2015 268 26 September

Excess in the yield of J/$\psi$ at very low $\textit{p}_{\rm T}$ ALICE
Collaboration††thanks: See Appendix A for the list of collaboration members
ALICE Collaboration

We report on the first measurement of an excess in the yield of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ at very low transverse
momentum ($p_{\rm T}$ $<$ 0.3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$)
in peripheral hadronic Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV,
performed by ALICE at the CERN LHC. Remarkably, the measured nuclear
modification factor of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in the
rapidity range $2.5<y<4$ reaches about 7 (2) in the $p_{\rm T}$ range 0–0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ in the
$\mathrm{70\mbox{--}90\%}$ ($\mathrm{50\mbox{--}70\%}$) centrality class. The
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ production cross section
associated with the observed excess is obtained under the hypothesis that
coherent photoproduction of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ is
the underlying physics mechanism. If confirmed, the observation of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ coherent photoproduction in
Pb–Pb collisions at impact parameters smaller than twice the nuclear radius
opens new theoretical and experimental challenges and opportunities. In
particular, coherent photoproduction accompanying hadronic collisions may
provide insight into the dynamics of photoproduction and nuclear reactions, as
well as become a novel probe of the Quark-Gluon Plasma.

The aim of experiments with ultra-relativistic heavy-ion collisions is the
study of nuclear matter at high temperature and pressure, where Quantum
Chromodynamics (QCD) predicts the existence of a deconfined state of hadronic
matter, the Quark-Gluon Plasma (QGP). Heavy quarks are expected to be produced
in the primary partonic scatterings and to interact with this partonic matter,
making them ideal probes of the QGP. According to the color screening
mechanism [1], quarkonium states are suppressed in the QGP, with different
dissociation probabilities for the various states depending on the temperature
of the medium. On the other hand, regeneration models predict charmonium
production via the (re)combination of charm quarks during [2, 3, 4] or at the
end [5, 6] of the deconfined phase. ALICE measurements of the
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ nuclear modification factor
($R_{\rm{AA}}$) [7, 8, 9, 10] and elliptic flow [11] in Pb–Pb collisions at a
center-of-mass energy of $\sqrt{s_{\rm NN}}$ = 2.76 TeV, as well as the
comparison of the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ nuclear
modification factor in p–Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV [12,
13] with that in Pb–Pb, support the regeneration scenario.

In this letter, we report on the measurement of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ production in hadronic Pb–Pb
collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at very low $p_{\rm T}$ ($p_{\rm
T}$ $<$ 0.3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$). We find an excess
in the yield of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ with respect
to expectations from hadroproduction. A plausible explanation is that the
excess is caused by coherent photoproduction of J/$\psi$. In this process,
quasi-real photons coherently produced by the strong electromagnetic field of
one of the lead nuclei interact, also coherently, with the gluon field of the
other nucleus, to produce a J/$\psi$. This process proceeds, at leading order
in perturbative QCD, through the interchange of two gluons in a singlet color
state, probing thus the square of the gluon distribution in the target. The
coherence conditions impose a maximum transverse momentum for the produced
J/$\psi$ of the order of one over the nuclear radius, so the production occurs
at very low $p_{\rm T}$. The study of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ photoproduction processes in
hadron colliders is known in Ultra-Peripheral collisions (UPC) and several
results are already available in this field at RHIC[14] and at the LHC [15,
16]. These measurements give insight into the gluon distribution of the
incoming Pb nuclei over a broad range of Bjorken-$x$ values, providing
information complementary to the study of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ hadroproduction in p–Pb and
Pb–Pb collisions. However, coherent
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ photoproduction has never been
observed in nuclear collisions with impact parameters smaller than twice the
radius of the nuclei. Although the extension to interactions where the nuclei
interact hadronically raises several questions, e.g. how the break-up of the
nuclei affects the coherence requirement, we find no other convincing
explanation. Assuming, therefore, this mechanism causes the observed excess,
we obtain the corresponding cross section in the $\mathrm{30\mbox{--}50\%}$,
$\mathrm{50\mbox{--}70\%}$ and $\mathrm{70\mbox{--}90\%}$ centrality classes.

The ALICE detector is described in [17, 18]. At forward rapidity ($2.5<y<4$)
the production of quarkonium states is measured via their $\mu^{+}\mu^{-}$
decay channel in the muon spectrometer down to $p_{\rm{T}}=0$. The Silicon
Pixel Detector (SPD), the scintillator arrays (V0) and the Zero Degree
Calorimeters (ZDC) were also used in this analysis. The SPD is located in the
central barrel of ALICE, while the V0 and ZDC are located on both sides of the
interaction point. The pseudorapidity coverages of these detectors are
$|\eta|<2$ (first SPD layer), $|\eta|<1.4$ (second SPD layer), $2.8<\eta<5.1$
(V0A), $-3.7<\eta<-1.7$ (V0C) and $|\eta|>8.7$ (ZDC). The SPD provides the
coordinates of the primary interaction vertex. The minimum bias trigger (MB)
required a signal in the V0 detectors at forward and backward rapidity. In
addition to the MB condition, the dimuon opposite-sign trigger ($\mu\mu$MB),
used in this analysis, required at least one pair of opposite-sign track
segments detected in the muon spectrometer triggering system, each with a
$p_{\rm T}$ above the 1 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
threshold of the online trigger algorithm. The background induced by the beam
and electromagnetic processes was further reduced by the V0 and ZDC timing
information and by requiring a minimum energy deposited in the neutron ZDC
(ZNA and ZNC) [19]. The energy thresholds were $\sim$ 450 GeV for ZNA and
$\sim$ 500 GeV for ZNC and were placed approximately three standard deviations
below the energy deposition of a 1.38 TeV neutron. The data sample used for
this analysis amounts to about $17\times 10^{6}$ $\mu\mu$MB triggered Pb–Pb
collisions, corresponding to an integrated luminosity $\mathcal{L}_{\rm
int}\approx 70$$\mu$b-1. The centrality determination was based on a fit of
the V0 amplitude distribution as described in [20]. A selection corresponding
to the 90% most central collisions was applied; for these events the MB
trigger was fully efficient. In each centrality class, the average number of
participant nucleons $\langle N_{\mathrm{part}}\rangle$ and average value of
the nuclear overlap function were derived from a Glauber model calculation
[21].

J/$\psi$ candidates were formed by combining pairs of opposite-sign (OS)
tracks reconstructed in the geometrical acceptance of the muon spectrometer
and matching a track segment above the 1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ $p_{\rm T}$ threshold in the
trigger chambers [10].

Figure 1:  (Color online) Raw OS dimuon $p_{\rm T}$ distribution for the
invariant mass range 2.8 $<$ $m_{\mu^{+}\mu^{-}}$ $<$ 3.4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$ and centrality class
$\mathrm{70\mbox{--}90\%}$. Vertical error bars are the statistical
uncertainties. The red line represents the $p_{\rm T}$ distribution of
coherently photoproduced J/$\psi$ as predicted by the STARLIGHT MC generator
[22] in Pb–Pb ultra-peripheral collisions and convoluted with the response
function of the muon spectrometer. The normalization of the red line is given
by the measured number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in
excess reported in Table 1 after correction for the $\psi$(2S) feed-down and
incoherent contributions (see text).

In Fig. 1, the $p_{\rm T}$ distribution of OS dimuons, without combinatorial
background subtraction, is shown for the invariant mass range 2.8
$<m_{\mu^{+}\mu^{-}}<$ 3.4 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$
in the centrality class $\mathrm{70\mbox{--}90\%}$. A remarkable excess of
dimuons is observed at very low $p_{\rm T}$ in this centrality class. Such an
excess has not been observed in the like-sign dimuon $p_{\rm T}$ distribution,
neither reported in previous measurements in proton-proton collisions [23, 24,
25, 26, 27, 28].

Figure 2:  (Color online) Invariant mass distributions of OS dimuons in the
$p_{\rm T}$ range 0–0.3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The
centrality classes are $\mathrm{0\mbox{--}10\%}$ (top) and
$\mathrm{70\mbox{--}90\%}$ (bottom). Vertical error bars are the statistical
uncertainties.

The raw number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in five
centrality classes ($\mathrm{0\mbox{--}10\%}$, $\mathrm{10\mbox{--}30\%}$,
$\mathrm{30\mbox{--}50\%}$, $\mathrm{50\mbox{--}70\%}$ and
$\mathrm{70\mbox{--}90\%}$) and three $p_{\rm T}$ ranges (0–0.3, 0.3–1, 1–8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) was extracted by fitting the
OS dimuon invariant mass distribution using a binned likelihood approach. Two
functions were considered to describe the
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ signal shape: a Crystal Ball
function [29] and a pseudo-Gaussian function [30]. The tails of the
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ signal functions were fixed
using Monte Carlo (MC) simulations for both hadronic [8] and photoproduction
hypotheses [15]. Depending on the $p_{\rm T}$ range and centrality class under
study, two or three functional forms were used to describe the background
under the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ signal peak. In
addition, the fit range was varied. It has also been checked that changing the
invariant mass bin width does not significantly modify the results. Fig. 2
shows typical fits in the $p_{\rm T}$ range 0–0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for the
$\mathrm{0\mbox{--}10\%}$ and $\mathrm{70\mbox{--}90\%}$ centrality classes.
The extracted $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ signals are the
average of the results obtained making all the combinations of signal shapes,
background shapes and fitting ranges, while the systematic uncertainties are
given by the RMS of the results. The extracted
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ signals and the corresponding
statistical and systematic uncertainties are quoted in the second column of
Table 1 for the very low $p_{\rm T}$ range.

In each centrality class and $p_{\rm T}$ range, the $R_{\rm{AA}}$ was obtained
from the measured number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
($N^{{\rm J}/\psi}_{{\rm AA}}$) corrected for acceptance and efficiency
–$({\cal A}\times\epsilon)^{{\rm h~{}J}/\psi}_{{\rm AA}}$ – (assuming pure
hadroproduction with no polarization), branching ratio ($\rm
BR_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi\rightarrow l^{+}l^{-}}$) and
normalized to the equivalent number of MB events ($N_{\rm events}$), average
nuclear overlap function ($\left\langle\rm T_{AA}\right\rangle$) and proton-
proton inclusive $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ production
cross section ($\sigma^{{\rm h~{}J}/\psi}_{{\rm pp}}$), as detailed in [8] and
shown in Eq. (1):

$R_{{\rm AA}}^{{\rm h~{}J}/\psi}=\frac{N^{{\rm J}/\psi}_{{\rm AA}}}{\rm
BR_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi\rightarrow
l^{+}l^{-}}\times\it{N}_{\rm events}\times({\cal A}\times\epsilon)^{{\rm
h~{}J}/\psi}_{{\rm AA}}\times\left\langle\rm
T_{AA}\right\rangle\times\sigma^{{\rm h~{}J}/\psi}_{{\rm pp}}}.$ (1)

In the $p_{\rm T}$ range 1–8 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ cross section in pp
collisions at $\sqrt{s}=2.76~{}\mathrm{TeV}$ was directly extracted from the
ALICE measurement [26], while in the $p_{\rm T}$ ranges 0–0.3 and 0.3–1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, due to limited statistics, it
was obtained by fitting the measured $p_{\rm T}$ distribution with the
following parametrization [31]:

$\frac{{\rm d}^{2}\sigma^{{\rm h~{}J}/\psi}_{{\rm pp}}}{{\rm d}p_{\rm T}{\rm
d}y}=\frac{c\times\sigma_{\rm\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}\times
p_{\rm T}}{1.5\times\langle p_{\rm
T}\rangle^{2}}\left(1+a^{2}\left(\frac{p_{\rm T}}{\langle p_{\rm
T}\rangle}\right)^{2}\right)^{-n},$ (2)

where $a=\Gamma(3/2)\Gamma(n-3/2)/\Gamma(n-1)$, $c=2a^{2}(n-1)$, and
$\sigma_{\rm J/\psi}$, $\langle p_{\rm T}\rangle$ and $n$ are free parameters
of the fit. A Lévy–Tsallis function [32, 33] and UA1 function [34] were also
used to fit the data in order to assess systematic uncertainties. In addition,
the validity of the procedure was confirmed using the
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ data sample in pp collisions
at 7 TeV [23], where the larger statistics at very low $p_{\rm T}$ allows for
a direct measurement of the cross sections: the values obtained with this
procedure in the $p_{\rm T}$ ranges 0–0.3 and 0.3–1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ agree within 11% (1.2$\sigma$)
and 4% (0.6$\sigma$), respectively, with the measured cross sections.

The procedures for the determination of the various systematic uncertainties
are the same as those followed in [8], apart from the reference pp cross
section in the $p_{\rm T}$ ranges 0–0.3 and 0.3–1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, which incorporate the
uncertainties on the fitting procedure described above. In Fig. 3, systematic
uncertainties were separated into 4 categories according to their degree of
correlation with centrality and $p_{\rm T}$: uncorrelated in $p_{\rm T}$ and
centrality (open boxes), which contain the systematic uncertainties on the
signal extraction in Pb–Pb (1-23%); fully correlated as a function of $p_{\rm
T}$ but not as a function of centrality (shaded areas), which contain the
uncertainties on the nuclear overlap function (3.2-7%), on the determination
of the centrality classes (0.7-7.7%) and on the centrality dependence of the
tracking (0-1%) and trigger efficiencies (0-1%); fully correlated as a
function of centrality but not as a function of $p_{\rm T}$ (quoted as global
systematics in the legend), which contain the uncertainties on the
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ cross section from pp
collisions (statistical (3.6-6.9%) and uncorrelated systematic (3.2-8.0%)), on
the MC input parametrization (0.5-2%) and on the tracking (10-11%), trigger
(2.2-3.6%) and matching efficiencies (1%); and fully correlated in $p_{\rm T}$
and centrality (quoted as common global systematics), which contain the
correlated systematic uncertainty on the pp reference cross section (5.8%) and
the uncertainty on the number of equivalent minimum bias events (3.5%).

The $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ $R_{\rm{AA}}$ shown in
Fig. 3 exhibits a strong increase in the $p_{\rm T}$ range 0–0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for the most peripheral Pb–Pb
collisions. This observation is surprising and none of the transport models
[2, 3] that well describe the previous measurements [7, 8, 10] predict such a
pattern at LHC energies.

Figure 3:  (Color online) $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
$R_{\rm{AA}}$ as a function of $\langle N_{\mathrm{part}}\rangle$ for 3
$p_{\rm T}$ ranges in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV. See
text for details on uncertainties. When assuming full transverse polarization
of the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in Pb-Pb collisions, as
expected if $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ are coherently
photoproduced, the $R_{\rm{AA}}$ values increase by about 21$\%$ in the range
0 $<\mbox{$p_{\rm T}$}~{}<$ 0.3 GeV/c.

To quantify the excess of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ at
very low $p_{\rm T}$, we subtracted the number of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ expected from hadroproduction
in Pb–Pb collisions. The following parametrization of the number of hadronic
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ ($N^{{\rm h~{}J}/\psi}_{{\rm
AA}}$) as a function of $p_{\rm T}$ in a given centrality class was used:

$\frac{{\rm d}N^{{\rm h~{}J}/\psi}_{{\rm AA}}}{{\rm d}\mbox{$p_{\rm
T}$}}={\cal N}\times\frac{{\rm d}\sigma^{{\rm h~{}J}/\psi}_{{\rm pp}}}{{\rm
d}\mbox{$p_{\rm T}$}}\times R_{{\rm AA}}^{{\rm h~{}J}/\psi}\times({\cal
A}\times\epsilon)^{{\rm h~{}J}/\psi}_{{\rm AA}}.$ (3)

The factor ${\cal N}$ is fixed by normalizing the integral of Eq. (3) in the
$p_{\rm T}$ range 1–8 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ to the
number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ measured in the same
range, where the hadroproduction component is dominant. The second term is
given by the fit of the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
$p_{\rm T}$-differential cross section measured in pp collisions [26] using
Eq. (2). The third term is a parametrization of the $R_{{\rm AA}}^{{\rm
h~{}J}/\psi}$ as a function of $p_{\rm T}$ from the ALICE measurements in
Pb–Pb collisions at 2.76 TeV [10, 8]. These measurements are available in
three centrality classes ($\mathrm{0\mbox{--}20\%}$,
$\mathrm{20\mbox{--}40\%}$, $\mathrm{40\mbox{--}90\%}$). To calculate the
hadroproduction component in the $\mathrm{10\mbox{--}30\%}$
($\mathrm{30\mbox{--}50\%}$) centrality class, parameterizations obtained in
both $\mathrm{0\mbox{--}20\%}$ and $\mathrm{20\mbox{--}40\%}$
($\mathrm{20\mbox{--}40\%}$ and $\mathrm{40\mbox{--}90\%}$) were considered. A
Woods-Saxon like parametrization, which describes the prediction of transport
models on $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ production in heavy-
ion collisions at low $p_{\rm T}$ [2, 3], was used in all the centrality
classes:

$R_{{\rm AA}}^{{\rm h~{}J}/\psi}(\mbox{$p_{\rm T}$})=R_{\rm
AA}^{0}+\frac{\Delta_{R_{\rm AA}}}{1+\exp\Bigl{(}\frac{p_{\rm T}-p_{\rm
T}^{0}}{\sigma_{p_{\rm T}}}\Bigr{)}}.$ (4)

$R_{\rm AA}^{0}$, $\sigma_{p_{\rm T}}$ and $\Delta_{R_{\rm AA}}$ are free
parameters of the fit while the $p_{\rm T}^{0}$ parameter was either
unconstrained or fixed to $M_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}$
to force an evolution of $R_{{\rm AA}}^{{\rm h~{}J}/\psi}$ at very low $p_{\rm
T}$ in agreement with the predictions of the transport models [2, 3]. In
addition, a first order polynomial and a constant were used in the most
peripheral class. Two fitting ranges in $p_{\rm T}$ were considered, either
0-8 or 1-8 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ since the first bin
could be biased by the presence of the very low $p_{\rm T}$
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ excess. Finally, the last term
in Eq. (3) is a parametrization of the acceptance times efficiency of hadronic
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ ($({\cal
A}\times\epsilon)^{{\rm h~{}J}/\psi}_{{\rm AA}}$) – determined from MC
simulations of the muon spectrometer response function – with either a third-
order polynomial or the ratio of two Lévy–Tsallis functions. Simulations were
performed with an embedding technique where MC
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ particles are injected into
real events and then reconstructed [8]. The results of the various
parameterizations are averaged in a given range in $p_{\rm T}$ and centrality
and the RMS of the results is included in the systematic uncertainty on the
expected number of hadronic J/$\psi$.

The excess in the number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
measured in the $p_{\rm T}$ range 0–0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ after subtracting the hadronic
component is given in the fourth column of Table 1.

Cent. (%) | $N^{{\rm J}/\psi}_{{\rm AA}}$ | $N^{{\rm h~{}J}/\psi}_{{\rm AA}}$ | $N^{{\rm excess~{}J}/\psi}_{{\rm AA}}$ | d$\sigma_{\mathrm{J}\kern-0.14003pt/\kern-0.35002pt\psi}^{\rm coh}/$d$y$ ($\mu$b)
---|---|---|---|---
0–10 | $339\pm 85\pm 78$ | 406 $\pm$ 14 $\pm$ 55 |  $<$ 251 |  $<$ 318
10–30 | $373\pm 87\pm 75$ | 397 $\pm$ 10 $\pm$ 61 |  $<$ 237 |  $<$ 290
30–50 | $187\pm 37\pm 15$ | 126 $\pm$ 4 $\pm$ 15 | 62 $\pm$ 37 $\pm$ 21 | 73 $\pm$ 44 ${}^{+26}_{-27}$ $\pm$ 10
50–70 | $89\pm 13\pm 2$ | 39 $\pm$ 2 $\pm$ 5 | 50 $\pm$ 14 $\pm$ 5 | 58 $\pm$ 16 ${}^{+8}_{-10}$ $\pm$ 8
70–90 | $59\pm 9\pm 3$ | 8 $\pm$ 1 $\pm$ 1 | 51 $\pm$ 9 $\pm$ 3 | 59 $\pm$ 11 ${}^{+7}_{-10}$ $\pm$ 8
Table 1: Raw number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
($N^{{\rm J}/\psi}_{{\rm AA}}$), expected raw number of hadronic
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ ($N^{{\rm h~{}J}/\psi}_{{\rm
AA}}$) and measured excess in the number of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ ( $N^{{\rm
excess~{}J}/\psi}_{{\rm AA}}$), all three numbers in the $p_{\rm T}$ range
(0–0.3) $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, and
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ coherent photoproduction cross
section in Pb–Pb collisons at $\sqrt{s_{\rm NN}}$ = 2.76 TeV, with their
statistical and uncorrelated systematic uncertainties. A correlated systematic
uncertainty also applies to the cross section. In the most central classes, an
upper limit (95$\%$ CL) on the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
yield excess and on the cross section is given.

The statistical uncertainty is the quadratic sum of the uncertainties on the
measured number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in the
$p_{\rm T}$ ranges 0–0.3 and 1-8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The latter is used in the
normalization factor of Eq. (3). The systematic uncertainty is the quadratic
sum of the uncertainties on the signal extraction in 0-0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ (see Table 1) and on the
parametrization of the hadronic component (13.0$\%$, 12.5$\%$ and 12$\%$ in
the $\mathrm{70\mbox{--}90\%}$, $\mathrm{50\mbox{--}70\%}$ and
$\mathrm{30\mbox{--}50\%}$ centrality classes, respectively, see Table 1). The
significance of the excess is 5.4$\sigma$, 3.4$\sigma$ and 1.4$\sigma$ in the
$\mathrm{70\mbox{--}90\%}$, $\mathrm{50\mbox{--}70\%}$ and
$\mathrm{30\mbox{--}50\%}$ centrality classes, respectively. For the two
central classes, only the 95% confidence level limit could be computed. To
cross-check the robustness of these results, the excess was re-evaluated
assuming a rough parametrization of the $R_{{\rm AA}}^{{\rm h~{}J}/\psi}$
based on two extreme cases: (i) a constant suppression independent of $p_{\rm
T}$ ($R_{{\rm AA}}^{{\rm h~{}J}/\psi}$($p_{\rm T}$ $<$ 0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) = $R_{{\rm AA}}^{{\rm
h~{}J}/\psi}$(1 $<$ $p_{\rm T}$ $<$ 8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$)), which minimizes the hadronic
contribution, and (ii) no suppression at all at low $p_{\rm T}$ ($R_{{\rm
AA}}^{{\rm h~{}J}/\psi}$($p_{\rm T}$ $<$ 0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) = 1), which gives the maximum
possible hadronic contribution. Even with these simplified and extreme
assumptions, the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ excess
remains significant and compatible with the results reported in Table 1 within
less than 1 (3) times the quoted systematic uncertainty for the
$\mathrm{70\mbox{--}90\%}$ ($\mathrm{50\mbox{--}70\%}$) centrality class.

A plausible explanation of the measured excess is
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ photoproduction. The cross
section for this process increases with energy and at the LHC becomes
comparable to the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ hadronic
cross section. Moreover, the shape of the $p_{\rm T}$ distribution in the
region of the observed excess is similar to that of a coherently photoproduced
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ [15], where the photon is
emitted by the electromagnetic field of the source nucleus, and then the
target nucleus interacts coherently with the photon to produce the
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$, like in Pb–Pb ultra-
peripheral collisions. The average transverse momentum of coherently
photoproduced $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ is around 0.055
GeV/$c$. Detailed MC simulations show that detector effects widen
reconstructed distribution by approximately a factor of two (see red line in
Fig. 1) and that 98$\%$ of coherently photoproduced
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ are contained in the $p_{\rm
T}$ interval [0, 0.3] GeV/$c$.

Assuming that coherent photoproduction causes the excess at very low $p_{\rm
T}$, the corresponding cross section can be obtained as described in reference
[15]. The fraction of processes where the coherently emitted photon couples
only to single nucleon, so called incoherent photoproduction of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$, and passed the data selection
is $f_{\mathrm{I}}=0.14^{+0.16}_{-0.05}$, while the contribution of coherently
produced $\psi(2S)$ with a $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
among the decay products which passes the data selection is
$f_{\mathrm{D}}=0.10\pm 0.06$. Both fractions are used to correct the found
excess to extract the number of coherent
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$. This number was then
corrected for the acceptance times efficiency (${\cal A}\times\epsilon$ =
11.31 $\pm$ 0.04$\%$) taking into account that photoproduced
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ are expected to be
transversally polarized, for branching ratio and normalized to the integrated
luminosity and the width of the rapidity range. For the
$\mathrm{70\mbox{--}90\%}$ centrality class, the cross section per unit of
rapidity amounts to 59 $\pm$ 11 (stat)${}^{+7}_{-10}$ (uncor. syst) $\pm$ 8
(cor. syst) $\mu$b (see Table 1, where the values for the other centrality
classes are also reported). The uncorrelated centrality dependent systematic
uncertainties contain, in addition to the one on the measured excess, the
uncertainties on the incoherent and $\psi(2S)$ feed-down contributions (see
above), on the determination of the centrality classes (0.7-7.7$\%$), on the
trigger efficiency (0-1$\%$), on the tracking efficiency (0-1$\%$) and on the
tracking and trigger efficiency loss as a function of centrality (0-3$\%$).
The correlated systematic uncertainties contain the uncertainty on the
branching ratio (1$\%$), on the luminosity (${}^{+7.8}_{-6.5}\%$), on the
tracking (11$\%$), trigger (3.6$\%$) and matching efficiencies (1$\%$) and on
the MC input parametrization (3$\%$).

In UPC of lead nuclei at $\sqrt{s_{\rm NN}}$ = 2.76 TeV one expects the
incoherent yield in the $p_{\rm T}$ range 0.3–1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ to be about 30$\%$ of the
coherent yield in the $p_{\rm T}$ range 0–0.3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ [15]. Assuming the same
behavior in peripheral collisions, one would expect a 23$\%$ (4$\%$)
contribution of incoherent $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ to
the total number of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ measured
in the $\mathrm{70\mbox{--}90\%}$ ($\mathrm{50\mbox{--}70\%}$) centrality
class in the $p_{\rm T}$ range 0.3–1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The significance of the
present data sample is not sufficient to confirm the presence of incoherent
photoproduction in this $p_{\rm T}$ range.

The probability of a random coincidence of a MB collision and a coherent
production of a $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in a UPC
satisfying the dimuon trigger, in the same bunch crossing, has been evaluated.
In the overall data sample, only one random coincidence is expected for the
full centrality range, corresponding to 0.6 coincidences in the
$\mathrm{30\mbox{--}90\%}$ centrality class.

To our knowledge there is no numerical prediction for the cross section of
coherent photoproduction of $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in
peripheral collisions. Given that the nuclei also undergo a hadronic
interaction, it is not clear how to incorporate the coherence conditions. To
have a rough estimate, we considered the extreme assumption that all the
charges in the source and all the nucleons in the target contribute to the
photonuclear cross section as in coherent UPC (see also [35]). The photon
flux, see e.g. [36], was obtained integrating in the impact parameter range
corresponding to the centrality class. We used two different approaches: the
vector dominance model of [37], normalized to the measured UPC data [15, 16],
and the perturbative QCD model of [36] with the parameterization of [38]. In
both cases we obtain a cross section in the $\mathrm{70\mbox{--}90\%}$
centrality class of about 40 $\mu$b, which is of the same order of magnitude
as our measurement. Note that the most peripheral class corresponds to the
hadronic interaction of just a few nucleons ($N_{\rm part}\approx 11$), so the
interaction is close to the ultra-peripheral case and the comparison to the
estimate seems reasonable. Another interesting hypothesis, not considered,
would be that only the spectators in the target are the ones that interact
coherently with the photon. In this case, the $p_{\rm T}$ distribution of the
excess would get wider as the centrality increases, providing an experimental
tool to discriminate among potential models. Indeed, as the size of the
spectator region decreases with centrality, the maximum $p_{\rm T}$, given by
the coherence condition and the uncertainty principle, would increase.

In summary, we reported on the ALICE measurement of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ production at very low $p_{\rm
T}$ and forward rapidity in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76
TeV. A strong increase of the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
$R_{\rm{AA}}$ is observed in the range $0\leq p_{\rm T}<0.3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for the
$\mathrm{70\mbox{--}90\%}$ ($\mathrm{50\mbox{--}70\%}$) centrality class,
where $R_{\rm{AA}}$ reaches a value of about 7 (2). The excess has been
quantified with a significance of 5.4 (3.4) $\sigma$ assuming a smooth
evolution of the $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
hadroproduction at low $p_{\rm T}$. Coherent photoproduction of
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ is a plausible physics
mechanism at the origin of this excess. Following this assumption, the
coherent photoproduction cross section has been extracted for the centrality
classes $\mathrm{30\mbox{--}50\%}$, $\mathrm{50\mbox{--}70\%}$ and
$\mathrm{70\mbox{--}90\%}$ while an upper limit is given for
$\mathrm{0\mbox{--}10\%}$ and $\mathrm{10\mbox{--}30\%}$. It would be very
challenging for existing theoretical models, which only include hadronic
processes, to explain this excess. The survival of an electromagnetically
produced charmonium in a nuclear collision merits theoretical investigation.
In addition, coherent photoproduced
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ may be formed in the initial
stage of the collisions and could therefore interact with the QGP, resulting
in a modification of the measured cross section with respect to the
expectation of theoretical models. In particular, one expects a partial
suppression of photoproduced $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$
due to color screening of the heavy quark potential in the QGP. The
regenerated $\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ in the QGP exhibit
a wider $p_{\rm T}$ distribution and do not contribute to the measured excess,
making this measurement a potentially powerful tool to constrain the
suppression/regeneration components in the models. Experimentally, the
increase of the LHC heavy ion luminosity during Run 2 will lead to a factor 10
larger data sample, thus improving the precision of the present measurement
and opening the possibility to determine whether the
$\mathrm{J}\kern-0.20004pt/\kern-0.50003pt\psi$ excess at very low $p_{\rm T}$
is also present in the most central collisions.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: State
Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds
Kidagan, Armenia; Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de
Amparo à Pesquisa do Estado de São Paulo (FAPESP); National Natural Science
Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC); Ministry of Education and
Youth of the Czech Republic; Danish Natural Science Research Council, the
Carlsberg Foundation and the Danish National Research Foundation; The European
Research Council under the European Community’s Seventh Framework Programme;
Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3,
the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA,
France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und
Technologie (BMBF) and the Helmholtz Association; General Secretariat for
Research and Technology, Ministry of Development, Greece; Hungarian Orszagos
Tudomanyos Kutatasi Alappgrammok (OTKA) and National Office for Research and
Technology (NKTH); Department of Atomic Energy and Department of Science and
Technology of the Government of India; Istituto Nazionale di Fisica Nucleare
(INFN) and Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi”, Italy; MEXT Grant-in-Aid for Specially Promoted Research,
Japan; Joint Institute for Nuclear Research, Dubna; National Research
Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT),
Direccion General de Asuntos del Personal Academico(DGAPA), México, Amerique
Latine Formation academique - European Commission (ALFA-EC) and the EPLANET
Program (European Particle Physics Latin American Network); Stichting voor
Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway
(NFR); National Science Centre, Poland; Ministry of National
Education/Institute for Atomic Physics and National Council of Scientific
Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry of Education
and Science of Russian Federation, Russian Academy of Sciences, Russian
Federal Agency of Atomic Energy, Russian Federal Agency for Science and
Innovations and The Russian Foundation for Basic Research; Ministry of
Education of Slovakia; Department of Science and Technology, South Africa;
Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas
(CIEMAT), E-Infrastructure shared between Europe and Latin America (EELA),
Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta de Galicia
(Consellería de Educación), Centro de Aplicaciones Tecnológicas y Desarrollo
Nuclear (CEADEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy
Agency); Swedish Research Council (VR) and Knut $\&$ Alice Wallenberg
Foundation (KAW); Ukraine Ministry of Education and Science; United Kingdom
Science and Technology Facilities Council (STFC); The United States Department
of Energy, the United States National Science Foundation, the State of Texas,
and the State of Ohio; Ministry of Science, Education and Sports of Croatia
and Unity through Knowledge Fund, Croatia; Council of Scientific and
Industrial Research (CSIR), New Delhi, India; Pontificia Universidad Católica
del Perú.

## References

  * [1] T. Matsui and H. Satz, “$J/\psi$ Suppression by Quark-Gluon Plasma Formation,” Phys. Lett. B178 (1986) 416.
  * [2] X. Zhao and R. Rapp, “Medium Modifications and Production of Charmonia at LHC,” Nucl.Phys. A859 (2011) 114–125.
  * [3] Y.-P. Liu, Z. Qu, N. Xu, and P.-F. Zhuang, “$J/\psi$ Transverse Momentum Distribution in High Energy Nuclear Collisions at RHIC,” Phys. Lett. B678 (2009) 72–76.
  * [4] R. L. Thews, M. Schroedter, and J. Rafelski, “Enhanced $J/\psi$ production in deconfined quark matter,” Phys. Rev. C63 (2001) 054905, arXiv:hep-ph/0007323 [hep-ph].
  * [5] P. Braun-Munzinger and J. Stachel, “(Non)thermal aspects of charmonium production and a new look at $J/\psi$ suppression,” Phys. Lett. B490 (2000) 196–202.
  * [6] A. Andronic, P. Braun-Munzinger, K. Redlich, and J. Stachel, “The thermal model on the verge of the ultimate test: particle production in Pb-Pb collisions at the LHC,” J. Phys. G38 (2011) 124081.
  * [7] ALICE Collaboration, B. Abelev et al., “$J/\psi$ suppression at forward rapidity in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV,” Phys. Rev. Lett. 109 (2012) 072301, arXiv:1202.1383 [hep-ex].
  * [8] ALICE Collaboration, B. Abelev et al., “Centrality, rapidity and transverse momentum dependence of J/$\psi$ suppression in Pb-Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV,” Phys. Lett. B734 (2014) 314–327, arXiv:1311.0214 [nucl-ex].
  * [9] ALICE Collaboration, J. Adam et al., “Inclusive, prompt and non-prompt J/$\psi$ production at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV,” JHEP 07 (2015) 051, arXiv:1504.07151 [nucl-ex].
  * [10] ALICE Collaboration, J. Adam et al., “Differential studies of inclusive J/$\psi$ and $\psi$(2S) production at forward rapidity in Pb-Pb collisions at $\mathbf{\sqrt{{\textit{s}}_{{}_{NN}}}}$ = 2.76 TeV,” arXiv:1506.08804 [nucl-ex].
  * [11] ALICE Collaboration, E. Abbas et al., “J/$\psi$ Elliptic Flow in Pb-Pb Collisions at $\sqrt{s_{NN}}$=2.76 TeV,” Phys. Rev. Lett. 111 (2013) 162301, arXiv:1303.5880 [nucl-ex].
  * [12] ALICE Collaboration, B. Abelev et al., “$J/\psi$ production and nuclear effects in p-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV,” JHEP 1402 (2014) 073, arXiv:1308.6726 [nucl-ex].
  * [13] ALICE Collaboration, J. Adam et al., “Rapidity and transverse-momentum dependence of the inclusive J/$\psi$ nuclear modification factor in p-Pb collisions at $\sqrt{s_{N\ N}}=$ 5.02 TeV,” JHEP 06 (2015) 055, arXiv:1503.07179 [nucl-ex].
  * [14] PHENIX Collaboration, S. Afanasiev et al., “Photoproduction of J/psi and of high mass e+e- in ultra-peripheral Au+Au collisions at s**(1/2) = 200-GeV,” Phys. Lett. B679 (2009) 321–329, arXiv:0903.2041 [nucl-ex].
  * [15] ALICE Collaboration, B. Abelev et al., “Coherent $J/\psi$ photoproduction in ultra-peripheral Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV,” Phys.Lett. B718 (2013) 1273–1283, arXiv:1209.3715 [nucl-ex].
  * [16] ALICE Collaboration, E. Abbas et al., “Charmonium and $e^{+}e^{-}$ pair photoproduction at mid-rapidity in ultra-peripheral Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV,” Eur. Phys. J. C73 (2013) 2617, arXiv:1305.1467 [nucl-ex].
  * [17] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC,” JINST 3 (2008) S08002.
  * [18] ALICE Collaboration, B. Abelev et al., “Performance of the ALICE Experiment at the CERN LHC,” Int. J. Mod. Phys. A29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
  * [19] ALICE Collaboration, B. Abelev et al., “Measurement of the Cross Section for Electromagnetic Dissociation with Neutron Emission in Pb-Pb Collisions at $\sqrt{s_{NN}}$ = 2.76 TeV,” Phys. Rev. Lett. 109 (2012) 252302, arXiv:1203.2436 [nucl-ex].
  * [20] ALICE Collaboration, B. Abelev et al., “Centrality determination of Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV with ALICE,” Phys.Rev. C88 no. 4, (2013) 044909, arXiv:1301.4361 [nucl-ex].
  * [21] M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, “Glauber modeling in high energy nuclear collisions,” Ann. Rev. Nucl. Part. Sci. 57 (2007) 205–243, arXiv:nucl-ex/0701025 [nucl-ex].
  * [22] STARLIGHT website (2013) . http://starlight.hepforge.org/.
  * [23] ALICE Collaboration, B. Abelev et al., “Measurement of quarkonium production at forward rapidity in $pp$ collisions at $\sqrt{s}=7$ TeV,” Eur. Phys. J. C74 no. 8, (2014) 2974, arXiv:1403.3648 [nucl-ex].
  * [24] ALICE Collaboration, K. Aamodt et al., “Rapidity and transverse momentum dependence of inclusive J/psi production in $pp$ collisions at $\sqrt{s}=7$ TeV,” Phys. Lett. B704 (2011) 442–455, arXiv:1105.0380 [hep-ex].
  * [25] ALICE Collaboration, B. Abelev et al., “$J/\psi$ Production as a Function of Charged Particle Multiplicity in $pp$ Collisions at $\sqrt{s}=7$ TeV,” Phys. Lett. B712 (2012) 165–175, arXiv:1202.2816 [hep-ex].
  * [26] ALICE Collaboration, B. Abelev et al., “Inclusive $J/\psi$ production in $pp$ collisions at $\sqrt{s}=2.76$ TeV,” Phys. Lett. B718 (2012) 295–306, arXiv:1203.3641 [hep-ex].
  * [27] LHCb Collaboration, R. Aaij et al., “Measurement of $J/\psi$ production in $pp$ collisions at $\sqrt{s}=7~{}\rm{TeV}$,” Eur. Phys. J. C71 (2011) 1645, arXiv:1103.0423 [hep-ex].
  * [28] LHCb Collaboration, R. Aaij et al., “Measurement of $J/\psi$ production in $pp$ collisions at $\sqrt{s}=2.76$ TeV,” JHEP 1302 (2013) 041, arXiv:1212.1045 [hep-ex].
  * [29] J. E. Gaiser.  PhD thesis, Stanford, 1982.  Appendix-F, SLAC-R-255.
  * [30] R. Shahoyan.  PhD thesis, Institute Superior Técnico, Universidade Tecnica de Lisboa, 2001.
  * [31] F. Bossu, Z. del Valle, A. de Falco, M. Gagliardi, S. Grigoryan, et al., “Phenomenological extrapolation of the inclusive $J/\psi$ cross section to proton-proton collisions at 2.76 TeV and 5.5 TeV,” arXiv:1103.2394 [nucl-ex].
  * [32] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,” J. Statist. Phys. 52 (1988) 479–487.
  * [33] STAR Collaboration, B. Abelev et al., “Strange particle production in p+p collisions at $\sqrt{s}$ = 200 GeV,” Phys. Rev. C75 (2007) 064901, arXiv:nucl-ex/0607033 [nucl-ex].
  * [34] UA1 Collaboration, C. Albajar et al., “A Study of the General Characteristics of $p\bar{p}$ Collisions at $\sqrt{s}$ = 0.2 TeV to 0.9 TeV,” Nucl. Phys. B335 (1990) 261.
  * [35] M. Kłusek-Gawenda and A. Szczurek, “Photoproduction of $J/\psi$ mesons in peripheral and semi-central heavy ion collisions,” arXiv:1509.03173 [nucl-th].
  * [36] G. Baur, K. Hencken, D. Trautmann, S. Sadovsky, and Y. Kharlov, “Coherent gamma gamma and gamma-A interactions in very peripheral collisions at relativistic ion colliders,” Phys. Rept. 364 (2002) 359–450, arXiv:hep-ph/0112211 [hep-ph].
  * [37] S. Klein and J. Nystrand, “Exclusive vector meson production in relativistic heavy ion collisions,” Phys. Rev. C60 (1999) 014903, arXiv:hep-ph/9902259 [hep-ph].
  * [38] V. Guzey, E. Kryshen, M. Strikman, and M. Zhalov, “Evidence for nuclear gluon shadowing from the ALICE measurements of PbPb ultraperipheral exclusive $J/{\psi}$ production,” Phys.Lett. B726 (2013) 290–295, arXiv:1305.1724 [hep-ph].

##  Appendix A The ALICE Collaboration

J. Adam40, D. Adamová84, M.M. Aggarwal88, G. Aglieri Rinella36, M. Agnello110,
N. Agrawal48, Z. Ahammed132, S.U. Ahn68, S. Aiola136, A. Akindinov58, S.N.
Alam132, D. Aleksandrov80, B. Alessandro110, D. Alexandre101, R. Alfaro
Molina64, A. Alici12,104, A. Alkin3, J.R.M. Almaraz119, J. Alme38, T. Alt43,
S. Altinpinar18, I. Altsybeev131, C. Alves Garcia Prado120, C. Andrei78, A.
Andronic97, V. Anguelov94, J. Anielski54, T. Antičić98, F. Antinori107, P.
Antonioli104, L. Aphecetche113, H. Appelshäuser53, S. Arcelli28, R.
Arnaldi110, O.W. Arnold37,93, I.C. Arsene22, M. Arslandok53, B. Audurier113,
A. Augustinus36, R. Averbeck97, M.D. Azmi19, A. Badalà106, Y.W. Baek67, S.
Bagnasco110, R. Bailhache53, R. Bala91, A. Baldisseri15, R.C. Baral61, A.M.
Barbano27, R. Barbera29, F. Barile33, G.G. Barnaföldi135, L.S. Barnby101, V.
Barret70, P. Bartalini7, K. Barth36, J. Bartke117, E. Bartsch53, M. Basile28,
N. Bastid70, S. Basu132, B. Bathen54, G. Batigne113, A. Batista Camejo70, B.
Batyunya66, P.C. Batzing22, I.G. Bearden81, H. Beck53, C. Bedda110, N.K.
Behera50, I. Belikov55, F. Bellini28, H. Bello Martinez2, R. Bellwied122, R.
Belmont134, E. Belmont-Moreno64, V. Belyaev75, G. Bencedi135, S. Beole27, I.
Berceanu78, A. Bercuci78, Y. Berdnikov86, D. Berenyi135, R.A. Bertens57, D.
Berzano36, L. Betev36, A. Bhasin91, I.R. Bhat91, A.K. Bhati88, B.
Bhattacharjee45, J. Bhom128, L. Bianchi122, N. Bianchi72, C. Bianchin57,134,
J. Bielčík40, J. Bielčíková84, A. Bilandzic81, R. Biswas4, S. Biswas79, S.
Bjelogrlic57, J.T. Blair118, D. Blau80, C. Blume53, F. Bock94,74, A.
Bogdanov75, H. Bøggild81, L. Boldizsár135, M. Bombara41, J. Book53, H.
Borel15, A. Borissov96, M. Borri83,124, F. Bossú65, E. Botta27, S. Böttger52,
C. Bourjau81, P. Braun-Munzinger97, M. Bregant120, T. Breitner52, T.A.
Broker53, T.A. Browning95, M. Broz40, E.J. Brucken46, E. Bruna110, G.E.
Bruno33, D. Budnikov99, H. Buesching53, S. Bufalino27,36, P. Buncic36, O.
Busch94,128, Z. Buthelezi65, J.B. Butt16, J.T. Buxton20, D. Caffarri36, X.
Cai7, H. Caines136, L. Calero Diaz72, A. Caliva57, E. Calvo Villar102, P.
Camerini26, F. Carena36, W. Carena36, F. Carnesecchi28, J. Castillo
Castellanos15, A.J. Castro125, E.A.R. Casula25, C. Ceballos Sanchez9, J.
Cepila40, P. Cerello110, J. Cerkala115, B. Chang123, S. Chapeland36, M.
Chartier124, J.L. Charvet15, S. Chattopadhyay132, S. Chattopadhyay100, V.
Chelnokov3, M. Cherney87, C. Cheshkov130, B. Cheynis130, V. Chibante
Barroso36, D.D. Chinellato121, S. Cho50, P. Chochula36, K. Choi96, M.
Chojnacki81, S. Choudhury132, P. Christakoglou82, C.H. Christensen81, P.
Christiansen34, T. Chujo128, S.U. Chung96, C. Cicalo105, L. Cifarelli12,28, F.
Cindolo104, J. Cleymans90, F. Colamaria33, D. Colella59,33,36, A. Collu74,25,
M. Colocci28, G. Conesa Balbastre71, Z. Conesa del Valle51, M.E.
ConnorsII,136, J.G. Contreras40, T.M. Cormier85, Y. Corrales Morales110, I.
Cortés Maldonado2, P. Cortese32, M.R. Cosentino120, F. Costa36, P. Crochet70,
R. Cruz Albino11, E. Cuautle63, L. Cunqueiro36, T. Dahms93,37, A. Dainese107,
A. Danu62, D. Das100, I. Das51,100, S. Das4, A. Dash121,79, S. Dash48, S.
De120, A. De Caro31,12, G. de Cataldo103, C. de Conti120, J. de Cuveland43, A.
De Falco25, D. De Gruttola12,31, N. De Marco110, S. De Pasquale31, A.
Deisting97,94, A. Deloff77, E. DénesI,135, C. Deplano82, P. Dhankher48, D. Di
Bari33, A. Di Mauro36, P. Di Nezza72, M.A. Diaz Corchero10, T. Dietel90, P.
Dillenseger53, R. Divià36, Ø. Djuvsland18, A. Dobrin57,82, D. Domenicis
Gimenez120, B. Dönigus53, O. Dordic22, T. Drozhzhova53, A.K. Dubey132, A.
Dubla57, L. Ducroux130, P. Dupieux70, R.J. Ehlers136, D. Elia103, H. Engel52,
E. Epple136, B. Erazmus113, I. Erdemir53, F. Erhardt129, B. Espagnon51, M.
Estienne113, S. Esumi128, J. Eum96, D. Evans101, S. Evdokimov111, G.
Eyyubova40, L. Fabbietti93,37, D. Fabris107, J. Faivre71, A. Fantoni72, M.
Fasel74, L. Feldkamp54, A. Feliciello110, G. Feofilov131, J. Ferencei84, A.
Fernández Téllez2, E.G. Ferreiro17, A. Ferretti27, A. Festanti30, V.J.G.
Feuillard15,70, J. Figiel117, M.A.S. Figueredo124,120, S. Filchagin99, D.
Finogeev56, F.M. Fionda25, E.M. Fiore33, M.G. Fleck94, M. Floris36, S.
Foertsch65, P. Foka97, S. Fokin80, E. Fragiacomo109, A. Francescon30,36, U.
Frankenfeld97, U. Fuchs36, C. Furget71, A. Furs56, M. Fusco Girard31, J.J.
Gaardhøje81, M. Gagliardi27, A.M. Gago102, M. Gallio27, D.R. Gangadharan74, P.
Ganoti36,89, C. Gao7, C. Garabatos97, E. Garcia-Solis13, C. Gargiulo36, P.
Gasik37,93, E.F. Gauger118, M. Germain113, A. Gheata36, M. Gheata62,36, P.
Ghosh132, S.K. Ghosh4, P. Gianotti72, P. Giubellino110,36, P. Giubilato30, E.
Gladysz-Dziadus117, P. Glässel94, D.M. Goméz Coral64, A. Gomez Ramirez52, V.
Gonzalez10, P. González-Zamora10, S. Gorbunov43, L. Görlich117, S. Gotovac116,
V. Grabski64, O.A. Grachov136, L.K. Graczykowski133, K.L. Graham101, A.
Grelli57, A. Grigoras36, C. Grigoras36, V. Grigoriev75, A. Grigoryan1, S.
Grigoryan66, B. Grinyov3, N. Grion109, J.M. Gronefeld97, J.F. Grosse-
Oetringhaus36, J.-Y. Grossiord130, R. Grosso97, F. Guber56, R. Guernane71, B.
Guerzoni28, K. Gulbrandsen81, T. Gunji127, A. Gupta91, R. Gupta91, R. Haake54,
Ø. Haaland18, C. Hadjidakis51, M. Haiduc62, H. Hamagaki127, G. Hamar135, J.W.
Harris136, A. Harton13, D. Hatzifotiadou104, S. Hayashi127, S.T. Heckel53, M.
Heide54, H. Helstrup38, A. Herghelegiu78, G. Herrera Corral11, B.A. Hess35,
K.F. Hetland38, H. Hillemanns36, B. Hippolyte55, R. Hosokawa128, P. Hristov36,
M. Huang18, T.J. Humanic20, N. Hussain45, T. Hussain19, D. Hutter43, D.S.
Hwang21, R. Ilkaev99, M. Inaba128, M. Ippolitov75,80, M. Irfan19, M. Ivanov97,
V. Ivanov86, V. Izucheev111, P.M. Jacobs74, M.B. Jadhav48, S. Jadlovska115, J.
Jadlovsky115,59, C. Jahnke120, M.J. Jakubowska133, H.J. Jang68, M.A. Janik133,
P.H.S.Y. Jayarathna122, C. Jena30, S. Jena122, R.T. Jimenez Bustamante97, P.G.
Jones101, H. Jung44, A. Jusko101, P. Kalinak59, A. Kalweit36, J. Kamin53, J.H.
Kang137, V. Kaplin75, S. Kar132, A. Karasu Uysal69, O. Karavichev56, T.
Karavicheva56, L. Karayan97,94, E. Karpechev56, U. Kebschull52, R. Keidel138,
D.L.D. Keijdener57, M. Keil36, M. Mohisin KhanIII,19, P. Khan100, S.A.
Khan132, A. Khanzadeev86, Y. Kharlov111, B. Kileng38, D.W. Kim44, D.J. Kim123,
D. Kim137, H. Kim137, J.S. Kim44, M. Kim44, M. Kim137, S. Kim21, T. Kim137, S.
Kirsch43, I. Kisel43, S. Kiselev58, A. Kisiel133, G. Kiss135, J.L. Klay6, C.
Klein53, J. Klein36,94, C. Klein-Bösing54, S. Klewin94, A. Kluge36, M.L.
Knichel94, A.G. Knospe118, T. Kobayashi128, C. Kobdaj114, M. Kofarago36, T.
Kollegger97,43, A. Kolojvari131, V. Kondratiev131, N. Kondratyeva75, E.
Kondratyuk111, A. Konevskikh56, M. Kopcik115, M. Kour91, C. Kouzinopoulos36,
O. Kovalenko77, V. Kovalenko131, M. Kowalski117, G. Koyithatta
Meethaleveedu48, I. Králik59, A. Kravčáková41, M. Kretz43, M. Krivda101,59, F.
Krizek84, E. Kryshen36, M. Krzewicki43, A.M. Kubera20, V. Kučera84, C. Kuhn55,
P.G. Kuijer82, A. Kumar91, J. Kumar48, L. Kumar88, S. Kumar48, P.
Kurashvili77, A. Kurepin56, A.B. Kurepin56, A. Kuryakin99, M.J. Kweon50, Y.
Kwon137, S.L. La Pointe110, P. La Rocca29, P. Ladron de Guevara11, C. Lagana
Fernandes120, I. Lakomov36, R. Langoy42, C. Lara52, A. Lardeux15, A.
Lattuca27, E. Laudi36, R. Lea26, L. Leardini94, G.R. Lee101, S. Lee137, F.
Lehas82, R.C. Lemmon83, V. Lenti103, E. Leogrande57, I. León Monzón119, H.
León Vargas64, M. Leoncino27, P. Lévai135, S. Li70,7, X. Li14, J. Lien42, R.
Lietava101, S. Lindal22, V. Lindenstruth43, C. Lippmann97, M.A. Lisa20, H.M.
Ljunggren34, D.F. Lodato57, P.I. Loenne18, V. Loginov75, C. Loizides74, X.
Lopez70, E. López Torres9, A. Lowe135, P. Luettig53, M. Lunardon30, G.
Luparello26, A. Maevskaya56, M. Mager36, S. Mahajan91, S.M. Mahmood22, A.
Maire55, R.D. Majka136, M. Malaev86, I. Maldonado Cervantes63, L.
MalininaIV,66, D. Mal’Kevich58, P. Malzacher97, A. Mamonov99, V. Manko80, F.
Manso70, V. Manzari36,103, M. Marchisone126,27,65, J. Mareš60, G.V.
Margagliotti26, A. Margotti104, J. Margutti57, A. Marín97, C. Markert118, M.
Marquard53, N.A. Martin97, J. Martin Blanco113, P. Martinengo36, M.I.
Martínez2, G. Martínez García113, M. Martinez Pedreira36, A. Mas120, S.
Masciocchi97, M. Masera27, A. Masoni105, L. Massacrier113, A. Mastroserio33,
A. Matyja117, C. Mayer117, J. Mazer125, M.A. Mazzoni108, D. Mcdonald122, F.
Meddi24, Y. Melikyan75, A. Menchaca-Rocha64, E. Meninno31, J. Mercado Pérez94,
M. Meres39, Y. Miake128, M.M. Mieskolainen46, K. Mikhaylov58,66, L.
Milano36,74, J. Milosevic22, L.M. Minervini103,23, A. Mischke57, A.N.
Mishra49, D. Miśkowiec97, J. Mitra132, C.M. Mitu62, N. Mohammadi57, B.
Mohanty132,79, L. Molnar113,55, L. Montaño Zetina11, E. Montes10, D.A. Moreira
De Godoy113,54, L.A.P. Moreno2, S. Moretto30, A. Morreale113, A. Morsch36, V.
Muccifora72, E. Mudnic116, D. Mühlheim54, S. Muhuri132, M. Mukherjee132, J.D.
Mulligan136, M.G. Munhoz120, R.H. Munzer37,93, S. Murray65, L. Musa36, J.
Musinsky59, B. Naik48, R. Nair77, B.K. Nandi48, R. Nania104, E. Nappi103, M.U.
Naru16, H. Natal da Luz120, C. Nattrass125, K. Nayak79, T.K. Nayak132, S.
Nazarenko99, A. Nedosekin58, L. Nellen63, F. Ng122, M. Nicassio97, M.
Niculescu62, J. Niedziela36, B.S. Nielsen81, S. Nikolaev80, S. Nikulin80, V.
Nikulin86, F. Noferini12,104, P. Nomokonov66, G. Nooren57, J.C.C. Noris2, J.
Norman124, A. Nyanin80, J. Nystrand18, H. Oeschler94, S. Oh136, S.K. Oh67, A.
Ohlson36, A. Okatan69, T. Okubo47, L. Olah135, J. Oleniacz133, A.C. Oliveira
Da Silva120, M.H. Oliver136, J. Onderwaater97, C. Oppedisano110, R. Orava46,
A. Ortiz Velasquez63, A. Oskarsson34, J. Otwinowski117, K. Oyama94,76, M.
Ozdemir53, Y. Pachmayer94, P. Pagano31, G. Paić63, S.K. Pal132, J. Pan134,
A.K. Pandey48, P. Papcun115, V. Papikyan1, G.S. Pappalardo106, P. Pareek49,
W.J. Park97, S. Parmar88, A. Passfeld54, V. Paticchio103, R.N. Patra132, B.
Paul100, H. Pei7, T. Peitzmann57, H. Pereira Da Costa15, E. Pereira De
Oliveira Filho120, D. Peresunko80,75, C.E. Pérez Lara82, E. Perez Lezama53, V.
Peskov53, Y. Pestov5, V. Petráček40, V. Petrov111, M. Petrovici78, C. Petta29,
S. Piano109, M. Pikna39, P. Pillot113, O. Pinazza104,36, L. Pinsky122, D.B.
Piyarathna122, M. Płoskoń74, M. Planinic129, J. Pluta133, S. Pochybova135,
P.L.M. Podesta-Lerma119, M.G. Poghosyan85,87, B. Polichtchouk111, N.
Poljak129, W. Poonsawat114, A. Pop78, S. Porteboeuf-Houssais70, J. Porter74,
J. Pospisil84, S.K. Prasad4, R. Preghenella104,36, F. Prino110, C.A.
Pruneau134, I. Pshenichnov56, M. Puccio27, G. Puddu25, P. Pujahari134, V.
Punin99, J. Putschke134, H. Qvigstad22, A. Rachevski109, S. Raha4, S.
Rajput91, J. Rak123, A. Rakotozafindrabe15, L. Ramello32, F. Rami55, R.
Raniwala92, S. Raniwala92, S.S. Räsänen46, B.T. Rascanu53, D. Rathee88, K.F.
Read125,85, K. Redlich77, R.J. Reed134, A. Rehman18, P. Reichelt53, F.
Reidt94,36, X. Ren7, R. Renfordt53, A.R. Reolon72, A. Reshetin56, J.-P.
Revol12, K. Reygers94, V. Riabov86, R.A. Ricci73, T. Richert34, M. Richter22,
P. Riedler36, W. Riegler36, F. Riggi29, C. Ristea62, E. Rocco57, M. Rodríguez
Cahuantzi2,11, A. Rodriguez Manso82, K. Røed22, E. Rogochaya66, D. Rohr43, D.
Röhrich18, R. Romita124, F. Ronchetti72,36, L. Ronflette113, P. Rosnet70, A.
Rossi30,36, F. Roukoutakis89, A. Roy49, C. Roy55, P. Roy100, A.J. Rubio
Montero10, R. Rui26, R. Russo27, E. Ryabinkin80, Y. Ryabov86, A. Rybicki117,
S. Sadovsky111, K. Šafařík36, B. Sahlmuller53, P. Sahoo49, R. Sahoo49, S.
Sahoo61, P.K. Sahu61, J. Saini132, S. Sakai72, M.A. Saleh134, J. Salzwedel20,
S. Sambyal91, V. Samsonov86, L. Šándor59, A. Sandoval64, M. Sano128, D.
Sarkar132, E. Scapparone104, F. Scarlassara30, C. Schiaua78, R. Schicker94, C.
Schmidt97, H.R. Schmidt35, S. Schuchmann53, J. Schukraft36, M. Schulc40, T.
Schuster136, Y. Schutz36,113, K. Schwarz97, K. Schweda97, G. Scioli28, E.
Scomparin110, R. Scott125, M. Šefčík41, J.E. Seger87, Y. Sekiguchi127, D.
Sekihata47, I. Selyuzhenkov97, K. Senosi65, S. Senyukov3,36, E.
Serradilla10,64, A. Sevcenco62, A. Shabanov56, A. Shabetai113, O. Shadura3, R.
Shahoyan36, A. Shangaraev111, A. Sharma91, M. Sharma91, M. Sharma91, N.
Sharma125, K. Shigaki47, K. Shtejer9,27, Y. Sibiriak80, S. Siddhanta105, K.M.
Sielewicz36, T. Siemiarczuk77, D. Silvermyr34,85, C. Silvestre71, G.
Simatovic129, G. Simonetti36, R. Singaraju132, R. Singh79, S. Singha79,132, V.
Singhal132, B.C. Sinha132, T. Sinha100, B. Sitar39, M. Sitta32, T.B. Skaali22,
M. Slupecki123, N. Smirnov136, R.J.M. Snellings57, T.W. Snellman123, C.
Søgaard34, J. Song96, M. Song137, Z. Song7, F. Soramel30, S. Sorensen125, F.
Sozzi97, M. Spacek40, E. Spiriti72, I. Sputowska117, M. Spyropoulou-
Stassinaki89, J. Stachel94, I. Stan62, G. Stefanek77, E. Stenlund34, G.
Steyn65, J.H. Stiller94, D. Stocco113, P. Strmen39, A.A.P. Suaide120, T.
Sugitate47, C. Suire51, M. Suleymanov16, M. SuljicI,26, R. Sultanov58, M.
Šumbera84, A. Szabo39, A. Szanto de ToledoI,120, I. Szarka39, A.
Szczepankiewicz36, M. Szymanski133, U. Tabassam16, J. Takahashi121, G.J.
Tambave18, N. Tanaka128, M.A. Tangaro33, M. Tarhini51, M. Tariq19, M.G.
Tarzila78, A. Tauro36, G. Tejeda Muñoz2, A. Telesca36, K. Terasaki127, C.
Terrevoli30, B. Teyssier130, J. Thäder74, D. Thomas118, R. Tieulent130, A.R.
Timmins122, A. Toia53, S. Trogolo27, G. Trombetta33, V. Trubnikov3, W.H.
Trzaska123, T. Tsuji127, A. Tumkin99, R. Turrisi107, T.S. Tveter22, K.
Ullaland18, A. Uras130, G.L. Usai25, A. Utrobicic129, M. Vajzer84, M. Vala59,
L. Valencia Palomo70, S. Vallero27, J. Van Der Maarel57, J.W. Van Hoorne36, M.
van Leeuwen57, T. Vanat84, P. Vande Vyvre36, D. Varga135, A. Vargas2, M.
Vargyas123, R. Varma48, M. Vasileiou89, A. Vasiliev80, A. Vauthier71, V.
Vechernin131, A.M. Veen57, M. Veldhoen57, A. Velure18, M. Venaruzzo73, E.
Vercellin27, S. Vergara Limón2, R. Vernet8, M. Verweij134, L. Vickovic116, G.
ViestiI,30, J. Viinikainen123, Z. Vilakazi126, O. Villalobos Baillie101, A.
Villatoro Tello2, A. Vinogradov80, L. Vinogradov131, Y. VinogradovI,99, T.
Virgili31, V. Vislavicius34, Y.P. Viyogi132, A. Vodopyanov66, M.A. Völkl94, K.
Voloshin58, S.A. Voloshin134, G. Volpe135, B. von Haller36, I. Vorobyev37,93,
D. Vranic97,36, J. Vrláková41, B. Vulpescu70, A. Vyushin99, B. Wagner18, J.
Wagner97, H. Wang57, M. Wang7,113, D. Watanabe128, Y. Watanabe127, M.
Weber112,36, S.G. Weber97, D.F. Weiser94, J.P. Wessels54, U. Westerhoff54,
A.M. Whitehead90, J. Wiechula35, J. Wikne22, M. Wilde54, G. Wilk77, J.
Wilkinson94, M.C.S. Williams104, B. Windelband94, M. Winn94, C.G. Yaldo134, H.
Yang57, P. Yang7, S. Yano47, C. Yasar69, Z. Yin7, H. Yokoyama128, I.-K. Yoo96,
J.H. Yoon50, V. Yurchenko3, I. Yushmanov80, A. Zaborowska133, V. Zaccolo81, A.
Zaman16, C. Zampolli104, H.J.C. Zanoli120, S. Zaporozhets66, N. Zardoshti101,
A. Zarochentsev131, P. Závada60, N. Zaviyalov99, H. Zbroszczyk133, I.S.
Zgura62, M. Zhalov86, H. Zhang18, X. Zhang74, Y. Zhang7, C. Zhang57, Z.
Zhang7, C. Zhao22, N. Zhigareva58, D. Zhou7, Y. Zhou81, Z. Zhou18, H. Zhu18,
J. Zhu113,7, A. Zichichi28,12, A. Zimmermann94, M.B. Zimmermann36,54, G.
Zinovjev3, M. Zyzak43

Affiliation Notes

I Deceased

II Also at: Georgia State University, Atlanta, Georgia, United States

III Also at Department of Applied Physics, Aligarh Muslim University, Aligarh,
India

IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia

Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

2 Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

3 Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

5 Budker Institute for Nuclear Physics, Novosibirsk, Russia

6 California Polytechnic State University, San Luis Obispo, California, United
States

7 Central China Normal University, Wuhan, China

8 Centre de Calcul de l’IN2P3, Villeurbanne, France

9 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

10 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

11 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

12 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico
Fermi”, Rome, Italy

13 Chicago State University, Chicago, Illinois, USA

14 China Institute of Atomic Energy, Beijing, China

15 Commissariat à l’Energie Atomique, IRFU, Saclay, France

16 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

17 Departamento de Física de Partículas and IGFAE, Universidad de Santiago de
Compostela, Santiago de Compostela, Spain

18 Department of Physics and Technology, University of Bergen, Bergen, Norway

19 Department of Physics, Aligarh Muslim University, Aligarh, India

20 Department of Physics, Ohio State University, Columbus, Ohio, United States

21 Department of Physics, Sejong University, Seoul, South Korea

22 Department of Physics, University of Oslo, Oslo, Norway

23 Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari, Italy

24 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN Rome,
Italy

25 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

26 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

27 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

29 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

30 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

31 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

32 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy

33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

34 Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

35 Eberhard Karls Universität Tübingen, Tübingen, Germany

36 European Organization for Nuclear Research (CERN), Geneva, Switzerland

37 Excellence Cluster Universe, Technische Universität München, Munich,
Germany

38 Faculty of Engineering, Bergen University College, Bergen, Norway

39 Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

40 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

41 Faculty of Science, P.J. Šafárik University, Košice, Slovakia

42 Faculty of Technology, Buskerud and Vestfold University College, Vestfold,
Norway

43 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

44 Gangneung-Wonju National University, Gangneung, South Korea

45 Gauhati University, Department of Physics, Guwahati, India

46 Helsinki Institute of Physics (HIP), Helsinki, Finland

47 Hiroshima University, Hiroshima, Japan

48 Indian Institute of Technology Bombay (IIT), Mumbai, India

49 Indian Institute of Technology Indore, Indore (IITI), India

50 Inha University, Incheon, South Korea

51 Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-
IN2P3, Orsay, France

52 Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

53 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

54 Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

55 Institut Pluridisciplinaire Hubert Curien (IPHC), Université de Strasbourg,
CNRS-IN2P3, Strasbourg, France

56 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

57 Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands

58 Institute for Theoretical and Experimental Physics, Moscow, Russia

59 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

60 Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

61 Institute of Physics, Bhubaneswar, India

62 Institute of Space Science (ISS), Bucharest, Romania

63 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

64 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico

65 iThemba LABS, National Research Foundation, Somerset West, South Africa

66 Joint Institute for Nuclear Research (JINR), Dubna, Russia

67 Konkuk University, Seoul, South Korea

68 Korea Institute of Science and Technology Information, Daejeon, South Korea

69 KTO Karatay University, Konya, Turkey

70 Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

71 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France

72 Laboratori Nazionali di Frascati, INFN, Frascati, Italy

73 Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

74 Lawrence Berkeley National Laboratory, Berkeley, California, United States

75 Moscow Engineering Physics Institute, Moscow, Russia

76 Nagasaki Institute of Applied Science, Nagasaki, Japan

77 National Centre for Nuclear Studies, Warsaw, Poland

78 National Institute for Physics and Nuclear Engineering, Bucharest, Romania

79 National Institute of Science Education and Research, Bhubaneswar, India

80 National Research Centre Kurchatov Institute, Moscow, Russia

81 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

82 Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands

83 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

84 Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež u
Prahy, Czech Republic

85 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

86 Petersburg Nuclear Physics Institute, Gatchina, Russia

87 Physics Department, Creighton University, Omaha, Nebraska, United States

88 Physics Department, Panjab University, Chandigarh, India

89 Physics Department, University of Athens, Athens, Greece

90 Physics Department, University of Cape Town, Cape Town, South Africa

91 Physics Department, University of Jammu, Jammu, India

92 Physics Department, University of Rajasthan, Jaipur, India

93 Physik Department, Technische Universität München, Munich, Germany

94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany

95 Purdue University, West Lafayette, Indiana, United States

96 Pusan National University, Pusan, South Korea

97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany

98 Rudjer Bošković Institute, Zagreb, Croatia

99 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

100 Saha Institute of Nuclear Physics, Kolkata, India

101 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

102 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru

103 Sezione INFN, Bari, Italy

104 Sezione INFN, Bologna, Italy

105 Sezione INFN, Cagliari, Italy

106 Sezione INFN, Catania, Italy

107 Sezione INFN, Padova, Italy

108 Sezione INFN, Rome, Italy

109 Sezione INFN, Trieste, Italy

110 Sezione INFN, Turin, Italy

111 SSC IHEP of NRC Kurchatov institute, Protvino, Russia

112 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

113 SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France

114 Suranaree University of Technology, Nakhon Ratchasima, Thailand

115 Technical University of Košice, Košice, Slovakia

116 Technical University of Split FESB, Split, Croatia

117 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland

118 The University of Texas at Austin, Physics Department, Austin, Texas, USA

119 Universidad Autónoma de Sinaloa, Culiacán, Mexico

120 Universidade de São Paulo (USP), São Paulo, Brazil

121 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

122 University of Houston, Houston, Texas, United States

123 University of Jyväskylä, Jyväskylä, Finland

124 University of Liverpool, Liverpool, United Kingdom

125 University of Tennessee, Knoxville, Tennessee, United States

126 University of the Witwatersrand, Johannesburg, South Africa

127 University of Tokyo, Tokyo, Japan

128 University of Tsukuba, Tsukuba, Japan

129 University of Zagreb, Zagreb, Croatia

130 Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne,
France

131 V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

132 Variable Energy Cyclotron Centre, Kolkata, India

133 Warsaw University of Technology, Warsaw, Poland

134 Wayne State University, Detroit, Michigan, United States

135 Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

136 Yale University, New Haven, Connecticut, United States

137 Yonsei University, Seoul, South Korea

138 Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany


∎

11institutetext: Yuta Harayama 22institutetext: Department of Electrical
Engineering, Faculty of Engineering, Fukuoka Institute of Technology, 3-30-1
Wajiro-higashi, Higashi-ku, Fukuoka 811-0295, Japan
33institutetext: Jiro Kitagawa 44institutetext: Department of Electrical
Engineering, Faculty of Engineering, Fukuoka Institute of Technology, 3-30-1
Wajiro-higashi, Higashi-ku, Fukuoka 811-0295, Japan
44email<EMAIL_ADDRESS>
# Superconductivity in Al-Nb-Ti-V-Zr multicomponent alloy

Yuta Harayama  Jiro Kitagawa

(Received: date / Accepted: date)

###### Abstract

The superconducting high-entropy alloys (HEAs) recently attract considerable
attention due to their exciting properties, such as the robustness of
superconductivity against atomic disorder and extremely high-pressure. The
well-studied crystal structure of superconducting HEAs is body-centered-cubic
(bcc) containing Nb, Ti, and Zr atoms. The same elements are contained in
Al5Nb24Ti40V5Zr26, which is a recently discovered bcc HEA and shows a gum-
metal-like behavior after cold rolling. The gum metal is also an interesting
system, exhibiting superelasticity and low Young’s modulus. If gum metals show
superconductivity and can be used as a superconducting wire, the gum-metal HEA
superconductors might be the next-generation superconducting wire materials.
Aiming at a fundamental assessment of as-cast Al-Nb-Ti-V-Zr multicomponent
alloys including Al5Nb24Ti40V5Zr26, we have investigated the structural and
superconducting properties of the alloys. All alloys investigated show the
superconductivity, and the valence electron concentration dependence of the
superconducting critical temperature is very close to those of typical
superconducting bcc HEAs.

###### Keywords:

multicomponent alloy high-entropy alloy superconductivity gum metal

##  1 Introduction

High-entropy alloy (HEA) is a new class of materials and was initially
proposed for simple crystal structures such as face-centered-cubic, body-
centered-cubic (bcc), and hexagonal-closed packing in which more than five
elements, each having the atomic fraction between 5% and 35%, randomly occupy
one crystallographic siteGao:book ; Murty:book . Nowadays, the HEA concept is
adopted in many alloys with multiple Wyckoff positions, oxides, chalcogenides,
etc.Kitagawa:Metals ; Musico:APLMat ; Jiang:Science . The definition of HEA
other than by the atomic concentration relies on the order of mixing entropy
$\Delta S_{\mathrm{mix}}$: low-entropy alloys as having $\Delta
S_{\mathrm{mix}}$ less than 0.69$R$ ($R$ is the gas constant), medium-entropy
alloys with $\Delta S_{\mathrm{mix}}$ between 0.69$R$ and 1.60$R$, and HEAs
with $\Delta S_{\mathrm{mix}}$ of 1.60$R$ or largerOtto:ActaMater . The high
atomic-disorder leads to the severe lattice distortion effect, and especially
bcc HEAs show the enhancement of mechanical properties, which attract
researchers all over the world. The enhancement of property beyond the simple
mixture of those of constituent elements is also observed as, for example,
outstanding thermal stability or enhanced magnetic frustrationSun:MRL ;
Marik:ScrMat .

The HEA superconductivity is one of the hot topics of the HEA research field
due to its exotic propertiesKitagawa:Metals ; Sun:PRM . For example, the
superconductivity is robust against atomic disorder and highly insensitive to
the application of extremely high-pressureRohr:PNAC ; Guo:PNAC . Although the
bcc HEA superconductors have been well studiedRohr:PNAC ; Guo:PNAC ;
Kozelj:PRL ; Rohr:PRM ; Marik:JALCOM ; Ishizu:RINP ; Nelson:SciRep ; Zhang:PRR
; Kim:ActaMater , several HEAs with multisite crystal structures such as the
CsCl-type, A15, NaCl-type, $\sigma$-phase, and layered structures also show
the interesting superconductivitiesStolze:ChemMater ; Wu:SCM ; Mizuguchi:JPSJ
; Yamashita:DalTra ; Liu:JALCOM ; Sogabe:APE ; Sogabe:SSC . While the relation
between the superconductivity and the high-entropy state is unclear in many
systems, in high-entropy (La0.2Ce0.2Pr0.2Nd0.2Sm0.2)O0.5F0.5BiS2 with the
BiS2-based superconducting layer and the REO (RE: rare earth) blocking layer,
the bulk nature of superconductivity is improved compared to PrO0.5F0.5BiS2
with the low-entropy state, which suggests that the mixing entropy at the
blocking layer severely affects the superconducting stateSogabe:APE ;
Sogabe:SSC .

The gum metals, which have received considerable attention due to their
unusual mechanical behaviors such as superelasticity and low Young’s
modulusSaito:Science , possess chemical compositions similar to those of bcc
HEA superconductors. The unusual properties are obtained after the cold
rolling of as-cast materials. The valence electron concentration per atom
(VEC) of the gum metals is 4.24, which is appropriate for the appearance of
the superconductivity of $d$-electron alloy superconductors. Recently
Al5Nb24Ti40V5Zr26 is reported as a gum-metal-like HEAZherebtsov:Int . If gum
metals show superconductivity, they are highly advantageous for making
superconducting wires, and this kind of material may be a good candidate for
the next-generation superconducting wire.

In this paper, we have started from Al5Nb24Ti40V5Zr26, and characterized the
structural and superconducting properties of Al5NbxTi35V5Zr55-x and
Al5NbxTi59-xV5Zr31 alloys in the as-cast form. The superconducting properties
were investigated by measuring the ac magnetic susceptibility and the
electrical resistivity. This study will contribute to the basic understanding
of superconductivity in gum metals in the future.

##  2 Materials and methods

Eight polycrystalline samples with different atomic compositions, as listed in
Table 1, were synthesized by a home-made arc furnace. The constituent elements
of Al (99.99 %), Nb (99.9 %), Ti (99.9 %), V (99.9 %), and Zr (99.5%), were
arc-melted on a water-cooled Cu hearth in an Ar atmosphere. The samples
received no heat treatment.

The X-ray diffraction (XRD) patterns of prepared samples were checked by an
X-ray diffractometer (XRD-7000L, Shimadzu, Kyoto, Japan) with Cu-K$\alpha$
radiation. We used thin slabs cut from the as-cast samples due to their high
ductility. The microstructure of each sample was investigated by a field
emission scanning electron microscope (FE-SEM, JSM-7100F; JEOL, Akishima,
Japan). The atomic compositions of the samples were determined by an energy
dispersive X-ray (EDX) spectrometer equipped to the FE-SEM.

The temperature dependence of ac magnetic susceptibility $\chi_{ac}$ ($T$) in
an alternating field of 5 Oe at 800 Hz, between 2.8 K and 300 K, was measured
by a mutual inductance method using a GM refrigerator (UW404, Ulvac
cryogenics, Kyoto, Japan). The temperature dependence of electrical
resistivity $\rho$ ($T$) between 2.8 K and 300 K was measured by the
conventional dc four-probe method using the GM refrigerator.

Table 1: Atomic composition determined by EDX measurement, lattice parameter $a$, $\delta$, and $\Delta S_{\mathrm{mix}}/R$ of prepared samples. Sample | Atomic composition | a (Å) | $\delta$ | $\Delta S_{\mathrm{mix}}/R$
---|---|---|---|---
Al5Nb24Ti40V5Zr26 | Al5.1(3)Nb25(1)Ti38.6(6)V4.6(2)Zr27(1) | 3.349(3) | 5.28 | 1.359
Al5Nb14Ti35V5Zr41 | Al5.1(3)Nb14.6(5)Ti33.6(3)V4.9(4)Zr41.8(4) | 3.407(4) | 5.72 | 1.308
Al5Nb24Ti35V5Zr31 | Al4.8(2)Nb25.7(7)Ti33.6(3)V4.5(5)Zr31.4(3) | 3.368(1) | 5.53 | 1.373
Al5Nb34Ti35V5Zr21 | Al5.0(1)Nb33.5(6)Ti33.5(3)V5.2(3)Zr22.9(5) | 3.342(2) | 5.06 | 1.362
Al5Nb44Ti35V5Zr11 | Al4.6(2)Nb45.1(8)Ti34.1(3)V4.7(1)Zr11.5(7) | 3.314(2) | 4.18 | 1.271
Al5Nb14Ti45V5Zr31 | Al4.7(2)Nb12.9(4)Ti47.7(5)V5.5(3)Zr29.2(5) | 3.372(1) | 5.40 | 1.297
Al5Nb34Ti25V5Zr31 | Al4.9(2)Nb32.7(5)Ti27.7(3)V6.0(4)Zr28.7(7) | 3.371(2) | 5.65 | 1.376
Al5Nb44Ti15V5Zr31 | Al5.0(2)Nb40.9(7)Ti17.6(2)V5.8(3)Zr30.6(7) | 3.371(1) | 5.77 | 1.308

##  3 Results and discussion

The XRD pattern of Al5Nb24Ti40V5Zr26 is characterized by a single-phase bcc
with the lattice parameter $a=$3.349 $\AA$, which is consistent with the
reported value 3.350 $\AA$Zherebtsov:Int  (see Table 1 and the inset of Figure
1(a)). Al5Nb24Ti40V5Zr26 exhibits the diamagnetic signal and the zero
resistivity as shown in Figs. 1(a) and 1(b), respectively. In the measurement
of the real part of ac magnetic susceptibility $\chi_{ac}^{{}^{\prime}}$
($T$), the superconducting critical temperature $T_{\mathrm{c}}$ is determined
as being the intercept of the linearly extrapolated diamagnetic slope with the
normal state signalRohr:PNAC ; Hamamoto:MRX  (see the broken lines in Fig.
1(a)). $T_{\mathrm{c}}$ in $\rho$ ($T$) measurement is determined from the
onset of the transition. The inset of Fig. 1(b) shows the $\rho$ data in the
whole measured temperature range, which indicates the weak temperature
dependence in the normal state due to the atomic disorder.

Figure 1: (a) Temperature dependence of real part of $\chi_{ac}$ for
Al5Nb24Ti40V5Zr26. The inset is the XRD pattern of Al5Nb24Ti40V5Zr26. (b)
Temperature dependence of $\rho$ for Al5Nb24Ti40V5Zr26 at low temperatures.
The inset is $\rho$ in the whole measured temperature range. Figure 2: X-ray
diffraction patterns of (a) Al5NbxTi35V5Zr55-x and (b) Al5NbxTi59-xV5Zr31,
respectively. The origin of each pattern is shifted by an integer value for
clarity. (c) Nb content dependences of lattice parameter of Al5NbxTi35V5Zr55-x
and Al5NbxTi59-xV5Zr31.

Figures 2(a) and 2(b) show the XRD patterns of Al5NbxTi35V5Zr55-x and
Al5NbxTi59-xV5Zr31, respectively. In each sample, the diffraction peaks can be
well indexed by a bcc structure. The lattice parameters are obtained by a
least-mean square method (see Table 1) and plotted as a function of Nb content
$x$ in Fig. 2(c). For Al5NbxTi35V5Zr55-x, the lattice parameter shrinks with
increasing $x$, which is contrasted with the almost $x$-independent lattice
parameters in Al5NbxTi59-xV5Zr31. The SEM images of representative samples are
displayed in Figures 3(a) and 3(b), indicating no apparent impurity phase.
Each elemental mapping also supports the homogeneous elemental distribution.
Table 1 shows the atomic compositions of the samples determined by EDX
measurements. The respective composition agrees with the stating composition.

Figure 3: SEM images of (a) Al5Nb24Ti35V5Zr31 and (b) Al5Nb34Ti25V5Zr31,
respectively. The elemental mappings are also shown.

Shown in Figs. 4(a) and 4(b) are $\chi_{ac}^{{}^{\prime}}$ ($T$) of
Al5NbxTi35V5Zr55-x and Al5NbxTi59-xV5Zr31, respectively. All samples exhibit
diamagnetic signals. In both alloy systems, $T_{\mathrm{c}}$ systematically
increases with increasing Nb concentration. Figures 5(a) and 5(b) exhibit
$\rho$ ($T$) of Al5NbxTi35V5Zr55-x and Al5NbxTi59-xV5Zr31, respectively, which
are normalized by the room temperature values listed in Table 2. The
temperature dependence in the normal state tends to be weaker with decreasing
Nb content. In each alloy system, the $x$=14 sample exhibit a negative
temperature coefficient of resistivity, suggesting an occurrence of carrier
localization. The insets are $\rho$ ($T$) at low temperatures, all showing
drops to zero resistivity. Table 2 summarizes $T_{\mathrm{c}}$’s in
$\chi_{ac}^{{}^{\prime}}$ ($T$) and $\rho$ ($T$) measurements, which are
determined by the same methods in Al5Nb24Ti40V5Zr26.

Figure 4: Temperature dependences of real part of $\chi_{ac}$ for (a) Al5NbxTi35V5Zr55-x and (b) Al5NbxTi59-xV5Zr31, respectively. Figure 5: Temperature dependences of $\rho$ normalized by room temperature (RT) values for (a) Al5NbxTi35V5Zr55-x and (b) Al5NbxTi59-xV5Zr31, respectively. The insets are $\rho$ ($T$) at low temperatures. Table 2: VEC, $T_{\mathrm{c}}$’s determined by $\chi_{ac}$ and $\rho$ measurements, and $\rho$ at room temperature of prepared samples. Sample | VEC |  $T_{\mathrm{c}}$ (K) |  $T_{\mathrm{c}}$ (K) |  $\rho$ at room
---|---|---|---|---
|  | by $\chi_{ac}$ | by $\rho$ | temperature ($\mu\Omega$cm)
Al5Nb24Ti40V5Zr26 | 4.24 | 5.50 | 5.36 | 102.3
Al5Nb14Ti35V5Zr41 | 4.14 | 4.73 | 4.40 | 88.3
Al5Nb24Ti35V5Zr31 | 4.24 | 5.45 | 5.43 | 111.5
Al5Nb34Ti35V5Zr21 | 4.34 | 6.47 | 6.48 | 105.2
Al5Nb44Ti35V5Zr11 | 4.44 | 6.75 | 6.66 | 69.4
Al5Nb14Ti45V5Zr31 | 4.14 | 4.96 | 4.65 | 111.6
Al5Nb34Ti25V5Zr31 | 4.34 | 6.18 | 6.38 | 61.3
Al5Nb44Ti15V5Zr31 | 4.44 | 6.98 | 7.01 | 76.6

Here we discuss the relationship between $T_{\mathrm{c}}$ and the parameter
$\delta$ or mixing entropy $\Delta S_{\mathrm{mix}}$. The parameter $\delta$
is employed in the material design of HEAs and means the degree of the atomic
size difference among the constituent elementsGao:book ; Murty:book . This was
calculated for an $n$-component alloy as follows:

$\delta=100\times\sqrt{\sum^{n}_{i=1}c_{i}\left(1-\frac{r_{i}}{\bar{r}}\right)^{2}},$
(1)

where $c_{i}$ and $r_{i}$ are the atomic fraction and the atomic radius of the
$i$-th element, respectively, and $\bar{r}$ is the composition-weighted
average atomic radius. The values of $r_{i}$ are taken from
ref.Miracle:ActaMater . $\Delta S_{\mathrm{mix}}$ is given by

$\Delta S_{\mathrm{mix}}=-R\sum^{n}_{i=1}c_{i}lnc_{i},$ (2)

where $R$ is the gas constant. As mentioned in the introduction, there are two
well-accepted definitionsGao:book ; Murty:book  for HEAs. Although the three
alloys Al5Nb24Ti35V5Zr31, Al5Nb34Ti35V5Zr21, and Al5Nb34Ti25V5Zr31 fulfill the
definition by the atomic percentage, each having 5 % $\leq$ $c_{i}$ $\leq$ 35
%, $\Delta S_{\mathrm{mix}}$’s of all alloys investigated are rather smaller
than 1.60$R$ (see also Table 1). Figures 6(a) and 6(b) explain the $\delta$ or
$\Delta S_{\mathrm{mix}}/R$ dependences of $T_{\mathrm{c}}$ for both alloy
systems. For Al5NbxTi35V5Zr55-x, $T_{\mathrm{c}}$ increases with decreasing
$\delta$, which is contrasted with the $\delta$ dependence of $T_{\mathrm{c}}$
in Al5NbxTi59-xV5Zr31. This means the robustness of superconductivity against
the lattice distortion, which would be one of the characteristics of bcc HEA
superconductors. In both alloy systems, $T_{\mathrm{c}}$ shows the non-
monotonous $\Delta S_{\mathrm{mix}}$ dependences. Therefore, $T_{\mathrm{c}}$
does not severely rely on the high-entropy effect.

Figure 6: (a)$T_{\mathrm{c}}$ vs $\delta$ plot and (b)$T_{\mathrm{c}}$ vs
$\Delta S_{\mathrm{mix}}/R$ plot for Al5NbxTi35V5Zr55-x and
Al5NbxTi59-xV5Zr31.

Figure 7 shows the VEC dependence of $T_{\mathrm{c}}$ for Al-Nb-Ti-V-Zr
multicomponent alloys, which is compared to those of crystalline 4$d$ metal
solid solutionsSun:PRM  (the dotted line) and typical superconducting bcc
HEAsRohr:PNAC ; Kozelj:PRL ; Marik:JALCOM ; Ishizu:RINP  (Ta-Nb-Hf-Zr-Ti,
Nb20Re20Zr20Hf20Ti20, and Hf21Nb25Ti15V15Zr24). Although $T_{\mathrm{c}}$’s of
these HEAs are relatively lower than those of 4$d$ metal solid solutions at a
fixed VEC, the VEC dependence is similar to each other; $T_{\mathrm{c}}$ seems
to form a broad maximum at approximately VEC=4.7. The VEC dependence of
$T_{\mathrm{c}}$ of Al-Nb-Ti-V-Zr multicomponent alloy falls on those of bcc
HEAs, whereas $\Delta S_{\mathrm{mix}}$’s of the present alloys are lower.
Ternary alloys Nb-Ti-Zr are also superconductorsRoberts:JPCRD , and the data
is plotted in Figure 7 (Nb50Ti10Zr40: $T_{\mathrm{c}}=$10.3 K, Nb35Ti15Zr50:
$T_{\mathrm{c}}=$8.95 K, Nb35Ti60Zr5: $T_{\mathrm{c}}=$8.6 K, and
Nb21Ti61Zr18: $T_{\mathrm{c}}=$6.8 K). The plot well agrees with the Matthias
rule of 4$d$ metal solid solutions. Therefore, a multicomponent alloy composed
of five elements might generally show the lowered $T_{\mathrm{c}}$ compared to
simple 4$d$ metal solid solutions.

Figure 7: VEC dependences of $T_{\mathrm{c}}$ for alloys denoted in figure
legend. The same dependence is also shown for crystalline 4$d$ metal solid
solutions by the dotted line. Data for the dotted line is from ref.Sun:PRM .

Several superconductors maintain the superconducting state after the cold
rolling processRaabe:ActaMater ; Guryev:JPCS ; Idczak:PLA . Thus we can expect
the same result for the present alloys. It would be important to elucidate the
relationship between the mechanical properties of Al-Nb-Ti-V-Zr alloys,
including gum-metal composition, and the superconducting properties in order
to know whether the gum-metal HEA superconductors can be candidate for the
next-generation superconducting wire or not.

##  4 Summary

We have characterized new multicomponent alloy superconductors Al-Nb-Ti-V-Zr
including Al5Nb24Ti40V5Zr26 which exhibits a gum-metal-like behavior after the
cold rolling. All as-cast samples crystallize into the bcc structure with no
obvious secondary phase. The lattice parameters of Al5NbxTi35V5Zr55-x and
Al5NbxTi59-xV5Zr31 exhibit the different $x$ dependences. Al5NbxTi35V5Zr55-x
shows the shrink of lattice parameter with increasing $x$, whereas the almost
$x$-independent lattice parameters are observed in Al5NbxTi59-xV5Zr31.
Nonetheless, the similar VEC dependence of $T_{\mathrm{c}}$ is confirmed for
both alloy systems. Although the ternary superconducting Nb-Ti-Zr alloys well
obey the Matthias rule of crystalline 4$d$ metal solid solutions, the present
alloys show lower $T_{\mathrm{c}}$’s compared to ternary Nb-Ti-Zr alloys.
However, the VEC dependence of $T_{\mathrm{c}}$ of Al-Nb-Ti-V-Zr alloys falls
on those of the typical bcc HEA superconductors. Therefore, a multicomponent
alloy composed of five elements might generally behave as an HEA
superconductor, even if the mixing entropy is rather smaller than 1.60$R$.
This study will be useful for the fundamental understanding of
superconductivity in gum metals.

###### Acknowledgements.

J.K. is grateful for the support provided by Comprehensive Research
Organization of Fukuoka Institute of Technology.

## References

  * (1) Gao,M. C., Yeh, J. -W., Liaw, P. K., Zhang, Y.: High-Entropy Alloys: Fundamentals and Applications, (Swizerland: Springer, 2015)
  * (2) Murty, B. S. Yeh, J. -W., Ranganathan, S., Bhattacharjee, P. P.: High-Entropy Alloys. 2nd ed., (Amsterdam: Elsevier, 2019)
  * (3) Kitagawa, J., Hamamoto, S., Ishizu, N.: Cutting Edge of High-Entropy Alloy Superconductors from the Perspective of Materials Research, Metals 10, 1078 (2020)
  * (4) Musicó, B. L., Gilbert, D., Ward, L. Z., Page, K., George, E., Yan, J., Mandrus, D., Keppens, V.: The emergent field of high entropy oxides: Design, prospects, challenges, and opportunities for tailoring material properties, APL Materials 8, 040912 (2020)
  * (5) Jiang, B., Yu, Y., Cui, J., Liu, X., Xie, L., Liao, J., Zhang, Q., Huang, Y., Ning, S., Jia, B., Zhu, B., Bai, S., Chen, L., Pennycook, S. J., He, J.: High-entropy-stabilized chalcogenides with high thermoelectric performance, Science 371, 830-834 (2021)
  * (6) Otto, F., Yang, Y., Bei, H., George, E. P.: Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys, Acta Mater. 61 2628-2638 (2013)
  * (7) Sun, L., Luo, Y., Ren, X., Gao, Z., Du, T., Wu, Z., Wang, J.: A multicomponent $\gamma$-type (Gd1/6Tb1/6Dy1/6Tm1/6Yb1/6Lu1/6)2Si2O7 disilicate with outstanding thermal stability, Mater. Res. Lett. 8 424-430 (2020)
  * (8) Marik, S., Singh, D., Gonano, B., Veillon, F., Pelloquin, D., Bréard, Y.: Enhanced magnetic frustration in a new high entropy diamond lattice spinel oxide. Scr. Mater.186, 366-369 (2020)
  * (9) Sun, L., Cava, R. J.: High-entropy alloy superconductors: Status, opportunities, and challenges, Phys. Rev. Mater. 3, 090301 (2019)
  * (10) von Rohr, F. O., Winiarski, M. J., Tao, J., Klimczuk, T., Cava, R. J.: Effect of electron count and chemical complexity in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor, Proc. Natl. Acad. Sci.113, E7144-E7150 (2016)
  * (11) Guo, J., Wang, H., von Rohr, F., Wang, Z., Cai, S., Zhou, Y., Yang, K., Li, A., Jiang, S., Wu, Q., Cava, R. J., Sun, L.: Robust zero resistance in a superconducting high-entropy alloy at pressures up to 190 GPa, Proc. Natl. Acad. Sci. 114, 13144-13147 (2017)
  * (12) Koželj, P., Vrtnik, S., Jelen, A., Jazbec, S., Jagličić, Z., Maiti, S., Feuerbacher, M., Steurer, W, Dolinšek, J.: Discovery of a superconducting high-entropy alloy, Phys. Rev. Lett. 113, 107001 (2014)
  * (13) von Rohr, F. O., Cava, R. J.: Isoelectronic substitutions and aluminium alloying in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor, Phys. Rev. Mater. 2, 034801 (2018)
  * (14) Marik, S., Varghese, M., Sajilesh, K. P., Singh, D., Singh, R. P.: Superconductivity in equimolar Nb-Re-Hf-Zr-Ti high entropy alloy, J. Alloys and Compd. 769, 1059-1063 (2018)
  * (15) Ishizu, N., Kitagawa, J.: New high-entropy alloy superconductor Hf21Nb25Ti15V15Zr24, Res. Phys. 13, 102275 (2019)
  * (16) Nelson, W. L., Chemey, A. T., Hertz, M., Choi, E., Graf, D. E., Latturner, S., Albrecht-Schmitt, T. E., Wei, K., Baumbach, R. E.: Superconductivity in a uranium containing high entropy alloy, Sci. Rep. 10, 4717 (2020)
  * (17) Zhang, X., Winter, N., Witteveen, C., Moehl, T., Xiao, Y., Krogh, F., Schilling, A., von Rohr, F. O.: Preparation and characterization of high-entropy alloy (TaNb)1-x(ZrHfTi)x superconducting films, Phys. Rev. Res. 2, 013375 (2020)
  * (18) Kim, G., Lee, M. -H., Yun, J. H., Rawat, P., Jung, S. -G., Choi, W., You, T. -S., Kim, S. J., Rhyee, J. -S.: Strongly correlated and strongly coupled s-wave superconductivity of the high entropy alloy Ta1/6Nb2/6Hf1/6Zr1/6Ti1/6 compound, Acta Mater. 186, 250-256 (2020)
  * (19) Stolze, K., Tao, J., von Rohr, F. O., Kong, T., Cava, R. J.: Sc-Zr-Nb-Rh-Pd and Sc-Zr-Nb-Ta-Rh-Pd high-entropy alloy superconductors on a CsCl-type lattice, Chem. Mater. 30, 906-914 (2018)
  * (20) Wu, J., Liu, B., Cui, Y., Zhu, Q., Xiao, G., Wang, H., Wu, S., Cao, G., Ren, Z.: Polymorphism and superconductivity in the V-Nb-Mo-Al-Ga high-entropy alloys, Sci. China Mater. 63, 823-831 (2020)
  * (21) Mizuguchi, Y.: Superconductivity in high-entropy-alloy telluride AgInSnPbBiTe5, J. Phys. Soc. Jpn. 88, 124708 (2019)
  * (22) Yamashita, A., Jha, R., Goto, Y., Matsuda, T. D., Aoki, Y., Mizuguchi, Y.: An Efficient way of increasing the total entropy of mixing in high-entropy-alloy compounds: a case of NaCl-type (Ag,In,Pb,Bi)Te${1-x}$Sex (x = 0.0, 0.25, 0.5) superconductors, Dalton Trans. 49, 9118-9122 (2020)
  * (23) Liu, B., Wu, J., Cui, Y., Zhu, Q., Xiao, G., Wu, S., Cao, G., Ren, Z.: Superconductivity and paramagnetism in Cr-containing tetragonal high-entropy alloys, J. Alloys and Compd. 159293 869, (2021)
  * (24) Sogabe, R., Goto, Y., Mizuguchi, Y.: Superconductivity in REO0.5F0.5BiS2 with high entropy-alloy-type blocking layers, Appl. Phys. Express 11, 053102 (2018)
  * (25) Sogabe, R., Goto, Y., Abe, T., Moriyoshi, C., Kuroiwa, Y., Miura, A., Tadanaga, K., Mizuguchi, Y.: Improvement of superconducting properties by high mixing entropy at blocking layers in BiS2-based superconductor REO0.5F0.5BiS2, Solid State Commun. 295, 43-49 (2019)
  * (26) Saito, T., Furuta, T., Hwang, J. -H., Kuramoto, S., Nishino, K., Suzuki, N., Chen, R., Yamada, A., Ito, K., Seno, Y., Nonaka, T., Ikehata, H., Nagasako, N., Iwamoto, C., Ikuhara, Y., Sakuma, T.: Multifunctional alloys obtained via a dislocation free plastic deformation mechanism. Science 300, 464-467 (2003)
  * (27) Zherebtsov, S., Yurchenko, N., Panina, E., Tikhonovsky, M., Stepanov, N.: Gum-like mechanical behavior of a partially ordered Al5Nb24Ti40V5Zr26 high entropy alloy, Intermetallics 116, 106652 (2020)
  * (28) Hamamoto, S., Kitagawa, J.: Superconductivity in oxygen-added Zr5Pt3, Mater. Res. Express 5, 106001 (2018)
  * (29) Miracle, D. B., Senkov, O. N.: A critical review of high entropy alloys and related concepts, Acta Mater. 122, 448-511 (2017)
  * (30) Roberts, B. W.: Survey of superconductive materials and critical evaluation of selected properties, J. Phys. Chem. Ref. Data 5, 581-821 (1976)
  * (31) Raabe, D., Hangen, U.: Correlation of microstructure and type II superconductivity of a heavily cold rolled Cu-20mass% Nb in situ composite, Acta Mater. 44, 953-961 (1996)
  * (32) Guryev, V. V., Shavkin, S. V., Kruglov, V. S., Volkov, P. V., Vasiliev, A. L., Ovcharov, A. V., Likhachev, I. A., Pashaev, E. M., Svetogorov, R. D., Zubavichus, Y. V.: Apparent anisotropy effects of upper critical field in high-textured superconducting Nb-Ti tapes, J. Phys.: Conf. Ser. 747, 012034 (2016)
  * (33) Idczak, R., Nowak, W., Babij, M., Tran, V. H.: Type-II superconductivity in cold-rolled tantalum, Phys. Lett. A 384, 126750 (2020)