# Methodology to determine the spin-parity of muon-philic $\boldsymbol{X}$
boson in $\boldsymbol{J/\psi\rightarrow\mu^{-}\mu^{+}X}$ decay

Manimala Mitra<EMAIL_ADDRESS>Institute of Physics, Sachivalaya Marg,
Bhubaneswar 751005, India  Homi Bhabha National Institute, BARC Training
School Complex, Anushaktinagar, Mumbai 400094, India  Dibyakrupa Sahoo
<EMAIL_ADDRESS>Institute of Physics, Sachivalaya Marg, Bhubaneswar
751005, India  Homi Bhabha National Institute, BARC Training School Complex,
Anushaktinagar, Mumbai 400094, India

###### Abstract

The present anomaly in muon anaomalous magnetic moment can be explained by the
presence of a muon-philic $X$ boson which could be a scalar particle or a
vector particle with mass less than twice the mass of muon. The muon-philic
$X$ boson could interestingly not be a parity eigenstate as well. If there
exists such a boson, irrespective of its parity, it can be directly observed
in the decay $J/\psi\to\mu^{-}\mu^{+}X$ where $X$ remains invisible. We show
that by using the angular distribution or the distribution of events in the
square Dalitz plot, along with two well defined dimensionless ratios, one can
clearly distinguish among the various spin-parity possibilities. This would
constitute an important probe of both the existence and the nature of this new
physics possibility.

##  I Introduction

It is well known that the anomalous magnetic moment of muon,
$a_{\mu}=\big{(}g_{\mu}-2\big{)}/2$ where $g_{\mu}$ is the $g$-factor of muon,
is sensitive to contributions from various new physics possibilities via
quantum loops (see Ref. [1] for a recent review on contributions from various
specific new physics possibilities on $a_{\mu}$). Therefore, a difference
between the experimental measurement of $a_{\mu}$ and its standard model (SM)
prediction is considered to be a good probe of new physics. The precise
experimental measurement of muon anomalous magnetic moment as reported by the
E821 experiment $\Big{(}a_{\mu}^{\textrm{exp}}\Big{)}$ at Brookhaven National
Laboratory (BNL) [2] is found to be larger than the existing most precise
theoretical prediction for the same from the SM
$\Big{(}a_{\mu}^{\textrm{SM}}\Big{)}$ [3]:

$\Delta a_{\mu}\equiv
a_{\mu}^{\textrm{exp}}-a_{\mu}^{\textrm{SM}}=279\left(76\right)\times
10^{-11}.$ (1)

This $3.7\sigma$ discrepancy can be considered as a tantalizing hint of the
presence of some new physics. It is expected that this discrepancy might
increase in the near future once results from the E989 experiment at Fermilab
[4] are available which would improve the existing experimental measurement by
a factor of four. The J-PARC New g-2/EDM experiment at KEK, Japan [5] is also
going to probe this discrepancy with more precision. If the discrepancy goes
beyond the accepted discovery threshold of $5\sigma$ it would only imply that
there is definitively some new physics contributing via the quantum loops.
However, to pin point the nature of the new physics it is pertinent that we
directly probe the various new physics possibilities in other experiments.

In one of the simplest new physics possibilities one introduces a new,
electrically neutral, spin-$0$ or spin-$1$ boson, say $X$, with exclusively
muon-philic interaction so as to avoid possible constraints from various other
experimental studies. The $X$ boson can have positive or negative parity, i.e.
it could be a scalar, pseudo-scalar, vector or axial-vector particle, or it
could even not be a parity eigenstate. To denote these possibilities in a
unified manner let us write $X\equiv X_{s^{\pm}}$ where $s=0,1$ denotes the
spin and $\pm$ signify the parity. It is well known that for a scalar
$\left(X_{0^{+}}\right)$, pseudo-scalar $\left(X_{0^{-}}\right)$, vector
$\left(X_{1^{+}}\right)$ or axial-vector $\left(X_{1^{-}}\right)$ boson
coupling exclusively to muon via the following interaction Lagrangians,

$\displaystyle\mathscr{L}_{\mu}^{\textrm{S}}$
$\displaystyle=-g_{0+}\,X_{0^{+}}\;\overline{\mu}\,\mu,$ (2a)
$\displaystyle\mathscr{L}_{\mu}^{\textrm{P}}$
$\displaystyle=-i\,g_{0-}\,X_{0^{-}}\;\overline{\mu}\,\gamma^{5}\,\mu,$ (2b)
$\displaystyle\mathscr{L}_{\mu}^{\textrm{V}}$
$\displaystyle=-g_{1+}\,\left(X_{1^{+}}\right)_{\alpha}\;\overline{\mu}\,\gamma^{\alpha}\,\mu,$
(2c) $\displaystyle\mathscr{L}_{\mu}^{\textrm{A}}$
$\displaystyle=-g_{1-}\,\left(X_{1^{-}}\right)_{\alpha}\;\overline{\mu}\,\gamma^{\alpha}\gamma^{5}\,\mu,$
(2d)

with mass $m_{X}\lesssim 2m_{\mu}$ where $m_{\mu}$ is the mass of muon (so
that $X$ is invisible), we get the following contributions to $\Delta a_{\mu}$
at leading-order [1] from Fig. 1,

$\displaystyle\Delta a_{\mu}^{\textrm{S}}$
$\displaystyle=\frac{g_{0+}^{2}}{8\pi^{2}}\int_{0}^{1}\frac{m_{\mu}^{2}\,\big{(}1-z\big{)}\,\big{(}1-z^{2}\big{)}}{m_{\mu}^{2}\,\big{(}1-z\big{)}^{2}+m_{X}^{2}\,z}\,\mathrm{d}z,$
(3a) $\displaystyle\Delta a_{\mu}^{\textrm{P}}$
$\displaystyle=-\;\frac{g_{0-}^{2}}{8\pi^{2}}\int_{0}^{1}\frac{m_{\mu}^{2}\,\big{(}1-z\big{)}^{3}}{m_{\mu}^{2}\,\big{(}1-z\big{)}^{2}+m_{X}^{2}\,z}\,\mathrm{d}z,$
(3b) $\displaystyle\Delta a_{\mu}^{\textrm{V}}$
$\displaystyle=\frac{g_{1+}^{2}}{8\pi^{2}}\int_{0}^{1}\frac{2\,m_{\mu}^{2}\,z\,\big{(}1-z\big{)}^{2}}{m_{\mu}^{2}\,\big{(}1-z\big{)}^{2}+m_{X}^{2}\,z}\,\mathrm{d}z,$
(3c) $\displaystyle\Delta a_{\mu}^{\textrm{A}}$
$\displaystyle=-\;\frac{g_{1-}^{2}}{8\pi^{2}}\int_{0}^{1}\frac{2m_{\mu}^{2}\big{(}1-z\big{)}\big{(}m_{X}^{2}z\left(3+z\right)+2m_{\mu}^{2}\left(1-z\right)^{2}\big{)}}{m_{X}^{2}\,\left(m_{\mu}^{2}\,\big{(}1-z\big{)}^{2}+m_{X}^{2}\,z\right)}\,\mathrm{d}z,$
(3d)

where $g_{s\pm}$ are the various coupling constants introduced in Eq. (2). It
is clear that when $X$ is not an eigenstate of parity, it simply implies that
we could have both scalar and pseudo-scalar couplings for spin-$0$ case and
both vector and axial-vector couplings for spin-$1$ case. In such cases, one
would have to add the corresponding contributions to $\Delta a_{\mu}$ to
explain the observed anomaly in Eq. (1).

Figure 1: Contribution from the muon-philic boson $X$ to $\Delta a_{\mu}$.

There exist possible UV complete models that can provide interactions as
required in our Eq. (2), see Ref. [1]. Inevitably, these UV complete models
introduce additional interactions which put constraint on the relevant
parameter space from other processes. For the scalar case, one example is the
type-$X$ two Higgs doublet model [6, 7, 8]. As was recently shown in [9], a
light scalar can accommodate both muon $g-2$ anomaly as well as the KOTO
anomaly in $K_{L}\to\pi^{0}\nu\overline{\nu}$ decay [10, 11]. Similarly, for
the vector case, an example of UV complete model could be the
$U(1)_{L_{\mu}-L_{\tau}}$ model which conserves the difference between muon
and tau lepton number, in addition to being anomaly free [12, 13, 14]. In a
recent study [15] it was shown that such a model could accommodate both muon
$g-2$ anomaly and the anomaly reported by the Atomki experiment in
${}^{8}\textrm{Be}^{*}$ [16, 17]. The mass of the new scalar or vector
particles is in the MeV region which is also the region of interest to us.
However, in this paper we are not concerned with the UV completion of the
simplistic muon-philic model that we have considered. Instead we will focus on
how the existence of the $X$ boson can be studied and how its spin-parity can
be determined. This would offer a direct probe of the nature of the new
physics under our consideration.

It is clear from Eq. (3) that the pseudo-scalar and axial-vector contributions
have opposite sign compared with contributions from scalar and vector cases.
This would imply that pseudo-scalar and axial-vector contributions would push
the theoretical value farther from the experimental value, and can not explain
the observed anomaly of Eq. (1) when considered separately. Therefore, purely
from the point of view of muon anomalous magnetic moment one usually considers
only the scalar and vector new physics scenarios. In a recent work of one of
the authors [18] it was explored how the decay $J/\psi\to\mu^{-}\mu^{+}X$ can
indeed be used to probe this sort of new physics in a conclusive and
independent manner at the BES III experiment. This decay mode can be compared
to the analogous process $e^{+}e^{-}\to\mu^{-}\mu^{+}X$ proposed in context of
Belle II [19] which has a large number of competing background processes that
must be carefully considered. The $X$ boson in the final state is electrically
neutral and does not decay (in the simplest muon-philic scenario as
exemplified by Eq. (2) above) leaving no track in the detector. As explained
in detail in [18] the most dominant SM background for the decay
$J/\psi\to\mu^{-}\mu^{+}X$ arises from final state radiation which can be
readily handled experimentally by employing a cut on the missing energy
distribution. The feasibility of observing the decay process is exemplified by
the fact that around $30$ to $300$ events for the scalar case and about $300$
to $2000$ events for the vector case are expected at BES III after the
aforementioned missing energy cut is applied [18].

It is important to note that our paper differs significantly from Ref. [18] by
the facts that  (1) we consider all the four spin-parity possibilities of $X$
as well as the possibility of $X$ not being a parity eigenstate, instead of
only scalar and vector cases as in [18],  (2) we show that for the case of $X$
being not a parity eigenstate the parameter space allowed by muon $g-2$ is
widened enhancing the branching ratios for the decay
$J/\psi\to\mu^{-}\mu^{+}X$ making their experimental observation more
feasible, and  (3) we provide a completely different methodology to ascertain
the various spin-parity possibilities of $X$ using the difference in
distribution patterns in conventional Dalitz plot, angular distribution,
square Dalitz plot as well as by using two experimentally accessible
dimensionless ratios.

Our paper is organized as follows. In Sec. II we find out the region of
parameter space allowed by the existing anomaly in muon anomalous magnetic
moment, considering the simple muon-philic interactions of Eq. (2). This is
followed by an analytical analysis of the decay $J/\psi\to\mu^{-}\mu^{+}X$ for
all the various spin-parity possibilities of $X$ in Sec. III. Along the way,
in Sec. IV, we numerically show the differences in patterns of distribution of
events in different kinds of Dalitz plots and angular distributions for the
various spin-parity possibilities, and discuss how they can be used in
conjunction with two dimensionless experimentally measurable ratios to
distinguish the various spin-parity possibilities. Finally we conclude in Sec.
V highlighting the main ideas and the future prospect of our study.

##  II Constraints on pure muon-philic interactions from muon anomalous
magnetic moment

Figure 2: The coupling constants $g_{0+}$ and $g_{1+}$ as allowed by $\Delta
a_{\mu}$ at $2\sigma$ level for $m_{X}\lesssim 2m_{\mu}$. Here $X$ is
considered to be a parity eigenstate, either a scalar or vector.

(a) A part of the allowed parameter space for $g_{0+}$ and $g_{0-}$.

(b) A part of the allowed parameter space for $g_{1+}$ and $g_{1-}$.

Figure 3: The region of parameter space allowed by $\Delta a_{\mu}$ at
$2\sigma$ level when $X$ is not a parity eigenstate, shown for a few chosen
values of $m_{X}\lesssim 2m_{\mu}$. The allowed region for the specific
$m_{X}$ value is the region bounded by the corresponding colored and dashed
lines.

By ascribing the anomaly in muon anomalous magnetic moment to muon-philic
interactions alone we can readily find out the allowed range of values for the
coupling constants $g_{s\pm}$ where $s=0,1$. Allowing the current discrepancy
in Eq. (1) at $2\sigma$ level and considering Eq. (3) and taking the $X$ boson
as a particle with definite parity, the scalar coupling constant $g_{0+}$ and
the vector coupling constant $g_{1+}$ are allowed to vary in the green colored
bands of Fig. 2.

If, instead, we relax the condition that the $X$ boson must be a parity
eigenstate, the coupling constants $g_{0+}$ and $g_{0-}$ are together allowed
for spin-$0$ case, and for spin-$1$ case both $g_{1+}$ and $g_{1-}$ are
allowed. Because of the fact that we have two parameters to fit one data, the
allowed region naturally widens, as can be seen from Fig. 3. Interestingly, it
is the negative sign in front of Eqs. (3b) and (3d) which enable this widening
in parameter space. In Fig. 3 the region allowed by $\Delta a_{\mu}$ at
$2\sigma$ level is shown for the specific $m_{X}$ values of $10$ MeV, $110$
MeV and $210$ MeV as the region bounded by the corresponding colored and
dashed lines. It is interesting that one can consider much larger values than
what is allowed if $X$ were to be a parity eigenstate. It is also clear from
Fig. 3 that the special cases of $g_{0+}=g_{0-}$ are also allowed for most of
the $m_{X}$ values.

Since the branching ratio of any process that would probe $X$ would be, in
general and at least, proportional to square of the coupling constant, a
larger value of the coupling constant would imply bigger branching ratio.
Therefore, the scenario where $X$ is not a parity eigenstate could be probed
better in experiment. Nevertheless, as we have seen from Figs. 2 and 3 the
study of muon anomalous magnetic moment alone can not decipher the nature of
the new physics. In order to find out the nature of new physics we need to
supplement exploration of $\Delta a_{\mu}$ with some other study, such as the
decay $J/\psi\to\mu^{-}\mu^{+}X$. By analyzing the Dalitz plot distributions
of $J/\psi\to\mu^{-}\mu^{+}X$ or its angular distribution in the center-of-
momentum frame of $\mu^{-}\mu^{+}$ one should, in principle, distinguish
between the various new physics possibilities. In the following we develop
this methodology in detail.

##  III Study of the decay $\boldsymbol{J/\psi\to\mu^{-}\mu^{+}X}$ with all
spin-parity possibilities of $\boldsymbol{X}$

Figure 4: Feynman diagrams for the decay $J/\psi\to\mu^{-}\mu^{+}X$. The
notation for $4$-momenta of all the particles is also shown here.

The decay $J/\psi\to\mu^{-}\mu^{+}X_{s^{\pm}}$ takes place via the Feynman
diagrams as shown in Fig. 4. The electrically neutral $X$ boson can arise from
either of the muon legs, and considering only the muon-philic interactions of
Eq. (3) it is stable and remains invisible in the mass regime $m_{X}\lesssim
2m_{\mu}$ which is the region of our interest. Considering the $X$ boson to be
a parity eigenstate, it was shown in Ref. [18] that this decay can be studied
at BES III. As noted in the previous section, from Fig. 3 we find that when
$X$ is not a parity eigenstate the coupling constants can have much larger
values and, therefore, it is evident that this possibility is experimentally
interesting.

Since we are considering a three-body decay, the allowed phase-space is fully
described by only two variables, such as two energies, or two invariant mass-
squares, or one invariant mass square and an angle. Below we consider a few of
these pairs of variables and find out the expressions for corresponding
distributions.

###  III.1 The normal Dalitz plot distribution in terms of two invariant mass-
squares

Denoting the $4$-momenta of $J/\psi$, $\mu^{-}$, $\mu^{+}$ and $X$ by $p_{J}$,
$p_{-}$, $p_{+}$ and $p_{X}$ respectively, let us define the following three
invariant mass-squares $s$, $t$ and $u$,

$\displaystyle s$
$\displaystyle=\left(p_{+}+p_{-}\right)^{2}=\left(p_{J}-p_{X}\right)^{2},$
(4a) $\displaystyle t$
$\displaystyle=\left(p_{+}+p_{X}\right)^{2}=\left(p_{J}-p_{-}\right)^{2},$
(4b) $\displaystyle u$
$\displaystyle=\left(p_{-}+p_{X}\right)^{2}=\left(p_{J}-p_{+}\right)^{2}.$
(4c)

The three invariant mass-squares are not independent since
$s+t+u=m_{J}^{2}+m_{X}^{2}+2m_{\mu}^{2}$, where $m_{J}$ is the mass of
$J/\psi$. Taking the invariant mass-squares $t$ and $u$ as the two parameters,
the differential decay rate for the decay $J/\psi\to\mu^{-}\mu^{+}X_{s^{\pm}}$
can be expressed by

$\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}t\;\mathrm{d}u}\equiv\frac{\mathrm{d}^{2}\Gamma\left(J/\psi\to\mu^{-}\mu^{+}X_{s^{\pm}}\right)}{\mathrm{d}t\;\mathrm{d}u}=\frac{\alpha^{2}\,g_{s\pm}^{2}\,f_{J}^{2}}{27\,\pi\,m_{J}^{5}\,Y}\left|A_{s^{\pm}}\right|^{2},$
(5)

where $\alpha$ is the fine-structure constant, $f_{J}=0.407$ GeV [20] is the
decay constant of the $J/\psi$,
$Y=\left(t-m_{\mu}^{2}\right)^{2}\left(u-m_{\mu}^{2}\right)^{2}$, and
$\left|A_{s^{\pm}}\right|^{2}$ are some function of $t$, $u$ and the masses
involved, as given in Appendix A.

All differences among the scalar, pseudo-scalar, vector and axial-vector
possibilities are present in the expressions for
$\left|A_{s^{\pm}}\right|^{2}$ as shown in Eq. (25). The distribution
expressed in Eq. (5) (which is the normal Dalitz plot distribution) is unique
in the sense that the invariant mass-squares $t$ and $u$ do not depend on the
frame of reference.

This must be noted that when $X$ is not a parity eigenstate, the differential
decay rate is easily obtained, analytically, by simply adding the two
contributions one would have if $X$ had definite parity, i.e.

$\frac{\mathrm{d}^{2}\Gamma_{s}}{\mathrm{d}t\;\mathrm{d}u}\equiv\frac{\mathrm{d}^{2}\Gamma\left(J/\psi\to\mu^{-}\mu^{+}X_{s}\right)}{\mathrm{d}t\;\mathrm{d}u}=\frac{\mathrm{d}^{2}\Gamma_{s^{+}}}{\mathrm{d}t\;\mathrm{d}u}+\frac{\mathrm{d}^{2}\Gamma_{s^{-}}}{\mathrm{d}t\;\mathrm{d}u}.$
(6)

From Eq. (6) it is clear that, in general,
$\Gamma\left(J/\psi\to\mu^{-}\mu^{+}X_{s}\right)>\Gamma\left(J/\psi\to\mu^{-}\mu^{+}X_{s^{+}}\right)$.
The decay rate $\Gamma\left(J/\psi\to\mu^{-}\mu^{+}X_{s}\right)$ also gets
further enhanced due to the fact that when $X$ is not a parity eigenstate the
allowed parameter space has a much wider spread as seen from Fig. 3 vis-à-vis
Fig. 2. For example, the value of $g_{0+}$ could be about $5$ times larger
when $X$ is not a parity eigenstate than when $X$ is purely scalar, and thus
one can expect that the number of $J/\psi\to\mu^{-}\mu^{+}X_{0}$ events for
the generic spin-$0$ case would be larger than $25$ times the number of
$J/\psi\to\mu^{-}\mu^{+}X_{0^{+}}$ events for the scalar case. Similar
arguments also hold for the spin-$1$ case.

Instead of the $t$ vs. $u$ Dalitz plot considered above, one could also think
of another normal Dalitz plot using $E_{-}$ and $E_{+}$, where $E_{\pm}$
denotes the energy of $\mu^{\pm}$ in the rest frame of $J/\psi$. These two
Dalitz plot distributions are related to one another by

$\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}E_{-}\;\mathrm{d}E_{+}}=4\,m_{J}^{2}\,\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}t\;\mathrm{d}u},$
(7)

arising from the simple observation that in the rest frame of $J/\psi$ we have

$\displaystyle t$ $\displaystyle=m_{J}^{2}+m_{\mu}^{2}-2m_{J}E_{-},$ (8a)
$\displaystyle u$ $\displaystyle=m_{J}^{2}+m_{\mu}^{2}-2m_{J}E_{+}.$ (8b)

For our analysis either of these normal Dalitz plots would serve the same
purpose. However, for our numerical study in Sec. IV we have chosen the $t$
vs. $u$ Dalitz plot due to its Lorentz invariant nature.

###  III.2 The angular distribution in the center-of-momentum frame of the
muon pair

Figure 5: The center-of-momentum frame of the muon pair, equivalently the
Gottfried-Jackson frame.

To arrive at another useful distribution we need to consider the Gottfried-
Jackson frame of reference, which is essentially the center-of-momentum frame
of the muon pair. Let the angle subtended by the direction of flight of
$\mu^{-}$ in this frame with respect to the direction of flight of $J/\psi$
(equivalently that of $X_{s^{\pm}}$ as well) be $\theta$, see Fig. 5. In this
frame of reference we find that,

$\displaystyle t$ $\displaystyle=a+b\cos\theta,$ (9a) $\displaystyle u$
$\displaystyle=a-b\cos\theta,$ (9b)

where

$\displaystyle a$
$\displaystyle=\frac{1}{2}\left(m_{J}^{2}+m_{X}^{2}+2m_{\mu}^{2}-s\right),$
(10a) $\displaystyle b$
$\displaystyle=\frac{1}{2}\sqrt{1-\frac{4m_{\mu}^{2}}{s}}\sqrt{\lambda\left(s,m_{J}^{2},m_{X}^{2}\right)},$
(10b)

with the Källén function being given by

$\lambda\left(x,y,z\right)=x^{2}+y^{2}+z^{2}-2\left(xy+yz+zx\right).$

Using Eqs. (9) and (10) we can make a change of variables and write down the
following expression for the differential decay rate in the Gottfried-Jackson
frame in terms of $s$ and $\cos\theta$,

$\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}s\;\mathrm{d}\cos\theta}=\frac{2\,m_{J}\,b\,\sqrt{s}}{m_{J}^{2}+s-m_{X}^{2}}\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}t\;\mathrm{d}u}.$
(11)

Note that while going from Eq. (5) to (11) the effect of time dilation has
been taken into consideration, and the frame dependency of Eq. (11)
essentially stems from terms proportional to various powers of $\cos\theta$
after substituting $t$ and $u$ using Eq. (9).

###  III.3 The square Dalitz plot distribution

Another alternative distribution, favored by experimentalists, is the one
called square Dalitz plot. The idea of square Dalitz plot first appeared in a
BaBar paper [21], and recently it has been used in a LHCb study [22] as well.
For our case, the expression for distribution of events in the square Dalitz
plot can be obtained from Eq. (11) by making the following change of
variables,

$m^{\prime}=\frac{1}{\pi}\arccos\left(2\frac{\sqrt{s}-2m_{\mu}}{m_{J}-m_{X}-2m_{\mu}}-1\right),\qquad\theta^{\prime}=\frac{1}{\pi}\theta,$
(12)

such that both $m^{\prime}$ and $\theta^{\prime}$ vary between $0$ and $1$. It
is easy to show that

$\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}m^{\prime}\;\mathrm{d}\theta^{\prime}}=Z\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}s\;\mathrm{d}\cos\theta},$
(13)

where

$\displaystyle Z$
$\displaystyle=\frac{\pi^{2}}{2}\sin\left(\pi\,m^{\prime}\right)\;\sin\left(\pi\,\theta^{\prime}\right)\;\Big{(}m_{J}-m_{X}-2m_{\mu}\Big{)}$
$\displaystyle\quad\times\left(\Big{(}m_{J}-m_{X}-2m_{\mu}\Big{)}\,\Big{(}1+\cos\left(\pi\,m^{\prime}\right)\Big{)}+4m_{\mu}\right).$
(14)

This square Dalitz plot provides a clearer view of the peaks in the
differential decay rate as compared to the normal Dalitz plot and as we will
see in Sec. IV they play a vital role in our study.

###  III.4 Information in the angular distribution

Before we study the patterns in the various distributions mentioned above, it
is helpful to do a detailed analysis of the angular distribution, Eq. (11), in
particular. We find that the angular distribution for all the spin-parity
possibilities can be described in a unified manner by using the orthogonal
Legendre polynomials in the following manner,

$\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}s\;\mathrm{d}\cos\theta}=\frac{g_{s\pm}^{2}\,C}{Y}\bigg{(}\mathcal{T}_{s\pm}+\mathcal{U}_{s\pm}\,P_{2}\left(\cos\theta\right)+\mathcal{V}_{s\pm}\,P_{4}\left(\cos\theta\right)\bigg{)},$
(15)

where

$C=\left(\frac{2\,\alpha^{2}\,f_{J}^{2}}{27\,\pi\,m_{J}^{4}}\right)\left(\frac{b\,\sqrt{s}}{m_{J}^{2}+s-m_{X}^{2}}\right),$
(16)

$P_{2}(x)=\tfrac{1}{2}\left(3x^{2}-1\right)$,
$P_{4}(x)=\tfrac{1}{8}\left(35x^{4}-30x^{2}+3\right)$ denote the Legendre
polynomials of order $2$ and $4$ respectively, and the angular coefficients
$\mathcal{T}_{s\pm}$, $\mathcal{U}_{s\pm}$ and $\mathcal{V}_{s\pm}$ are as
given in Appendix B.

Due to the orthogonal nature of the Legendre polynomials in Eq. (15), all the
individual terms $\mathcal{T}_{s\pm}$, $\mathcal{U}_{s\pm}$ and
$\mathcal{V}_{s\pm}$ explicitly shown in Eq. (26) of Appendix B can be
obtained via the following integrations following the method of moments [23,
24],

$\displaystyle\mathcal{T}_{s\pm}$
$\displaystyle=\frac{1}{2\,g_{s\pm}^{2}C}\int_{-1}^{1}Y\,\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}s\;\mathrm{d}\cos\theta}\;\mathrm{d}\cos\theta,$
(17a) $\displaystyle\mathcal{U}_{s\pm}$
$\displaystyle=\frac{5}{2\,g_{s\pm}^{2}\,C}\int_{-1}^{1}Y\,P_{2}\left(\cos\theta\right)\,\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}s\;\mathrm{d}\cos\theta}\;\mathrm{d}\cos\theta,$
(17b) $\displaystyle\mathcal{V}_{s\pm}$
$\displaystyle=\frac{9}{2\,g_{s\pm}^{2}\,C}\int_{-1}^{1}Y\,P_{4}\left(\cos\theta\right)\,\frac{\mathrm{d}^{2}\Gamma_{s^{\pm}}}{\mathrm{d}s\;\mathrm{d}\cos\theta}\;\mathrm{d}\cos\theta.$
(17c)

Extraction of these angular coefficients by Eq. (17) help us to define the
following two ratios,

$\mathcal{R}_{1}^{s\pm}=\mathcal{U}_{s\pm}/\mathcal{T}_{s\pm},\qquad\mathcal{R}_{2}^{s\pm}=\mathcal{V}_{s\pm}/\mathcal{T}_{s\pm},$
(18)

which are independent of the coupling constants $g_{s\pm}$. From Eqs. (26i)
and (26j) in Appendix B it is clear that for spin-$0$ case (both scalar and
pseudo-scalar) $R_{2}^{0\pm}=0$ while from Eqs. (26k) and (26l) we get
$R_{2}^{1\pm}\neq 0$ for spin-$1$ case. Therefore, $R_{2}^{s\pm}$ can easily
distinguish between spin-$0$ and spin-$1$ cases. Nevertheless, the ratio
$R_{1}^{s\pm}$ also has distinct features for the various spin-parity
possibilities. We shall numerically show in the next section that these two
ratios can indeed be used to distinguish the various spin-parity
possibilities.

It should be noted that when $X$ is not a parity eigenstate, the angular
distribution would have the following form,

$\displaystyle\frac{\mathrm{d}^{2}\Gamma_{s}}{\mathrm{d}s\;\mathrm{d}\cos\theta}=\frac{C}{Y}\Bigg{(}\mathcal{T}_{s}+\mathcal{U}_{s}\,P_{2}\left(\cos\theta\right)+\mathcal{V}_{s}\,P_{4}\left(\cos\theta\right)\Bigg{)},$
(19)

where

$\displaystyle\mathcal{T}_{s}$
$\displaystyle=g_{s+}^{2}\,\mathcal{T}_{s+}+g_{s-}^{2}\,\mathcal{T}_{s-},$
(20a) $\displaystyle\mathcal{U}_{s}$
$\displaystyle=g_{s+}^{2}\,\mathcal{U}_{s+}+g_{s-}^{2}\,\mathcal{U}_{s-},$
(20b) $\displaystyle\mathcal{V}_{s}$
$\displaystyle=g_{s+}^{2}\,\mathcal{V}_{s+}+g_{s-}^{2}\,\mathcal{V}_{s-}.$
(20c)

We can also define two ratios similar to the ones in Eq. (18),

$\mathcal{R}_{1}^{s}=\mathcal{U}_{s}/\mathcal{T}_{s},\qquad\mathcal{R}_{2}^{s}=\mathcal{V}_{s}/\mathcal{T}_{s},$
(21)

which, however, do depend on the coupling constants $g_{s\pm}$. Interestingly
when $X$ is not a parity eigenstate, we only need to know its spin, which can
be easily inferred from $\mathcal{R}_{2}^{s}$ alone, since for spin-$0$ case
$\mathcal{R}_{2}^{0}=0$ and for spin-$1$ case $\mathcal{R}_{2}^{1}\neq 0$.

It should be noted that although the angular distribution of Eq. (11) is
defined in the Gottfried-Jackson frame, the ratios as defined in Eqs. (18) and
(21) are valid in all frames of reference, since they are function of the
invariant mass-square $s$ alone.

It is possible to do the integration over $s$ and define the following ratios
as well,

$\left\langle\mathcal{R}_{1}^{s\pm}\right\rangle=\frac{\int
ds\,\mathcal{U}_{s\pm}}{\int
ds\,\mathcal{T}_{s\pm}},\qquad\left\langle\mathcal{R}_{2}^{s\pm}\right\rangle=\frac{\int
ds\,\mathcal{V}_{s\pm}}{\int ds\,\mathcal{T}_{s\pm}}.$ (22)

Once again, for the spin-$0$ case we expect
$\left\langle\mathcal{R}_{2}^{0\pm}\right\rangle=0$ and for the spin-$1$ case
$\left\langle\mathcal{R}_{2}^{1\pm}\right\rangle\neq 0$.

There is one easy prescription to numerically measure the ratios
$\left\langle\mathcal{R}_{1,2}^{s\pm}\right\rangle$. For this we can consider
the $t$ vs. $u$ Dalitz plot, or the $s$ vs. $\cos\theta$ distribution of
events. For every event we calculate the values of
$Y=\left(\left(a-m_{\mu}^{2}\right)^{2}-b^{2}\,\cos^{2}\theta\right)^{2}$,
$P_{2}\left(\cos\theta\right)$ and $P_{4}\left(\cos\theta\right)$. Then we sum
over all the values of $Y$, $Y\,P_{2}\left(\cos\theta\right)$ and
$Y\,P_{4}\left(\cos\theta\right)$ to obtain $\left\langle Y\right\rangle$,
$\left\langle YP_{2}\left(\cos\theta\right)\right\rangle$ and $\left\langle
YP_{4}\left(\cos\theta\right)\right\rangle$ respectively. Finally we use the
following expressions to measure the values of
$\left\langle\mathcal{R}_{1,2}^{s\pm}\right\rangle$,

$\left\langle\mathcal{R}_{1}^{s\pm}\right\rangle=\frac{\left\langle
Y\,P_{2}\left(\cos\theta\right)\right\rangle}{\left\langle
Y\right\rangle},\qquad\left\langle\mathcal{R}_{2}^{s\pm}\right\rangle=\frac{\left\langle
Y\,P_{4}\left(\cos\theta\right)\right\rangle}{\left\langle Y\right\rangle}.$
(23)

Within experimental accuracy, if
$\left\langle\mathcal{R}_{2}^{s\pm}\right\rangle=0$, then we have a spin-$0$
$X$ boson, else the $X$ boson has spin-$1$.

##  IV Numerical study

###  IV.1 Canonical branching ratios and expected number of events at BESIII

Before we analyze the distribution patterns and ratios to distinguish the
various spin-parity possibilities of $X$, it would be helpful to know whether
such decays can indeed be probed experimentally. For this study we consider
the BESIII experiment as a natural choice because at BESIII a large number
$(\sim 10^{11})$ of on-shell $J/\psi$ mesons will be produced at rest [25, 26,
27] which would help in inferring the $4$-momentum of the invisible $X$ in a
much easy and clean manner. Let us denote the canonical branching ratios for
the decays $J/\psi\to\mu^{-}\mu^{+}X_{s^{\pm}}$ by
$\overline{\textup{Br}}\left(J/\psi\to\mu^{-}\mu^{+}X_{s^{\pm}}\right)$ and
they are defined as the usual branching ratios sans the coupling constants
i.e.

$\overline{\textup{Br}}\left(J/\psi\to\mu^{-}\mu^{+}X_{s^{\pm}}\right)=\frac{1}{g_{s\pm}^{2}}\frac{\Gamma\left(J/\psi\to\mu^{-}\mu^{+}X_{s^{\pm}}\right)}{\Gamma_{J/\psi}},$
(24)

where $\Gamma_{J/\psi}$ is the experimentally measured total decay rate of
$J/\psi$. In Fig. 6 we have shown the variation of the canonical branching
ratios with the mass of $X$ for its various spin-parity possibilities. The
distinct trend of rise in the canonical branching ratio for the axial-vector
case in the limit $m_{X}\to 0$ is easily discernible from the $m_{X}^{-2}$
factor in Eq. (25d). It must be noted that in evaluation of the canonical
branching ratios shown in Fig. 6 we have included a cut on the missing energy
at $E_{\textrm{missing}}=140$ MeV as suggested in Ref. [18] to completely
eliminate the SM background events arising from final state radiation in the
form of $J/\psi\to\mu^{-}\mu^{+}\gamma$, especially the soft photon ones since
at BESIII photons with energy less than $20$ MeV can not be detected at the
detector [28]. Details of the background study can be found in Ref. [18].

Figure 6: The canonical branching ratios, as defined in Eq. (24), for various
spin parity possibilities of $X$. The evaluation includes a cut on the missing
energy at $140$ MeV to eliminate the significant SM background from final
state radiation arising from $J/\psi\to\mu^{-}\mu^{+}\gamma$ events.

The canonical branching ratios are helpful in predicting the number of signal
events, i.e. number of $J/\psi\to\mu^{-}\mu^{+}X_{s}$ decays, one would expect
at BESIII if the muon-philic $X$ boson were to describe the muon $g-2$
anomaly. In Fig. 7 we show the expected number of such signal events across
the parameter space allowed by anomalous magnetic moment of muon (region shown
before in Fig. 3), for three representative masses $m_{X}=10$ MeV, $110$ MeV
and $210$ MeV. The high number of events shown in Fig. 7 are possible only
when one considers the $X$ boson to not be a parity eigenstate. This is due to
the widening of the parameter space allowed by the presence of additional
coupling constants $g_{0-}$ and $g_{1-}$ for the spin-$0$ and spin-$1$ cases
respectively.

Figure 7: Expected number of $J/\psi\to\mu^{-}\mu^{+}X_{s}$ events out of a
total of $10^{11}$ number of $J/\psi$ decays including a missing energy cut at
$140$ MeV.

It is nevertheless interesting and important to numerically study and find out
how to distinguish the individual spin-parity possibilities irrespective of
the muon anomalous magnetic moment consideration. For this we focus on a
numerical study of the various distributions and the ratios that were
presented, analytically, in the previous section.

###  IV.2 Patterns in distributions, ratios and discussion

To study how the patterns of distribution differ for the different spin-parity
possibilities of $X$ as well as how these patterns evolve when we go from
lower values of $m_{X}$ to higher values of $m_{X}$, we once again consider
the three representative masses, $m_{X}=10$ MeV, $110$ MeV and $210$ MeV. We
will analyze the $t$ vs. $u$ Dalitz plot distribution of Eq. (5), the $s$ vs.
$\cos\theta$ angular distribution of Eq. (11) and the $m^{\prime}$ vs.
$\theta^{\prime}$ distribution also known as the square Dalitz plot
distribution as described by Eq. (13). To make a meaningful comparison across
the various spin-parity possibilities, we have normalized the distributions by
their maximum values which helps the patterns become more visually acute and
easy to grasp. Due to this normalization by the maximum value of the
distribution, all the distributions shown do not depend on the size of the
coupling constants $g_{s\pm}$.

To put the distribution patterns into proper perspective we have also included
distribution of $1000$ simulated Monte Carlo events generated after applying a
cut on the missing energy at $140$ MeV as mentioned before.

#### Normal Dalitz plot distribution:

Let us first consider the $t$ vs. $u$ Dalitz plots, see Fig. 8. It is clear
that for $m_{X}=10$ MeV, all the four distributions, corresponding to the four
distinct spin-parity possibilities, are extremely flat in most of the allowed
region except at the kinematic boundary. If we go to $m_{X}=110$ MeV, the
distribution peaks are found to be indeed close to the boundary, but are more
prominent than before. Here we can see that for spin-$0$ case there is no peak
close to origin, while for spin-$1$ case the peak sits nearer to the origin.
Considering $m_{X}=210$ MeV we find that the distribution still retains the
characteristic locations of the peaks as mentioned before, but the scalar and
pseudo-scalar distributions can now be apparently distinguished, whereas its
still difficult to distinguish between vector and axial-vector cases.

#### The $\boldsymbol{s}$ vs. $\boldsymbol{\cos\theta}$ distribution:

Considering the $s$ vs. $\cos\theta$ distributions as shown in Fig. 9, we find
that for $m_{X}=10$ MeV, there are not enough useful distinguishing features.
However, if we consider $m_{X}=110$ MeV and $210$ MeV, it is possible to
distinguish between all the four spin-parity cases, albeit the fact that the
distribution peaks are still close to the boundary of the plots.

#### Square Dalitz plot distribution:

Considering the square Dalitz plot distributions as shown in Fig. 10 for
$m_{X}=10$ MeV, $110$ MeV and $210$ MeV, we find that the differences between
all the four spin-parity possibilities which were kind of hidden in other
distributions, do show up very clearly. In fact for the low mass of $m_{X}=10$
MeV the differences are much clearly visible, when we compare, for example,
the patterns of vector and axial-vector cases of $m_{X}=210$ MeV. The square
Dalitz plot is indeed a very powerful discerning distribution due to the fact
that the distribution peaks which are located at the boundaries in other
distributions correspond to internally observed peaks here.

#### Ratios:

Finally looking at the ratios $\mathcal{R}_{1,2}^{s\pm}$, we find from Figs.
11 that using $\mathcal{R}_{2}^{s\pm}=0$ as a criteria one can easily
distinguish the spin-$0$ and spin-$1$ cases. For $m_{X}=10$ MeV case we find
that for axial-vector scenario the $\mathcal{R}_{2}^{1-}$ is extremely tiny
but non-zero. In this case one can clearly use the curves for
$\mathcal{R}_{1}^{1\pm}$ to distinguish the various spin-parity possibilities
without any ambiguity. Therefore, both $\mathcal{R}_{1}^{s\pm}$ and
$R_{2}^{s\pm}$ should be used to distinguish among the four spin-parity
possibilities.

It would indeed be more practical to employ both the ratios and the
distributions, especially the square Dalitz plot distribution to decipher the
spin-parity of the $X$ boson in the decay $J/\psi\to\mu^{-}\mu^{+}X$.

Figure 8: Expected patterns in normal $t$ vs. $u$ Dalitz plot distributions
are shown on the left panel of each of the subfigures, and on the right panel
are the distributions of $1000$ simulated events after applying a missing
energy cut at $140$ MeV.

Figure 9: Expected patterns in $s$ vs. $\cos\theta$ distributions are shown on
the left panel of each of the subfigures, and on the right panel are the
distributions of $1000$ simulated events after applying a missing energy cut
at $140$ MeV.

Figure 10: Expected patterns in the square Dalitz plot distributions are shown
on the left panel of each of the subfigures, and on the right panel are the
distributions of $1000$ simulated events after applying a missing energy cut
at $140$ MeV.

Figure 11: The variation of the ratios $\mathcal{R}_{1,2}^{s\pm}$ for
$m_{X}=10$ MeV with respect to the invariant mass-square $s$.

##  V Conclusion

The present anomaly in muon anomalous magnetic moment can be considered as a
tantalizing hint of the presence of some new physics. The simplest new physics
that can contribute involves purely muon-philic interactions and one needs
only to hypothesize that there exists a spin-$0$ or spin-$1$ boson (say, $X$)
taking part in these interactions. If the $X$ boson is a parity eigenstate,
then only scalar and vector possibilities are allowed from the muon anomalous
magnetic moment. Interestingly the allowed paramater space for the coupling
constants widens if one considers $X$ to be not a parity eigenstate.

Irrespective of the parity of the $X$ boson, and considering its mass
$m_{X}\lesssim 2m_{\mu}$ as suggested by the muon anomalous magnetic moment
and other experimental studies, the electrically neutral $X$ boson can be
definitively probed by the decay $J/\psi\to\mu^{-}\mu^{+}X$. This decay not
only provides an excellent avenue to test this specific muon-philic new
physics possibility, but it also can be utilized to ascertain whether $X$ is a
parity eigenstate or not, and if it is a parity eigenstate we can probe both
its spin and parity. Due to the widening of parameter space for parity non-
eigenstate scenario, decay with such a $X$ would have larger branching
fraction than the one which is a parity eigenstate.

Since the decay $J/\psi\to\mu^{-}\mu^{+}X$ is a three-body decay, there are a
multitude of distributions that can be studied. We find that the square Dalitz
plot distribution as well as the angular distribution of events in the center-
of-momentum frame of the muon pair, do indeed exhibit the distinguishing
features among all the four spin-parity possibilities, viz. scalar, pseudo-
scalar, vector and axial-vector cases. We also provide two dimensionless
ratios, obtained from the angular distribution, which are also useful to
ascertain the spin-parity of $X$. The search for decay
$J/\psi\to\mu^{-}\mu^{+}X$ or similar decay such as $\phi\to\mu^{-}\mu^{+}X$
would constitute an important strategy in our search for definitive signature
of new physics.

###### Acknowledgements.

M.M. acknowledges the financial support from the DST INSPIRE Faculty research
grant (IFA-14-PH-99), and thanks Indo-French Centre for the Promotion of
Advanced Research for the support (grant no: 6304-2). D.S. is thankful to
Donghun Lee for discussions on the numerical study.

##  Appendix A Expressions for $\boldsymbol{\left|A_{s^{\pm}}\right|^{2}}$

The expressions for $\left|A_{s^{\pm}}\right|^{2}$ contributing to Eq. (5) are
as given below.

$\displaystyle\left|A_{0^{+}}\right|^{2}$
$\displaystyle=\left(T^{2}+U^{2}\right)\left(4m_{\mu}^{2}-m_{X}^{2}\right)\left(2m_{\mu}^{2}+m_{J}^{2}\right)+TU\left(T+U\right)\left(T+U+2\left(4m_{\mu}^{2}-m_{X}^{2}\right)\right)$
$\displaystyle\quad+TU\left(\left(4m_{\mu}^{2}-m_{X}^{2}\right)^{2}-m_{X}^{2}\left(4m_{\mu}^{2}-m_{X}^{2}\right)+8m_{J}^{2}m_{\mu}^{2}\right),$
(25a) $\displaystyle\left|A_{0^{-}}\right|^{2}$
$\displaystyle=-m_{J}^{2}\,m_{X}^{2}\,\left(T^{2}+U^{2}\right)+\left(T+U\right)^{2}\,\left(T\,U-2\,m_{X}^{2}\,m_{\mu}^{2}\right)-2\,m_{X}^{2}\,T\,U\,\left(T+U-m_{X}^{2}\right),$
(25b) $\displaystyle\left|A_{1^{+}}\right|^{2}$
$\displaystyle=2\left(T^{2}+U^{2}\right)\bigg{(}TU-\left(m_{J}^{2}+2m_{\mu}^{2}\right)\left(m_{X}^{2}+2m_{\mu}^{2}\right)\bigg{)}-4M^{2}TU\left(T+U-M^{\prime
2}\right),$ (25c) $\displaystyle\left|A_{1^{-}}\right|^{2}$
$\displaystyle=\frac{2}{m_{X}^{2}}\Bigg{(}2\,T\,U\,\bigg{(}m_{\mu}^{2}\,\left(T+U\right)^{2}-m_{X}^{2}\,\left(M^{\prime
2}-2\,m_{\mu}^{2}\right)\,\left(T+U\right)+m_{X}^{2}\,\left(2\,m_{\mu}^{2}\,\left(4\,m_{\mu}^{2}-3\,m_{X}^{2}-2\,m_{J}^{2}\right)+\left(m_{X}^{2}+m_{J}^{2}\right)^{2}\right)\bigg{)}$
$\displaystyle\hskip
28.45274pt+m_{X}^{2}\,\left(T\,U+\left(2\,m_{\mu}^{2}+m_{J}^{2}\right)\,\left(4\,m_{\mu}^{2}-m_{X}^{2}\right)\right)\,\left(T^{2}+U^{2}\right)\Bigg{)},$
(25d)

with $T=t-m_{\mu}^{2}$, $U=u-m_{\mu}^{2}$,
$M^{2}=m_{J}^{2}+m_{X}^{2}+2m_{\mu}^{2}$ and $M^{\prime
2}=m_{J}^{2}+m_{X}^{2}-2m_{\mu}^{2}$.

##  Appendix B Expressions for angular coefficients
$\boldsymbol{\mathcal{T}_{s\pm}}$, $\boldsymbol{\mathcal{U}_{s\pm}}$ and
$\boldsymbol{\mathcal{V}_{s\pm}}$

The expressions for the angular coefficients $\mathcal{T}_{s\pm}$,
$\mathcal{U}_{s\pm}$ and $\mathcal{V}_{s\pm}$ appearing in Eq. (15) are as
follows,

$\displaystyle\mathcal{T}_{0+}$
$\displaystyle=2\,\left(a-m_{\mu}^{2}\right)^{2}\,\left(2\,a^{2}+4\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,a+10\,m_{\mu}^{4}-6\,m_{X}^{2}\,m_{\mu}^{2}+8\,m_{J}^{2}\,m_{\mu}^{2}+m_{X}^{4}-m_{J}^{2}\,m_{X}^{2}\right)$
$\displaystyle\quad-\frac{2}{3}\,\left(2\,a^{2}+4\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,a-6\,m_{\mu}^{4}-2\,m_{X}^{2}\,m_{\mu}^{2}+m_{X}^{4}+m_{J}^{2}\,m_{X}^{2}\right)\,b^{2}$
(26a) $\displaystyle\mathcal{T}_{0-}$
$\displaystyle=4\,\left(a-m_{\mu}^{2}\right)^{2}\,\left(2\,a^{2}-4\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,a+2\,m_{\mu}^{4}-2\,m_{X}^{2}\,m_{\mu}^{2}+m_{X}^{4}-m_{J}^{2}\,m_{X}^{2}\right)$
$\displaystyle\quad-\frac{4}{3}\,\left(2\,a^{2}-4\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,a+2\,m_{\mu}^{4}+2\,m_{X}^{2}\,m_{\mu}^{2}+m_{X}^{4}+m_{J}^{2}\,m_{X}^{2}\right)\,b^{2},$
(26b) $\displaystyle\mathcal{T}_{1+}$
$\displaystyle=-\frac{24}{15}\,b^{4}+\frac{8}{3}\,\left(2\,M^{2}\,a-4\,m_{\mu}^{4}-2\,M^{2}\,m_{\mu}^{2}-2\,m_{X}^{2}\,m_{\mu}^{2}-2\,m_{J}^{2}\,m_{\mu}^{2}-M^{2}\,M^{\prime
2}-m_{J}^{2}\,m_{X}^{2}\right)\,b^{2}$
$\displaystyle\quad+8\,\left(a-m_{\mu}^{2}\right)^{2}\,\left(a^{2}-2\,m_{\mu}^{2}\,a-2\,M^{2}\,a-3\,m_{\mu}^{4}+2\,M^{2}\,m_{\mu}^{2}-2\,m_{X}^{2}\,m_{\mu}^{2}-2\,m_{J}^{2}\,m_{\mu}^{2}+M^{2}\,M^{\prime
2}-m_{J}^{2}\,m_{X}^{2}\right),$ (26c) $\displaystyle\mathcal{T}_{1-}$
$\displaystyle=-\frac{4}{5}\,m_{X}^{2}\,b^{4}-\frac{4}{3}\,b^{2}\,\bigg{(}4\,m_{\mu}^{2}\,a^{2}-8\,m_{\mu}^{4}\,a+4\,m_{X}^{2}\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,M^{\prime
2}\,a+4\,m_{\mu}^{6}-4\,m_{X}^{2}\,m_{\mu}^{4}+2\,m_{X}^{2}\,M^{\prime
2}\,m_{\mu}^{2}$ $\displaystyle\hskip
85.35826pt-4\,m_{X}^{4}\,m_{\mu}^{2}-8\,m_{J}^{2}\,m_{X}^{2}\,m_{\mu}^{2}+m_{X}^{6}+3\,m_{J}^{2}\,m_{X}^{4}+m_{J}^{4}\,m_{X}^{2}\bigg{)}$
$\displaystyle\quad+4\,\left(a-m_{\mu}^{2}\right)^{2}\,\bigg{(}4\,m_{\mu}^{2}\,a^{2}+m_{X}^{2}\,a^{2}-8\,m_{\mu}^{4}\,a+2\,m_{X}^{2}\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,M^{\prime
2}\,a+4\,m_{\mu}^{6}+13\,m_{X}^{2}\,m_{\mu}^{4}+2\,m_{X}^{2}\,M^{\prime
2}\,m_{\mu}^{2}$ $\displaystyle\hskip
85.35826pt-8\,m_{X}^{4}\,m_{\mu}^{2}+m_{X}^{6}+m_{J}^{2}\,m_{X}^{4}+m_{J}^{4}\,m_{X}^{2}\bigg{)},$
(26d) $\displaystyle\mathcal{U}_{0+}$
$\displaystyle=-\frac{4}{3}\,\left(2\,a^{2}+4\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,a-6\,m_{\mu}^{4}-2\,m_{X}^{2}\,m_{\mu}^{2}+m_{X}^{4}+m_{J}^{2}\,m_{X}^{2}\right)\,b^{2},$
(26e) $\displaystyle\mathcal{U}_{0-}$
$\displaystyle=-\frac{8}{3}\,\left(2\,a^{2}-4\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,a+2\,m_{\mu}^{4}+2\,m_{X}^{2}\,m_{\mu}^{2}+m_{X}^{4}+m_{J}^{2}\,m_{X}^{2}\right)\,b^{2},$
(26f) $\displaystyle\mathcal{U}_{1+}$
$\displaystyle=\frac{16}{3}\,\left(2\,M^{2}\,a-4\,m_{\mu}^{4}-2\,M^{2}\,m_{\mu}^{2}-2\,m_{X}^{2}\,m_{\mu}^{2}-2\,m_{J}^{2}\,m_{\mu}^{2}-M^{2}\,M^{\prime
2}-m_{J}^{2}\,m_{X}^{2}\right)\,b^{2}-\frac{32}{7}\,b^{4},$ (26g)
$\displaystyle\mathcal{U}_{1-}$
$\displaystyle=-\frac{16}{7}\,m_{X}^{2}\,b^{4}-\frac{8}{3}\,\bigg{(}4\,m_{\mu}^{2}\,a^{2}-8\,m_{\mu}^{4}\,a+4\,m_{X}^{2}\,m_{\mu}^{2}\,a-2\,m_{X}^{2}\,M^{\prime
2}\,a+4\,m_{\mu}^{6}-4\,m_{X}^{2}\,m_{\mu}^{4}+2\,m_{X}^{2}\,M^{\prime
2}\,m_{\mu}^{2}$ $\displaystyle\hskip
85.35826pt-4\,m_{X}^{4}\,m_{\mu}^{2}-8\,m_{J}^{2}\,m_{X}^{2}\,m_{\mu}^{2}+m_{X}^{6}+3\,m_{J}^{2}\,m_{X}^{4}+m_{J}^{4}\,m_{X}^{2}\bigg{)}\,b^{2},$
(26h) $\displaystyle\mathcal{V}_{0+}$ $\displaystyle=0,$ (26i)
$\displaystyle\mathcal{V}_{0-}$ $\displaystyle=0,$ (26j)
$\displaystyle\mathcal{V}_{1+}$ $\displaystyle=-\frac{64}{35}\,b^{4},$ (26k)
$\displaystyle\mathcal{V}_{1-}$
$\displaystyle=-\frac{32}{35}\,m_{X}^{2}\,b^{4}.$ (26l)

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# Designing Participatory AI: Creative Professionals’ Worries and Expectations
about Generative AI

Nanna Inie<EMAIL_ADDRESS>Center for Computing Education Research (CCER), IT
University of CopenhagenRued Langgaards Vej 7CopenhagenDenmark2300 ,  Jeanette
Falk<EMAIL_ADDRESS>Dep. of Artificial Intelligence and
Human Interfaces, University of SalzburgJakob-Haringer-Straße
8SalzburgAustria5020 and  Steven Tanimoto<EMAIL_ADDRESS>Paul G. Allen
School of Computer Science & Engineering, University of Washington1410 NE
Campus ParkwaySeattleUSA

(2023)

###### Abstract.

Generative AI, i.e., the group of technologies that automatically generate
visual or written content based on text prompts, has undergone a leap in
complexity and become widely available within just a few years. Such
technologies potentially introduce a massive disruption to creative fields.
This paper presents the results of a qualitative survey ($N$ = 23)
investigating how creative professionals think about generative AI. The
results show that the advancement of these AI models prompts important
reflections on what defines creativity and how creatives imagine using AI to
support their workflows. Based on these reflections, we discuss how we might
design participatory AI in the domain of creative expertise with the goal of
empowering creative professionals in their present and future coexistence with
AI.

participatory AI, participatory design, generative AI, creative professionals,
creativity support

††journalyear: 2023††copyright: rightsretained††conference: Extended Abstracts
of the 2023 CHI Conference on Human Factors in Computing Systems; April 23–28,
2023; Hamburg, Germany††booktitle: Extended Abstracts of the 2023 CHI
Conference on Human Factors in Computing Systems (CHI EA ’23), April 23–28,
2023, Hamburg, Germany††doi: 10.1145/3544549.3585657††isbn:
978-1-4503-9422-2/23/04††ccs: Computing methodologies
Philosophical/theoretical foundations of artificial intelligence††ccs: Human-
centered computing Empirical studies in HCI††ccs: Human-centered computing HCI
design and evaluation methods

##  1\. Introduction and background

Recent developments in generative AI, i.e., AI technologies that automatically
generate visual or written content based on text prompts, have led to much
speculation and concern about what these developments may mean for different
professions in the future, particularly for professionals where creativity
accounts for a sizable part of their everyday work (Press, 2023). Potential
“threats” that generative AI models may pose for creative professionals
(“creatives”) include the ability to automate generation of high(er) quality
content (text, code, images, and video), increased content variety, and
personalized content based on preferences of individual users and consumers.
Some current discourse about generative AI models frame them as threatening
the ownership and agency of creatives. See, e.g., (Metz, 2022; Baio, 2022;
Heikkilä, 2022) for interviews with artists whose work was — unbeknownst to
them — used to train AI models that generated images in the style of the
artists’ work. Rogers critically discusses this scenario in terms of ‘the
attribution problem with generative AI’ (Rogers, 2022).

Conversely, other creatives express curiosity and excitement about the
potential this technology may offer, e.g., (Yang, 2022). Regardless of whether
generative AI is seen as a blessing or curse, it is both timely and of
research value to answer questions about how it and creatives can most
fruitfully coexist.

One response to perceived threats posed by AI is the notion of participatory
AI, where the goal is to include ‘wider publics’ in the development and
deployment of AI systems (Birhane et al., 2022). Historically, the emergence
of participatory design (PD) in the 1970s was motivated by efforts to
rebalance “power and agency in the professional realm” (Bannon et al., 2018)
in order to empower workers to “codetermine the development of the information
system and of their workplace” (Clement and Van den Besselaar, 1993). In light
of this historical backdrop, participatory AI is expected to empower those
affected by the development of novel technologies by enforcing values of
inclusion, plurality, collective safety, and ownership (Birhane et al., 2022).

One step in the direction of participatory AI is to understand the needs of
people and communities affected. Related research in this direction includes
Singh et al., who explored which assumptions and expectations creative writers
have for a supporting AI tool (Singh et al., 2022); Guzdial et al., who
explored designers’ expectations for AI-driven game-level editors (Guzdial et
al., 2019); and Zhu et al., who argued for a better understanding of game
designers’ needs when co-creating with AI (Zhu et al., 2018).

Our paper contributes to this objective by surfacing and categorizing concerns
and expectations that creatives of different types currently have about the
effect of generative AI on their work. It represents the authors’ first
empirical research into the question of How might we design and perform
participatory AI? This question is particularly relevant to those who design
and develop AIs for creatives and those who design and develop creativity
support tools that use AI technology.

Our findings, albeit preliminary, identify important topics that may inform
participatory design of generative AI so creatives can “influence digital
technologies that will change their work practices or everyday life” (Bødker
et al., 2022), the goal of participatory design in its essence. Our
contributions include the following. (1) We introduce new conceptions about
what constitutes creativity in relation to generative AI. (2) We categorize
some reasons why creatives are and are not concerned about novel generative
AI. (3) We categorize reasons why some creatives are curious and excited about
AI and how it might augment their creative processes. (4) We discuss possible
foci for the design of participatory AI aimed at helping creative
professionals Understand AI, Cope with AI, Adapt to AI, and Exploit AI.

##  2\. Methods

We conducted a qualitative survey with open-ended questions designed to
encourage longer answers and reflection. The survey format let respondents
participate asynchronously, while allowing us to discover themes and
directions for further in-depth research. The survey was circulated to the
authors’ networks of creative professionals as well as on social media. The
call was posted as an open question of ‘Are you a creative
professional/professional creative, and do you have opinions about generative
AI that you would like to share with us?’ The term ‘creative’ was left to
self-definition, and we asked the respondents to explain the role of
creativity in their profession. We collected responses over a period of
approximately two months in late 2022. We offered a draw of five $25 gift
cards to Amazon as symbolic compensation for participation. The study and
survey were approved by the ethical committees of the authors’ universities.

###  2.1. Participants

We received 23 responses to the survey from creatives residing in Denmark
(10), Germany (4), the United Kingdom (4), USA (3), Turkey (1), and Morocco
(1). Respondents were between 21 and 55 years old, distributed as 21-25 (4),
26-30 (1), 31-35 (8), 36-40 (3), 41-45 (6), and 51-55 (1). 10 respondents
identified as female, 12 as male, and 1 as non-binary. The respondents worked
in a variety of fields, from computer science research to design of UX/UI and
games to teaching. Most respondents came from software-oriented creative
domains, and our findings should be read with this limitation in mind (see
Section 5 for a discussion of this limitation). We were more interested in
people self-qualifying as a “creative professional” where creativity plays a
significant role in their work, than we were in specific job titles. The
responses, as well as a detailed overview of respondents, are presented in the
supplementary material.

###  2.2. Survey and analysis

The survey consisted of both demographic questions and six questions related
to our research interest (which we list below). We designed the questions to
elicit respondents’ general understanding of and attitudes towards AI and
creativity. We sought to prompt a deeper level of reflection and tried to
avoid overloading respondents with questions.

  1. (1)

In your own words, how would you define what AI (Artificial Intelligence) is?

  2. (2)

Do you believe computers can be creative? Why/why not?

  3. (3)

A standard definition of a creative idea is that it is: 1. original (new,
either to the creator or to human history in general), 2. useful (in some
context), and 3. surprising (it seems unlikely but possible). Given this
definition, do you believe a computer/an AI algorithm can generate creative
ideas? Why/why not?111This definition is a compilation of three-criterion
definitions by, e.g., Boden (Boden, 2004) and Simonton (Simonton, 2012).

  4. (4)

Are you excited about AI contributing to creative work in your profession?
Why/why not?

  5. (5)

Do you worry about AI replacing creative work in your profession? Why/why not?

  6. (6)

Which role do you think AI will play in your profession in the near and far
future?

Questions (4) and (5) were swapped for approximately half the respondents (in
two different instances of the survey) to avoid priming respondents in any
specific direction.

We performed a thematic analysis as described by Braun and Clarke (Braun and
Clarke, 2012) on the responses. We tagged responses individually with
different codes and then clustered them into sub-themes, which we highlight in
bold throughout Section 3.

##  3\. Survey responses

###  3.1. How intelligent or creative is generative AI?

In order to inform the design of participatory AI, it is relevant to
understand how creatives currently conceive of AI and its limits. These
factors can inform decisions about how to design participation processes to,
for instance, include more or less information and discussion about the state
of AI.

####  3.1.1. What is AI?

Answers to the question “In your own words, how would you define AI?” varied,
especially on two scales: technical depth (from superficial to deep
understanding) and agency of AI (from no agency to high agency). In terms of
technical depth, some respondents, naturally, had a deeper understanding of AI
algorithms than others, e.g., from “… digital solutions that are trained to be
helpful in specific ways” (P21) (technically superficial) to “A system capable
of making dynamic choices based on input, dynamic as in non-binary evaluation
of input referencing data model, a model which would ideally evolve through
feedback of external verification of multiple processes’ (P2) (technically
advanced).

We also saw interesting variation in the level of agency ascribed to the AI
system, from no agency at all: “AI is a set of rules, defined by humans, which
a computer can follow.” (P3) to a high degree of agency: “it’s a computer that
over time improves itself in the tasks it has to solve by collecting
information and inputs from humans” (P7). These understandings may influence
creatives’ judgments of the degree to which AI can support them and contribute
to/replace tasks in their creative processes.

We tagged 7 responses as portraying a relatively deep technical understanding
with no agency to the computer. Six responses were tagged with a more
superficial technical understanding and no agency ascribed to the computer. 10
responses were tagged as superficial technical understanding with a high
degree of computational agency, and no responses were tagged as deep technical
understanding and high agency of the computer. An overview is shown in the
supplementary material, Figure 1.

####  3.1.2. New definitions of creativity

The presence of generative AI encourages us to reevaluate and question our
understanding of creativity and creative ideas. Most respondents who denied
that AIs can be considered creative disputed the computer’s capacity to
generate original output since it is trained only on already existing (human)
input. However, one respondent wrote in answer to “Do you believe computers
can be creative?”: “I kind of resent it - but yeah. If creativity is defined
as something useful and new, then yeah I think so. Even though AI’s [sic] rely
on training data and existing man-made patterns (which some might use to
criticize AI’s as being derivative or as simply reproducing what already
exists) the process of combining stuff into a new “something” isn’t really
THAT different from what humans do… it’s just bigger in scale and I guess you
might argue that humans are also just “trained on” a bunch of data… we also
carry around a repertoire of input we can draw on to come up with ideas […]
ideas are always rooted in some pre-existing thing(s)” (P5). Another
participant noted that “What is my brain if not a computer that takes in all
this provided data and produces its own result from a mix of the inputs? If
that result is ‘creative’, then why is an AI not?” (P20).

This understanding is consistent with a traditional definition of creative
ideas as being ‘novel’, ‘useful’, and ‘surprising’, e.g., (Boden, 2004;
Simonton, 2012). However, one respondent noted that “Computers aren’t creative
by themselves as they only follow the orders that someone gives them” (P6). In
P6’s understanding, creativity entails agency or initiative, which is not
historically a property of the three-criterion definition of creativity.

Intention and sentience were described as criteria for creativity by some
respondents: “There is not intention” (P1), “Creativity stems from personal
experiences/knowledge/emotions and the need to express/communicate/use this
[…] Creativity lies not in the creation, but in why we create. Programs can
emulate this, but without true sentience, it will always be [an] emulation”
(P10), and “The computer still isn’t creative, it’s still just doing what it’s
told […] Maybe I think it needs feelings to be truly creative?” (P23).

Other conditions for creativity were also evoked in the answers, such as
(self-)awareness: “I think that true creativity requires a sense of self and
self-awareness” (P8). “They are not creative in themselves; they are producing
content unaware of the value they just created” (P21). Even experiences and
inspiration were evoked: “Computers can solve problems and create art and
everything, but it will all be logic and calculated and not because it got a
sudden burst of inspiration or remembered something that happened in the
second grade” (P23).

Even if we do not assume that these definitions should be unanimously
integrated into a scholarly or theoretical definition of creativity, it is
interesting that reflecting on creativity in relation to the role of
generative AI raises different conceptions of what creativity entails.

###  3.2. I Am Not Worried (Yet)

Only three of our 23 respondents unambiguously answered yes to being worried
about AI replacing their work: “Yes, the market needs to adjust heavily and I
don’t think the revolution will be entirely peaceful” (P2); “the idea of AI is
mostly uncanny right now.” (P4), and “Yes I [worry]. (…) a lot of tasks such
as writing micro copy for websites etc which UX writers currently do would be
automated” (P14). Three more noted that they worry to some degree, or that
they worry but are optimistic, e.g.: “I worry about it, but I hope the reality
will be that AI becomes another tool” (P5).

Nine respondents noted that they did not worry at all, while six reported that
they do not worry yet, e.g. “for now only the boring parts would be replaced.
But this take-my-job-away argument was made countless times in history, there
will always be something new. We can’t be held back by this fear” (P12). We
group reasons for concern (aside from losing work) into the following themes.

##### 1\. Worse quality output.

P8 observed: “It concerns me already that video games are becoming something
of an echo chamber, and the sheer volume of games being released are diluting
the market and making it harder for indie games to get the recognition they
need to do well.” The concern expressed here is not only that humans may
become obsolete in the development process, but that the volume of output (in
this case, of games) that AI (co-)creation makes possible will increase
quantity but reduce quality of video games.

P9 wrote “I certainly don’t intend to replace all my hires with AI but some
people will. They may achieve early success and they may also bring the genre
into disrepute if they pump out a lot of lazy AI-written content.” This
indicates worries that extend beyond individuals and their job security to
concerns about an entire genre of creative content. This perspective assumes
that AI produces creative output of worse quality than humans produce, which
we could consider a reason not to worry about AI-generated content. However,
in this case, the potential of such content to ‘dilute’ or ‘bring into
disrepute’ a whole genre or field presents a threat or concern to some
creatives.

##### 2\. Weakening the creative process.

Most respondents pointed out that humans will still be required in AI-
facilitated creative processes or that the computer will simply help automate
the ‘boring tasks.’ However, a few also reflected on what that might mean to
the creative processes, e.g., “I also don’t like the way AI image generators
get you results instantly. They skip the creative process and just take you
straight to the result… […] that just overlooks a super important part of a
creative process, which is exploration. And emergence, where stuff just kind
of comes out of the process but you never imagined it would. Or happy
accidents! In that sense I think AIs could actually lead to a stagnation in
the history of creativity, if AI turns out to weaken the “creative muscle”’
(P5).

P11 further noted that “the meaning of ‘creative’ seems to be increasingly
twisted to mean merely ‘original/surprising,’ and partly because there is a
tendency for many to be unaware of the amount of creativity that my work
involves. […] A lot is being lost.” This observation raises seminal questions
similar to those raised in other fields where complex human thought processes
have historically been replaced or at least disrupted, such as the
introduction of calculators in algebra: How does it affect human cognition if
computational processes take over (part of) our thinking? Will we lose our
ability to use those parts of our brain, or will it simply free up cognitive
reserve to consider new and more significant issues?

##### 3\. Copyright issues.

Generative AI works only because a dataset exists that it can be trained on,
and this raises new copyright issues, as P16 notes, “the ethical implications
of AI stealing other people’s work without credit […] make me a bit wary.”
Many established artists have raised concerns about this issue since those
whose art is currently visible on the internet lack means to opt out of image
training databases or otherwise control how their art is used (Metz, 2022;
Baio, 2022; Heikkilä, 2022; Sparkes, 2022). Interestingly, this concern was
mentioned directly by only one respondent, suggesting that either it is not a
matter that appears to be a threat to creatives we surveyed or that they
expect that a technological solution will emerge to address it; indeed,
measures to protect intellectual properties of images, such as watermarks, are
currently being developed (Zhang et al., 2018).

Reasons for not worrying about generative AI having a deleterious effect on
their professions were described in three themes:

##### 1\. AI cannot produce output without human input.

As described in Section 3.1.2, several respondents questioned a computer’s
ability to produce truly original output. This was also described as a reason
not to worry about AI replacing creative production or problem solving since
human input is needed for datasets to be trained on and verified: “Being able
to generate a Rothko at the click of a button is only possible because Rothko
himself had original thoughts - that isn’t creativity” (P8), and “human input
is still needed to verify and maintain AI’s work” (P22).

#####  2\. AI output is not _convincing_.

Several respondents also noted that they do not find AI-generated output
completely ‘convincing’ or original: “I don’t see any authentic or convincing
AI in artistic fields at all” (P8); “I know it can create pretty, but I don’t
think it can create “Wow! I have never seen anything like it!”” (P23); and “at
the moment it’s a tool that when used skillfully can create awesome images,
but there still needs to be someone with creative taste and an eye for imagery
at the helm. AIs also tend to generate ‘samey’ images to me” (P20). Although
this theme resembles the preceding one (AI needs human input to produce
output), which pertains more to requiring a human in the process of creating
and maintaining generative AIs, whereas the current theme critiques generative
AIs’ output.

##### 3\. My work/creative process is too complex for AI to imitate.

Finally, several respondents observed that their work process is too complex
for AI to replace it: “No, the complexity and dependencies is [sic] too high
in my work” (P21); “[I do not worry] for user interface design, there’s so
much to consider and think through that I can’t see an AI making something
fluid yet” (P16). Particularly in processes of original problem solving and
client communication, human cognition was described as indispensable: “Even
the new code that they write is still going to be unoriginal in terms of
problem solving” (P15); “We work very closely with clients and our work
requires a lot of thought process behind it. Our main product is communication
ideas and solving problems visually. Often we can do that better with a
scribble than a fancy looking piece of art. You can never ask the AI about the
intention/thoughts/feelings behind the product” (P10).

###  3.3. Exciting Times Ahead!

Thirteen respondents noted that they are more or less unequivocally excited
about AI contributing to creative work in their profession (such as “Yes!” or
“Absolutely, exciting times ahead!” (P12)). Four volunteered some version of
“yes and no,” e.g., “To some extent. I think some people will be able to use
it in a nice way” (P7). We grouped specific reasons for being excited about
the advent and adoption of generative AI technology in creative professions
into three themes:

##### 1\. AI can raise productivity for the individual or for larger
processes.

Several respondents imagined AI being used to raise productivity, either in
terms of individual efficiency (e.g., eliminating repetitive tasks and thus
allowing creatives to focus on ‘more important’ work): “there are things that
are more efficient to leave to machines which should pair with things that
humans will be better at for the foreseeable future.” (P19)) or in terms of
cultivating higher output rates by streamlining processes: “it would
streamline many of the standard questions in the field” (P1).

##### 2\. AI can offer inspiration.

In fields that require creativity, it is perhaps not surprising that
respondents highlighted using quickly generated output as a source of
inspiration in their creative process. Creative professionals often rely on
readily available examples of design for inspiration (Herring et al., 2009),
and the availability of AI to generate innumerable novel examples was seen as
a powerful opportunity for ‘opening up new solution spaces,’ e.g.: “It will
allow me to iterate through a much bigger possibility space” (P12); and “it
will make some work a lot easier/more efficient as you can try out different
ideas in a very short amount of time” (P6). In this role, AI is imagined to
augment what we call the divergent parts of the creative process by offering
examples and opening up novel and larger solution spaces (Dorst and Cross,
2001).

##### 3\. AI can lead to higher quality output.

Finally, some respondents highlighted the opportunity for AI to yield higher
quality output, partially for the two reasons above (offering novel
inspiration and freeing up time to work on tasks more central to the creative
core), and partially due to qualities inherent in the AI itself: “Any creative
work is better as a team effort and differences are a driving force. AI is
very different and I want to work with them” (P2); “it’s a powerful tool that
can enhance my work. […] I can see it slotting into a step between browsing
Pinterest for reference art and sketching my own stuff” (P20). Two respondents
also mentioned using AI for convergent parts of the creative process, for
instance, decision making and evaluation: “It can augment decision making”
(P14); and “it opens up to possibilities to create new solutions and evaluate
in new ways” (P21), although specific ways for evaluation to occur were not
described further.

##  4\. Discussion: Opportunities for participation

Although complex, it seems prudent and timely to tackle the issue of how to
encourage populations to participate in the development of AI more broadly
(Birhane et al., 2022). We consolidate our preliminary analysis into four
categories of potential focus for the design of participatory AI for
creatives: (1) Understanding AI, (2) Coping with AI, (3) Adapting to AI, and
(4) Exploiting AI. These categories align with the participatory design
approach presented by Sanders (Sanders, 2002) by considering what end-users
know (= understand AI), feel (= coping with AI), do (= adapt to AI), and dream
(= exploit AI). The categories offer a framework for engaging professional
creatives in participatory AI design in a meaningful way. One could ask
questions that align with the framework, e.g., “How might we help future users
understand this technology” or “How might we help future users adapt to new
work flows?”

###  4.1. Understanding AI

Some survey responses identify a superficial understanding of the technical
side of AI. This is acceptable, just as it is not a requirement of driving a
car that one understands how the engine works. However, creatives will be
better prepared to use AI as creativity support tools and design materials if
they have a working understanding of the tools and their limitations (Dove et
al., 2017; Long and Magerko, 2020; Falk and Inie, 2022), particularly the
level of agency that computers can be ascribed (as we saw, no responses that
demonstrated a deep level of technical understanding also portrayed the
computer as having a high degree of agency).

We suggest that facilitating a truthful understanding of AI is the first step
in empowering these users to co-create with AI technology. It is easy to brush
this responsibility off as a creatives-only undertaking. However, we believe
that AI developers share an ethical responsibility to make their systems
accessible and explainable to a broader public, in line with the HCI research
agenda for explainable, accountable and intelligible systems (Abdul et al.,
2018).

###  4.2. Coping with AI

In the longer term, it is inevitable that AI-generated content of many kinds
will be ubiquitous in most of our lives. How should we cope? We posit that
creatives should hone their skills in creating and in evaluating creativity.
The responses to our survey suggest that they can recognize and celebrate
indispensable human properties of creativity and art, e.g.: “human[-like]
creativity is due to a combination of experiences and impressions that are
connected in ways that are largely defined by human culture, and also
feelings/sensations […] that are mostly haphazard, and which AI don’t have”
(P11). Sharing worries, excitement, and coping strategies — including avoiding
AI, see, e.g, (Plunkett, 2022; Zhang et al., 2018; Joseph Saveri Law Firm &
Matthew Butterick, 2023) — as well as celebrating what is uniquely creative
about human approaches seems an important and achievable goal of designing
participatory AI. We imagine a future where generative AI openly celebrates
the sources from which its data are harvested, and where creators of
generative AI include input from end-users in their design processes.

###  4.3. Adapting to AI

When photography was invented, artists adjusted their activities to focus less
on realism and more on interpretation, whether through impressionism,
abstraction, or surrealism (see, e.g., (Silva, 2022) for a more elaborate
discussion of this). As writing, translation, paraphrasing and poetry become
increasingly automated, professional writers and editors may become “bosses to
bots,” instructing them on what to write, how to tailor material, and what to
re-write when results do not meet professional or personal standards.

Where by coping we mean respectfully considering the new reality that these
technologies bring about, by adapting we suggest more comprehensive inclusion
of creatives in the development of specific generative AI models. Several
respondents shared excitement about the possibilities of using AI to help
automate bureaucracy, repetitive tasks, and boring work. The responsibility of
facilitating adaptation, however, does not fall only on creatives. By
understanding creative needs and processes, generative AI developers may
tailor AI systems to help specific professions and crafts in a way that is not
only meaningful for creatives, but that may enhance the development of AI
itself, similar to how PD was originally meant not only to improve information
systems but also to empower workers (Clement and Van den Besselaar, 1993).

###  4.4. Exploiting AI

Photography changed what painters did, but it also opened up a field and a new
profession: photographer. Technologies such as ChatGPT will change what
writers do. Journalists are likely to spend more of their efforts on
investigation and acquiring stories and less time on wordsmithing the reports
on those stories. A mystery writer may give increased attention to plot
features and less to the word-by-word narrative. Completely new tools and
media may come out of the new AI technologies, including new types of creative
jobs; as P3 notes, “the far future might include both 2D and 3D assets,
generated in real time, as the player interacts with the experience […]
Experiences still need to be controlled, to ensure a good user experience.
Therefore it would probably increase the number of creative/technical
positions within game companies.” (P3).

We hypothesize that such technology can reach its full potential only if
creative professionals truly participate in its development. AI has sometimes
been described as “a new shiny hammer in search of nails” (Vardi, 2021), i.e.,
the technology or tool is being developed ahead of its specific purpose. We
posit that if generative AI is developed with participation from creatives,
there is a chance not only of better integration of AI in specific creative
work practices, but also of leveraging creative competencies to imagine
completely new avenues for these technologies.

##  5\. Conclusion and future work

The insights presented in this abstract illustrate some of the ways in which
creative professionals speculate about and anticipate how AI may impact their
creative work practices. Based on the insights, we encourage engaging
creatives in the development of generative AI, both in developing concrete
technology and in managing larger project issues as representatives of their
peers, in line with the ideals of participatory design (Sanders, 2002; Bødker
et al., 2022). Pathways for developing more participatory AI should consider
how creatives may better understand, cope with, adapt to as well as exploit
AI.

While the scope of our study is limited, we believe that both technology
development and opinions towards AI are changing so quickly that it is
relevant to share these preliminary results. We hope they will spark
discussions and inform future research into how to develop and use AI in a way
that encourages and requires participation of the people who will be affected
most by these technologies in the future. Since most creative fields
represented in our study are software-oriented, it is possible that the
expressed views are more open and welcoming towards AI. Future research should
include a more evenly distributed representation from different creative
fields as well as obtain richer data by conducting interview studies.

Furthermore, the respondents came from different creative industries, and
their everyday work lives may therefore not necessarily be impacted in the
same ways by generative AI. We have also not characterized how each
individual’s understanding of AI relates to, for instance, their level of
worry or expectations since we believe this would require a larger participant
group and deeper investigation.

Future work could categorize different creative industries and identify which
and how specific work tasks within these industries may be impacted by
generative AI, as well as investigate different ways to support these creative
practices with AI.

###### Acknowledgements.

This research has been supported by the VILLUM Foundation, grant 37176
(ATTiKA: Adaptive Tools for Technical Knowledge Acquisition) and by the
Austrian Science Fund (FWF) [P34226-N].

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##  Appendix A Respondents overview

P# | Age |  Country | Gender |  “Please describe your profession and how creativity plays a role in your profession/work” (slightly shortened for overview)
---|---|---|---|---
1 | 41-45 |  USA | Female |  Librarian, My work involves a lot of creative problem solving to address user needs.
2 | 36-40 |  Denmark | Male |  Digital designer, game designer, creative use of concepts and interfaces to tailor experiences and evoke emotions.
3 | 31-35 |  Denmark | Male |  Designing, programming and testing games. Creativity is important in designing a game, since it helps the rest of the team to understand where the goal of the game is.
4 | 36-40 |  Turkey | Female |  I am a researcher in academia and creativity plays a key role in terms of connecting dots on different topics, organize and elaborate my ideas clearly, be fluent on different subjects and flexible in terms of changing my perspectives when needed.
5 | 41-45 |  Denmark | Male |  3d artist / illustrator. I work in a team tasked with coming up with new game concept prototypes. My day job involves a lot of hands-on art creation, where different types of creativity is a big part - in concepting new stuff, or in problem solving, or simply in painting something
6 | 21-25 |  Germany | Female |  Media Designer, I need to come up with creative ideas for campaigns and minigames on websites.
7 | 31-35 |  Denmark | Male |  I’m a game designer / developer. I do everything from coding, drawing, animation and ui/ux design. Creativity plays a large role in everything I do
8 | 26-30 |  UK | Female |  I work in games production, so am responsible for the scheduling and scope of PC and console videogame projects. There’s a significant element of creative problem-solving in my job in terms of administration and organisation, as well as need for creativity in helping to create the games themselves
9 | 41-45 |  UK | Female |  video game writer / developer
10 | 31-35 |  Denmark | Female |  Creative Producer. I work with concept art and manage concept artists
11 | 51-55 |  Denmark | Female |  I work as a fixer, coordinator, and assistant. Because my job is to make people shine, regardless of their intrinsic potential, I have to be extremely creative (and imaginitive and persuasive) in finding ways to accomplish this, both in terms of finding solutions and in convincing clients to adopt my suggestions.
12 | 36-40 |  Germany | Male |  Software Engineer, sometimes coding needs to be creative
13 | 41-45 |  Germany | Female |  Research Assistent
14 | 31-35 |  UK | Male |  I am a computer scientist. As any other researcher, much of my work involves using creative methods - designing experiments, writing papers, analysing data etc
15 | 21-25 |  USA | Female |  student with an interest in art and design
16 | 21-25 |  USA | Non-binary |  Student in HCI and Design, with the goal of becoming a user interface designer or similar. Creativity is necessary to solve design problems and create visuals to explain solutions.
17 | 31-35 |  Germany | Male |  I research computational creativity, I am also an educator.
18 | 41-45 |  UK | Male |  Creative
19 | 31-35 |  Denmark | Male |  Experience Design for websites
20 | 31-35 |  Denmark | Male |  By day I’m a UI/UX artist. In past I’ve worked as a concept artist.
21 | 41-45 |  Denmark | Male |  Project management and design, finding new solutions on a daily basis…
22 | 21-25 |  Morocco | Male |  I’m a PhD student working on extracting entities and relations from morphological descriptions. Creativity is crucial for my work especially in coming up with solutions, presenting the explainability behind the provided solution as well as for presenting it to non technical meeting.
23 | 31-35 |  Denmark | Female |  I teach simple programming and computer game development to 11-13 year olds. They work through the design process, ideation, sketching, creating original pixel art and coding their own games.

Table 1. Overview of survey respondents

An overview of survey respondents, including participant number, age, residing
country, gender and response to the question: Please describe your profession
and how creativity plays a role in your profession/work. The responses have
been slightly shortened due to space limitations.

##  Appendix B Graph of responses to “What is AI?”

Figure 1. Screenshot of the distribution of answers in terms of their
technical depth and ascribed agency of AI.