# Anatomy of Higgs mass in Supersymmetric Inverse Seesaw Models

Eung Jin Chun<EMAIL_ADDRESS>Korea Institute for Advanced Study, Seoul
130-722, Korea  V. Suryanarayana Mummidi<EMAIL_ADDRESS>Sudhir K
Vempati<EMAIL_ADDRESS>Centre for High Energy Physics, Indian
Institute of Science, Bangalore 560012

###### Abstract

We compute the one loop corrections to the CP even Higgs mass matrix in the
supersymmetric inverse seesaw model to single out the different cases where
the radiative corrections from the neutrino sector could become important. It
is found that there could be a significant enhancement in the Higgs mass even
for Dirac neutrino masses of $\mathcal{O}$(30) GeV if the left-handed
sneutrino soft mass is comparable or larger than the right-handed neutrino
mass. In the case where right-handed neutrino masses are significantly larger
than the supersymmety breaking scale, the corrections can utmost account to an
upward shift of 3 GeV. For very heavy multi TeV sneutrinos, the corrections
replicate the stop corrections at 1-loop. We further show that general gauge
mediation with inverse seesaw model naturally accommodates a 125 GeV Higgs
with TeV scale stops.

###### pacs:

73.21.Hb, 73.21.La, 73.50.Bk

##  I Introduction

The discovery of the Higgs boson Aad:2012tfa ; Chatrchyan:2012tx ;
Chatrchyan:2012ufa  of the standard model has put severe constraints on its
supersymmetric extensions. In particular, for light stops masses (below 1
TeV), maximal stop mixing is required to generate a Higgs mass $\sim$125 GeV
Hall:2011aa ; Draper:2011aa ; Christensen:2012ei ; Aparicio:2012iw ;
Baer:2012uya ; Arbey:2012dq ; Cao:2012fz . Many supersymmetry breaking models
have already been strongly constrained by this requirement Heinemeyer:2011aa ;
AlbornozVasquez:2011aa ; Arbey:2011aa ; Arbey:2011ab ; Carena:2011aa ;
Baer:2011ab ; Kadastik:2011aa ; Buchmueller:2011ab ; Ellis:2012aa .

On the other hand, neutrino masses constitute one of the strongest signatures
of physics beyond standard model. It is imperative that any supersymmetric
extension of the standard model should also contain an explanation for non-
zero neutrino masses. Among many ideas to generate tiny neutrino massse, the
inverse seesaw model Mohapatra:1986bd  is interesting as it is applicable at
the weak scale with neutrino Yukawa couplinig of order one, and thus testable
at colliders like LHC.

In the present work, we revisit the consequences of the inverse seesaw model
for the lightest CP even Higgs boson mass Gogoladze:2012jp ; Guo:2013sna . We
find parameter regions in which the one-loop corrections to the light Higgs
mass can be very significant, leading to an increase of ${\cal O}(10)$ GeV,
for the neutrino Yukawa coupling larger than about 0.2. This is in the line of
observations of Refs. Babu:2008ge ; Martin:2009bg  which explored the role of
extra vector like matter at TeV scale in increasing the light Higgs mass. We
then apply these corrections to phenomenological minimal supersymmetric
standard models (PMSSM) and general gauge mediaed supersymmetry breaking
models (GMSB) where the Higgs mass can become 125 GeV for supersymmetry
breaking scale around TeV.

The paper is organized as follows. In the next section, we present one loop
corrections to the Higgs mass and study the various parameter regimes. In the
section 3, we work out two numerical examples in (1) PMSSM (2) General gauge
mediated supersymmetric inverse seesaw model. We conclude in the section 4.
Appendix A contains the main formulae, whereas appendices B and C contain RGE
equations and some ancillary formulae.

##  II One loop corrections to the Higgs mass in MSSM

The inverse seesaw model is characterized by a small lepton number violating
mass, unlike the Type-I seesaw, the right-handed neutrinos can be as light as
TeV or even below, with their Yukawa couplings of order one. This is achieved
by having an additional singlet field, which we denote by S. The
superpotential for this model is given as

$W_{\text{SISM}}=W_{\text{MSSM}}+Y_{N}LH_{u}N^{c}+M_{R}N^{c}S+\mu_{S}SS$ (1)

where $W_{MSSM}$ stands for the standard MSSM superpotential,

$\displaystyle W_{MSSM}=Y_{U}QU^{c}H_{u}+Y_{D}QD^{c}H_{d}+Y_{E}LE^{c}H_{d}+\mu
H_{u}H_{d}$ (2)

and $N^{c}$ and S are singlet fields carrying lepton number +1,-1
respectively.

We consider one right-handed neutrino and one singlet S field in the
discussion. It can be easily generalized to the case of two/three generations.
The mechanism of how neutrino gets mass is well documented in the literature.
We revisit it here briefly. In the basis, $\\{{\nu}_{L},{N^{c}},{S}\\}$, the
mass matrix, $M_{\nu}$, for the neutral leptons is given by

$M_{{\nu}}=\left(\begin{array}[]{ccc}0&m_{D}&0\\\ m_{D}&0&M_{R}\\\
0&M_{R}&\mu_{S}\end{array}\right)$ (3)

Where $m_{D}=Y_{N}\,\langle H_{u}\rangle$. The eigenvalues are given as

$\displaystyle m_{\nu_{1}}$ $\displaystyle\approx$
$\displaystyle{m_{D}^{2}\,\mu_{S}\over M_{R}^{2}}$ $\displaystyle m_{\nu_{2}}$
$\displaystyle\approx$ $\displaystyle-\left({m_{D}^{2}\over
2\,M_{R}}+M_{R}\right)$ $\displaystyle m_{\nu_{3}}$ $\displaystyle\approx$
$\displaystyle\left({m_{D}^{2}\over 2\,M_{R}}+M_{R}\right)$

$m_{\nu_{1}}$ is the lightest neutrino eigenvalue proportional to the lepton
number violating parameter $\mu_{S}$, the other two eigenvalues are almost
degenerate $\sim M_{R}$.

Since the inverse seesaw model is typically a low scale model, unlike the
traditional seesaw mechanisms, one wonders if they can give large enough
contribution to the light CP-even Higgs boson mass. This is more important to
explore in the regions where $m_{D}$ can be relatively large $\gtrsim
10~{}\text{GeV}$. It should be noted that the range in $m_{D}$
$\simeq(0.2-0.3)v$ for has been explored by collider searches
Bandyopadhyay:2012px ; Banerjee:2013fga . There are constraints, however, on
the size of $m_{D}$ for a given value of $M_{R}$ from electroweak precision
tests delAguila:2008pw :

$m_{D}\lesssim 0.05~{}M_{R}$ (4)

This constraint is strictly for the electron and muon generations. For the
third generation, it is slightly weaker, at the level of 0.07. This requires
$M_{R}\simeq 3$ TeV for $m_{D}$ close to the top quark mass. To compute the
corrections to the light Higgs mass from the neutrino sector, we use the one
loop effective potential methods of Coleman-Weinberg Coleman:1973jx . The
methods have been used to derive the well-known one-loop corrections from the
top-stop sector Ellis:1991zd ; Drees:1991mx  and we extend them to the
neutrino sector in the inverse seesaw model.

The scalar potential in this model consists of

$V_{S}=V_{F}+V_{D}+V_{\text{soft}}$ (5)

where

$\displaystyle V_{F}$ $\displaystyle=$
$\displaystyle|Y_{e}EH_{d}+Y_{N}H_{u}N|^{2}+|Y_{u}Qu^{c}+\mu
H_{d}+Y_{N}LN^{c}|^{2}+|Y_{N}LH_{u}+M_{R}S|^{2}+|M_{R}N^{c}+\mu_{S}S|^{2}+\ldots$
$\displaystyle V_{D}$ $\displaystyle=$
$\displaystyle\frac{1}{8}(g^{2}+g^{\prime 2})\,(|H_{u}|^{2}-|H_{d}|^{2})$
$\displaystyle V_{\text{soft}}$ $\displaystyle=$ $\displaystyle
A_{N}LH_{u}N^{c}+B_{M}NS+B_{\mu_{S}}SS+H.c+\ldots\,.$ (6)

In the basis, $\\{\tilde{\nu}_{L},\tilde{N^{c}},\tilde{S}\\}$, the mass
matrix, $\mathcal{M}_{\tilde{\nu}}^{2}$, for the sneutrinos is given by

$\mathcal{M}_{\tilde{\nu}}^{2}=\left(\begin{array}[]{ccc}m_{L}^{2}+D_{L}+m_{D}^{2}&m_{D}\,(A_{N}-\mu\cot\beta)&M_{R}\,m_{D}\\\
&m_{D}^{2}+m_{N}^{2}+M_{R}^{2}&B_{M}+M_{R}\,\mu_{S}\\\
&*&M_{R}^{2}+\mu_{S}^{2}+m_{\tilde{S}}^{2}\end{array}\right).$ (7)

In the above matrix, elements with $*$ correspond to symmetric entries of the
mass matrix. The eigenvalues of the above mass matrix can be easily derived in
the limit $\mu_{S}\ll m_{D}\ll M_{R}$, as required by the inverse seesaw
mechanism and the electroweak precision tests. In the leading order of
$m_{D}M_{R}/d_{2},m_{D}X_{N}/d_{1}\ll 1$, they are given as

$\displaystyle m_{\tilde{\nu}_{1}}^{2}$ $\displaystyle\approx$ $\displaystyle
m_{L}^{2}+m_{D}^{2}\left(1+{M_{R}^{2}\over d_{2}}+{X_{N}^{2}\over
d_{1}}\right)$ $\displaystyle m_{\tilde{\nu}_{2}}^{2}$ $\displaystyle\approx$
$\displaystyle m_{N}^{2}+M_{R}^{2}+m_{D}^{2}\left(1-{X_{N}^{2}\over
d_{1}}\right)$ $\displaystyle m_{\tilde{\nu}_{3}}^{2}$ $\displaystyle\approx$
$\displaystyle m_{S}^{2}+M_{R}^{2}-{M_{R}^{2}\,m_{D}^{2}\over d_{2}}$

where

$\displaystyle d_{1}=m_{L}^{2}-m_{N}^{2}-M_{R}^{2}$ $\displaystyle
d_{2}=m_{L}^{2}-m_{S}^{2}-M_{R}^{2}\,.$

One-loop corrections for the Higgs mass matrix will be derived from the one-
loop effective scalar potential given by the standard form:

$V_{1-loop}(q^{2})={1\over
64\pi^{2}}\mathcal{S}Tr\mathcal{M}^{4}(h)~{}~{}\text{Log}\left({\mathcal{M}^{2}(h)\over
q^{2}}-{3\over 2}\right).$ (8)

In the basis $\Phi^{T}=(Re\\{H_{d}^{0}\\},Re\\{H_{u}^{0}\\})$, the corrections
to the CP even Higgs mass are given as

$\mathcal{M}^{2}=\mathcal{M}^{2}_{0}+\Delta\mathcal{M}^{2}_{t}+\Delta\mathcal{M}^{2}_{\nu}$

where $\mathcal{M}^{2}_{0}$ stands for the tree level mass matrix,
$\Delta\mathcal{M}^{2}_{t}$ and $\Delta\mathcal{M}^{2}_{\nu}$ are
contributions from the top/stop sector and the neutrino/sneutrino sectors
respectively. The full mass matrix has the form:

$\displaystyle\mathcal{M}_{11}^{2}$ $\displaystyle=$ $\displaystyle
M_{Z}^{2}\,\cos\beta^{2}+m_{A}^{2}\sin\beta^{2}+\Delta\mathcal{M}_{t_{11}}^{2}+\Delta\mathcal{M_{\nu}}_{11}^{2}$
$\displaystyle\mathcal{M}_{12}^{2}$ $\displaystyle=$
$\displaystyle-(M_{z}^{2}+m_{A}^{2})\cos\beta\sin\beta+\Delta\mathcal{M}_{t_{12}}^{2}+\Delta\mathcal{M_{\nu}}_{12}^{2}$
$\displaystyle\mathcal{M}_{22}^{2}$ $\displaystyle=$ $\displaystyle
M_{Z}^{2}\,\sin\beta^{2}+m_{A}^{2}\cos\beta^{2}+\Delta\mathcal{M}_{t_{22}}^{2}+\Delta\mathcal{M_{\nu}}_{22}^{2}$

where for the sake of completeness, we present the well known top/stop
contributions Ellis:1991zd ; Drees:1991mx  :

$\displaystyle\Delta\mathcal{M}_{t_{11}}^{2}$ $\displaystyle=$
$\displaystyle{3g_{2}^{2}\,m_{t}^{4}\over
16\pi^{2}M_{W}^{2}\sin\beta^{2}}\left(\mu\,X_{t}\over
m_{\tilde{t}_{1}}^{2}-m_{\tilde{t}_{2}}^{2}\right)^{2}g(m_{\tilde{t}_{1}}^{2},m_{\tilde{t}_{2}}^{2})$
$\displaystyle\Delta\mathcal{M}_{t_{12}}^{2}$ $\displaystyle=$
$\displaystyle{3g_{2}^{2}\,m_{t}^{4}\over
16\pi^{2}M_{W}^{2}\sin\beta^{2}}\left(\mu\,X_{t}\over
m_{\tilde{t}_{1}}^{2}-m_{\tilde{t}_{2}}^{2}\right)\log\left({m_{\tilde{t}_{1}}^{2}\over
m_{\tilde{t}_{2}}^{2}}\right)-{A_{t}\over\mu}\Delta\mathcal{M}_{t_{11}}^{2}$
$\displaystyle\Delta\mathcal{M}_{t_{22}}^{2}$ $\displaystyle=$
$\displaystyle{3g_{2}^{2}\,m_{t}^{4}\over
16\pi^{2}M_{W}^{2}\sin\beta^{2}}\left(2\,\log{Q^{2}\over
m_{t}^{2}}+{2A_{t}X_{t}\over
m_{\tilde{t}_{1}}^{2}-m_{\tilde{t}_{2}}^{2}}\log\left({m_{\tilde{t}_{1}}^{2}\over
m_{\tilde{t}_{2}}^{2}}\right)\right)+\left({A_{t}\over\mu}\right)^{2}\Delta\mathcal{M}_{t_{11}}^{2}$
(9)

In the following we write down the contribution from the neutrino sector in a
compact notation as follows:

$\displaystyle\Delta\mathcal{M_{\nu}}_{11}^{2}$ $\displaystyle=$
$\displaystyle
2\,k\left(\tilde{L}_{1}\,\tilde{B}_{11}^{2}+\tilde{L}_{2}\,\tilde{B}_{21}^{2}+\tilde{L}_{3}\,\tilde{B}_{31}^{2}+m_{\tilde{\nu}_{1}}^{2}\tilde{A}_{111}(\tilde{L}_{1}-1)+m_{\tilde{\nu}_{2}}^{2}\tilde{A}_{211}(\tilde{L}_{2}-1)+m_{\tilde{\nu}_{3}}^{2}\tilde{A}_{311}(\tilde{L}_{3}-1)\right)$
$\displaystyle\Delta\mathcal{M_{\nu}}_{22}^{2}$ $\displaystyle=$
$\displaystyle
2\,k\left(\tilde{L}_{1}\,\tilde{B}_{12}^{2}+\tilde{L}_{2}\,\tilde{B}_{22}^{2}+\tilde{L}_{3}\,\tilde{B}_{32}^{2}+m_{\tilde{\nu}_{1}}^{2}\tilde{A}_{122}(\tilde{L}_{1}-1)+m_{\tilde{\nu}_{2}}^{2}\tilde{A}_{222}(\tilde{L}_{2}-1)+m_{\tilde{\nu}_{3}}^{2}\tilde{A}_{322}(\tilde{L}_{3}-1)\right)$
$\displaystyle-$ $\displaystyle
4\,k\,\left(L_{2}\,B_{22}^{2}+L_{3}\,B_{32}^{2}+m_{\nu_{2}}^{2}A_{222}(L_{2}-1)+m_{\nu_{3}}^{2}A_{322}(L_{3}-1)\right)$
$\displaystyle\Delta\mathcal{M_{\nu}}_{12}^{2}$ $\displaystyle=$
$\displaystyle
2\,k\left(\tilde{L}_{1}\,\tilde{B}_{12}\tilde{B}_{11}+\tilde{L}_{2}\,\tilde{B}_{22}\tilde{B}_{21}+\tilde{L}_{3}\,\tilde{B}_{32}\tilde{B}_{31}+m_{\tilde{\nu}_{1}}^{2}\tilde{A}_{112}(\tilde{L}_{1}-1)+m_{\tilde{\nu}_{2}}^{2}\tilde{A}_{212}(\tilde{L}_{2}-1)\right.$
(10) $\displaystyle+$
$\displaystyle\left.m_{\tilde{\nu}_{3}}^{2}\tilde{A}_{312}(\tilde{L}_{3}-1)\right)$

In the above,

$\displaystyle g(A,B)$ $\displaystyle=$ $\displaystyle
2-{(A+B)\over(A-B)}\log{A\over B};~{}~{}~{}~{}k=\frac{2}{32\pi^{2}}$
$\displaystyle\tilde{L}_{i}$ $\displaystyle=$ $\displaystyle
Log\left(\frac{m_{\tilde{\nu}_{i}}^{2}}{Q^{2}}\right);~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}L_{i}=Log\left(\frac{m_{\nu_{i}}^{2}}{Q^{2}}\right)$
$\displaystyle X_{t}$ $\displaystyle=$ $\displaystyle A_{t}-\mu\cot\beta$

and $B_{ij}$ and $A_{ijk}$’s are given in the Appendix. While the above
formulae are written for a single generation of right handed and singlet
neutrinos, they can be easily generalized to three generations of right-handed
and singlet neutrinos. The neutrino contributions to the light Higgs mass,
though similar to those from the top/stop sector, have a couple of distinct
features: (a) there is no colour factor associated with the neutrino
contributions, so they typically lower than the top/stop contributions by a
factor three, (b) The fermionic contributions, from the right-handed neutrinos
can be significant, reducing the total contribution to the Higgs mass. This is
highly dependent on the hierarchies between the relevant parameters: the soft
masses and the right handed neutrino masses. To understand the overall
relevance of these contributions, we will consider a few interesting cases
below. Note that in our numerical analysis, we restrict
$m_{D}M_{R}/d_{2},m_{D}X_{N}/d_{1}$ to be less than 0.1.

####  II.0.1 case-1 : $M_{R}\approx m_{L}$

Figure 1: The lightest CP even Higgs boson mass as a function of $m_{D}$ for
$A_{N}=0$ (red) and $A_{N}=-1000$ GeV (green). In this plot other parameter
are fixed as $M_{R}=m_{L}=1500$ GeV, $m_{N}=1000$ GeV and $m_{S}=800$ GeV. The
stop mass parameters are fixed such that $m_{h}=120$ GeV without the neutrino
corrections.

In this case 111see Appendix-C, for approximate formulae for sneutrino
eigenvalues, we choose the right-handed neutrino mass scale close to the
(left-handed) slepton masses. To satisfy the electroweak precision tests,
$m_{D}$ should be typically smaller than $M_{R}$ by a factor 20. Neutrino
masses can be adjusted by choosing a sufficiently small $\mu_{S}$. In Fig. 1
we plot the light Higgs mass as a function of $m_{D}$ for two values of
$A_{N}$ = 0 (Red) and $A_{N}=-1000$ GeV (Green). The stop contributions are
chosen such that the lightest CP even Higgs mass, $m_{h}=120\,\text{GeV }$ and
rest of the contribution comes solely from the neutrino sector. As it can be
seen from the left panel, the Higgs mass has a significant increase from 120
GeV and the increase is possible even for $m_{D}$ values as small as 20 GeV
222$m_{D}$ values quoted here are at the $M_{SUSY}$ scale which has been fixed
at 1 TeV. as long as slepton mass $m_{L}$ is relatively heavy $\gtrsim$ 1TeV
in the same range of $M_{R}$. The rest of the slepton masses appearing in the
1-loop formula are chosen to be $m_{N}=1000$ GeV and $m_{S}=800$ GeV. As
expected increasing $A_{N}$ increases the higgs mass, but the effect varies
with increasing $m_{D}$. It should be noted that perturbative constraints
exist on the neutrino Yukawa couplings $y_{N}=m_{D}/v_{u}$. Requiring $y_{N}$
to be perturbative all the way up to the GUT scale, puts a constraint on
$y_{N}\leq 0.75$ Guo:2013sna . While we have considered $M_{R}\approx m_{L}$
in the present example, this is not strictly necessary. For example, instead
of $m_{L}$ in the above case, one can have a similar enhancement in the case
$M_{R}\approx m_{N}$, while $m_{L}$ being significantly lighter. $M_{R}\approx
m_{S}$ does not lead to significant enhancement because that $S$ does not
couple to the Higgs field, $H_{u}$.

Figure 2:  The red band corresponds to Higgs mass of range [124-126] GeV in
the plane of $m_{S}$ and $m_{N}$. The rest of the parameters are chosen as
$m_{L}=M_{R}=1500$ GeV, $m_{D}=75$ GeV and $A_{N}=0$. The stop mass parameters
are fixed such that $m_{h}=120$ GeV without the neutrino corrections.

In Fig. 2, $m_{L}$, $m_{D}$ and $A_{N}$ are fixed to be 1500 GeV, 75 GeV and 0
respectively. And the parameter space in $m_{N}$ and $m_{S}$ plane is plotted
with a restriction that Higgs mass should be in the range [124-126] GeV.
Evidently there is wide range of parameter space available which can give
Higgs mass of 125 GeV.

####  II.0.2 case-2: $M_{R}\gg m_{L}$

We now consider the case where $M_{R}$ is the largest mass scale in the
theory. This limit has been earlier considered in Ref.Guo:2013sna . In this
case, the enhancement in the light Higgs mass is much smaller and restricted
to a few GeV. This is because the neutrino 1-loop correction, which is
negative, significantly suppresses the total contribution from the neutrino
sector. This is illustrated in Fig. 3 where we have plotted $m_{h}$ as a
function of $A_{N}$ (left panel) and $m_{D}$ (right panel). The slepton masses
are fixed as $m_{L}=500$ GeV, $m_{N}=300$ GeV and $m_{S}=200$ GeV. The right-
handed neutrino mass is taken to be 5 TeV. As can be seen from the plots, the
enhancement is not significant in this case. This holds even with the
variation in $A_{N}$ (left panel) or $m_{D}$ (right panel). The maximum
enhancement achieved here is about two and half GeV.

Figure 3: The lightest CP even neutral Higgs boson is plotted for $M_{R}=5$
TeV with respect to $A_{N}$ (left panel) and $m_{D}$ (right panel). The rest
of the parameters are chosen to be $m_{L}=500$ GeV, $m_{N}=300$ GeV, and
$m_{S}=200$ GeV. The stop parameters are taken such that $m_{h}=120$ GeV.

####  II.0.3 case-3: $m_{L}=m_{N}=m_{S}\gg M_{R}$

This case replicates the stop corrections. All the sneutrino eigenvalues are
much larger than the neutrino ones and thus dominating over the negative
contributions. However, it turns out that the required sneutrino mass scale is
in TeV range ( around 2 TeV range for a 500 GeV $M_{R}$). This range is suited
for semi-split and split scenarios. This is depicted in the Fig. 4.

Figure 4: $m_{h}$ is plotted versus $m_{L}$ keeping $M_{R}=500$ GeV and
$A_{N}=0$ . The stop parameters are taken such that $m_{h}=120$ GeV.

####  II.0.4 case-4: $M_{R}=m_{SUSY}$

We now consider the case where $M_{R}~{}=M_{SUSY}$, where
$M_{SUSY}=\sqrt{m_{\tilde{t}_{1}}m_{\tilde{t}_{2}}}$. Fixing the stop
parameters such that $m_{h}=120$ GeV fixes, $M_{R}\approx M_{SUSY}\approx
1$TeV. $m_{N},m_{L}$ and $m_{S}$ are considered as free parameters. The
parameter space $m_{L}$ and $m_{N}$ which accommodates, Higgs mass in the
range 124–126 GeV for different values of $m_{S}$ with $A_{N}=0$ and
$A_{N}=-1$ TeV is shown in Fig. 5.333Points which contribute to poles in
sneutrino eigenvalues are removed and are responsible for discontinuity in the
plots

Figure 5: $m_{L}$ is plotted against $m_{N}$ with different values of $m_{S}$,
for a Higgs mass of 124-126 GeV. The rest of the parameters are chosen to be
$A_{N}=0$ (-1 TeV) and $m_{D}=50$ GeV for the left (right) panel. The stop
parameters are taken such that $m_{h}=120$ GeV

##  III Applications to PMSSM and GMSB

In the present section, we present two numerical examples as an application to
the above calculation.

###  III.1 PMSSM and Inverse Seesaw

Figure 6: For a fixed value of $M_{R}=1000\,(2500)$ GeV in the left (right)
panel, $M_{SUSY}$ is plotted against $X_{t}/M_{SUSY}$. Green (red) points are
with (without) neutrino contribution.

The phenomenological MSSM is low energy parameterisation of the supersymmetry
breaking soft terms in terms of 19-22 parameters (See for example,
Berger:2008cq ). To study the inverse seesaw model in the PMSSM setting the
following additional parameters $m_{N},m_{S},A_{N}$ are to be included.
Together with the existing parameters, the nine parameters which completely
fix the low energy neutral CP even Higgs mass matrix and their ranges are
given as: $m_{Q},m_{U},m_{L},m_{N},m_{S}\in[100,3000]$ GeV;
$A_{t},\mu\in[-1500,1500]$GeV; $Y_{N}\in[0.1,1]$.

In Fig. 6, we have plotted the regions of Higgs mass within the range
[123,128] GeV in the plane of $M_{SUSY}$ and $X_{t}/M_{\text{SUSY}}$. In the
left (right) panel right-handed neutrino mass is chosen to be 1 (2) TeV. The
$\tan\beta$ is fixed to be 10. The red points are the ones without
neutrino/sneutrino contributions and the green points are the ones where
neutrino/sneutrino contributions are added. As we can clearly see from the
figure, even if $m_{SUSY}$ is below 1 TeV, there is enough contribution from
the neutrino sector to a 125 GeV Higgs mass

As right-handed neutrino mass $M_{R}$ increases, we get closer to the case-2
discussed in the previous section where larger right-handed neutrino masses
make the contribution of right-handed neutrinos to Higgs mass negative, and
thus reducing the Higgs mass. This effect is seen in the right panel of Fig.
6.

###  III.2 GMSB and Inverse Seesaw

Minimal gauge mediation models have been strongly constrained by the recent
discovery of the Higgs mass of 125 GeV Draper:2011aa . This is because the
stop mixing parameter $X_{t}$ is predicted to be very small in these models.
The $X_{t}$ can be made large through renormalisation group corrections, but
this would require gluino masses to be greater than 8 TeV. Thus, the only way
these models can accommodate a light CP even neutral higgs boson with a mass
around 125 GeV is by increasing the masses of the stops beyond 4 TeV. This
range for the stop masses is far beyond the LHC reach. One can then consider
modification by including either messenger-matter interactions, new fields or
new interactions to achieve the Higgs mass within the required ball park. The
feature of small $X_{t}$ also persists in general gauge mediation which is an
umbrella of all possible gauge mediations both in the perturbative and non-
perturbative regime. A recent analysis of the Higgs mass in general gauge
mediation is presented in Ref. Grajek:2013ola .

Incorporating the inverse seesaw model in general gauge mediation could
generate the Higgs mass in the right ball park, due to the additional
corrections induced by the neutrinos. We study this possibility in the present
subsection. The set up of general gauge mediation we consider is specified by
the following boundary conditions at the messenger scale:

$\displaystyle M_{i}(X)$ $\displaystyle\approx$
$\displaystyle\frac{\Lambda}{16\pi^{2}}\sum_{i}\left(g_{i}^{2}(X)\right)$
$\displaystyle m_{\tilde{Q}}^{2}$ $\displaystyle\approx$
$\displaystyle\frac{2\Lambda^{2}}{(16\pi^{2})^{2}}\sum_{i}\left(g_{i}^{4}(X)~{}C_{i}(Q)\right)$
$\displaystyle m_{\tilde{U}}^{2}$ $\displaystyle\approx$
$\displaystyle\frac{2\Lambda^{2}}{(16\pi^{2})^{2}}\sum_{i}\left(g_{i}^{4}(X)~{}C_{i}(U)\right)$
$\displaystyle m_{\tilde{L}}^{2}$ $\displaystyle\approx$
$\displaystyle\frac{2\Lambda_{L}^{2}}{(16\pi^{2})^{2}}\sum_{i}\left(g_{i}^{4}(X)~{}C_{i}(L)\right)$
$\displaystyle m_{\tilde{e}}^{2}$ $\displaystyle\approx$
$\displaystyle\frac{2\Lambda_{L}^{2}}{(16\pi^{2})^{2}}\sum_{i}\left(g_{i}^{4}(X)~{}C_{i}(L)\right)$
$\displaystyle m_{\tilde{S}}^{2}$ $\displaystyle=$ $\displaystyle 0$
$\displaystyle m_{\tilde{N}}^{2}$ $\displaystyle=$ $\displaystyle 0$

Where $C_{i}(f)$ is the quadratic casimir of the field f and $g_{i}(X)$ is the
gauge coupling constant at the messenger scale $M_{X}$. And ’i’ runs over all
the gauge groups in the standard model. Except for sleptons all other
parameters, scalar squared masses and gaugino masses are set by $\Lambda$ at
the messenger scale where as slepton masses are set by $\Lambda_{L}$.
Typically, the soft masses of the singlets $m_{S}$ and $m_{N}$ are zero at the
mediation scale. At the weak scale $m_{N}$ does get generated by RGE
corrections whereas $m_{S}$ remains zero. Using the RGE given in the appendix,
the leading log estimate of $m_{N}$ at the weak scale is given by

$m_{N}^{2}(M_{\text{SUSY}})\approx-{1\over
16\pi^{2}}(m_{H_{u}}^{2}+m_{L}^{2}+m_{N}^{2})Y_{N}^{2}Log({M_{\text{mess}}\over
M_{\text{SUSY}}})$ (11)

This generates a large enough positive contribution to $m_{N}^{2}$ at the weak
scale as $m_{H_{u}}^{2}$ is negative at the weak scale from the requirement of
electroweak symmetry breaking. The question then remains whether with the
above boundary conditions it is possible to reproduce either of the conditions
$m_{N}\gtrsim M_{R}$ or $m_{L}\gtrsim M_{R}$ to enhance the Higgs mass
significantly.

Assuming as before only one right-handed neutrino and one singlet, we find
that it is indeed possible to generate a Higgs mass of 125 GeV. We have to
choose an appropriate boundary condition for the third generation sleptons
such that it is close to the $M_{R}$ mass. In the table 1 we present two
example points which have this characteristic. It is clear that the two
example points given in the table corresponds to the case $m_{L}$$\sim$
$M_{R}$ discussed in the section-2.

$m_{h}[GeV]$ | $y_{N}$ | $M_{R}[GeV]$ |  $m_{\tilde{t}_{1}}$[GeV] |  $m_{\tilde{t}_{2}}$ [GeV] |  $\Lambda$[GeV] |  $\Lambda_{L}$[GeV] |  $m_{L}$[GeV] |  $m_{N}$[GeV] |  $m_{S}$[GeV]
---|---|---|---|---|---|---|---|---|---
127.21 | 0.62 | 1787 | 943 | 1078 | $10^{5}$ | 5.2 $10^{5}$ | 1791 | 808 | 0
124 | 0.82 | 2056 | 940 | 1072 | $10^{5}$ | 6 $10^{5}$ | 2046 | 846 | 0
Table 1: Parameter space in general gauge mediated supersymmetric inverse
seesaw model

##  IV Summary

Inverse seesaw model has many interesting features and serves as an important
alternative to the regular seesaw model. Supersymmetric versions of this model
have been studied earlier in the literature. In the present work, we have
discussed the detailed anatomy of the one loop corrections to the neutral CP
even Higgs boson masses. We show that the corrections can be significant in
cases where the soft mass of either the singlet or the doublet sneutrino is
comparable or greater than the right-handed neutrino mass (for reasonable
values of Dirac coupling). An enhancement of 6-12 GeV or even more can be
easily achieved. This removes the requirement of a large stop mixing parameter
$X_{t}$ (for stop masses less than a TeV) in models where low scale inverse
seesaw mechanism is implemented.

An interesting application of this model lies in general gauge mediation where
we have shown that implementing inverse seesaw model can enhance the light
Higgs mass to the 125 GeV for stops less than a TeV, without resorting to any
mechanism to enhance the stop mixing parameter $X_{t}$.

Acknowledgments:
SKV is supported by DST Ramanujan Grant SR/S2/2008/RJN-25 of Govt of India.
VSM is supported by CSIR fellowship 09/079(2377)/2010-EMR-1. EJC was supported
by SRC program of NRF Grant No. 2009-0083526 funded by the Korea government
(MSIP) through Korea Neutrino Research Center.

##  Appendix A Appendix

Here we have collected the expressions for $B_{ij}$ and $A_{ijk}$’s which are
used in the calculation of one-loop corrected Higgs mass.

$\displaystyle B_{ij}$ $\displaystyle=$ $\displaystyle{\partial
m_{\nu_{i}}^{2}\over\partial H_{j}}$ $\displaystyle A_{ijk}$ $\displaystyle=$
$\displaystyle{\partial B_{ij}\over\partial H_{k}}$

$\tilde{B}_{12}=2\,y_{N}\,m_{D}\left(\frac{m_{L}^{2}-m_{S}^{2}}{d_{2}}+\frac{X_{N}A_{N}}{d_{1}}\right);~{}~{}~{}\tilde{B}_{11}=-2\,y_{N}\,m_{D}\frac{\mu\,X_{N}}{d_{1}};~{}~{}~{}~{}\tilde{B}_{22}=2\,y_{N}\,m_{D}-2\,y_{N}\,m_{D}\,\frac{X_{N}A_{N}}{d_{1}}\\\
$ $\tilde{B}_{21}={2\,y_{N}\,m_{D}\,\mu\,X_{N}\over
d_{1}};~{}~{}~{}\tilde{B}_{32}=-{2\,y_{N}\,m_{D}\,M_{R}^{2}\over
d_{2}};~{}~{}~{}\tilde{B}_{31}=0$ $\displaystyle\tilde{A}_{111}$
$\displaystyle=$
$\displaystyle\frac{2y_{N}^{2}\mu^{2}}{d_{1}};~{}~{}~{}~{}~{}~{}\tilde{A}_{112}=-{A_{N}\over\mu}\,\tilde{A}_{111};~{}~{}~{}~{}~{}\tilde{A}_{122}=2y_{N}^{2}(1+{A_{N}\over
d_{1}}+{M_{R}^{2}\over d_{2}})$ $\displaystyle\tilde{A}_{211}$
$\displaystyle=$
$\displaystyle-\tilde{A}_{111}:~{}~{}~{}~{}~{}\tilde{A}_{212}={A_{N}\over\mu}\,\tilde{A}_{111};~{}~{}~{}~{}~{}~{}~{}\tilde{A}_{222}=2y_{N}^{2}(1-{A_{N}\over
d_{1}})$ $\displaystyle\tilde{A}_{311}$ $\displaystyle=$ $\displaystyle
0:~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\tilde{A}_{312}=0:~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\tilde{A}_{322}=-2y_{N}^{2}{M_{R}^{2}\over
d_{2}}$ $\displaystyle B_{22}$ $\displaystyle=$ $\displaystyle
2|H_{u}|y_{N}^{2}+\frac{|H_{u}|^{3}y_{N}^{4}}{M_{R}^{2}};~{}~{}~{}~{}~{}~{}~{}~{}B_{32}=2|H_{u}|y_{N}^{2}+\frac{|H_{u}|^{3}y_{N}^{4}}{M_{R}^{2}}$
$\displaystyle A_{222}$ $\displaystyle=$ $\displaystyle
2y_{N}^{2}+\frac{3|H_{u}|^{2}y_{N}^{4}}{M_{R}^{2}};~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}A_{322}=2y_{N}^{2}+\frac{3|H_{u}|^{2}y_{N}^{4}}{M_{R}^{2}}$

where we have suppressed the generation indices.

##  Appendix B RGE equations in SISM

In the last section of the appendix we present the renormalisation group
equations for some of the superpotential and soft terms relevant to the
analysis of general gauge mediation. To derive the formulae we use the
standard formulae available in the literatureFalck:1985aa ; Martin:1993zk .
The notation we use is $t=Log({\mu\over m_{SUSY}})$.

$\displaystyle\frac{dy_{i}}{dt}$ $\displaystyle=$
$\displaystyle\frac{y_{i}}{16\pi^{2}}{\gamma_{i}}^{(1)}$
$\displaystyle\frac{d\mu}{dt}$ $\displaystyle=$
$\displaystyle\frac{\mu}{16\pi^{2}}\left[3y_{t}^{2}+3y_{b}^{2}+y_{N}^{2}+y_{\tau}^{2}-3g_{2}^{2}-{3\over
5}g_{1}^{2}\right]$ $\displaystyle\frac{d\mu_{s}}{dt}$ $\displaystyle=$
$\displaystyle 0$ $\displaystyle\frac{dM_{R}}{dt}$ $\displaystyle=$
$\displaystyle\frac{M_{R}}{16\pi^{2}}2y_{N}^{2}$

where

$\displaystyle{\gamma_{t}}^{(1)}$ $\displaystyle=$
$\displaystyle\left[y_{N}^{2}+6y_{t}^{2}+y_{b}^{2}-{16\over
3}g_{3}^{2}-3g_{2}^{2}-{13\over 15}g_{1}^{2}\right]$
$\displaystyle{\gamma_{b}}^{(1)}$ $\displaystyle=$
$\displaystyle\left[6y_{b}^{2}+y_{t}^{2}+{y_{\tau}}^{2}-{16\over
3}g_{3}^{2}-3g_{2}^{2}-{7\over 15}g_{1}^{2}\right]$
$\displaystyle{\gamma_{\tau}}^{(1)}$ $\displaystyle=$
$\displaystyle\left[y_{N}^{2}+3y_{b}^{2}+4{y_{\tau}}^{2}-3g_{2}^{2}-{9\over
5}g_{1}^{2}\right]$ $\displaystyle{\gamma_{y_{N}}}^{(1)}$ $\displaystyle=$
$\displaystyle\left[4y_{N}^{2}+3y_{t}^{2}+{y_{\tau}}^{2}-{3\over
5}g_{1}^{2}\right]$

$\displaystyle\frac{dm_{H_{u}}^{2}}{dt}$ $\displaystyle=$
$\displaystyle\frac{1}{16\pi^{2}}\left[3x_{t}+x_{N}-6g_{2}^{2}M_{2}-\frac{6}{5}g_{1}^{2}M_{1}^{2}+{3\over
5}g_{1}^{2}\xi\right]$ $\displaystyle\frac{dm_{H_{d}}^{2}}{dt}$
$\displaystyle=$
$\displaystyle\frac{1}{16\pi^{2}}\left[3x_{b}+x_{\tau}-6g_{2}^{2}M_{2}-\frac{6}{5}g_{1}^{2}M_{1}^{2}-{3\over
5}g_{1}^{2}\xi\right]$ $\displaystyle\frac{dm_{N}^{2}}{dt}$ $\displaystyle=$
$\displaystyle\frac{1}{16\pi^{2}}\left[2\,x_{N}\right]$
$\displaystyle\frac{dm_{S}^{2}}{dt}$ $\displaystyle=$ $\displaystyle 0$ (16)

where

$\displaystyle x_{t}$ $\displaystyle=$ $\displaystyle
2y_{t}^{2}\left(m_{H_{u}}^{2}+m_{Q_{3}}^{2}+m_{U_{3}}^{2}\right)+2A_{t}^{2}$
$\displaystyle x_{b}$ $\displaystyle=$ $\displaystyle
2y_{b}^{2}\left(m_{H_{d}}^{2}+m_{Q_{3}}^{2}+m_{d_{3}}^{2}\right)+2A_{b}^{2}$
$\displaystyle x_{\tau}$ $\displaystyle=$ $\displaystyle
2y_{\tau}^{2}\left(m_{H_{d}}^{2}+m_{L_{3}}^{2}+m_{e_{3}}^{2}\right)+2A_{\tau}^{2}$
$\displaystyle x_{N}$ $\displaystyle=$ $\displaystyle
2y_{N}^{2}\left(m_{H_{u}}^{2}+m_{L_{3}}^{2}+m_{N}^{2}\right)+2A_{N}^{2}$

##  Appendix C Approximate sneutrino egenvalues for $M_{R}\sim m_{L}$

$\displaystyle m_{\tilde{\nu}_{1}}^{2}$ $\displaystyle\approx$ $\displaystyle
m_{L}^{2}+m_{D}^{2}\left(1-\frac{m_{L}^{2}}{m_{S}^{2}}-\frac{X_{N}^{2}}{m_{N}^{2}}\right)$
$\displaystyle m_{\tilde{\nu}_{2}}^{2}$ $\displaystyle\approx$ $\displaystyle
m_{N}^{2}+m_{L}^{2}+m_{D}^{2}\left(1+\frac{X_{N}^{2}}{m_{N}^{2}}\right)$
$\displaystyle m_{\tilde{\nu}_{3}}^{2}$ $\displaystyle\approx$ $\displaystyle
m_{S}^{2}+m_{L}^{2}+m_{D}^{2}\,\frac{m_{L}^{2}}{m_{S}^{2}}$
$\displaystyle\tilde{B}_{11}$ $\displaystyle=$ $\displaystyle
2\,y_{N}\,m_{D}\,\frac{\mu\,X_{N}}{m_{N}^{2}};~{}~{}~{}\tilde{B}_{21}=-\tilde{B}_{11}$
$\displaystyle\tilde{B}_{12}$ $\displaystyle=$ $\displaystyle
2\,y_{N}\,m_{D}\,\left(1-\frac{m_{L}^{2}}{m_{S}^{2}}-\frac{X_{N}\,A_{N}}{m_{N}^{2}}\right)$
$\displaystyle\tilde{B}_{22}$ $\displaystyle=$ $\displaystyle
2\,y_{N}\,m_{D}\,\left(1+\frac{X_{N}\,A_{N}}{m_{N}^{2}}\right)$
$\displaystyle\tilde{B}_{32}$ $\displaystyle=$ $\displaystyle
2\,y_{N}\,m_{D}\frac{m_{L}^{2}}{m_{S}^{2}}$ $\displaystyle\tilde{A}_{111}$
$\displaystyle=$ $\displaystyle-{2\mu^{2}y_{N}^{2}\over
m_{N}^{2}};~{}~{}~{}~{}~{}~{}\tilde{A}_{112}=-{A_{N}\over\mu}\,\tilde{A}_{111}$
$\displaystyle\tilde{A}_{122}$ $\displaystyle=$ $\displaystyle
2y_{N}^{2}(1-{A_{N}^{2}\over m_{N}^{2}}-{M_{R}^{2}\over
m_{S}^{2}});~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\tilde{A}_{211}=-\tilde{A}_{111}$
$\displaystyle\tilde{A}_{212}$ $\displaystyle=$
$\displaystyle{A_{N}\over\mu}\,\tilde{A}_{111};~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}~{}\tilde{A}_{222}=2y_{N}^{2}(1+{A_{N}^{2}\over
m_{N}^{2}})$ $\displaystyle\tilde{A}_{322}$ $\displaystyle=$ $\displaystyle
2y_{N}^{2}{M_{R}^{2}\over m_{S}^{2}}$ (18)

Approximate formula for the bound on the mass of the lightest Higgs boson is
given by

$\displaystyle m_{h}^{2}$ $\displaystyle\leq$ $\displaystyle
M_{Z}^{2}\cos\beta^{2}+\Delta\mathcal{M_{t}}_{22}^{2}\sin\beta^{2}+\Delta\mathcal{M_{\nu}}_{22}^{2}\sin\beta^{2}$
(19)

$\Delta\mathcal{M}_{11}^{2}$ and $\Delta\mathcal{M}_{12}^{2}$ contribution is
very small, compared to $\Delta\mathcal{M}_{22}^{2}$, can be neglected. To
estimate nuetrino contribution to Higgs mass we have considered
$\Delta\mathcal{M_{\nu}}_{22}^{2}$ in the approximations $M_{R}\sim m_{L}$ and
$A_{N}$=0, which is given by

$\displaystyle\Delta\mathcal{M_{\nu}}_{22}^{2}$ $\displaystyle=$
$\displaystyle
2\,k\left(\tilde{L}_{1}\,\tilde{B}_{12}^{2}+\tilde{L}_{2}\,\tilde{B}_{22}^{2}+\tilde{L}_{3}\,\tilde{B}_{32}^{2}+m_{\tilde{\nu}_{2}}^{2}\tilde{A}_{222}(\tilde{L}_{2}-1)+m_{\tilde{\nu}_{3}}^{2}\tilde{A}_{322}(\tilde{L}_{3}-1)\right)$
(20)
$\displaystyle-4\,k\,\left(L_{2}\,B_{22}^{2}+L_{3}\,B_{32}^{2}+m_{\nu_{2}}^{2}A_{222}(L_{2}-1)+m_{\nu_{3}}^{2}A_{322}(L_{3}-1)\right)$

From Appendix-A, it is clear that A’s and B’s corresponding to right-handed
neutrino part is are small compared to that of sneutrinos. Thus fermion
contribution can be safely neglected (this is not true when
$m_{SUSY}$$\ll$$M_{R}$) and 20 becomes

$\displaystyle\Delta\mathcal{M_{\nu}}_{22}^{2}\over(2k)$
$\displaystyle\approx$ $\displaystyle
4m_{D}^{2}y_{N}^{2}\left[\tilde{L}_{2}+{M_{R}^{4}\over
m_{S}^{4}}L_{3}+{(M_{R}^{2}-m_{S}^{2})^{2}\over
m_{S}^{4}}\tilde{L}_{1}\right]$ (21)
$\displaystyle+2m_{\tilde{\nu}_{1}}^{2}y_{N}^{2}\left[({M_{R}^{2}\over
m_{S}^{2}}-1)\,(1-\tilde{L}_{1})\right]+2m_{\tilde{\nu}_{2}}^{2}y_{N}^{2}\left[\tilde{\tilde{L}}_{2}-1\right]$
$\displaystyle+2m_{\tilde{\nu}_{3}}^{2}y_{N}^{2}\left[{M_{R}^{2}\over
m_{S}^{2}}\,(\tilde{L}_{3}-1)\right]$

Typically all the sneutrino masses are of O($10^{6}$) (while log factors are
of O(1)) and can be taken to be equal.

$\displaystyle\Delta\mathcal{M_{\nu}}_{22}^{2}\over(2k)$
$\displaystyle\approx$ $\displaystyle
4m_{D}^{2}y_{N}^{2}\left[\tilde{L}_{2}+{M_{R}^{4}\over
m_{S}^{4}}\tilde{L}_{3}+{(M_{R}^{2}-m_{S}^{2})^{2}\over
m_{S}^{4}}\tilde{L}_{1}\right]+2\,m_{\tilde{\nu}}^{2}\,y_{N}^{2}\left[{M_{R}^{2}\over
m_{S}^{2}}\,{\tilde{L}_{3}\over\tilde{L}_{1}}\right.$ (22)
$\displaystyle\left.+(-2+\tilde{L}_{1}+\tilde{L}_{2})\,\right]$

From eq (22), it is evident that Higgs mass receives large correction from
sneutrino masses. As sneutrino masses implicitly depend on $m_{D}$, increase
in $m_{D}$ increases the Higgs mass.

## References

  * (1) G. Aad et al., “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Phys.Lett., vol. B716, pp. 1–29, 2012.
  * (2) S. Chatrchyan et al., “Combined results of searches for the standard model Higgs boson in $pp$ collisions at $\sqrt{s}=7$ TeV,” Phys.Lett., vol. B710, pp. 26–48, 2012.
  * (3) S. Chatrchyan et al., “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC,” Phys.Lett., vol. B716, pp. 30–61, 2012.
  * (4) L. J. Hall, D. Pinner, and J. T. Ruderman, “A Natural SUSY Higgs Near 126 GeV,” JHEP, vol. 1204, p. 131, 2012.
  * (5) P. Draper, P. Meade, M. Reece, and D. Shih, “Implications of a 125 GeV Higgs for the MSSM and Low-Scale SUSY Breaking,” Phys.Rev., vol. D85, p. 095007, 2012.
  * (6) N. D. Christensen, T. Han, and S. Su, “MSSM Higgs Bosons at The LHC,” 2012.
  * (7) L. Aparicio, D. Cerdeno, and L. Ibanez, “A 119-125 GeV Higgs from a string derived slice of the CMSSM,” JHEP, vol. 1204, p. 126, 2012.
  * (8) H. Baer, V. Barger, and A. Mustafayev, “Neutralino dark matter in mSUGRA/CMSSM with a 125 GeV light Higgs scalar,” JHEP, vol. 1205, p. 091, 2012.
  * (9) A. Arbey, M. Battaglia, A. Djouadi, and F. Mahmoudi, “The Higgs sector of the phenomenological MSSM in the light of the Higgs boson discovery,” JHEP, vol. 1209, p. 107, 2012.
  * (10) J.-J. Cao, Z.-X. Heng, J. M. Yang, Y.-M. Zhang, and J.-Y. Zhu, “A SM-like Higgs near 125 GeV in low energy SUSY: a comparative study for MSSM and NMSSM,” JHEP, vol. 1203, p. 086, 2012.
  * (11) S. Heinemeyer, O. Stal, and G. Weiglein, “Interpreting the LHC Higgs Search Results in the MSSM,” Phys.Lett., vol. B710, pp. 201–206, 2012.
  * (12) D. Albornoz Vasquez, G. Belanger, R. Godbole, and A. Pukhov, “The Higgs boson in the MSSM in light of the LHC,” Phys.Rev., vol. D85, p. 115013, 2012\.
  * (13) A. Arbey, M. Battaglia, and F. Mahmoudi, “Constraints on the MSSM from the Higgs Sector: A pMSSM Study of Higgs Searches, $B^{0}_{s}\to\mu^{+}\mu^{-}$ and Dark Matter Direct Detection,” Eur.Phys.J., vol. C72, p. 1906, 2012.
  * (14) A. Arbey, M. Battaglia, A. Djouadi, F. Mahmoudi, and J. Quevillon, “Implications of a 125 GeV Higgs for supersymmetric models,” Phys.Lett., vol. B708, pp. 162–169, 2012.
  * (15) M. Carena, S. Gori, N. R. Shah, and C. E. Wagner, “A 125 GeV SM-like Higgs in the MSSM and the $\gamma\gamma$ rate,” JHEP, vol. 1203, p. 014, 2012\.
  * (16) H. Baer, V. Barger, and A. Mustafayev, “Implications of a 125 GeV Higgs scalar for LHC SUSY and neutralino dark matter searches,” Phys.Rev., vol. D85, p. 075010, 2012.
  * (17) M. Kadastik, K. Kannike, A. Racioppi, and M. Raidal, “Implications of the 125 GeV Higgs boson for scalar dark matter and for the CMSSM phenomenology,” JHEP, vol. 1205, p. 061, 2012.
  * (18) O. Buchmueller, R. Cavanaugh, A. De Roeck, M. Dolan, J. Ellis, et al., “Higgs and Supersymmetry,” Eur.Phys.J., vol. C72, p. 2020, 2012.
  * (19) J. Ellis and K. A. Olive, “Revisiting the Higgs Mass and Dark Matter in the CMSSM,” Eur.Phys.J., vol. C72, p. 2005, 2012.
  * (20) R. Mohapatra and J. Valle, “Neutrino Mass and Baryon Number Nonconservation in Superstring Models,” Phys.Rev., vol. D34, p. 1642, 1986.
  * (21) I. Gogoladze, B. He, and Q. Shafi, “Inverse Seesaw in NMSSM and 126 GeV Higgs Boson,” Phys.Lett., vol. B718, pp. 1008–1013, 2013.
  * (22) J. Guo, Z. Kang, T. Li, and Y. Liu, “Higgs boson mass and complex sneutrino dark matter in the supersymmetric inverse seesaw models,” JHEP, vol. 1402, p. 080, 2014.
  * (23) K. Babu, I. Gogoladze, M. U. Rehman, and Q. Shafi, “Higgs Boson Mass, Sparticle Spectrum and Little Hierarchy Problem in Extended MSSM,” Phys.Rev., vol. D78, p. 055017, 2008.
  * (24) S. P. Martin, “Extra vector-like matter and the lightest Higgs scalar boson mass in low-energy supersymmetry,” Phys.Rev., vol. D81, p. 035004, 2010\.
  * (25) P. Bandyopadhyay, E. J. Chun, H. Okada, and J.-C. Park, “Higgs Signatures in Inverse Seesaw Model at the LHC,” JHEP, vol. 1301, p. 079, 2013.
  * (26) S. Banerjee, P. S. B. Dev, S. Mondal, B. Mukhopadhyaya, and S. Roy, “Invisible Higgs Decay in a Supersymmetric Inverse Seesaw Model with Light Sneutrino Dark Matter,” JHEP, vol. 1310, p. 221, 2013.
  * (27) F. del Aguila, J. de Blas, and M. Perez-Victoria, “Effects of new leptons in Electroweak Precision Data,” Phys.Rev., vol. D78, p. 013010, 2008.
  * (28) S. R. Coleman and E. J. Weinberg, “Radiative Corrections as the Origin of Spontaneous Symmetry Breaking,” Phys.Rev., vol. D7, pp. 1888–1910, 1973\.
  * (29) J. R. Ellis, G. Ridolfi, and F. Zwirner, “On radiative corrections to supersymmetric Higgs boson masses and their implications for LEP searches,” Phys.Lett., vol. B262, pp. 477–484, 1991.
  * (30) M. Drees and M. M. Nojiri, “One loop corrections to the Higgs sector in minimal supergravity models,” Phys.Rev., vol. D45, pp. 2482–2492, 1992\.
  * (31) C. F. Berger, J. S. Gainer, J. L. Hewett, and T. G. Rizzo, “Supersymmetry Without Prejudice,” JHEP, vol. 0902, p. 023, 2009.
  * (32) P. Grajek, A. Mariotti, and D. Redigolo, “Phenomenology of General Gauge Mediation in light of a 125 GeV Higgs,” JHEP, vol. 1307, p. 109, 2013\.
  * (33) N. K. Falck, “Renormalization Group Equations for Softly Broken Supersymmetry: The Most General Case,” Z.Phys., vol. C30, p. 247, 1986\.
  * (34) S. P. Martin and M. T. Vaughn, “Two loop renormalization group equations for soft supersymmetry breaking couplings,” Phys.Rev., vol. D50, p. 2282, 1994\.