Third family quasi-Yukawa unification: Higgsino dark matter, NLSP gluino and
all that

Qaisar Shafia,111E-mail<EMAIL_ADDRESS>Amit Tiwaria,222E-mail:
<EMAIL_ADDRESS>and Cem Salih $\ddot{\rm U}$nb,c,333E-mail:
<EMAIL_ADDRESS>
aBartol Research Institute, Department of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA
bDepartment of Physics, Bursa Uludag̃ University, TR16059 Bursa, Turkey
c Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física
Matemáticas y Computación, Campus del Carmen, Universidad de Huelva, Huelva
21071, Spain

We explore the implications of third family ($t-b-\tau$) quasi-Yukawa
unification (QYU) for collider and dark matter (DM) searches within the
framework of a supersymmetric $SU(4)_{c}\times SU(2)_{L}\times SU(2)_{R}$
model. The deviation from exact Yukawa unification is quantified through the
relation $y_{t}:y_{b}:y_{\tau}=|1+C|:|1-C|:|1+3C|$, with $C$ being a real
parameter ($|C|\leq 0.2$). We allow for the breaking of left-right symmetry
both by the soft scalar and gaugino mass parameters and obtain a variety of
viable solutions that predict the sparticle mass spectrum including LSP DM
(whose stability is guaranteed by a $Z_{2}$ gauge symmetry). We highlight
solutions that include an NLSP gluino with mass $\sim$ 1.3-2.5 TeV, which
should be accessible at LHC Run 3. There also exist NSLP stop solutions with
masses heavier than about 1.8 TeV, which are consistent with the LSP
neutralino dark matter relic density through stop-neutralino coannihilation.
We identify A-resonance solutions with DM mass $\sim$ 0.8 - 2 TeV, as well as
bino-chargino, bino-slepton and bino-stau co-annihilation scenarios. Finally,
we also identify Wino-like ($\sim 99\%$) and Higgsino-like ($\sim 99\%$)
solutions whose masses are heavier than about 1.5 TeV and 1 TeV, respectively.
These solutions are compatible with the desired dark matter relic density and
testable in ongoing and future direct detection experiments.

##  1 Introduction

Low scale supersymmetry (SUSY) remains an attractive extension of the Standard
Model (SM) for a number of reasons. Firstly, the gauge hierarchy problem
associated with quadratic divergences in the scalar sector of the SM is
significantly tamed in the presence of low scale SUSY. Secondly, while the SM
quartic Higgs coupling $\lambda$ is essentially a free parameter in the SM, in
the simplest supersymmetric extensions such as the Minimal Supersymmetric SM
(MSSM), $\lambda$ is related to the gauge couplings of the electroweak sector.
This feature allows one to provide an estimate for the upper bound of around
130 GeV or so on the SM Higgs mass in MSSM, which is in excellent agreement
with the experimentally measured value of 125.6 GeV ATLAS:2012yve ;
CMS:2013btf . Thanks to SUSY, the problem of $\lambda$ running to zero and
subsequently turning negative at a scale of around $10^{11}$ GeV is also
avoided. Finally, in the presence of TeV scale SUSY, the three SM gauge
couplings nicely unify at an energy scale close to $10^{16}$ GeV
Dimopoulos:1981yj ; Amaldi:1991cn ; Ellis:1990wk ; Langacker:1991an . This
last feature provides a strong motivation for considering supersymmetric grand
unified theories. Other good reasons include electric charge quantization,
unification of quarks and leptons in each family, and prediction of non-zero
neutrino masses, which is required by the observed solar, atmospheric and
reactor neutrino oscillation experiments (for a recent review and additional
references see Formaggio:2021nfz ). A particularly attractive example of grand
unification is provided by SUSY SO(10) which, among other things, also
predicts third family ($t-b-\tau$) Yukawa unification (YU) to a good
approximation Ananthanarayan:1991xp ; Ananthanarayan:1992cd . The consequences
for collider and dark matter physics that follow from YU have been extensively
studied in the literature (see Gomez:2020gav  for recent discussion and
additional references).

Motivated by the ongoing LHC Run 3 at CERN and the large number of dark matter
searches underway, we investigate the experimental consequences of third
family Quasi YU (QYU) Dar:2011sj ; Shafi:2015lfa ; Altin:2017sxx  in the
framework of $SU(4)_{c}\times SU(2)_{L}\times SU(2)_{R}$ ($422$ for short),
which is a maximal subgroup of $SO(10)$ Pati:1974yy  and retains some of the
key predictions of $SO(10)$ (for a recent discussion of b-tau Yukawa
unification in 422 see Ref. Ahmed:2022ibc ). We go beyond earlier
investigations with the assumption that the soft SUSY breaking scalar and
gaugino masses do not respect left-right symmetry, and the soft scalar masses
for the first two families are split from the third family which allows us to
probe a larger region of the parameter space compared to earlier studies.

We have explored the predictions for sparticle masses including dark matter
and NLSP candidates in the framework of a supersymmetric $422$ model which
incorporates third family QYU. An unbroken $Z_{2}$ gauge symmetry contained in
the $422$ model acts as matter parity and ensures the presence of a viable
neutralino dark matter candidate Kibble:1982dd . In addition to Bino-like DM
we also identify Wino-like and Higgsino-like dark matter solutions, which
yield the desired dark matter relic abundance with masses greater than or of
order 1.5 TeV and 1 TeV, respectively. We also identify stop-neutralino
coannihilation solutions for masses in the 1.8-2.3 TeV range. The NLSP gluino
mass lies in the 1.3-2.5 TeV range, which should be testable at the LHC Run 3.
Other solutions include the NLSP stau with mass between 1-2 TeV and
A-resonance solutions with the mass $m_{A}$ varying between 0.5 and 2.5 TeV.
In this context, the A-resonance solutions can also be tested through the
decay channel A, $H\longrightarrow\tau\tau$, which currently excludes the
solutions with $m_{A}\leq 2$ TeV in the large $\tan\beta$ region. We display
several benchmark points that highlight these solutions and also show that the
dark matter neutralino may be accessible in the current and near future
experiments.

This paper is organized as follows: In Section 2, we briefly describe QYU,
scanning procedure, the employed constraints and fundamental parameter space.
In section 3, we display the plots for the GUT scale mass parameters and the
implications for the mass spectra. Section 4 is devoted to the DM implications
including the relic density as well as the spin-independent and spin-dependent
scattering cross-sections. In this section, we display five benchmark points
and discuss the prospects to test QYU in the ongoing collider and DM
experiments.

##  2 Quasi-Yukawa Unification, Fundamental Parameters, Scanning Procedure and
Experimental Constraints

Precise third family Yukawa Unification (YU) is realized in supersymmetric
unified theories based on gauge groups such as SO(10) and $422$
Ananthanarayan:1991xp ; Ananthanarayan:1994qt . Quasi-Yukawa Unification (QYU)
is motivated by the desire to incorporate the observed fermion masses and
mixings, and a particularly simple yet realistic example of t-b-tau QYU is
provided by the relation Dar:2011sj ; Gomez:2002tj :

$y_{t}:y_{b}:y_{\tau}=(1+C):(1-C):(1+3C)~{},$ (1)

where $C$ is taken to be real, but it can be negative or positive. The
derivation of this relation in SO(10) and $422$ models can be found in
Ref.Dar:2011sj  and will not be repeated here. Our main goal in this paper is
to explore the phenomenological implications of this QYU condition in $422$
models that can be tested in ongoing collider and dark matter experiments. Our
investigation has some overlap with earlier work, but an important new
ingredient here is the violation of left-right symmetry by the soft SUSY
breaking parameters of the scalar and gaugino sectors of the model.

The soft supersymmetry breaking (SSB) terms in the Lagrangian include the mass
terms for the scalars and gauginos, as well as trilinear interactions of the
supersymmetric particles. However, these SSB terms cannot be arbitrary because
of the underlying GUT symmetry. Since we consider a symmetry breaking pattern
in which the LR symmetry is also broken, the set of free parameters includes
two different mass terms for the left and right handed fields. In addition, we
also assume a flavor symmetry at the GUT scale that distinguishes the third
family from the others, which doubles the number of mass terms for the scalar
matter fields. If we assign a parameter $x_{LR}$ which quantifies the LR
breaking in the scalar sector, one can derive the following relation for the
SSB mass terms for the matter fields:

$m_{\tilde{R}_{i}}=x_{LR}m_{\tilde{L}_{i}}~{},~{}i=1,2~{}(3)~{}{\rm
for~{}the~{}first~{}two~{}(third)~{}families}$ (2)

The relation among the SSB gaugino masses can be derived from the breaking of
$422$. When the $422$ symmetry breaks to the MSSM gauge group the hypercharge
generator remains unbroken and yields the following mass relation for the
gauginos:

$Y=\sqrt{\dfrac{3}{5}}I_{3R}+\sqrt{\dfrac{2}{5}}(B-L)\Rightarrow
M_{1}=\dfrac{3}{5}M_{2R}+\dfrac{2}{5}M_{3}~{},$ (3)

where $I_{3R}$ and $B-L$ are the diagonal generators of $SU(2)_{R}$ and
$SU(4)_{c}$ respectively, and $M_{1}$, $M_{2R}$ and $M_{3}$ are the SSB mass
terms for the gauginos associated with the $U(1)_{Y}$, $SU(2)_{R}$ and
$SU(4)_{c}$ gauge groups respectively. As stated for the scalar matter fields,
the LR symmetry breaking leads, in general, to $M_{2R}\neq M_{2L}$, where
$M_{2L}$ denotes the mass of the $SU(2)_{L}$ gaugino. If we assign a parameter
$y_{LR}$ to measure the LR breaking in the gaugino sector as
$M_{2R}=y_{LR}M_{2L}$, Eq.(2) yields

$M_{1}=\dfrac{3}{5}y_{LR}M_{2L}+\dfrac{2}{5}M_{3}~{}.$ (4)

We can summarize the the set of GUT scale free parameters and their ranges in
our scans as follows:

$\begin{array}[]{lcl}0\leq&m_{\tilde{L}_{1,2}},m_{\tilde{L}_{3}}&\leq
20~{}{\rm TeV}\\\ 0\leq&M_{2L}&\leq 5~{}{\rm TeV}\\\ -3\leq&M_{3}&\leq
5~{}{\rm TeV}\\\ -3\leq&A_{0}/m_{\tilde{L}_{3}}&\leq 3\\\
35\leq&\tan\beta&\leq 60\\\ 0\leq&{\rm x}_{{\rm LR}}&\leq 3\\\ -3\leq&{\rm
y}_{{\rm LR}}&\leq 3\\\ 0\leq&{\rm x}_{{\rm d}}&\leq 3\\\ -1\leq&{\rm x}_{{\rm
u}}&\leq 2~{},\\\ \end{array}$ (5)

where we assume a universal trilinear coupling denoted by $A_{0}$. Note that
we consider the same $x_{LR}$ to quantify the LR symmetry breaking for all the
families. We also impose non-universal Higgs boson masses at $M_{{\rm GUT}}$
which are parametrised as $m_{H_{d}}=x_{d}m_{\tilde{L}_{3}}$ and
$m_{H_{u}}=x_{u}m_{\tilde{L}_{3}}$. In addition to the fundamental parameters,
we only consider cases in which the bilinear Higgs mixing term is always
positive ($\mu>0$).

We perform random scans in the fundamental parameter space of $422$ by using
SPheno Porod:2003um ; Porod:2011nf  generated by SARAH Staub:2008uz ;
Staub:2015iza  for numerical calculations. After the GUT scale is determined
through renormalization group equations (RGEs) by imposing the unification
condition on the SM gauge couplings as $g_{1}=g_{2}\simeq g_{3}$, the RGEs
runs back from $M_{{\rm GUT}}$ to $M_{Z}$ scale together with the SSB terms
determined by the parameters given in Eq.(5). The SUSY mass spectra are
calculated at the two-loop level. For the Higgs boson mass, SPheno employs
also the self-energy contributions in addition to the two-loop corrections.
Besides, we use the method which runs the SM RGEs at three-loop level between
$M_{Z}$ and $M_{{\rm SUSY}}$ by using the effective Higgs potential and
imposing the matching condition at this scale. Note that we insert the central
value of the top quark mass ($m_{t}=173.3$ GeV CDF:2009pxd ; ATLAS:2021urs ).
Even though $1-2\sigma$ variations in the top quark mass do not affect the
SUSY spectrum, it can yield a $1-2$ GeV shift in the SM-like Higgs boson mass
AdeelAjaib:2013dnf ; Gogoladze:2014hca . In our scans, we accept only the
solutions in which the LSP is one of the MSSM neutralinos. At the final step
of the scans, we transfer the SPheno outputs to micrOMEGAs Belanger:2018ccd
to calculate the dark matter (DM) observables.

In the scanning procedure, we employ the Metropolis-Hastings algorithm
Baer:2008jn ; Belanger:2009ti . After generating the data, we successively
employ the mass bounds Agashe:2014kda , constraints from combined results for
rare $B-$meson decays CMS:2020rox ; Belle-II:2022hys ; HFLAV:2022pwe , and the
latest Planck Satellite measurements Planck:2018nkj  of the DM relic abundance
to constrain the LSP neutralino. We can summarize the experimental constraints
employed in our analyses as follows:

$\begin{array}[]{l}m_{h}=123-127~{}{\rm GeV}\\\ m_{\tilde{g}}\geq 2.1~{}{\rm
TeV}~{}(800~{}{\rm GeV}~{}{\rm if~{}it~{}is~{}NLSP})\\\ 1.95\times
10^{-9}\leq{\rm BR}(B_{s}\rightarrow\mu^{+}\mu^{-})\leq 3.43\times
10^{-9}\;(2\sigma)\\\ 2.99\times 10^{-4}\leq{\rm BR}(B\rightarrow
X_{s}\gamma)\leq 3.87\times 10^{-4}\;(2\sigma)\\\ 0.114\leq\Omega_{{\rm
CDM}}h^{2}\leq 0.126\;(5\sigma)~{}.\end{array}$ (6)

We have listed only the Higgs boson and gluino mass bounds, since they have
been updated model independently, although we also employ the model
independent mass bounds from the Linear electron-positron collider (LEP2)
ParticleDataGroup:2014cgo . Even though the parameters listed in Eq.(6) have
been measured experimentally with significant precision, we consider a few
$\sigma$ variations to compensate for the uncertainties in their theoretical
calculations arising from strong interaction coupling, the top quark mass, the
mixing in the squark sectors, etc. Gogoladze:2011aa ; AdeelAjaib:2013dnf ;
Degrassi:2002fi ; Bahl:2019hmm ; Bagnaschi:2017xid ; Athron:2016fuq ;
Allanach:2004rh ; Drechsel:2016htw . We employ a $5\sigma$ uncertainty in
constraining the relic abundance of LSP neutralino since the uncertainties in
its theoretical calculations exceed the statistical uncertainties in its
experimental measurements Bergeron:2017rdm ; Baer:2021tta . We identify the
solutions compatible with the QYU condition if the deviation in Yukawa
couplings quantified by the $C$ parameter satisfies $|C|\leq 0.2$. Note that
Eq.(1) leads to three different solutions for $C$ in terms of different
combinations of the Yukawa couplings. We also require the QYU compatible
solutions to yield the same $|C|$ in all three Yukawa couplings up to about
$10\%$ uncertainty.

##  3 QYU and Mass Spectrum

Figure 1: Plots in the $C-m_{\tilde{L}_{3}}$, $C-m_{\tilde{L}_{1,2}}$,
$C-M_{2L}$ and $C-M_{3}$ planes. All solutions are compatible with REWSB and
LSP neutralino conditions. Green points satisfy the mass bounds on the
sparticles and the constraints from rare B-decays. Orange points form a subset
of green and they are compatible with the QYU condition. Red points are a
subset of orange and satisfy the constraint on relic abundance of LSP
neutralino from Planck measurements within $5\sigma$. Yellow points form a
subset of orange with DM relic density lower than the $5\sigma$ constraints
from the Planck measurements.

Figure 2: Plots in the $C-x_{LR}$ and $C-y_{LR}$ planes. Color coding is the
same as in Figure 1.

Figure 3: Plots in the $C-A_{0}/m_{3\tilde{L}}$ and $C-\tan\beta$ planes
(top), and the RGE evolution of the Yukawa couplings (bottom). Color coding in
the top planes is the same as in Figure 1. The curves and vertical lines in
the bottom planes are defined in the panels.

Figure 4: Plots in the $m_{\tilde{t}_{1}}-m_{\tilde{\chi}_{1}^{0}}$ and
$m_{\tilde{g}}-m_{\tilde{\chi}_{1}^{0}}$ planes. All solutions are compatible
with REWSB and LSP neutralino conditions. Green points satisfy the mass bounds
on the sparticles and the constraints from rare B-decays. Orange points form a
subset of green and satisfy $\mid C\mid\leq 0.2$ as well as the QYU condition.
Points in red form a subset of orange and satisfy the constraint on relic
abundance of LSP neutralino from Planck measurements within $5\sigma$. Points
in yellow form a subset of orange with lower relic density than the Planck
measurements. The diagonal lines represent solutions in which the particles
shown are degenerate in mass.

In this section, we display the plots for the GUT scale mass parameters in
Figure 1 with plots in the $C-m_{\tilde{L}_{3}}$, $C-m_{\tilde{L}_{1,2}}$,
$C-M_{2L}$ and $C-M_{3}$ planes. All solutions are compatible with REWSB and
LSP neutralino conditions. Green points satisfy the mass bounds on the
sparticles and the constraints from rare B-decays. Orange points form a subset
of green and they are compatible with the QYU condition. Red points are a
subset of orange and satisfy the constraint on relic abundance of LSP
neutralino from Planck measurements within $5\sigma$. Yellow points form a
subset of orange with DM relic density lower than the $5\sigma$ constraints
from the Planck measurements. The $C-m_{\tilde{L}_{3}}$ plane shows that the
QYU condition on the Yukawa couplings at $M_{{\rm GUT}}$ can be realized in a
wide range as $0.3\lesssim m_{\tilde{L}_{3}}\lesssim 20$ TeV. The solutions
with low $m_{\tilde{L}_{3}}$ yield a relatively large deviation from YU
($|C|\gtrsim 0.12$), and the DM relic density bounds it at about 0.18 from
below (red solutions). Besides, the lighter solutions lead to the SM-like
Higgs boson mass at about 123 GeV, and the central value of the Higgs boson
mass ($\sim 125.6$ GeV) favors the solutions with $m_{\tilde{L}_{3}}\gtrsim 1$
TeV. The SSB mass term for the first two families compatible with the QYU
condition can also be light, but the solutions consistent with the DM relic
density can be realized if $m_{\tilde{L}_{1,2}}\gtrsim 3$ TeV, as shown in the
$|C|-m_{\tilde{L}_{1,2}}$ plane. The bottom panels of Figure 1. Similar
observation can be seen from the bottom panels where the SSB masses for
$SU(2)_{L}$ and $SU(3)_{c}$ gauginos are plotted. Note that the fade region in
the $C-M_{3}$ plane ($-600\lesssim M_{3}\lesssim 600$ GeV) is excluded by the
current mass bound on gluino.

The masses for the right-handed partners of the SUSY scalars and gauginos can
be considered through the LR symmetry breaking parametrized by $x_{LR}$ and
$y_{LR}$ which are displayed in Figure 2 with plots in the $C-x_{LR}$ and
$C-y_{LR}$ planes. Color coding is the same as in Figure 1. The $C-x_{LR}$
plane shows that LR breaking in the scalar sector is compatible with the QYU
condition and the other constraints can measure in the range $0.7\lesssim
x_{LR}\lesssim 2.2$. Even though it is possible to realize QYU if the scalar
sector is LR symmetric ($x_{LR}=1$), as seen from the $C-y_{LR}$ plane, QYU is
mostly realized if LR symmetry is broken in the gaugino sector
($|y_{LR}|\gtrsim 1$). In addition, large LR breaking in the gaugino sector
can allow very small deviations in YU ($|C|\gtrsim 2\%$). Note that such
solutions are realized also for $y_{LR}\sim 1$ and $|C|\sim(1-1.2)\times
10^{-2}$, which can be considered recovering YU. However, these solutions
yield a large relic abundance of LSP neutralino and are excluded by the
current Planck measurements within $5\sigma$.

We continue our discussion with the correlation of QYU with $\tan\beta$ and
the SSB trilinear scalar interacting term in Figure 3, which also shows the
RGE evolution of the Yukawa couplings between $M_{{\rm GUT}}$ and $M_{Z}$.
Color coding in the top planes is the same as in Figure 1. The curves and
vertical lines in the bottom planes are defined in the legend. The
$C-\tan\beta$ plane shows a nearly linear correlation between $C$ and
$\tan\beta$, which indicates that the deviation from YU increases
proportionally with $\tan\beta$. One can realize a negligible deviation for
$\tan\beta\sim 45$. This value of $\tan\beta$ is also suitable for exact YU
(see, for instance, Hussain:2018xiy ; Antusch:2019gmc ; Gomez:2020gav ;
Hicyilmaz:2021onw ). The results in the $C-A_{0}/m_{3\tilde{L}}$ plane do not
show a specific correlation between $C$ and the trilinear scalar interacting
term, and the QYU condition requires $-2\lesssim A_{0}/m_{3\tilde{L}}\lesssim
3$.

These relations, especially one involving $\tan\beta$, can be understood
through the RGE evolution of the Yukawa couplings shown in the bottom plane of
Figure 3 for different $\tan\beta$ values. The Yukawa couplings receive
threshold correction at $M_{{\rm
SUSY}}\equiv\sqrt{m_{\tilde{t}_{R}}m_{\tilde{t}_{L}}}$, below which the SUSY
particles are assumed to decouple, where $m_{\tilde{t}_{L,R}}$ stand for the
left-handed and right-handed stops. These threshold corrections play an
important role in realizing YU consistent with the observed third-family
fermion masses. The bottom-quark Yukawa coupling, in particular, needs large
and negative threshold corrections in the case of YU Gogoladze:2010fu , which
can be recovered in our model for $\tan\beta\sim 45$ and $|C|\sim 0$. These
cases are represented with the point whose RGE evolution is shown in the
bottom-left plane of Figure 3. We note that $y_{b}$ needs a negative threshold
correction as large as $|\delta y_{b}|\simeq 0.2$ to yield a consistent bottom
quark mass at $M_{Z}$. However, moving away from the YU region, the impact of
the threshold corrections can be loosened. The bottom-right panel exemplifies
such solutions with correct fermion masses realized even with $|\delta
y_{b}|\sim 0.1$. Note that the curves shown crossing in the bottom figures do
not indicate unification at low scales, but occur only numerically in their
RGE evolution.

$\delta y_{b}\approx\dfrac{g_{3}^{2}}{12\pi^{2}}\dfrac{\mu
m_{\tilde{g}}\tan\beta}{m_{\tilde{b}}^{2}}+\dfrac{y_{t}^{2}}{32\pi^{2}}\dfrac{\mu
A_{t}\tan\beta}{m_{\tilde{t}}^{2}}.$ (7)

Eq.(7) also reveals the impact of the threshold corrections on the parameters
and mass spectrum. For $\mu>0$, the contributions from the gluino loop should
be suppressed which leads to next to LSP (NLSP) gluino solutions of mass
$m_{\tilde{g}}\lesssim 1$ TeV Raza:2014upa ; Gogoladze:2009ug ;
Gogoladze:2009bn . It also explains why one needs an appreciable LR breaking
($|y_{LR}|\sim 3$ as shown in Figure (2) to realize small deviations in YU
($|C|\sim 0$). However, as discussed above, the QYU solutions do not
necessarily employ large threshold corrections, so the upper bound on the
gluino mass from the YU condition disappears in our analyses. We display the
results for the stop and gluino masses versus the LSP neutralino mass in
Figure 4 in the $m_{\tilde{t}_{1}}-m_{\tilde{\chi}_{1}^{0}}$ and
$m_{\tilde{g}}-m_{\tilde{\chi}_{1}^{0}}$ planes. Color coding is the same as
in Figure 1. The diagonal lines designate the solutions with degenerate
masses. We obtain mass spectra in which the stop mass cannot be lighter than
about 1.5 TeV in the QYU parameter space (orange points), while the relic
density constraint raises this lower mass bound to about 1.8 TeV (red points),
where it also happens to be degenerate with the LSP neutralino in mass. These
nearly degenerate solutions play an important role in reducing the relic
abundance of LSP neutralino through stop-neutralino coannihilation scenario.
The heavy mass scales for the stop are mostly required in order to obtain the
correct SM Higgs boson mass Gomez:2022qrb . On the other hand, we realize NLSP
gluino solutions compatible with QYU condition with $m_{\tilde{g}}\gtrsim 800$
GeV, and the DM relic density constraint can be satisfied for
$m_{\tilde{g}}\gtrsim 1$ TeV. The possibility of small threshold corrections
also allows heavy gluino masses, and our scans yield gluino masses up to about
10 TeV. Although testing such heavy gluino solutions requires a much higher
center of mass energies and luminosities than currently available at the LHC,
the solutions with $2.1\leq m_{\tilde{g}}\lesssim 2.5$ TeV should be testable
during the LHC-Run3 experiments ATLAS:2022rcw .

##  4 DM Implications of QYU

Figure 5: Plots in the $m_{\tilde{\chi}_{1}^{\pm}}-m_{\tilde{\chi}_{1}^{0}}$,
$m_{\tilde{\tau}_{1}}-m_{\tilde{\chi}_{1}^{0}}$,
$m_{A}-m_{\tilde{\chi}_{1}^{0}}$ and $\tan\beta-m_{A}$ planes. The color
coding is the same as in Figure 4. The diagonal lines in the top panels
indicate the mass degenerate solutions for the particles shown, and the line
in the $m_{A}-m_{\tilde{\chi}_{1}^{0}}$ plane represents $A-$resonance
solutions ($m_{A}=2m_{\tilde{\chi}_{1}^{0}}$). The curves in the $\tan\beta-
m_{A}$ plane display the current exclusion region Bagnaschi:2018ofa ;
ATLAS:2020zms  for the CP-odd Higgs boson mass.

Figure 6: Spin-independent (left) and spin-dependent (right) scattering cross-
sections versus the LSP neutralino mass. The color coding is the same as in
Figure 4. The curves represent the current and projected exclusion curves from
several direct detection DM experiments, with the color coding given in the
respective panels. The current excluded regions are represented by the solid
curves, and the dashed curves display the projected experimental sensitivity.

Even though the MSSM provides a variety of different neutralino species (Bino,
Wino, Higgsinos) as DM candidates, the current relic density and direct
detection experiments have yielded a strong impact on the DM implications. The
Higgsino-like LSPs usually lead to large cross-sections in scattering with
nuclei, and together with the relic density constraints the current results
exclude the Higgsino-like LSP solutions if they are lighter than about 1 TeV
(see, for instance, Raza:2018jnh ; Hicyilmaz:2021khy ). Even though their
scattering cross-section is moderate, the Wino-like LSP solutions are
similarly constrained by the experiments. On the other hand, Bino-like LSP has
a relatively small scattering cross-section. However, considering the current
and future projected sensitivities in the direct detection experiments
Akerib:2018lyp ; Aalbers:2016jon ; Aprile:2020vtw ; Tanaka:2011uf ;
Khachatryan:2014rra ; Abbasi:2009uz ; Akerib:2016lao , these cross-sections
are expected to be tested soon.

The desired DM relic density with Bino-like LSP requires suitable
coannihilation processes, and as shown in Section 3, this is satisfied for a
gluino NLSP mass $m_{\tilde{g}}\gtrsim 1.3$ TeV. In addition, the stop-
neutralino coannihilation scenario is realized for $1.8\lesssim
m_{\tilde{t}_{1}}\simeq m_{\tilde{\chi}_{1}^{0}}\lesssim 2.5$ TeV.

In addition, we also identify chargino-neutralino and stau-neutralino
coannihilations scenarios, as well as $A-$resonance solutions as shown in
Figure 5, with plots in the
$m_{\tilde{\chi}_{1}^{\pm}}-m_{\tilde{\chi}_{1}^{0}}$,
$m_{\tilde{\tau}_{1}}-m_{\tilde{\chi}_{1}^{0}}$,
$m_{A}-m_{\tilde{\chi}_{1}^{0}}$ and $\tan\beta-m_{A}$ planes. The color
coding is the same as in Figure 1. The diagonal lines in the top panels
indicate the mass degenerate solutions for the particles shown, and the
$m_{A}-m_{\tilde{\chi}_{1}^{0}}$ plane displays $A-$resonance solutions
($m_{A}=2m_{\tilde{\chi}_{1}^{0}}$). The curves in the $\tan\beta-m_{A}$ plane
display the current exclusion limits Bagnaschi:2018ofa ; ATLAS:2020zms  on the
CP-odd Higgs boson mass versus $\tan\beta$. The
$m_{\tilde{\chi}_{1}^{\pm}}-m_{\tilde{\chi}_{1}^{0}}$ plane shows viable
chargino-neutralino coannihilation solutions compatible with the DM abundance
in a wide range with the chargino mass varying from about 250 GeV to 2.5 TeV.
The solutions with $m_{\tilde{\chi}_{1}^{0}}\lesssim 1.5$ TeV around the
diagonal line with the correct relic density (red points) usually lead to
Bino-like relic density with $M_{\tilde{B}}\lesssim M_{\tilde{W}}$, since the
Wino-like and Higgsino-Like LSP solutions ($M_{\tilde{W}}\ll M_{\tilde{B}}$)
are mostly excluded by the relic density constraints for
$m_{\tilde{\chi}_{1}^{0}}\lesssim 1.5$ TeV (see, for instance, Frank:2021nkq
). We also display solutions with stau-neutralino coannihilations in the
$m_{\tilde{\tau}_{1}}-m_{\tilde{\chi}_{1}^{0}}$ plane. Even though the stau is
heavy over most of the parameter space due to the QYU condition, the stau-
neutralino coannihilation solutions can be realized if the stau and LSP
neutralino are nearly degenerate in the mass range of about $1-2.5$ TeV.

Besides the coannihilation channels, the QYU scenario admits self
annihilations of LSP neutralinos into the CP-odd Higgs boson in a wide range,
namely $0.5\lesssim m_{A}\lesssim 2.5$ TeV, as shown in the
$m_{A}-m_{\tilde{\chi}_{1}^{0}}$ plane. The mass scale for $m_{A}$ is
constrained by the $A\longrightarrow\tau\tau$ decay, which is displayed with
the dotted and solid curves in the $\tan\beta-m_{A}$ plane. With a mass
heavier than a few hundred GeV, the neutral heavy Higgs bosons ($A$ and $H$)
decay into a pair of $\tau-$leptons at a level of about $15\%$, which is large
enough to exclude the solutions with $m_{A}\lesssim 2$ TeV Bagnaschi:2018ofa ;
ATLAS:2020zms . A recent analysis CMS:2018oxh  has shown that experiments at
the LHC-Run3 and High-Luminosity LHC (HL-LHC) can probe the CP-odd Higgs boson
up to about 2.5 TeV. Our results in the $\tan\beta-m_{A}$ plane show that QYU
solutions are abundantly realized for $2<m_{A}<2.5$ TeV, which should be
tested at LHC Run-3.

Another probe for the QYU solutions can be provided in the direct detection
experiments of DM. Figure 6 shows our results for the cross-sections for the
spin-independent (left) and spin-dependent (right) scattering of DM on nuclei
versus the LSP mass. The color coding is the same as in Figure 1. The solid
(dashed) curves represent the current (future projected) exclusion curves from
several direct detection DM experiments, with color coding given in the legend
for each plane. The $\sigma_{{\rm SI}}-m_{\tilde{\chi}_{1}^{0}}$ shows that
the LZ experiment Akerib:2018lyp  can currently exclude the QYU solutions with
spin-independent cross-section on the order of about $4\times 10^{-11}$ pb and
the LSP of about 1 TeV, while XENON1T has extended this exclusion limit to
about $4\times 10^{-12}$ pb in the same region. The solutions whose cross-
sections are above these bounds will be re-tested by the Darwin experiment in
the near future Aalbers:2016jon . Furthermore, the projected sensitivity of
XENON experiment (the curve from XENONnT) should be able to probe QYU
solutions at the level of about $8\times 10^{-13}$ pb Aprile:2020vtw . We also
present our results for the spin-dependent scattering cross-section, and as
seen from the $\sigma_{{\rm SD}}-m_{\tilde{\chi}_{1}^{0}}$, with the cross-
sections a few orders of magnitude lower than the experimental bounds
Tanaka:2011uf ; Khachatryan:2014rra ; Abbasi:2009uz ; Akerib:2016lao , we have
to wait for further upgrades in the experiments listed in the legend.

| Point 1 | Point 2 | Point 3 | Point 4 | Point 5 | Point 6
---|---|---|---|---|---|---
$m_{\tilde{L}_{1,2}}$ | 5016 | 9007 | 10049 | 3037 | 5063 | 2981
$m_{\tilde{L}_{3}}$ | 5316 | 7167 | 8031 | 2493 | 4562 | 3153
$M_{1}$ | 998.7 | -2638 | -3842 | 2544 | 3672 | 7675
$M_{2}$ | 585.1 | 2803 | 2853 | 1390 | 1989 | 4797
$M_{3}$ | 3564 | 484.3 | 727.4 | 2990 | 4313 | 4230
$A_{0}/m_{\tilde{L}_{3}}$ | -0.191 | -1.5 | -2 | -0.793 | -0.76 | -1.1
$\tan\beta$ | 55.4 | 52.2 | 54.1 | 54.8 | 55.8 | 53.1
$x_{LR}$ | 1.3 | 1.6 | 1.8 | 1.6 | 1.7 | 2.1
$y_{LR}$ | -1.2 | -1.7 | -2.4 | 1.6 | 1.6 | 2.1
$m_{\tilde{R}_{1,2}}$ | 6405 | 14051 | 18517 | 4782 | 8748 | 6298
$m_{\tilde{R}_{3}}$ | 6788 | 11181 | 14799 | 3926 | 7884 | 6662
$\mu$ | 1627 | 8762 | 10877 | 2807 | 5327 | 1086
$m_{h}$ | 125 | 124 | 125.7 | 123.9 | 125.3 | 125.6
$m_{H}$ | 2973 | 4973 | 4660 | 3578 | 3878 | 2447
$m_{A}$ | 2973 | 4973 | 4660 | 3578 | 3878 | 2447
$m_{H^{\pm}}$ | 2974 | 4972 | 4655 | 3579 | 3877 | 2450
$m_{\tilde{\chi}_{1}^{0}}$,$m_{\tilde{\chi}_{2}^{0}}$ |  426.6,  454.7 |  1227, 2466 |  1785, 2496 |  1137,  1153 |  1674,  1676 |  1087,  1090
$m_{\tilde{\chi}_{3}^{0}}$,$m_{\tilde{\chi}_{4}^{0}}$ | 1632, 1634 | 8691, 8691 | 10915, 10915 | 2815, 2817 | 5326, 5326 | 3520, 3992
$m_{\tilde{\chi}_{1}^{\pm}}$,$m_{\tilde{\chi}_{2}^{\pm}}$ |  454.8, 1634 | 2466, 8691 | 2496, 10915 |  1153, 2817 |  1677, 5327 |  1088, 3991
$m_{\tilde{g}}$ | 7509 | 1319 | 1914 | 6258 | 8920 | 8621
$m_{\tilde{u}_{1}}$,$m_{\tilde{u}_{2}}$ | 7854, 8783 | 9098, 14023 | 10080, 18539 | 6031, 7012 | 8835, 11306 | 8184, 9612
$m_{\tilde{t}_{1}}$,$m_{\tilde{t}_{2}}$ | 6035, 7065 | 4052, 9017 |  1873, 11948 | 4534, 5196 | 6633, 8771 | 5864, 7613
$m_{\tilde{d}_{1}}$,$m_{\tilde{d}_{2}}$ | 7854, 8814 | 9098, 14101 | 10080, 18591 | 6031, 7041 | 8836, 11304 | 8185, 9493
$m_{\tilde{b}_{1}}$,$m_{\tilde{b}_{2}}$ | 6037, 7621 | 4050, 9465 | 1869, 12879 | 4539, 5596 | 6634, 9494 | 5867, 8105
$m_{\tilde{\nu}_{e}}$,$m_{\tilde{\nu}_{\tau}}$ | 3971, 4981 | 5419, 9107 | 4916, 10153 | 1224, 3124 | 3115, 5210 | 3009, 4428
$m_{\tilde{e}_{1}}$,$m_{\tilde{e}_{2}}$ | 4978, 6444 | 9100, 14155 | 10142, 18617 | 3122, 4931 | 5206, 8864 | 4424, 6894
$m_{\tilde{\tau}_{1}}$,$m_{\tilde{\tau}_{2}}$ | 3971, 4706 | 5419, 8903 | 4916, 11641 |  1219, 2497 | 3115, 6198 | 3011, 5357
$\sigma_{{\rm SI}}$ | $2.22\times 10^{-12}$ | $4\times 10^{-15}$ | $2\times 10^{-15}$ | $2.04\times 10^{-12}$ | $3.01\times 10^{-12}$ | $2.82\times 10^{-11}$
$\sigma_{{\rm SD}}$ | $2.78\times 10^{-8}$ | $1.2\times 10^{-11}$ | $5.2\times 10^{-12}$ | $3.91\times 10^{-9}$ | $2.68\times 10^{-9}$ | $7.27\times 10^{-8}$
$\Omega h^{2}$ | 0.121 | 0.121 | 0.12 | 0.122 | 0.115 | 0.117
$C$ | 0.107 | 0.117 | 0.155 | 0.17 | 0.177 | 0.093

Table 1: Benchmark points satisfying the mass bounds, the constraints from
rare B-meson decays, Planck bounds within $5\sigma$ and the QYU condition with
$\mid C\mid\leq 0.2$. All masses are given in GeV. Point 1 represents
chargino-neutralino coannihilation, and Point 2 exemplifies solutions in which
the DM relic density is satisfied entirely through the gluino-neutralino
coannihilation processes, while Point 3 depicts solutions for the stop-
neutralino coannihilation scenario. Point 4 displays solutions for stau-
neutralino coannihilation scenario. Points 5 and 6 represent the solutions for
Wino-like and Higgsino-like LSP neutralino solutions respectively.

Finally, before concluding, we present six benchmark points in Table 1 which
exemplify our findings. All points are selected to be consistent with the
constraints applied in our analyses together with the QYU condition. All
masses are given in GeV, and the DM scattering cross-sections are in pb. We
show the NLSP species in red, and the masses of particles, which are relevant
to the discussion in bold. Point 1 represents Bino-like LSP neutralino
solutions whose spin-independent scattering cross-section lies just below the
current exclusion bound provided by the XENON1T experiment, and it is expected
to be tested very soon. These solutions will also be tested by Darwin. Since
the spectrum involves heavy SUSY scalars, the relic abundance of LSP
neutralino for such solutions can be reconciled with the Planck measurements
through chargino-neutralino coannihilation processes. Point 2 exemplifies
solutions in which the DM relic density is satisfied entirely through gluino-
neutralino coannihilation processes with $m_{\tilde{g}}\gtrsim 1.3$ TeV. We
exemplify the stop-neutralino coannihilation scenario with Point 3. Points 2
and 3 also represent Bino-like LSP solutions, but in comparison with Point 1,
they lead to small spin-independent scattering cross-sections which fall below
the neutrino floor and need more statistics to be tested in the direct
detection DM experiments. Point 4 displays a stau-neutralino coannihilation
scenario, and we observe that this is accompanied by chargino-neutralino
coannihilation processes in order to achieve the desired dark matter relic
abundance. Even though the LSP is Bino-like as in the previous points, it
should be testable in direct detection experiments in the near future. Points
5 and 6 depict solutions for Wino-like and Higgsino-Like LSP solutions, with
masses greater than about 1.5 TeV, and 1 TeV respectively. Point 6 also
depicts a spectrum in which the CP-odd Higgs boson mass is about 2.5 TeV,
which should be testable at HL-LHC through $A,H\rightarrow\tau\tau$ events.

##  5 Conclusion

We have explored the predictions for sparticle masses including dark matter
and NLSP candidates in the framework of a supersymmetric $SU(4)_{c}\times
SU(2)_{L}\times SU(2)_{R}$ model which incorporates third family quasi-Yukawa
unification. An unbroken $Z_{2}$ gauge symmetry contained in the $422$ model
acts as matter parity and ensures the presence of a viable neutralino dark
matter candidate. Our solutions contain Bino-like, Wino-like and Higgsino-like
DM solutions accompanied by a variety of NLSP candidates including gluino,
stop, stau and chargino. The NLSP gluino can be as light as 1.3 TeV, which
should be accessible at the LHC Run 3, while stop-neutralino coannihilations
become relevant for $1.8\lesssim m_{\tilde{t}_{1}}\simeq
m_{\tilde{\chi}_{1}^{0}}\lesssim 2.3$ TeV. The NLSP slepton masses are in the
$0.9-3$ TeV range, and these solutions are also involved in chargino-
neutralino coannihilation processes in order to realize a consistent relic
density of LSP neutralino. The Wino-like and Higgsino-like LSP neutralino
solutions are associated with masses of order 1.5 and 1 TeV respectively.
There also exist A-resonance solutions with the $m_{A}$ mass varying between
0.5 and 2.5 TeV. In this context, the A-resonance solutions can also be tested
through the decay channel $A,H\longrightarrow\tau\tau$, which currently
excludes solutions with $m_{A}$ $\lesssim$ 2 TeV in the large $tan\beta$
region. We display several benchmark points that highlight these solutions and
show that the dark matter neutralino may be accessible in collider and other
dark matter searches.

## Acknowledgment

AT is partially supported by the Bartol Research Institute, University of
Delaware. The research of CSU is supported in part by the Spanish MICINN,
under grant PID2019-107844GB-C22. CSU would like to thank Instituto Física
Theórica of Universidad Autónoma de Madrid, where part of his research has
been conducted. We acknowledge Information Technologies (IT) resources at the
University of Delaware, specifically the high performance computing resources
for the calculation of results presented in this paper. CSU also acknowledges
the resources supporting this work in part were provided by the CEAFMC and
Universidad de Huelva High Performance Computer (HPC@UHU) located in the
Campus Universitario el Carmen and funded by FEDER/MINECO project
UNHU-15CE-2848.

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# Tubu-io Decentralized Application Development & Test Workbench

1st Ercan Işık  TUBU
İstanbul, Turkey
<EMAIL_ADDRESS>2nd Melih Birim  TUBU
İstanbul, Turkey
<EMAIL_ADDRESS>3rd Enis Karaarslan  Department of Computer Engineering
Muğla Sıtkı Koçman University
Muğla, Turkey
<EMAIL_ADDRESS>
###### Abstract

Decentralized services are increasingly being developed and their proper usage
in different areas is being experimented with. Autonomous codes, which are
also called smart contracts, can be developed with Integrated Development
Environments (IDE). However, these tools lack live environment tests. The
underlying blockchain technologies are also evolving and it is not easy to
catch all the developments. There is a need for an easy-to-use interface by
which the developers can see the results of their codes. Tubu-io decentralized
application development workbench is developed to serve as an efficient way
for the programmers to deploy smart contracts on the blockchain networks and
interact with them easily. It can also be used for teaching decentralized
application programming for junior blockchain developers on blockchain
testbeds. Finally, it will have an effect in decreasing the development time
and the costs of developing decentralized application projects.

###### Index Terms:

Blockchain, decentralized solution, decentralized application, dapp, smart
contract

##  I Introduction

Decentralized solutions have the potential to change how we do transactions.
Trust can be provided without an intermediary; secure and private transactions
can be possible between peers. Blockchain is a decentralized ledger technology
that can be used for such processes [1]. Smart contracts are introduced with
Ethereum [2] that is used to form autonomous programs. These immutable codes
can be called from their stored addresses and enables to run deterministic
programming on the nodes of the blockchain network. Decentralized applications
(DAPP) use these codes to give decentralized services. Several blockchain
frameworks can be used to develop and deploy alike codes such as Ethereum [2],
Hyperledger Fabric[4], Corda[5], Quorum[6] However, deploying the smart
contracts on a blockchain network and interact with the system is a complex
task. Tubu-io DAPP development workbench is developed to enable a user-
friendly interface for the developers.

##  II DAPP DEVELOPMENT WORKBENCH

There are several integrated development environments (IDE) like remix,
truffle and embark which provide tools in writing smart contracts[7]. However,
these tools lack the interaction with the blockchain network. Tubu-io
blockchain development workbench is a web platform by which the developers can
easily interact with the defined blockchain networks. The developers can
deploy their smart contracts to their blockchain networks and interact with
them.

The proposed system is shown in Figure 1. Tubu-io can be installed on a
separate web server or one of the blockchain nodes. A separate web server
would be a better choice to form a more secure design. There are two main
users of the system:

  * •

Blockchain Developers: The developers will use the web interface to deploy and
test decentralized applications.

  * •

Dev Community: The developers of the Tubu-io. The project welcomes the
community in developing the system.

Figure 1: Tubu-io System

Tubu-io system arcitecture is shown in Figure 2. The system forms of four sub
modules:

  * •

Secure User/Wallet Management

  * •

REST API

  * •

Smart Contract Management

  * •

Version Management

Figure 2: Tubu-io System Architecture

Tubu-io can connect to internal (defined) networks, and also external networks
as well. It currently supports the Ethereum based Quorum blockchain platforms,
but other blockchain platforms will be integrated in future releases.
Blockchain networks are defined to the system from the user interface by
adding the new network actions. Since blockchain networks need specific TCP
ports to listen to the network connections, it is required to open these ports
to external networks on the system and the firewall. When the available
networks are defined on the system, creating the decentralized application is
simplified with its web interface. The following steps should be taken:

  * •

Connect to an available network

  * •

Create a new application

  * •

Deploy Contract

  * •

Access the deployed smart contracts via REST-API and tubu.IO SDK’s

Once smart contracts are deployed, users can interact with that smart contract
by calling the "Invoke” or “Call” methods. The application details section of
the system provides the necessary information for this. The users can reach
their blockchain network with the software development kit (SDK) of the used
blockchain framework without any need for any other dependency. The current
functions are the following:

  * •

Share the Application: This is used to share the application with the
specified system users.

  * •

Create API Key: API Key is required for the DAPP to interact with the
contracts.

  * •

Deploying New Version: A new version of a pre-deployed contract can be
deployed on the blockchain.

  * •

Accessing Contract Details: The methods, versions, accounts of the specific
contract can be accessed.

  * •

Using SDKs: Tubu-io can be used with the SDKs that are written in widely-used
programming languages such as NodeJS, Java, Python and Go.

##  III IMPLEMENTATION

Tubu-io is developed using Javascript programming language, node.js, Vue.js,
and web3.js library is used. Web3.js is a collection of Javascript API
libraries developed by the ChainSafe Organization. It is used for interacting
with remote Ethereum nodes. Solidity is used for the smart contracts.

Tubu-io API is written in Javascript and allows the developers to use get and
set requests, smart contract creation endpoints. The developers may use any
programming language and should send requests to the Tubu-io API. Request
libraries for each programming language are needed to use the Tubu-io API. SDK
is developed to ease these processes for the widely used programming languages
such as Python, NodeJS, Java, and Go.

Tubu-io is installed on a web server and developers can register and then log
in to the system through the web interface. The official web service can be
reached from https://app.tubu.io. Projects may install Tubu-io on their
private servers as well. Tubu-io web interface is shown in Fig. 2 and Fig. 3.
It is used in several projects and the project repo can be reached from [10].
A detailed usage document can also be reached from [8].

Figure 3: Tubu-io Web Interface Figure 4: Tubu-io Web Interface

##  IV CONCLUSION

There is a need to make blockchain solution development easier and make this
process cheaper. Some countries like China see the potential and the need for
this. China launched a national blockchain network in 100 cities to decrease
the costs of such enterprise blockchain solutions[9].

Tubu-io decentralized application development workbench is the first step at
decreasing the costs of developing blockchain projects. This tool can help
non-novice users to develop decentralized solutions easier. It has been used
in several projects so far. The source codes will be shared with the Apache
license. It currently supports the Quorum network. Hyperledger Besu [11] is
being tested and released soon. Other platforms like Hyperledger Fabric are
planned to be integrated in the future. The details of the system design will
be given in an upcoming paper.

## ACKNOWLEDGMENT

We would like to thank Şafak Öksüzer, Berkay, Umutcan Korkmaz, Hüseyin Emre
Arı and Yunus Emre Turğut for their contributions to the development of TUBU-
IO. We would also like to thank Cemal Dak for his contribution in the
graphics.

## References

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