#  SuSeFLAV 1.2: program for supersymmetric mass spectra with seesaw mechanism
and rare lepton flavor violating decays

Debtosh Chowdhury  Centre for High Energy Physics,Indian Institute of Science,
Bangalore 560 012, India  Raghuveer Garani  Physikalisches Institut der
Universität Bonn, Nußalle 12, D-53115 Bonn, Germany  Sudhir K. Vempati

###### Abstract

Accurate supersymmetric spectra are required to confront data from direct and
indirect searches of supersymmetry.
SuSeFLAV111http://cts.iisc.ernet.in/Suseflav/main.html is a numerical tool
which is capable of computing supersymmetric spectra precisely for various
supersymmetric breaking scenarios applicable even in the presence of flavor
violation. The program solves MSSM RGEs with complete $3\times 3$ flavor
mixing at 2-loop level and one loop finite threshold corrections to all MSSM
parameters by incorporating radiative electroweak symmetry breaking
conditions. The program also incorporates the Type-I seesaw mechanism with
three massive right handed neutrinos at user defined mass scales and mixing.
It also computes branching ratios of flavor violating processes such as
$l_{j}\,\rightarrow\,l_{i}\gamma$, $l_{j}\;\rightarrow\,3~{}l_{i}$,
$b\,\rightarrow\,s\gamma$ and supersymmetric contributions to flavor
conserving quantities such as $(g_{\mu}-2)$. A large choice of executables
suitable for various operations of the program are provided.

###### keywords:

MSSM , Right Handed Neutrinos , Lepton Flavor Violation.

††journal: Computer Physics Communications

PROGRAM SUMMARY

Manuscript Title: SuSeFLAV: program for supersymmetric mass spectra with
seesaw mechanism and rare lepton flavor violating decays
Authors: Debtosh Chowdhury, Raghuveer Garani, Sudhir K. Vempati
Program Title: SuSeFLAV
Journal Reference:
Catalogue identifier:
Licensing provisions: GNU Public License
Programming language: Fortran 95
Computer: Personal Computer, Work-Station
Operating system: Linux, Unix
RAM:
Number of processors used: Single
Supplementary material:
Keywords: MSSM, Right Handed Neutrinos, Lepton Flavor Violation.
Classification:
External routines/libraries:
Subprograms used:
Nature of problem: Determination of masses and mixing of supersymmetric
particles within the context of MSSM with conserved R-parity with and without
the presence of Type-I seesaw. Inter-generational mixing is considered while
calculating the mass spectrum. Supersymmetry breaking parameters are taken as
inputs at a high scales specified by the mechanism of supersymmetry breaking.
RG equations including full inter-generational mixing are then used to evolve
these parameters up to the electroweak breaking scale. The low energy
supersymmetric spectrum is calculated at the scale where successful radiative
electro-weak symmetry breaking occurs. At weak scale Standard Model fermion
masses, gauge couplings are determined ncluding the supersymmetric radiative
corrections. Once the spectrum is computed, the program proceeds to various
lepton flavor violating observables (e.g., BR$(\mu\ \rightarrow\ e\gamma)$,
BR$(\tau\ \rightarrow\ \mu\gamma)$ etc.) at the weak scale.

Solution method: Two loop RGEs with full $3\times 3$ flavor mixing for all
supersymmetry breaking parameters are used to compute the low energy
supersymmetric mass spectrum. Adaptive step size Runge-Kutta method is used to
solve the RGEs numerically between the high scale and the electroweak breaking
scale. Iterative procedure is employed to get the consistent radiative
electroweak symmetry breaking condition. The masses of the supersymmetric
particles are computed at 1-loop order. The third generation SM particles and
the gauge couplings are evaluated at the 1-loop order including supersymmetric
corrections. A further iteration of the full program is employed such that the
SM masses and couplings are consistent with the supersymmetric particle
spectrum.

Restrictions:

Unusual features:

Additional comments:
Several executables are presented for the user.
Running time: 0.2 seconds on a Intel(R) Core(TM) i5 CPU 650 with 3.20 GHz.

##  1 Introduction

Low energy supersymmetry [1] is currently being probed by the Large Hadron
Collider (LHC) at CERN and the Tevatron collider at the Fermilab222The
Tevatron collider has recently stopped functioning.. On the other hand, there
is already a huge amount of information which has been collected and is being
collected which gives information on low energy supersymmetric Lagrangian
indirectly. For example, the flavor experiments in the hadronic and the
leptonic sectors place strong constraints on the flavor off-diagonal entries
in the Lagrangian. Similarly, the astrophysical data on dark matter which has
been improved with the latest WMAP 7-year results [2] also strongly restricts
the parameter space where the mass and the couplings of the lightest
supersymmetric particle (LSP) correspond to the observed relic density. While
experimental evidence for supersymmetry is definitely far more superior
compared to the indirect detection of supersymmetry, the power of indirect
experimental data to constrain the parameter space cannot be underestimated.
Furthermore, as it is well known even if there is a positive experimental
signal at the LHC, it would be very hard to reconstruct the supersymmetric
breaking Lagrangian unambiguously due to the large number of degeneracies
present in the parameter space which can give similar signals at the colliders
[3]. It has also been noted that flavor violating observables and dark matter
could help to break these degeneracies [4].

Obviously, the flavor observables depend on the supersymmetric model in which
they are calculated. Unfortunately, most of the present supersymmetric mass
spectrum calculators do not take in to consideration the effect of flavor
violation in the running of soft mass parameters either in the hadronic sector
or the leptonic sector333The recent version of SPheno [38] is an exception..
In hadronic sector, typically the CKM is considered to be the only source of
flavor violation, while this works very well, as long as one restricts to the
scheme of Minimal Flavor Violation (MFV), in a more general scheme of
supersymmetric models, such an assumption cannot be supported. Recently
‘observed’ deviations from the Standard Model CKM paradigm [5, 6] might find
explanations in terms of a supersymmetric standard model with some amount of
flavor violation [7]. To study the associated phenomenology of such kinds of
models either for dark matter relic density, collider searches or other
theoretical aspects such as threshold corrections to fermion masses, gauge
coupling unification etc., would require precise computation of the mass
spectrum in these models.

In the leptonic sector, the case for flavor violation is even more stronger.
Firstly, neutrinos have non-zero masses and secondly their flavor mixing is
large as has been observed in the neutrino oscillation experiments. Most of
mechanisms of generating neutrino masses and mixing inevitably lead to large
flavor violation in supersymmetric theories. One of the simplest ways to
generate neutrino masses is the so called ‘seesaw mechanism’. In the present
work, we have restricted ourselves to Type-I seesaw mechanism, though the
program can be generalized to incorporate other seesaw mechanisms by adding
the corresponding RGEs. The Type-I seesaw mechanism444For a summary of the
seesaw mechanisms, please see [8]. has three singlet right handed neutrinos
added to the Standard Model which leads to two additional terms, the Dirac
mass term combining the left and right neutrino fields and the lepton number
violating Majorana mass term for the right handed singlet fields. The
interplay between these two terms leads to small Majorana masses to the left
handed neutrinos in the limit of heavy Majorana masses for the right
neutrinos. The supersymmetric version of the seesaw mechanism was proposed
long ago [9] and some of its consequences for leptonic flavor violations have
immediately been noticed. Over the years, other theoretical/phenomenological
consequences of having right handed neutrinos has been observed. In the
following we list some of them.

  * 1.

$Y_{b}-Y_{\tau}$ Unification: The presence of right handed neutrinos could
significantly modify regions where $\tau-b$ Yukawa couplings unify at the GUT
scale in unified theories like SO(10) or SU(5) [10, 11, 12, 13]. This is due
to the fact that the neutrino Dirac Yukawa couplings enter the renormalization
group equations (RGE) of the $Y_{b}$ and $Y_{\tau}$ at 2-loop level and
$Y_{t}$ at the 1-loop. This is enough to change the $Y_{b}/Y_{\tau}$ ratio at
the weak scale, if the neutrino Yukawa couplings are large.

  * 2.

Lepton Flavor Violation: As mentioned previously, one of the main consequences
of the seesaw mechanism in supersymmetric theories is the violation of lepton
numbers leading to rare flavor violating decays [9]. This flavor violation
will be generated through the RGE even if the supersymmetry breaking mechanism
at the high scale conserves flavor as in mSUGRA. In particular GUT models, the
generated flavor violations could be large enough to strongly constrain
observability of supersymmetry at the LHC [14, 16, 17, 18]. On going
experiments like MEG and future experiments like PRISM/PRIME and Super-B
factories have enhanced sensitivity to large amounts of parameter space even
with small mixing and small $\tan\beta$ [16, 18].

  * 3.

Dark Matter: One of the most surprising phenomenological aspects of seesaw
mechanism and SUSY-GUT models has been the impact on Dark matter
phenomenology. The presence of a single right handed neutrino with a large
Yukawa coupling could significantly enhance the efficiency of the electroweak
symmetry breaking and thus making the focus point region unviable within
mSUGRA like models [19, 20]. Similarly, GUT effects can significantly effect
the stau co-annihilation region [19]. The co-annihilation region and the focus
point regions seem to be most vulnerable to these effects in other GUT models
and mSUGRA incorporating Type-II or Type-III seesaw mechanisms [21]. It has
been recently realized that even flavor effects could play a role in the relic
density calculations in the early universe [22].

  * 4.

Hadronic flavor violation: Incorporating Type-I seesaw mechanism in Grand
Unified Theories (GUT) also has effects on the hadronic sector. For example,
CP violation in the neutrino sector could be transmitted to the quark sector
in SU(5) or SO(10) theories [23, 24]. The large phases of the neutrino mass
matrix can be transmitted to the hadronic sector with effects in $K$ and $B$
physics phenomenology. More generally in GUT theories, hadronic and leptonic
flavor violations are related to each other by the underlying GUT symmetry
[25].

  * 5.

Collider Signals: Lepton flavor violation which might be inevitable due to the
presence of a seesaw mechanism, can lead to flavor violation in the sleptonic
sector as we have mentioned above. Such flavor violation can be studied at the
colliders by measuring the mass differences between the sleptons by observing
such as sleptonic oscillations etc. [26, 27, 28, 29].

  * 6.

Gauge Coupling Unification: Finally, let us note that it has been pointed that
the presence of massive right handed neutrinos with large yukawa couplings in
the MSSM Lagrangian improves the accurate unification of the gauge couplings
because $\alpha_{3}$ gets contribution from the right handed neutrinos through
the RGE running at the two loop level [30].

The above points provide enough justification to determine the supersymmetric
mass spectrum in seesaw models at a high precision level including the effects
due to flavor violation555Programs like SuperIso[31] and SUSYFLAVOR[32]
compute the hadronic flavor violating processes for the given supersymmetric
spectrum at low energy with high precision. . Unfortunately, while there exist
very good spectrum calculators for supersymmetric theories like ISASUSY [33],
SuSpect [34] and SOFTSUSY [35], they do not consider full flavor violating
structure in the computation of the soft spectrum either in their RGE’s or
their mass matrices666 However there are programs which consider flavor
violation in their mass matrices. The program SPICE [36] computes mass
matrices with full flavor violation without considering intergenerational
mixing in the RGE. After this work has appeared we have been informed that
SOFTSUSY also has a new version where flavor violation is considered [37]..
For these reasons, present versions of these programs might not be suitable
for attacking problems listed above unless one significantly modifies them.
Our program was written to address this deficiency in publicly available
codes. We, however point out that the recent version of SPheno [39] is very
similar to the program we are presenting here. It has full flavor structure
for the soft masses as well as Yukawas at the 2-loop level and considers the
full $6\times 6$ mass matrices for the sparticles. The preliminary version of
our program was first presented at [40]. The present version is an expanded
and more structured version of the same. This paper explains the code in
detail. We attempted to link the physics discussion with the file structure of
the code wherever possible such that the user can modify the code with minimal
efforts.

SuSeFLAV is a program written in Fortran 95 in a fixed length format. The
recommended compiler for this program is gfortran available in various
distributions of Linux. The program can be made executable using other Fortran
compilers too, such as ifort, by modifying the Makefile in the main directory.
In addition to studying the spectrum of supersymmetric particles the code also
computes leptonic flavor violating decays and some hadronic decays. We have
implemented the SLHA 2.2 [41] format for dealing with the input parameters and
output data. This way, the output of the code can be fed in to other publicly
available programs either for computing Dark Matter relic density or for
calculating supersymmetric particle decays and production cross-sections at
LHC etc. While the main set of RGE’s are written for Type-I seesaw mechanism,
extending the program for other seesaw mechanisms or even other models would
require coding the RGE’s from respective models. However, other parts of the
code, like mass spectrum, one-loop corrections etc., which are given in
separate files in the source directory can be used to suit the user’s needs.

The rest of the paper is organized as follows. In section 2 we describe the
MSSM Lagrangian with Type-I seesaw mechanism. In section 3, we discuss the
various supersymmetry breaking scenarios considered in SuSeFLAV. In section 4
we describe the calculation of the low energy supersymmetric spectrum
implemented in the program. In section 5 we briefly describe about various
theoretical constraints we impose on the sparticle spectrum in SuSeFLAV. In
section 6 we discuss about the various low energy observables computed in the
program. In section 7 we show the instructions on how to install and execute
SuSeFLAV. In A we write down all the tree level mass matrices of the
sparticles and in B we outline all the one-loop radiative corrections to these
parameters SuSeFLAV. In C we graphically show the file structure in SuSeFLAV.
We close with a comparison chart of sparticle masses with other available
codes in D.

##  2 Minimal Supersymmetric Seesaw Model

Since 1998, ever increasing data from neutrino sector has firmly established
that neutrinos have non-zero masses and that their flavors mix with two of
their angles being close to maximal and the third angle is non-zero [42]. One
of the elegant mechanisms to generate non-zero neutrino masses is through the
seesaw mechanism [43], where right handed singlet fields are added to the
Standard Model particle spectrum. These singlet neutrinos break lepton number
typically at a scale much larger than the standard model scale through their
Majorana masses.

Supersymmetric version of the seesaw mechanism is straight forward extension
of the Minimal Supersymmetric Standard Model [1] by adding right handed
neutrino superfields. The field content of the MSSMRN(MSSM $+$ Right Handed
Neutrinos) and their transformation properties under the gauge group
${\mathcal{G}}_{{\rm SM}}\equiv{\rm SU}(3)_{c}\otimes{\rm
SU}(2)_{L}\otimes{\rm U}(1)_{Y}$ is given as

$\displaystyle{L}$ $\displaystyle:$
$\displaystyle\left(1,2,-\frac{1}{2}\right);\quad{e^{c}}:\left(1,1,+1\right);\qquad{\nu^{c}}:\left(1,1,0\right);$
$\displaystyle Q$ $\displaystyle:$
$\displaystyle\left(3,2,+\frac{1}{6}\right);\quad{u^{c}}:\left({\bar{3}},1,-\frac{2}{3}\right);\quad{d^{c}}:\left({\bar{3}},1,\frac{1}{3}\right);$
(1) $\displaystyle H_{u}$ $\displaystyle:$
$\displaystyle\left(1,2,+\frac{1}{2}\right);\quad
H_{d}:\left(1,2,-\frac{1}{2}\right).$

where $Q$ and $L$ stand for the $SU(2)_{L}$ doublet quarks and leptons,
$u^{c}$, $d^{c}$, $e^{c}$ and $\nu^{c}$ stand for the $SU(2)_{L}$ singlet
quarks and leptons, and the two Higgs doublet chiral superfields are denoted
by $H_{u}$ and $H_{d}$. At the seesaw scale and above, $q^{2}\gtrsim
M_{R}^{2}$, the superpotential takes the form :

$\displaystyle\mathcal{W}\ =\ $ $\displaystyle{\bf
Y}^{d}_{ij}d^{c}_{i}Q_{j}H_{d}+{\bf Y}^{u}_{ij}u^{c}_{i}Q_{j}H_{u}+{\bf
Y}^{e}_{ij}e^{c}_{i}L_{j}H_{d}$ $\displaystyle+{\bf
Y}^{\nu}_{ij}{\nu}^{c}_{i}L_{j}H_{u}+\mu
H_{u}H_{d}-\frac{1}{2}{M_{R}}_{i}{\nu}^{c}_{i}{\nu}^{c}_{i},$ (2)

where $i,j=\\{1,2,3\\}$ are generation indices. Note that the right handed
neutrino Majorana mass matrix is diagonal. The SU(2) and SU(3) contractions
are suppressed in the above Lagrangian. In the program, the seesaw scale is
taken to be $q^{2}=M_{R_{3}}^{2}$. At this scale, the right handed neutrino
mass matrix can be diagonalized by a rotation of the right handed neutrino
fields. The Dirac Yukawa matrix ${\bf Y}^{\nu}$ is defined at this scale in
the basis where the right handed neutrino mass matrix is diagonal. SuSeFLAV
considers the inputs at the scale $M_{R_{3}}$ where right handed neutrino
masses as well as the neutrino Dirac Yukawa coupling matrix. Finally it should
be noted that in the present version of SuSeFLAV, the ordering of the right
handed neutrino mass eigenvalues is taken as $M_{R_{1}}\lesssim
M_{R_{2}}\lesssim M_{R_{3}}$. We have not included the option of inverted
hierarchy for the right handed neutrinos in the present version. The program
will abort if such a choice is made.

Below the seesaw scale, once the right handed neutrinos are integrated out, we
are left with the five dimensional operator defining the the light neutrino
mass matrix as

$\displaystyle\mathcal{W}\ =\ $ $\displaystyle{\bf
Y}^{d}_{ij}d^{c}_{i}Q_{j}H_{d}+{\bf Y}^{u}_{ij}u^{c}_{i}Q_{j}H_{u}+{\bf
Y}^{e}_{ij}e^{c}_{i}L_{j}H_{d}$ $\displaystyle+\mu
H_{u}H_{d}+\frac{\kappa_{ij}}{\Lambda}\;L_{i}H_{u}L_{j}H_{u}$ (3)

The light neutrino mass matrix is given at the weak scale after the ${\rm
SU(2)}_{L}\times{\rm U(1)}_{Y}$ breaking as

$\mathcal{M}_{\nu}=\frac{\kappa_{ij}}{\Lambda}\;\langle H_{u}^{0}\rangle^{2}$
(4)

where $\Lambda$ represents the right handed neutrino mass scale or the seesaw
scale and $\langle H_{u}^{0}\rangle$ is the vev of the $H_{u}$ superfield. The
five dimensional operator is renormalized from the seesaw scale to the
electroweak scale. These corrections can be significant for inverse hierarchal
and degenerate spectrum for neutrino masses [44]. The present version of the
program does not contain the renormalization for the light neutrinos, we refer
users to use the existing programs like REAP [44]. The main reason for not
including the RG effects for light neutrinos has been the famous ambiguity in
relating the light neutrino masses to the neutrino Yukawa couplings [45].
Furthermore, we are more interested in the effects of seesaw mechanism on the
soft supersymmetric masses and couplings. However, we do provide the option
for the users to define the Yukawa matrices in terms of the Casas-Ibarra
${\cal R}$-parameterization [45]. In this parametrization the neutrino Yukawa
matrix ${\bf Y}^{\nu}$ is defined in terms of light neutrino masses as well as
the right handed neutrino masses. In ${\cal R}$-parametrization, ${\bf
Y}^{\nu}$ at the seesaw scale defined as

${\bf Y}^{\nu}=\frac{1}{\langle H_{u}^{0}\rangle^{2}}\ {\cal
D}_{\sqrt{M_{R}}}\,{\cal R}\,{\cal D}_{\sqrt{\cal{M_{\nu}}}}\,{\bf
U}^{\dagger}_{PMNS}$ (5)

where ${\bf U}_{{\rm PMNS}}$ is the Pontecorvo-Maki-Nakagawa-Sakata matrix
[46] and ${\cal R}$ is any $3\times 3$ orthogonal matrix. The ${\cal
D}_{\sqrt{M_{R}}}$ and ${\cal D}_{\sqrt{\cal{M_{\nu}}}}$ are defined as

$\displaystyle{\cal D}_{\sqrt{M_{R}}}\ =$ $\displaystyle\ {\rm
diagonal}\left(\sqrt{M_{R_{1}}},\,\sqrt{M_{R_{2}}},\,\sqrt{M_{R_{3}}}\right)$
(6) $\displaystyle{\cal D}_{\sqrt{\cal{M_{\nu}}}}\ =$ $\displaystyle\ {\rm
diagonal}\left(\sqrt{\kappa_{1}},\,\sqrt{\kappa_{2}},\,\sqrt{\kappa_{3}}\right)$
(7)

where $\kappa_{1}$, $\kappa_{2}$ and $\kappa_{3}$ are light neutrino mass
eigenvalues. It is important to note that $\cal R$ can be complex in nature
also, but in the present version of SuSeFLAV we take $\cal R$ to be real
orthogonal matrix. One can parametrize the $\cal R$ matrix in terms of 3
angles but in SuSeFLAV we have not parametrized the $\cal R$ matrix and left
all the 9 elements of $\cal R$ as user defined input. Various other
parametrization of the ${\bf Y}_{\nu}$ matrix have also been carried out in
[47]. Users interested in using the R-parameterization can use sinputs-rpar.in
in the main directory for their computations.

In addition to the user defined ${\bf Y}^{\nu}$ at the seesaw scale, we also
provide two other choices for ${\bf Y}^{\nu}$ and $M_{R}$ based on Grand
Unified Models like SO(10). Both these cases consider hierarchal masses for
the light neutrinos (${\mathcal{M}}_{\nu}$). These are

  1. 1.

CKM Case:

In this case the ${\bf Y}^{\nu}$ and $M_{R}$ are given as

$\displaystyle{\bf Y}^{\nu}=$ $\displaystyle\begin{pmatrix}h_{u}&0&0\\\
0&h_{c}&0\\\ 0&0&h_{t}\end{pmatrix}{\bf V}_{\text{CKM}}$ (8)
$\displaystyle\text{Diagonal}[M_{R}]=$
$\displaystyle\\{M_{R_{3}},M_{R_{2}},M_{R_{1}}\\}=\\{10^{14},10^{9},10^{6}\\}~{}\text{GeV}$

where $h_{u},h_{c},h_{t}$ are the Yukawa couplings of the up, charm and the
top quarks and ${\bf V}_{\text{CKM}}$ is the quark sector mixing matrix.

  2. 2.

PMNS Case:

In this case the ${\bf Y}^{\nu}$ and $M_{R}$ are given as

$\displaystyle{\bf Y}^{\nu}$ $\displaystyle=$
$\displaystyle\left(\begin{array}[]{ccc}h_{u}&0&0\\\ 0&h_{c}&0\\\
0&0&h_{t}\end{array}\right){\bf U}_{\text{PMNS}}$ (12)
$\displaystyle\text{Diagonal}[M_{R}]$ $\displaystyle=$
$\displaystyle\\{M_{R_{3}},M_{R_{2}},M_{R_{1}}\\}=\\{10^{14},10^{9},10^{6}\\}~{}\text{GeV}$

where ${\bf U}_{{\rm PMNS}}$ is the leptonic mixing matrix. Both ${\bf
V}_{\text{CKM}}$ and ${\bf U}_{\text{PMNS}}$ are defined in the SuSemain.f
file in the src/ directory. Below the seesaw scale, $q^{2}\lesssim
M_{R_{3}}^{2}$, the right handed neutrinos (and sneutrinos) decouple from the
theory, and the model is defined by MSSM.

The soft supersymmetric breaking terms in the seesaw enhanced MSSM are same as
in the MSSM together with the additional terms involving the right handed
sneutrinos. These include the mass terms for the gauginos, mass squared terms
for all the scalar particles and also the bilinear terms and trilinear terms:

$\displaystyle-\mathcal{L}_{\text{soft}}\ \supset\ $
$\displaystyle\frac{1}{2}\left(M_{1}\widetilde{B}\widetilde{B}+M_{2}\widetilde{W}\widetilde{W}+M_{3}\tilde{g}\tilde{g}\right)$
$\displaystyle+m_{H_{u}}^{2}|H_{u}|^{2}+m_{H_{d}}^{2}|H_{d}|^{2}+{\bf
m}_{\tilde{L}_{ij}}^{2}\tilde{L}_{i}^{\star}\tilde{L}_{j}+{\bf
m}^{2}_{\widetilde{e}^{c}_{ij}}\widetilde{e^{c}}^{\star}_{i}\widetilde{e}^{c}_{j}+{\bf
m}^{2}_{\widetilde{\nu^{c}}_{ij}}\widetilde{\nu^{c}}^{\star}_{i}\widetilde{\nu^{c}}_{j}+\ldots$
$\displaystyle+B_{\mu}H_{u}H_{d}+{\bf
B}_{M_{ij}}\widetilde{\nu^{c}_{i}}\widetilde{\nu^{c}_{j}}+h.c.$
$\displaystyle+\tilde{{\bf
A}}_{ij}^{u}\widetilde{Q}_{i}\widetilde{u}^{c}_{j}H_{u}+\tilde{{\bf
A}}_{ij}^{d}\widetilde{Q}_{i}\widetilde{d}^{c}_{j}H_{d}+\tilde{{\bf
A}}_{ij}^{e}\widetilde{L}_{i}\widetilde{e}^{c}_{j}H_{d}+\tilde{{\bf
A}}_{ij}^{\nu}\widetilde{L}_{i}\widetilde{\nu}^{c}_{j}H_{u}$ (13)

We use the factorization $\tilde{{\bf A}}^{u}\equiv{\bf A}^{u}{\bf Y}^{u}$,
for all the trilinear couplings at the weak scale777The RGEs are however,
defined in terms of $\tilde{\bf A}^{f}$, which sets the format for inputs at
the high scale. In mSUGRA, we have $\tilde{\bf A}^{f}=A_{0}\textbf{1}$. As
noted before, at the energies $q^{2}\lesssim M_{R_{3}}^{2}$, the right handed
sneutrinos also decouple from the theory, along with the right handed
neutrinos. In the program, we decouple the right handed neutrinos sequentially
at different scales : the heaviest right handed neutrino at $M_{R_{3}}$ and
the second heaviest one at $M_{R_{2}}$ and the lightest one at$M_{R_{1}}$.

The right handed neutrinos can be easily removed from the model to recover
MSSM without right handed neutrinos, by choosing ${\bf Y}^{\nu}=\textbf{0}$.
This automatically decouples the right handed neutrinos in the theory. An
explicit option is also provided in the input files, where by turning on/off
the parameter rhn, one can either include/remove right handed neutrinos in the
theory. Finally, let us note that quantum effects above the scale of seesaw
$q^{2}\gg M_{R_{3}}^{2}$ will make the mass matrix $M_{R}$ non-diagonal. The
running of the Majorana mass matrix can also effect the ${\bf B}_{M}$ term in
the soft potential, described below, at the 1-loop level. The ${\bf B}_{M}$
can have implications for flavor physics and EDMs, if it is large through
finite terms. These effects [48] are not computed in SuSeFLAV.

The complete set of 2-loop RGE for a general superpotential and MSSM are
presented in [49]. For the supersymmetric seesaw model, we use the RGE’s from
[50].

##  3 SUSY Breaking Mechanisms

Supersymmetry is broken spontaneously in a hidden sector and is then
communicated to the MSSM sector through the ‘messenger sector’. The messengers
could be gauge interactions or gravitational interactions. The result of this
communication leads to soft supersymmetry breaking terms in the MSSM. While
the form of the soft Lagrangian Eq. (2) is itself not dependent on the
mediation mechanism, the physical quantities i.e., the masses, the couplings
etc., are determined in terms of few ‘fundamental’ parameters depending on the
mediation mechanism. Popular among such supersymmetry breaking schemes are (i)
minimal Supergravity (mSUGRA) (ii) Gauge Mediated Supersymmetry Breaking
(GMSB) (iii) Anomaly Mediated Supersymmetry Breaking (AMSB) (iv) Gaugino
mediation (v) Moduli mediation etc. among a host of other possibilities [51].
In addition there could be variations within each of the above schemes. In the
SuSeFLAV, we have in-built (i) mSUGRA and some of its variations: (a) Non-
Universal Higgs Models (NUHM), (b) Non-Universal Gaugino Models (NUGM) and (c)
Complete Non-Universal Model (CNUM) and (ii) Gauge Mediated Supersymmetry
Breaking (GMSB) models. The corresponding input files are given in the
examples/ directory. An input file with completely non-universal soft
parameters is also presented for supergravity mediation, where the users can
define the boundary conditions of their choice. For other supersymmetric
breaking models, the users can modify appropriately the slha.in file and run
the program accordingly. In the section below we describe the two
supersymmetric breaking scenarios considered in SuSeFLAV.

###  3.1 mSUGRA and its variations

Supersymmetry is broken spontaneously in a hidden sector and the communicated
to the visible sector through the gravitational interactions. If the
supergravity Kähler metric is canonical in matter fields, the soft terms
resultant after integrating out the supergravity multiplet (while keeping the
gravitino mass fixed), are universal in nature [52]. The property universal
refers to the flavor space i.e. all the soft terms take the same value
irrespective of the flavor at the mediation scale. In SuSeFLAV we have
considered the mediation scale to be $M_{\text{GUT}}$. At this scale, all the
soft terms are determined by four parameters and the sign of the
$\mu$-parameter.

  1. 1.

At $M_{\text{GUT}}$ the gaugino masses are universal to a value $M_{1/2}$,
i.e.

$M_{1}(M_{\text{GUT}})=M_{2}(M_{\text{GUT}})=M_{3}(M_{\text{GUT}})\equiv
M_{1/2}$ (14)

  2. 2.

The scalar and the Higgs masses are given by the parameter $m_{0}^{2}$ at
$M_{\text{GUT}}$.

$\displaystyle{\bf m}^{2}_{{\tilde{Q}}_{i}}(M_{GUT})={\bf
m}^{2}_{{\tilde{u}}_{R_{i}}}(M_{GUT})$ $\displaystyle={\bf
m}^{2}_{{\tilde{d}}_{R_{i}}}(M_{GUT})={\bf
m}^{2}_{{\tilde{L}}_{i}}(M_{GUT})={\bf m}^{2}_{{\tilde{l}}_{i}}(M_{GUT})\equiv
m^{2}_{0}\;{\bf 1}$ $\displaystyle m^{2}_{{H}_{u}}(M_{GUT})$
$\displaystyle=m^{2}_{{H}_{d}}(M_{GUT})\equiv m^{2}_{0}\;$ (15)

  3. 3.

The trilinear couplings are given by the parameter $A_{0}$ at $M_{\text{GUT}}$

${\tilde{\bf A}}^{u}_{ij}(M_{GUT})={\tilde{\bf
A}}^{d}_{ij}(M_{GUT})={\tilde{\bf A}}^{l}_{ij}(M_{GUT})\equiv A_{0}\;{\bf
1}_{ij}$ (16)

To specify the spectrum at the weak scale, two more parameters need to be
fixed. First is the ratio of the vacuum expectation values (vevs) of the two
Higgs fields, $\tan\beta=v_{u}/v_{d}$. Second is a discrete parameter, the
sign of $\mu$ or the Higgsino mass parameter. The magnitude of $\mu$ is fixed
by the radiative electroweak symmetry breaking mechanism which has been
incorporated in the program.

####  3.1.1 Non-Universal Models

In models based on Grand Unified theories, it has been proposed that the
strictly universal feature of the soft masses might not be valid and in fact
some amount of non-universalities can enter in a model-dependent fashion. For
example, in models where the hidden sector gauge kinetic function is no longer
singlet under the GUT group, gaugino masses would become non-universal at the
high scale. However the non-universalities enter in a predictive fashion when
a particular gauge group is chosen, as the ratios of the gaugino masses are
now fixed by the Clebsch-Gordan coefficients of respective decomposition.
These ratios are well known for the GUT models based on various gauge groups,
e.g., SU(5) [53, 54, 55, 56], SO(10) [57, 58, 59]. Without resorting to any
particular model, we have incorporated non-universal gaugino mass scenario in
SuSeFLAV, by considering

$M_{1}(M_{GUT})\;\neq\;M_{2}(M_{GUT})\;\neq\;M_{3}(M_{GUT}).$ (17)

The user has the freedom of choosing any ratios among these three parameters
at GUT scale. The corresponding input file is sinputs-nugm.in. A second class
of non-universality which has been incorporated in SuSeFLAV is for the Higgs
[60]. It has been argued that since in Grand Unified theories (GUTs) like
SO(10), all the matter sits in a single representation where as the Higgs sits
in separate representation, the universality of the soft masses need not
include Higgs, especially when supersymmetry breaking mediation happens close
to the GUT scale. It has also been realized that introducing such non-
universality makes the $\mu$ parameter free and thus leading to completely
different phenomenology at the weak scale especially for dark matter. Thus the
boundary conditions at the high scale in our notation are given by

$\displaystyle{\bf m}^{2}_{{\tilde{Q}}_{i}}(M_{GUT})=\;$ $\displaystyle{\bf
m}^{2}_{{\tilde{u}}_{R_{i}}}(M_{GUT})=\;{\bf
m}^{2}_{{\tilde{d}}_{R_{i}}}(M_{GUT})=\;{\bf
m}^{2}_{{\tilde{L}}_{i}}(M_{GUT})={\bf m}^{2}_{{\tilde{l}}_{i}}(M_{GUT})\equiv
m^{2}_{0}\;{\bf 1}$ $\displaystyle m^{2}_{{H}_{u}}(M_{GUT})\equiv
m^{2}_{10}\;\;\;;\;\;\;m^{2}_{{H}_{d}}(M_{GUT})\equiv m^{2}_{20}$ (18)

Note that we intermittently use the notation $m_{10}$ and $m_{20}$ for the
Higgs mass parameters as defined above in the non-universal Higgs mass model.
The input file for this case sinputs-nuhm.in. It should be noted that a
negative sign for any soft-mass as input would mean a negative sign for that
soft-mass squared in the program.

In addition to these non-universal input files, a completely generic input
file called sinputs-cnum.in is provided where the user can provide all the
supersymmetric breaking parameters at the high scale (mSUGRA) without any
assumptions on their structure. This input file is more suited for models with
flavor structure at the high scale.

###  3.2 GMSB

The second class of supersymmetric breaking models incorporated in SuSeFLAV is
Gauge Mediated Supersymmetric Breaking (GMSB). As before, supersymmetry is
broken spontaneously in the hidden sector, but now communicated to the MSSM
sector through gauge interactions. The minimal set of models under this
category goes under the name, Minimal Messenger Model (MMM) [61]. In this
model, a set of messenger superfields transforming as complete representations
of SU(5) ($\supset\mathcal{G}_{\text{SM}}$) gauge group and couple directly to
a singlet field which parameterized the supersymmetry breaking in the hidden
sector. Supersymmetry breaking is then transmitted to the MSSM through SM
gauge interactions. The following superpotential represents the messenger
sector coupling to the hidden sector

${\cal W}=\lambda X\Phi_{i}\bar{\Phi}_{i}$ (19)

where $\Phi$ and $\bar{\Phi}$ are messenger sector superfields transforming as
$5$ and $\bar{5}$ of SU(5) and $i$ runs for the number of messenger sector
superfields, typically $i=[1,5]$. The $X$ superfield representing the hidden
sector is parameterized by the vacuum expectation values for both its scalar
component $\langle X\rangle$ as well as its auxiliary component $\langle
F_{X}\rangle$. Gauge interactions with the messenger fields lead to gauginos
attaining masses at 1-loop which at the Messenger scale are given by

$M_{a}\left(M_{mess}\right)=\frac{\alpha_{a}\left(M_{mess}\right)}{4\pi}\;\Lambda\;g\left(\frac{\Lambda}{M_{mess}}\right)\sum_{i}n_{a}(i);$
(20)

where the Messenger scale $M_{mess}=\lambda\langle X\rangle$ and
$\Lambda=\langle F_{X}\rangle/\langle X\rangle$. Here $n_{a}(i)$ is the Dynkin
index for the messenger pair $\Phi,\overline{\Phi}$ and the sum runs over all
the messengers in each group.

The scalars attain their masses from the 2-loop diagrams. These are given as

$m^{2}_{s}(M_{mess})=2\Lambda^{2}\;f\left(\frac{\Lambda}{M_{mess}}\right)\;\sum_{a,i}n_{a}(i)\;C_{a}\;\left(\frac{\alpha_{a}(M_{mess})}{4\pi}\right)^{2}$
(21)

Where $C_{a}$ is the quadratic Casimir invariant of the MSSM fields and the
function $g(x)$ and $f(x)$ are defined in [62] and [63] respectively. The
leading order contribution to the tri-linear couplings comes from the 2-loop
diagrams but they are suppressed by an extra $\alpha/4\pi$ factor compared to
the gaugino masses. Thus to an very good approximation we can take

${\tilde{\bf A}}^{u,d,l}_{ij}(M_{Mess})\simeq 0$ (22)

Thus in minimal GMSB model considered in SuSeFLAV we have the following 5
parameters as inputs

$\tan\beta,\;{\rm sign}(\mu),\;M_{mess},\;\Lambda{\rm~{}and~{}}n.$ (23)

The input file sinput-gmsb.in and mgmsb1.1.in and so on, are built-in files to
specify the inputs of the GMSB model in the examples/ directory of SuSeFLAV.

##  4 Calculation of Supersymmetric Spectrum

Figure 1: Flowchart of the program

Once the user chooses the particular model of supersymmetry breaking by typing
in the various parameters in the relevant input file, the program computes the
spectrum at the weak scale, checks for the various direct and indirect search
limits and computes the various observables including the flavor violating
ones like $\mu\to e+\gamma$. The computation of the spectrum involves several
complicated intermediate steps which has been already explained in detail by
various existing programs [64, 65]. In SuSeFLAV we follow a similar approach
in computing the spectrum, however including flavor mixing as well as
couplings with right handed neutrinos. In Fig. (1), we have shown the
flowchart of the computation of the spectrum and the observables in the
program. We can summarize the computation in terms of three steps which
however, are not independent of each other as the procedure involves
significant number of iterations.

  * 1.

RGE evolution: Using the MSSM RGE for the Yukawa and gauge couplings, run all
the known SM parameters like gauge couplings, Yukawa couplings up to the scale
of supersymmetry breaking. In the case of mSUGRA, run to the scale where the
gauge couplings corresponding to ${\rm SU}(2)_{L}$ ($g_{2}$) and ${\rm
U}(1)_{Y}$ $\left(g_{1}\equiv\sqrt{\frac{3}{5}}\;g_{Y}\right)$ meet, this
determines the GUT scale ($M_{{\rm GUT}}$). At the SUSY breaking scale
($M_{\text{GUT}}$ in case of mSUGRA and $M_{\text{mess}}$ in case of GMSB),
with the user defined input parameters and using the GUT scale SM parameters
as the boundary conditions, run all the MSSM RGEs including those for the soft
terms all the way down to $M_{{\rm SUSY}}$. For the initial run $M_{{\rm
SUSY}}$ is defined to be 1 TeV. If seesaw mechanism is switched on, the
program takes in to consideration the running of user defined neutrino Yukawa
couplings between the seesaw scale and the supersymmetric breaking scale in
both directions.

  * 2.

Radiative Electroweak symmetry breaking: The resultant soft parameters at the
$M_{\text{SUSY}}$ are used to check if they satisfy the tree level electroweak
symmetry breaking conditions and compute the $\mu$ parameter. The full one
loop effective potential corrections are then computed using the ‘tree level’
$\mu$ parameter, which is then used to derive the 1-loop corrections to the
$\mu$ parameter. This is repeated iteratively until the $\mu$ parameter
converges.

  * 3.

Convergence of the Spectrum: In the final step, we run all the soft terms to
the scale $M_{Z}$ where corrections to the SM parameters are added. We compute
the supersymmetric corrections to the SM gauge couplings and the third
generation fermion masses ($t$, $b$ and $\tau$). The resultant masses are fed
in to the RGE routine as shown in Fig. (1) and the soft spectrum is evaluated
and run to MZ scale. This full iteration is continued until the SM third
generation fermion masses converges to user defined precision (usually ${\cal
O}(10^{-3}-10^{-4})$). Once this masses get converged we calculate various low
energy observables (e.g. ${\rm BR}(\mu\to e\gamma)$, ${\rm BR}(b\to s\gamma)$
etc.). In section 6 we have discussed the low energy observables SuSeFLAV
calculates.

In the following we describe each of these steps in more detail.

###  4.1 RGE Evolution

The standard model fermion masses and gauge couplings are the inputs to the
program at the weak scale, taken to be equal to the Z-boson mass $M_{Z}$ in
the program. The parameters are divided in to two subsets depending on whether
radiative corrections are added or not. The parameters, masses of the first
two generations quarks and leptons, for which we do not add radiative
corrections are put in the file src/stdinputs.h. The values for these masses
are taken from PDG 2012 [66]. Most of the other parameters such as the
leptonic mixing matrix, ${\bf U}_{\text{PMNS}}$, the hadronic mixing matrix
(${\bf V}_{\text{CKM}}$) are defined in the file src/SuSemain.f. The
$\overline{\text{MS}}$ values of Z-boson mass, the pole masses of the top
quark $m_{t}^{pole}(m_{t})$ and tau lepton, $m_{\tau}^{pole}(m_{\tau})$ and
the $\overline{\text{MS}}$ mass of the bottom quark mass,
$m_{b}^{\overline{\text{MS}}}(m_{b})$, are left as user defined inputs. The
$\overline{\text{MS}}$ gauge couplings, electromagnetic, $\alpha_{em}(M_{Z})$
and the strong coupling, $\alpha_{s}(M_{Z})$ are also considered as inputs and
are contained in the input files. The $\overline{\text{MS}}$ inputs are
converted to $\overline{\text{DR}}$ as the RGEs are written in the
$\overline{\text{DR}}$ scheme. The conversion for the gauge couplings is given
by

$\alpha_{em}^{\overline{\text{DR}}}(M_{Z})=\left(\frac{1}{\alpha_{em}^{\overline{\text{MS}}}(M_{Z})}-\frac{1}{6\pi}\right)^{-1},\,\,\,\alpha_{s}^{\overline{\text{DR}}}(M_{Z})=\left({\frac{1}{\alpha_{s}^{\overline{\text{MS}}}(M_{Z})}-\frac{1}{4\pi}}\right)^{-1}$
(24)

The so defined $\alpha_{em}^{\overline{\text{DR}}}$ is in turn used to define
the $\overline{\text{DR}}$ values of the $\alpha_{1,2}$.

$\alpha_{1}(M_{Z})\equiv\frac{g_{1}^{2}}{4\pi}=\frac{5\alpha_{em}^{\overline{\text{DR}}}(M_{Z})}{3\cos^{2}\theta_{W}}\;,\quad\alpha_{2}(M_{Z})\equiv\frac{g_{2}^{2}}{4\pi}=\frac{\alpha_{em}^{\overline{\text{DR}}}(M_{Z})}{\sin^{2}\theta_{W}}$
(25)

In a similar fashion, the bottom mass is converted from the
$\overline{\text{MS}}$ to $\overline{\text{DR}}$ using [67, 68]

$m_{b}^{\overline{\text{DR}}}(M_{Z})=m_{b}^{\overline{\text{MS}}}(m_{b})\cdot\left[1-\frac{\alpha_{s}(M_{Z})}{3\pi}-\frac{23\alpha_{s}^{2}(M_{Z})}{72\pi^{2}}+\frac{3\alpha_{2}(M_{Z})}{32\pi}+\frac{13\alpha_{1}(M_{Z})}{288\pi}\right],$
(26)

where the coupling constants appearing in the parenthesis are their
$\overline{\text{DR}}$ values. The masses of the tau lepton and top quark are
converted from their pole masses using the following relations:

$\displaystyle m_{\tau}^{\overline{\text{DR}}}(M_{Z})$ $\displaystyle=$
$\displaystyle
m_{\tau}^{pole}\cdot\left[1-\frac{3}{8}\left(\alpha_{1}(M_{Z})-\frac{\alpha_{2}(M_{Z})}{4}\right)\right]$
$\displaystyle m_{t}^{\overline{\text{DR}}}(M_{Z})$ $\displaystyle=$
$\displaystyle m_{t}^{pole}\cdot\Delta_{m_{t}}^{QCD}$ (27)

where $\Delta_{m_{t}}^{QCD}$ is given by [69]

$\Delta_{m_{t}}^{QCD}=1-\frac{\alpha_{s}(m_{t})}{3\pi}\,\left(5-3\Delta_{tz}\right)-\alpha_{s}^{2}(m_{t})\,\left(0.538-\frac{43\Delta_{tz}}{24\pi}+\frac{3\Delta_{tz}^{2}}{8\pi^{2}}\right),$
(28)

with $\Delta_{tz}=2\ln\left(m_{t}^{pole}/M_{Z}\right)$ and

$\alpha_{s}(m_{t})=\frac{\alpha_{s}^{\overline{\text{DR}}}(M_{Z})}{1+\frac{3}{4\pi}{\alpha_{s}^{\overline{\text{DR}}}(M_{Z})\Delta_{tz}}}$
(29)

The $\overline{\text{DR}}$ corrected masses are used to define the $3\times 3$
Yukawa matrices at the $M_{Z}$ scale which form the inputs to the RGE.

$\displaystyle{\bf
Y}^{u}=\frac{\sqrt{2}}{v\sin\beta}\;\text{Diag}[m_{u},m_{c},m_{t}]\cdot{\bf
V}_{CKM}\;$ ; $\displaystyle\;{\bf
Y}^{d}=\frac{\sqrt{2}}{v\cos\beta}\;\text{Diag}[m_{d},m_{s},m_{b}]\;;$
$\displaystyle{\bf Y}^{e}=\frac{\sqrt{2}}{v\cos\beta}$
$\displaystyle\text{Diag}[m_{e},m_{\mu},m_{\tau}]$ (30)

We use the above defined Yukawas to run the full 2-loop RGEs from the weak
scale ($M_{Z}$) up to the scale at which the two gauge couplings ($g_{1}$ and
$g_{2}$) unify with an accuracy of 1%. For GMSB scenario this scale is set by
the user as messenger scale or $M_{\rm mess}$. In the case of right handed
neutrinos three intermediate scales get introduced in the theory. As mentioned
in the section 2, we consider the seesaw scale to be the mass of the heaviest
right handed neutrino, $M_{R_{3}}$. At this scale we set the neutrino Yukawa
(${\bf Y}^{\nu}$) and run the RGEs with this Yukawa up to the high scale. At
the high scale, depending on the model, we set the SUSY breaking boundary
conditions and then run the RGEs down to the heaviest right handed neutrino
mass scale i.e., $M_{R_{3}}$. Below this mass scale we decouple the heaviest
right handed neutrino by setting its couplings in the neutrino Yukawa matrix
to zero. From $M_{R_{3}}$ we run down the RGEs to the next heaviest right
handed neutrinos i.e., $M_{R_{2}}$ and then form $M_{R_{2}}$ to $M_{R_{1}}$.
Below each of these scale, i.e., $M_{R_{2}}$ and $M_{R_{1}}$, we decouple the
corresponding right handed neutrino by setting their couplings to zero. From
$M_{R_{1}}$ we run the RGEs down to the scale $M_{\rm SUSY}$. For the first
iteration we take a guess value for $M_{\rm SUSY}$ which is 1 TeV. From the
second iteration onwards the Electro-Weak Symmetry Breaking (EWSB) scale is
set to the geometric mean of the two stop masses or
$\sqrt{m_{\tilde{t}_{1}}\cdot m_{\tilde{t}_{2}}}$. At this scale we check for
the EWSB condition and then we calculate the supersymmetric spectrum. A
schematic picture of the integration of the RGE’s in mSUGRA with seesaw
mechanism is summarized in Fig. (2). In GMSB models, the high scale is the
messenger scale, $M_{\rm mess}$ instead of $M_{\rm GUT}$ and the procedure of
the integration is very similar. The seesaw mechanism can be incorporated in
this class of models as long as heaviest right handed neutrino is lighter than
the messenger scale ($M_{R_{3}}<M_{\rm mess}$).

Figure 2: Pictorial representation of evolution of RGEs

###  4.2 Radiative Electroweak Symmetry Breaking

The tree level EWSB conditions at the $M_{\rm SUSY}$ scale are defined as
below

$\displaystyle\left|\mu\right|^{2}$ $\displaystyle=$
$\displaystyle\frac{1}{2}\left[\tan 2\beta(m_{H_{u}}^{2}\tan\beta-
m_{H_{d}}^{2}\cot\beta)-M_{Z}^{2}\right]$ $\displaystyle B_{\mu}$
$\displaystyle=$ $\displaystyle\frac{\sin
2\beta}{2}\left[m_{H_{u}}^{2}+m_{H_{d}}^{2}+2|\mu|^{2}\right]$ (31)

where $m_{H_{u}}^{2}$ and $m_{H_{d}}^{2}$ are the RGE output at $M_{\rm
SUSY}$. For consistent electroweak symmetry breaking we require
$\left|\mu\right|^{2}>0$888Further, there should not be any tachyons in the
physical Higgs spectrum.. The tree level $|\mu|^{2}$ and RGE output of the
other SUSY soft masses is used to calculate the tree level spectrum as
described in A. Radiative corrections can however significantly modify the
tree level value of $\mu$. Using tree level sparticle spectrum, we calculate
the radiative corrections to the higgs potential up to one-loop order as given
by BPMZ [70]. The tadpoles modify the $m_{H_{u}}^{2}$ and $m_{H_{d}}^{2}$ as

$m_{H_{u}}^{2}\rightarrow m_{H_{u}}^{2}-\frac{t_{1}}{v_{1}}\quad;\quad
m_{H_{d}}^{2}\rightarrow m_{H_{d}}^{2}-\frac{t_{2}}{v_{2}}.$ (32)

With these radiatively corrected higges, using Eq. (4.2), we calculate the
radiatively corrected $|\mu|^{2}$. This is repeated iteratively until the
convergence of $|\mu|^{2}$ reaches the desired accuracy (default value is
$\mathcal{O}(10^{-4})$). This accuracy level can be changed by changing the
parameter tol in file src/ewsbiterate.f. There could be regions where the
$\mu$ parameter does not converge within a small number of iterations. In such
regions, the program considers the parameter point as $|\mu|$-non convergent.
Once $|\mu|$ has converged we calculate $B_{\mu}$ as

$B_{\mu}=\frac{\sin
2\beta}{2}\left[\overline{m}_{H_{u}}^{2}+\overline{m}_{H_{d}}^{2}+2|\mu|^{2}\right]$
(33)

It is important to note here that at $M_{\rm SUSY}$, SuSeFLAV checks for
D-flat directions in the potential as well as whether the potential is
unbounded from below. It also checks for charge and color breaking minima.
More details about these checks are discussed in the next section. Even if
these conditions are not satisfied the program still proceeds to compute the
spectrum however, a flag is raised and written in the output file.

Once $\mu$ is converged, the program uses it to compute complete one loop
corrections to the sparticle spectrum. We follow the work of BPMZ [70] in
computing these corrections999Current version of the program does not include
flavor violating contributions from sleptons to all the 1-loop corrections.
The sleptonic contributions are neglected in this version in the presence of
flavor violation.. Corrections to neutralinos and charginos are evaluated at
external momenta equal to $M_{\text{SUSY}}$ and the corrections to sfermion
masses are calculated at an external momenta equal to their pole mass as
prescribed by BPMZ. In B we have discussed more about these threshold
corrections to the sparticles. As mentioned before all the parameters of the
code are considered real, including the diagonalizing matrices. In determining
the neutral higgs masses the user has a choice to employ approximations for
two loop which are mostly top-stop enhanced [71] or full one loop tadpole
corrections as described in BPMZ or full one loop together with leading order
two loop corrections. We have implemented the two loop corrections due to
Slavich et. al [72] in our version 1.2. This is the default choice for the
Higgs spectrum in the present version.

###  4.3 Convergence of the Spectrum

In final step, the program evaluates the full one loop flavor conserving
supersymmetric threshold corrections to SM parameters. The parameters which
are corrected are $m_{t},\,m_{b},\,m_{\tau},\,\alpha_{s},\,\alpha_{em}$ and
$\sin^{2}\theta_{W}$. One loop corrected running masses are given by the
following,

$\Delta_{m_{t}}(M_{Z})=\Sigma_{t}^{BPMZ}+\Delta_{m_{t}}^{QCD},\quad
m_{t}(M_{Z})=m_{t}^{pole}\left[1+\Delta_{m_{t}}(M_{Z})\right]$ (34)

$m_{b}(M_{Z})^{\overline{DR}}_{MSSM}=\frac{m_{b}(M_{Z})^{\overline{DR}}_{SM}}{1+\Delta_{m_{b}}^{BPMZ}}$
(35)

$m_{\tau}(M_{Z})=m_{\tau}^{pole}\left[1+\Sigma_{\tau}^{BPMZ}\right]$ (36)

The quantity $\Sigma_{t}^{BPMZ}$, one loop correction to the top quark mass is
evaluated at external momenta equal to $m_{t}^{\overline{DR}}(M_{Z})$.
Whereas, $\Delta_{m_{b}}^{BPMZ}$ and $\Sigma_{\tau}^{BPMZ}$ are evaluated in
the limit of external momenta tending to zero. The expressions of these
parameters are described in the B. The three gauge couplings get corrected as
below

$\alpha_{1}(M_{Z})=\frac{5\alpha_{em}^{\overline{DR}}(M_{Z})}{3\left(1-\Delta_{\alpha_{em}}\right)\cos^{2}\theta_{W}}$
(37)
$\alpha_{2}(M_{Z})=\frac{\alpha_{em}^{\overline{DR}}(M_{Z})}{\left(1-\Delta_{\alpha_{em}}\right)\sin^{2}\theta_{W}}$
(38)

$\alpha_{3}(M_{Z})=\frac{\alpha_{s}(M_{Z})}{1-\Delta_{\alpha_{s}}}$ (39)

where $\Delta_{\alpha_{em}}$ and $\Delta_{\alpha_{s}}$ are one loop
corrections to the electromagnetic and strong coupling described in the B.
Note that $\sin^{2}\theta_{W}$ used in the above expressions is also
radiatively corrected. Iterative method is implemented to correctly evaluate
SUSY contributions to $\sin^{2}\theta_{W}$. The above corrected
$\alpha_{1}(M_{Z}),\alpha_{2}(M_{Z})$ and $\alpha_{3}(M_{Z})$ and also the
third generation SM fermions ($m_{t}$, $m_{b}$, $m_{\tau}$) masses are used as
the input for the next long iteration. The iteration continues until the SM
third generation fermions, namely top, bottom and tau mass are converged to
user defined precision (usually ${\cal O}(10^{-3})$). This precision can be
changed by the parameter named spectrum tolerance defined in the input files.
Once the SM fermion masses get converged the program proceeds to calculate the
various low energy observables. Finally, lets note that if both $LL$ and $RR$
type leptonic flavor violation is present, it could lead to corrections to
lepton self energies [73], which are not included in the present version of
the code.

##  5 Theoretical and Phenomenological Constraints

The requirement of consistent evaluation of supersymmetric spectrum involves a
check for theoretical constraints such as charge and color breaking minima
(CCB), scalar potential unbounded from below (UFB) and efficient electroweak
symmetry breaking at EWSB scale.

With every iterative step of the program SuSeFLAV checks for CCB and UFB
conditions at the tree level [74]. These conditions are governed by equations
40, 41 and are simultaneously implemented while computing the tree level $\mu$
parameter (checking for efficient EWSB, see section 4.2 for the complete
description).

$\displaystyle{\rm{\bf
CCB:}}\;\;\;\;3\left(m_{Q_{u}}^{2}+m_{f}^{2}+|\mu|^{2}+m_{H_{f}}^{2}\right)\geq\left|A_{f}\right|^{2}$
(40) $\displaystyle{\rm{\bf
UFB:}}\;\;\;\;\;m_{H_{u}}^{2}+m_{H_{d}}^{2}+2|\mu|^{2}\geq
2\left|B_{\mu}\right|^{2}{\;\rm at\;}Q>M_{EWSB}$ (41)

It is important to note that the complete MSSM spectrum is still calculated
even if CCB and UFB conditions are not satisfied. However, if the
supersymmetric scalar potential has a charge and color breaking minima which
is lower than electroweak minimum a warning flag CCB is generated. Similarly,
if the complete supersymmetric scalar is unbounded from below a warning flag
UFB is generated.

Apart form the above described theoretical constraints the program also
imposes additional phenomenological constraints on the obtained spectrum. From
the direct non-observation of charged dark matter in the Universe we require
$m_{\tilde{\tau}}>m_{\chi^{0}}$ or LSP being neutral. Regions for which this
condition is not true is excluded as $\tilde{\tau}$ LSP regions. Consequently
the flag is marked as LSPSTAU. Also, we require the the spectrum to be non-
tachyonic. If tachyonic spectrum is encountered it is flagged as TACSPEC. The
program also indicates the sector where the tachyon occurs, for example: a
tachyon in sleptonic sector is marked as TACSLP. Some lower bounds on various
sparticle masses that result from direct searches at colliders, e.g., the
lightest Higgs mass $m_{h}>114.5{\rm~{}GeV}$, and the Chargino mass
$m_{\chi^{\pm}}>103.5{\rm~{}GeV}$ [75] are also incorporated in the program.
Points failing to satisfy these bounds are flagged as LEPH and LEPC
respectively. The present version does not include recent direct search limits
from LHC [76].

##  6 Low Energy Observables

Once the complete supersymmetric spectrum is obtained we compute the following
low energy observables in SuSeFLAV.

  * 1.

Fine Tuning: In MSSM the standard model masses and gauge couplings, e.g.
$M_{Z}$, $m_{t}$, $m_{b}$ etc. are function of the input parameters of the
model, i.e., for mSUGRA $m_{0},\ M_{1/2},\ A_{0},\ \tan\beta\ {\rm and}\ {\rm
sign}(\mu)$. Now, we can recast the EWSB Eq. (4.2) as below:

$M_{\bar{Z}}^{2}=-2|\mu|^{2}+\tan 2\beta\left(m_{{H}_{u}}^{2}\tan\beta-
m_{{H}_{d}}^{2}\cot\beta\right),$ (42)

where, all the parameters on the right side of Eq. (42) are at the weak scale.
Given that $M_{Z}$ is know at a few percent level, it can be seen that some
amount of ‘tuning’ between the parameters in the right side is needed. Various
measures [77, 78, 79, 80] have been proposed to quantify the ‘tuning’ needed
in some input parameter. In SuSeFLAV, we have followed Barbieri and Giudice
[77, 80], in evaluating the fine tuning for a given parameter $\lambda_{i}$ of
the model as

$\frac{\delta
M_{Z}^{2}}{M_{Z}^{2}}=f(M_{Z}^{2},\lambda_{i})\;\frac{\delta\lambda_{i}}{\lambda_{i}}$
(43)

Where Barbieri-Giudice function or $f(M_{Z}^{2},\lambda_{i})$ is defined as

$f(M_{Z}^{2},\lambda_{i})=\frac{\lambda_{i}}{M_{Z}^{2}}\;\frac{\partial
M_{Z}^{2}}{\partial\lambda_{i}}$ (44)

We derive the fine tuning in $M_{Z}^{2}$ with respect to $\mu^{2}$ for which
$f(M_{Z}^{2},\mu^{2})$ takes the following form

$f(M_{Z}^{2},\mu^{2})=\frac{2|\mu|^{2}}{M_{Z}^{2}}\left[1+\frac{(\tan^{2}\beta+1)}{(\tan^{2}\beta-1)^{3}}\;\frac{4\tan^{2}\beta\;\left(m_{\overline{H}_{d}}^{2}-m_{\overline{H}_{u}}^{2}\right)}{\left(m_{\overline{H}_{d}}^{2}+m_{\overline{H}_{u}}^{2}\right)}\right].$
(45)

The fine tuning in $m_{t}$ with respect to $\mu^{2}$ or $f(M_{Z}^{2},m_{t})$
is expressed as follows

$f(m_{t},\mu^{2})=\frac{1}{2}f(M_{Z}^{2},\mu^{2})+\frac{1}{\tan^{2}\beta-1}\;\frac{2|\mu|^{2}}{m_{\overline{H}_{u}}^{2}+m_{\overline{H}_{d}}^{2}}$
(46)

  * 2.

Electro-Weak Precision Measurement: The electroweak observables $\rho$
parameter and $\sin^{2}\theta_{W}$ are defined in 47 and 48.

$\displaystyle\rho=\frac{M_{W}}{M_{Z}\cos\theta_{W}}$ (47)
$\displaystyle\sin^{2}\theta_{W}=1-\frac{M^{2}_{W}}{M^{2}_{Z}}$ (48)

At the tree level $\rho$ parameter is unity and $\sin^{2}\theta_{W}=0.2286$. A
deviation from these values are observed at one-loop level stemming from SM
and supersymmetric corrections to $W$ and $Z$ boson masses. A measure of this
deviation to $\rho$ parameter is given below

$\displaystyle\Delta\rho$
$\displaystyle=\frac{\Pi_{ZZ}(0)}{M_{Z}^{2}}-\frac{\Pi_{WW}(0)}{M_{W}^{2}}$
(49) $\displaystyle{\rm and\;}\rho$ $\displaystyle=\frac{1}{(1-\Delta\rho)}$
(50)

The correction to $\sin^{2}\theta_{W}$ is described in B. A precise
measurement of these parameters by LEP, SLC and Tevetron imposes stringent
constraints on $\Delta\rho$, requiring $\Delta\rho\lesssim 10^{-3}$ for a
physically viable spectrum.

  * 3.

BR($b\rightarrow s\gamma$) Constraint: Another sector where the effect of SUSY
particles can be seen is the radiative flavor changing decay of bottom quark,
$b\rightarrow s\gamma$ [81]. In the Standard model, this decay is mediated by
loops containing up sector quarks and $W$ bosons. In supersymmetric theories,
if CKM is the only source of hadronic flavor violation, additional
contributions to $b\rightarrow s\gamma$ process come from chargino loops
($\widetilde{\chi}^{\pm}$), stop ($\tilde{t}$) squarks loops and charged Higgs
bosons ($H^{\pm}$) loops. As in the perturbation theory the SM and
supersymmetric correction appear at the same order, the measurement of
BR($b\rightarrow s\gamma$) is a very powerful tool for constraining the SUSY
parameter space. In SuSeFLAV we have followed Bartl et al. [82], which
includes Standard model NLO as well as MSSM LO contributions. Like the other
observables, this branching ratio is calculated for all the valid points and
written in the SLHA file. More precise evaluations of this process are
available publicly in the [31, 32, 38, 83]. However, given that we are
concentrating on evaluation of flavor violating observables in the presence of
flavor violation in the soft sector, we would like upgrade our computation of
this processes in a future version to include gluino contributions which could
become important in the presence of squark flavor violating terms. Currently,
we refer our users to couple the output of our program to one of the above
existing codes depending on the accuracy required and input parameters they
are interested in. For example SuperIso [31] computes the process at NNLO. It
has an added advantage that it can compute other B-physics observables also.
As of now our program does not have an interface with SuperIso, but one can
link to it using one of its programs (cmssm.c etc ) to our code.

  * 4.

Anomalous Magnetic Moment of Muon $(g_{\mu}-2)$: The muon anomalous magnetic
moment ($g_{\mu}-2$) has been precisely measured by Muon $(g-2)$ collaboration
[84, 85]. Due to supersymmetric particles in the loop, ($g_{\mu}-2$) gets non-
negligible correction apart from the SM contribution. The experimentally
measured value of anomalous magnetic moment of muon is:

$a_{\mu}^{exp}\equiv\frac{(g_{\mu}-2)}{2}=(11659208\pm 6)\times 10^{-10}.$
(51)

Whereas, the difference in theoretical prediction by SM and experimental
value, i.e $a_{\mu}^{exp}-a_{\mu}^{SM}=(28.7\pm 8.0)\times 10^{-10}$ [86].
Here the difference arises because of the fact of different estimates of
hadronic vacuum polarization contribution. The contribution from the
supersymmetric particles to $(g_{\mu}-2)$ is through
$(\widetilde{\chi}^{0}-\tilde{\mu}/\tilde{\tau}/\tilde{e})$ loop or through
$(\widetilde{\chi}^{\pm}-\tilde{\nu})$ loop. Supersymmetric parameter space
can be severely constrained [87] as a supersymmetric explanation for the
discrepancy with the experiment prefers a ‘light’ supersymmetric spectrum.
Moreover, both these contributions are $\tan\beta$ enhanced, so large values
of $\tan\beta\,(\gtrsim 30)$ are more severely constrained. We have taken the
expression for one-loop contribution, due to supersymmetric particles, to the
$(g_{\mu}-2)$ from Hisano et al. [14]. For a given set of input parameter
SuSeFLAV calculates the $(g_{\mu}-2)$ and writes it into the SLHA file. Two
loop contributions are not added in the present version which could be
important in the very large tan$\beta$ regime [88]. One of the main reasons
for not including these contributions is the absence of two loop computations
including flavor violation in the sleptonic sector. The present version
includes flavor violating contributions at the 1-loop level which become
important when the seesaw is switched on. We hope to generalize the two loop
contributions including flavor violations in a future version.

  * 5.

Lepton Flavor Violating Decays: Subject to satisfying phenomenological
constraints at $M_{\rm SUSY}$, we evaluate decay rates of rare lepton flavor
violating processes. The decay rates and branching ratios for the following
processes are computed $\mu\,\rightarrow\,e\gamma$,
$\tau\,\rightarrow\,e\gamma$, $\tau\,\rightarrow\,\mu\gamma$,
$\mu\,\rightarrow\,e\gamma$, $\mu^{-}\,\rightarrow\,e^{+}e^{-}e^{-}$,
$\tau^{-}\,\rightarrow\,\mu^{+}\mu^{-}\mu^{-}$,
$\tau^{-}\,\rightarrow\,e^{+}e^{-}e^{-}$ and $\mu-e$ conversion rate in the
nuclei. The search for charged lepton flavor violating decays can play a
pivotal role in studying and discovering new physics beyond the standard model
at TeV scale and above.

Table 1: Present Experimental Bounds on LFV Processes Process | Experiment | Present upper bound
---|---|---
BR$(\mu\rightarrow e\,\gamma)$ | MEG [89] | $2.4\times 10^{-12}$
BR$(\mu\rightarrow e\,e\,e)$ | SINDRUM [90] | $1.0\times 10^{-12}$
CR$(\mu\rightarrow e\,{\rm in}\,{\bf Au})$ | SINDRUM-II [91] | $7\times 10^{-13}$
CR$(\mu\rightarrow e\,{\rm in}\,{\bf Ti})$ | SINDRUM-II [92] | $4.3\times 10^{-12}$
BR$(\tau\rightarrow\mu\,\gamma)$ | BABAR/Belle [93] | $4.4\times 10^{-8}$
BR$(\tau\rightarrow e\,\gamma)$ | BABAR/Belle [93] | $3.3\times 10^{-8}$
BR$(\tau\rightarrow\mu\,\mu\,\mu)$ | BABAR/Belle [93] | $2.0\times 10^{-8}$
BR$(\tau\rightarrow e\,e\,e)$ | BABAR/Belle [93] | $2.6\times 10^{-8}$

The amplitudes of these processes are also sensitive to the left-right mixing
in the sleptonic mass matrices in addition to the intergenerational mixing
[94]. In calculating the amplitudes we closely follow the notations and
expressions provided in [14, 15]. The contribution to $\mu-e$ conversion rate
in the nuclei is through penguin diagram where $\gamma$, $Z$ is exchanged and
through box diagrams containing $\tilde{\chi}^{0}-\tilde{l}_{i}-q_{u,d}$ loops
or $\tilde{\chi}^{-}-\tilde{\nu}_{i}-q_{u,d}$ loops. The current experimental
upper bound on various LFV processes is tabulated in Table 1.

In the current version of SuSeFLAV we use the tree level masses and full
$6\times 6$ slepton mixing matrix to calculate LFV observables. The output is
written in the BLOCK SuSeFLAVLOWENERGY in SLHA format.

  * 6.

Light Neutral Higgs Boson Mass: Recently, the ATLAS and CMS experiments at the
Large Hadron Collider (LHC) at CERN have reported the discovery of a Higgs
like boson with a statistical significance of more than $5$ sigma. Both the
experiments report the mass of this particle to be close to 125 GeV with the
exact numbers given by :

$\displaystyle m_{h}=125.3\pm 0.4~{}(\text{stat})\pm
0.5~{}(\text{sys})~{}~{}\text{GeV}~{}~{}~{}~{}~{}~{}\text{CMS
\cite[cite]{[\@@bibref{Number}{cmshiggs}{}{}]}}~{}~{}$ $\displaystyle
m_{h}=126.0\pm 0.4~{}(\text{stat})\pm
0.4~{}(\text{sys})~{}~{}\text{GeV}~{}~{}~{}~{}~{}~{}\text{ATLAS
\cite[cite]{[\@@bibref{Number}{atlashiggs}{}{}]}}~{}~{}$

In MSSM, this would correspond to the mass of lightest neutral CP-even Higgs
boson provided it has SM-like couplings [97]. Both these requirements put a
strong constraints on most models of supersymmetry breaking especially the
ones with universal boundary conditions[98]. In the universal class of models,
large values of the trilinear couplings are required to generate a light higgs
mass of that order. Two loop contributions to the higgs mass matrices are
important and cannot be neglected while studying the implications on model
parameter space. As mentioned earlier, SuSeFLAVcomputes the light higgs mass
at the two loop level making it appropriate for analysis of this constraint
over a wide range of supersymmetry breaking models. In particular,
implications on the supersymmetric seesaw models and the complementarity with
flavour processes has already been studied [99] assuming universal and non-
universal higgs boundary conditions. As of now the light higgs mass constraint
is not imposed automatically in the program. Since there are still some
theoretical and experimental uncertainties which are subject to modification
as more data pours in from LHC experiments, the exact range of the light higgs
mass is left to the user.

##  7 Executing SuSeFLAV

Instruction to compile and install the package is provided in README file.
SuSeFLAV uses the Diag package by T. Hanh to diagonalize the mass
matrices101010Note that LAPACK [100] library is a another option for an
earlier version of SuSeFLAV for diagonalizing mass matrices. It is available
on the website for downloading. We do not recommend the old version.. SuSeFLAV
package produces three executables when compiled, namely suseflav,
suseflavslha and suseflavscan in the bin/ sub-directory. To compute the
spectrum for a single point the usage of executables suseflav and suseflavslha
is recommended. The user must modify the corresponding input files sinputs.in
and slha.in where all the input parameters are specified. To scan the
parameter space the usage of the executable suseflavscan is recommended. The
corresponding input parameters are in the input file sinputs_scan.in.

###  7.1 Sample Input/Output

In this section we provide examples of input files which can be used to run
the program. SuSeFLAV has two input/output modes. This can be broadly
classified into SLHA I/O interface and non-SLHA or traditional SuSeFLAV I/O
interface. The directory examples/ contains a variety of input files with
which the user can run different models.

####  7.1.1 SLHA Interface

The main source file is runslha.f. To use the SLHA interface the user should
execute suseflavslha by modifying the corresponding input file slha.in. Note
that the user must rename the required SLHA file as slha.in to use that
particular file as input. To run the program type the following command at the
terminal

./suseflavslha

This sample input/output corresponds to point 10.1.5 [101] with Type-I see-saw
mechanism with maximal mixing in mSUGRA/CMSSM scenario.

    Block MODSEL                 # Select model
        1    1                   # sugra
        6    1                   # Quark Flavor Violation
    Block SMINPUTS               # Standard Model inputs
        1   1.279340000E+02      # alpha^(-1) SM MSbar(MZ)
        2   1.166390000E-05      # G_Fermi
        3   1.172000000E-01      # alpha_s(MZ) SM MSbar
        4   9.118760000E+01      # MZ(pole)
        5   4.230000000E+00      # mb(mb) SM MSbar
        6   1.727000000E+02      # mtop(pole)
        7   1.770000000E+00      # mtau(pole)
    Block MINPAR                 # Input parameters
        1   1.750000000E+02      # m0
        2   7.000000000E+02      # m12
        3   1.000000000E+01      # tanb
        4   1.000000000E+00      # sign(mu)
        5   0.000000000E+00      # A0
    Block SUSEFLAV            # Algorithm specific inputs
     1   1.000000000E-03      # spectrum tolerance
     5   2.000000000E+00      # 2-loop running (1 = 1loop; 2 = 2loop)
     3   1.000000000E+00      # print Control (0 = do not print output; 1 = print output)
     2   1.000000000E+00      # Right handed neutrino (1 = yes; 0 = no)
     4   1.000000000E+00      # RHN mixing : 1 = ckm; 2 =PMNS; 3 = user defined
     7   1.000000000E+06      # MR1, Lightest rhn decoupling scale
     8   1.000000000E+09      # MR2, second lightest rhn decoupling scale
     9   1.000000000E+14      # MR3, Heaviest rhn decoupling scale
     10  0.000000000E+00      # Dirac neutrino mixing matrix 1,1
     11  0.000000000E+00      # Dirac neutrino mixing matrix 1,2
     12  0.000000000E+00      # Dirac neutrino mixing matrix 1,3
     13  0.000000000E+00      # Dirac neutrino mixing matrix 2,1
     14  0.000000000E+00      # Dirac neutrino mixing matrix 2,2
     15  0.000000000E+00      # Dirac neutrino mixing matrix 2,3
     16  0.000000000E+00      # Dirac neutrino mixing matrix 3,1
     17  0.000000000E+00      # Dirac neutrino mixing matrix 3,2
     18  0.000000000E+00      # Dirac neutrino mixing matrix 3,3

The corresponding SLHA output is generated in slha.out

    # Spectrum Output in SUSY Les Houches Accord 2
    # SuSeFLAV v1.2.0
    # D. Chowdhury, R. Garani and S. K. Vempati, hep-ph/1109.3551
    # For bug reports or any other queries please send email to<EMAIL_ADDRESS>    # Created on 12.06.2012 at 17:30 Hrs
    #
    BLOCK SPINFO  #  Program information
         1   SuSeFLAV     # Spectrum calculator
         2   1.2.0        # Version number
    #
    BLOCK MODSEL  #  MODEL NAME
         1      1   # mSUGRA
         3      4   # mSUGRA + RHN
         6      3   # Lepton and quark flavor is violated
    #
    BLOCK MINPAR  # Input parameters
             1     1.75000000E+02   #  m0
             2     7.00000000E+02   #  m_1/2
             3     1.00000000E+01   #  tanbeta(mz)
             4     1.00000000E+00   #  sign(mu)
             5     0.00000000E+00   #  A0
    #
    BLOCK SMINPUTS  # Standard Model inputs
             1     1.27934000E+02   # alpha_em (M_Z)^MSbar
             2     1.16639000E-05   # G_F [GeV^-2]
             3     1.17200000E-01   # alpha_S(M_Z)^MSbar
             4     9.11876000E+01   # M_Z pole mass
             5     4.23000000E+00   # mb(mb)^MSbar
             6     1.72700000E+02   # mt pole mass
             7     1.77000000E+00   # mtau pole mass
    #
    BLOCK EXTPAR  # Extra Input parameters
             0     1.97682880E+16   # Unification Scale
    #
    BLOCK MASS  # Mass Spectrum
    # PDG code           mass       particle
            24     8.05095481E+01   # W+
            25     1.16435226E+02   # h
            35     9.79136838E+02   # H
            36     9.78810446E+02   # A
            37     9.82557324E+02   # H+
       1000001     1.29049183E+03   # ~d_1
       1000003     1.33317083E+03   # ~d_2
       1000005     1.33782720E+03   # ~d_3
       2000001     1.33783952E+03   # ~d_4
       2000003     1.39947428E+03   # ~d_5
       2000005     1.39948751E+03   # ~d_6
       1000002     1.08957331E+03   # ~u_1
       1000004     1.32515013E+03   # ~u_2
       1000006     1.34374200E+03   # ~u_3
       2000002     1.34410204E+03   # ~u_4
       2000004     1.39733996E+03   # ~u_5
       2000006     1.39738676E+03   # ~u_6
       1000011     3.12007210E+02   # ~l_1
       1000013     3.18856813E+02   # ~l_2
       1000015     3.18880311E+02   # ~l_3
       2000011     4.94924639E+02   # ~l_4
       2000013     4.96469065E+02   # ~l_5
       2000015     4.96470193E+02   # ~l_6
       1000012     4.87191917E+02   # ~nu_1
       1000014     4.90375557E+02   # ~nu_2
       1000016     4.90381909E+02   # ~nu_3
       1000021     1.57599127E+03   # ~g
       1000022     2.89580143E+02   # ~chi_10
       1000023     5.44321259E+02   # ~chi_20
       1000025     8.58605742E+02   # ~chi_30
       1000035     8.69437471E+02   # ~chi_40
       1000024     5.33851586E+02   # ~chi_1+
       1000037     8.62050764E+02   # ~chi_2+
    #
    BLOCK NMIX  # Neutralino Mixing Matrix
      1  1     9.97666897E-01   # N_11
      1  2    -1.03658855E-02   # N_12
      1  3     6.20427374E-02   # N_13
      1  4    -2.65332008E-02   # N_14
      2  1     2.32098394E-02   # N_21
      2  2     9.80197789E-01   # N_22
      2  3    -1.61409861E-01   # N_23
      2  4     1.12340793E-01   # N_24
      3  1     2.46412419E-02   # N_31
      3  2    -3.55274833E-02   # N_32
      3  3    -7.04937074E-01   # N_33
      3  4    -7.07950795E-01   # N_34
      4  1    -5.92863909E-02   # N_41
      4  2     1.94531848E-01   # N_42
      4  3     6.87867194E-01   # N_43
      4  4    -6.96764815E-01   # N_44
    #
    BLOCK UMIX  # Chargino Mixing Matrix U
      1  1     9.74989137E-01   # U_11
      1  2    -2.22252520E-01   # U_12
      2  1     2.22252520E-01   # U_21
      2  2     9.74989137E-01   # U_22
    #
    BLOCK VMIX  # Chargino Mixing Matrix V
      1  1     9.88224902E-01   # V_11
      1  2    -1.53008313E-01   # V_12
      2  1     1.53008313E-01   # V_21
      2  2     9.88224902E-01   # V_22
    #
    BLOCK USQMIX  # squark Mixing Matrix
      1  1     1.10996359E-03   # USQMIX_11
      1  2    -5.26653686E-03   # USQMIX_12
      1  3     3.55285163E-01   # USQMIX_13
      1  4     8.74704256E-04   # USQMIX_14
      1  5    -4.21826454E-03   # USQMIX_15
      1  6     9.34732542E-01   # USQMIX_16
      2  1     1.12595131E-02   # USQMIX_21
      2  2    -5.57113248E-02   # USQMIX_22
      2  3     9.23559656E-01   # USQMIX_23
      2  4     2.86784533E-02   # USQMIX_24
      2  5    -1.38092429E-01   # USQMIX_25
      2  6    -3.52015712E-01   # USQMIX_26
      3  1     2.97503603E-05   # USQMIX_31
      3  2    -9.98459110E-05   # USQMIX_32
      3  3     1.03612223E-03   # USQMIX_33
      3  4     9.77509497E-01   # USQMIX_34
      3  5     2.10888527E-01   # USQMIX_35
      3  6    -3.57456096E-04   # USQMIX_36
      4  1     2.18713035E-03   # USQMIX_41
      4  2     2.22241357E-03   # USQMIX_42
      4  3     1.33658497E-01   # USQMIX_43
      4  4    -2.08919254E-01   # USQMIX_44
      4  5     9.67647238E-01   # USQMIX_45
      4  6    -4.62304107E-02   # USQMIX_46
      5  1     9.82212602E-01   # USQMIX_51
      5  2     1.87753700E-01   # USQMIX_52
      5  3    -9.34002684E-04   # USQMIX_53
      5  4     5.08408180E-04   # USQMIX_54
      5  5    -2.40125319E-03   # USQMIX_55
      5  6     2.35206342E-04   # USQMIX_56
      6  1    -1.87418278E-01   # USQMIX_61
      6  2     9.80618229E-01   # USQMIX_62
      6  3     5.42538107E-02   # USQMIX_63
      6  4     2.10966003E-03   # USQMIX_64
      6  5    -9.57981337E-03   # USQMIX_65
      6  6    -1.49190697E-02   # USQMIX_66
    #
    BLOCK DSQMIX  # squark Mixing Matrix
      1  1     7.97027235E-03   # DSQMIX_11
      1  2    -3.83864371E-02   # DSQMIX_12
      1  3     9.76209913E-01   # DSQMIX_13
      1  4    -1.04373101E-05   # DSQMIX_14
      1  5    -2.41872348E-04   # DSQMIX_15
      1  6     2.13253615E-01   # DSQMIX_16
      2  1    -2.81490374E-03   # DSQMIX_21
      2  2     1.35643992E-02   # DSQMIX_22
      2  3    -2.12865830E-01   # DSQMIX_23
      2  4     1.79277418E-05   # DSQMIX_24
      2  5     9.89907963E-04   # DSQMIX_25
      2  6     9.76982723E-01   # DSQMIX_26
      3  1     6.10926291E-06   # DSQMIX_31
      3  2     5.89431513E-03   # DSQMIX_32
      3  3     6.86044622E-04   # DSQMIX_33
      3  4    -2.59132138E-05   # DSQMIX_34
      3  5     9.99981946E-01   # DSQMIX_35
      3  6    -9.45553891E-04   # DSQMIX_36
      4  1     2.96437790E-04   # DSQMIX_41
      4  2    -7.98684964E-07   # DSQMIX_42
      4  3     1.15232653E-05   # DSQMIX_43
      4  4     9.99999956E-01   # DSQMIX_44
      4  5     2.58944876E-05   # DSQMIX_45
      4  6    -1.50004569E-05   # DSQMIX_46
      5  1    -1.75678721E-01   # DSQMIX_51
      5  2     9.83552600E-01   # DSQMIX_52
      5  3     4.12376560E-02   # DSQMIX_53
      5  4     5.24615573E-05   # DSQMIX_54
      5  5    -5.82957991E-03   # DSQMIX_55
      5  6    -5.17098306E-03   # DSQMIX_56
      6  1     9.84411220E-01   # DSQMIX_61
      6  2     1.75875037E-01   # DSQMIX_62
      6  3    -1.15326259E-03   # DSQMIX_63
      6  4    -2.91633802E-04   # DSQMIX_64
      6  5    -1.04177570E-03   # DSQMIX_65
      6  6     1.44250146E-04   # DSQMIX_66
    #
    BLOCK SELMIX  # Slepton Mixing Matrix
      1  1     1.05172917E-05   # SELMIX_11
      1  2    -5.07243990E-05   # SELMIX_12
      1  3     1.03659288E-01   # SELMIX_13
      1  4     6.00795431E-08   # SELMIX_14
      1  5    -1.11136067E-05   # SELMIX_15
      1  6     9.94612864E-01   # SELMIX_16
      2  1    -3.08963419E-08   # SELMIX_21
      2  2     6.24290695E-03   # SELMIX_22
      2  3    -2.02732368E-06   # SELMIX_23
      2  4    -6.78386431E-09   # SELMIX_24
      2  5     9.99980513E-01   # SELMIX_25
      2  6     1.17032561E-05   # SELMIX_26
      3  1     2.98889602E-05   # SELMIX_31
      3  2    -6.33346635E-11   # SELMIX_32
      3  3     1.18627921E-08   # SELMIX_33
      3  4     1.00000000E+00   # SELMIX_34
      3  5     6.78606456E-09   # SELMIX_35
      3  6    -6.19572827E-08   # SELMIX_36
      4  1     9.84024127E-03   # SELMIX_41
      4  2    -4.73545901E-02   # SELMIX_42
      4  3     9.93448538E-01   # SELMIX_43
      4  4    -3.12319765E-07   # SELMIX_44
      4  5     2.98862230E-04   # SELMIX_45
      4  6    -1.03540457E-01   # SELMIX_46
      5  1     9.99950259E-01   # SELMIX_51
      5  2     2.09161645E-03   # SELMIX_52
      5  3    -9.70065714E-03   # SELMIX_53
      5  4    -2.98872962E-05   # SELMIX_54
      5  5    -1.30585027E-05   # SELMIX_55
      5  6     1.00054245E-03   # SELMIX_56
      6  1    -1.62739211E-03   # SELMIX_61
      6  2     9.98856442E-01   # SELMIX_62
      6  3     4.71237978E-02   # SELMIX_63
      6  4     4.78864799E-08   # SELMIX_64
      6  5    -6.23573698E-03   # SELMIX_65
      6  6    -4.86038870E-03   # SELMIX_66
    #
    BLOCK SNUMIX  # Sneutrino Mixing Matrix
      1  1     4.85609162E-03   # SNUMIX_11
      1  2    -2.34212181E-02   # SNUMIX_12
      1  3     9.99713892E-01   # SNUMIX_13
      2  1    -5.74301350E-02   # SNUMIX_21
      2  2     9.98069089E-01   # SNUMIX_22
      2  3     2.36616496E-02   # SNUMIX_23
      3  1     9.98337717E-01   # SNUMIX_31
      3  2     5.75286069E-02   # SNUMIX_32
      3  3    -3.50163123E-03   # SNUMIX_33
    #
    BLOCK ALPHA  # Higgs mixing
              -1.05473355E-01   # Mixing angle in the neutral Higgs boson sector
    #
    BLOCK HMIX Q=  1.20195104E+03  # DRbar Higgs Parameters
         1     8.50892351E+02   # mu(Q)
         2     9.63860969E+00   # tanbeta(Q)
         3     2.43818892E+02   # vev(Q)
         4     9.93075833E+05   # MA^2(Q)
    #
    BLOCK GAUGE Q=  1.20195104E+03  # The gauge couplings
         1     3.62957251E-01   # gprime(Q) DRbar
         2     6.42610014E-01   # g(Q) DRbar
         3     1.04880243E+00   # g_3(Q) DRbar
    #
    BLOCK TU Q=  1.20195104E+03  # The trilinear couplings
      1  1    -1.26688884E-01   # TURG_11
      1  2    -2.93067837E-02   # TURG_12
      1  3    -3.97143909E-04   # TURG_13
      2  1     2.93036897E+01   # TURG_21
      2  2    -1.26686864E+02   # TURG_22
      2  3    -5.37734251E+00   # TURG_23
      3  1    -1.11137936E+02   # TURG_31
      3  2     5.35228445E+02   # TURG_32
      3  3    -1.29451330E+04   # TURG_33
    #
    BLOCK TD Q=  1.20195104E+03  # The trilinear couplings
      1  1    -6.05492867E+00   # TDRG_11
      1  2    -1.02056677E-04   # TDRG_12
      1  3     2.38753240E-03   # TDRG_13
      2  1    -2.04113446E-03   # TDRG_21
      2  2    -1.21088577E+02   # TDRG_22
      2  3    -2.29965104E-01   # TDRG_23
      3  1     1.22702682E+00   # TDRG_31
      3  2    -5.90930668E+00   # TDRG_32
      3  3    -2.95665819E+03   # TDRG_33
    #
    BLOCK TE Q=  1.20195104E+03  # The trilinear couplings
      1  1    -1.44939639E-01   # TERG_11
      1  2    -2.31067898E-08   # TERG_12
      1  3    -4.08400006E-07   # TERG_13
      2  1    -4.82631701E-06   # TERG_21
      2  2    -3.02751406E+01   # TERG_22
      2  3     4.10638455E-04   # TERG_23
      3  1    -1.53360878E-03   # TERG_31
      3  2     7.38111171E-03   # TERG_32
      3  3    -5.16767721E+02   # TERG_33
    #
    BLOCK YU Q=  1.20195104E+03  # The top Yukawa coupling
      1  1     6.44039888E-06   # YU_11
      1  2     1.48968552E-06   # YU_12
      1  3     2.41182558E-08   # YU_13
      2  1    -1.48971566E-03   # YU_21
      2  2     6.44041987E-03   # YU_22
      2  3     2.72567759E-04   # YU_23
      3  1     7.22768067E-03   # YU_31
      3  2    -3.48078574E-02   # YU_32
      3  3     8.43790071E-01   # YU_33
    #
    BLOCK YD Q=  1.20195104E+03  # The down Yukawa coupling
      1  1     2.53400760E-04   # YD_11
      1  2    -1.10093360E-09   # YD_12
      1  3     2.56831364E-08   # YD_13
      2  1    -2.20186781E-08   # YD_21
      2  2     5.06812345E-03   # YD_22
      2  3    -2.47377375E-06   # YD_23
      3  1     1.31978305E-05   # YD_31
      3  2    -6.35600675E-05   # YD_32
      3  3     1.31856452E-01   # YD_33
    #
    BLOCK YE Q=  1.20195104E+03  # The tau Yukawa coupling
      1  1     2.77703519E-05   # YE_11
      1  2    -1.17975032E-11   # YE_12
      1  3     4.03483137E-10   # YE_13
      2  1    -2.46439380E-09   # YE_21
      2  2     5.80081939E-03   # YE_22
      2  3    -4.05872732E-07   # YE_23
      3  1     1.45732796E-06   # YE_31
      3  2    -7.01783388E-06   # YE_32
      3  3     9.96765043E-02   # YE_33
    #
    BLOCK MSOFT Q=  1.20195104E+03  # soft SUSY breaking masses at scale Q
             1     2.95504689E+02   # M_1
             2     5.45936065E+02   # M_2
             3     1.53262491E+03   # M_3
            21     2.14879878E+05   # M^2_Hd
            22    -6.96254426E+05   # M^2_Hu
            31     4.94404728E+02   # M_eL
            32     4.94396817E+02   # M_muL
            33     4.91242768E+02   # M_tauL
            34     3.15861187E+02   # M_eR
            35     3.15846380E+02   # M_muR
            36     3.11472426E+02   # M_tauR
            41     1.39829222E+03   # M_q1L
            42     1.39811849E+03   # M_q2L
            43     1.29136113E+03   # M_q3L
            44     1.34421791E+03   # M_uR
            45     1.34420302E+03   # M_cR
            46     1.11340022E+03   # M_tR
            47     1.33760077E+03   # M_dR
            48     1.33759064E+03   # M_sR
            49     1.33101944E+03   # M_bR
    #
    BLOCK MSQ2 Q=  1.20195104E+03  # M^2_Q soft SUSY breaking masses
      1  1     1.95522114E+06   # mSQRG_11
      1  2     1.03013845E+02   # mSQRG_12
      1  3    -2.38957910E+03   # mSQRG_13
      2  1     1.03013845E+02   # mSQRG_21
      2  2     1.95473530E+06   # mSQRG_22
      2  3     1.15080756E+04   # mSQRG_23
      3  1    -2.38957910E+03   # mSQRG_31
      3  2     1.15080756E+04   # mSQRG_32
      3  3     1.66761356E+06   # mSQRG_33
    #
    BLOCK MSU2 Q=  1.20195104E+03  # M^2_U soft SUSY breaking masses
      1  1     1.80692178E+06   # mSURG_11
      1  2    -5.84935042E-06   # mSURG_12
      1  3    -1.19615520E-02   # mSURG_13
      2  1    -5.84935042E-06   # mSURG_21
      2  2     1.80688177E+06   # mSURG_22
      2  3     4.19949204E+00   # mSURG_23
      3  1    -1.19615520E-02   # mSURG_31
      3  2     4.19949204E+00   # mSURG_32
      3  3     1.23966005E+06   # mSURG_33
    #
    BLOCK MSD2 Q=  1.20195104E+03  # M^2_D soft SUSY breaking masses
      1  1     1.78917582E+06   # mSDRG_11
      1  2    -9.47987536E-06   # mSDRG_12
      1  3     5.70618349E-03   # mSDRG_13
      2  1    -9.47987536E-06   # mSDRG_21
      2  2     1.78914873E+06   # mSDRG_22
      2  3    -5.49615942E-01   # mSDRG_23
      3  1     5.70618349E-03   # mSDRG_31
      3  2    -5.49615942E-01   # mSDRG_32
      3  3     1.77161275E+06   # mSDRG_33
    #
    BLOCK MSL2 Q=  1.20195104E+03  # M^2_L soft SUSY breaking masses
      1  1     2.44436035E+05   # mSLRG_11
      1  2     7.11764708E-01   # mSLRG_12
      1  3    -1.51306954E+01   # mSLRG_13
      2  1     7.11764708E-01   # mSLRG_21
      2  2     2.44428213E+05   # mSLRG_22
      2  3     7.28699498E+01   # mSLRG_23
      3  1    -1.51306954E+01   # mSLRG_31
      3  2     7.28699498E+01   # mSLRG_32
      3  3     2.41319457E+05   # mSLRG_33
    #
    BLOCK MSE2 Q=  1.20195104E+03  # M^2_E soft SUSY breaking masses
      1  1     9.97682891E+04   # mSERG_11
      1  2     6.08801261E-09   # mSERG_12
      1  3     1.01423906E-05   # mSERG_13
      2  1     6.08801261E-09   # mSERG_21
      2  2     9.97589360E+04   # mSERG_22
      2  3     1.15378509E-03   # mSERG_23
      3  1     1.01423906E-05   # mSERG_31
      3  2     1.15378509E-03   # mSERG_32
      3  3     9.70150720E+04   # mSERG_33
    #
    BLOCK SuSeFLAVLOWENERGY   #  PARAMETERS
             1     3.39444376E-03   # Delta rho parameter
             2     5.11182018E-10   # g_mu - 2
             3     3.73074715E-04   # Br(b -> s gamma)
             4     1.70603079E-13   # Br(tau -> mu gamma)
             5     7.32782350E-15   # Br(tau -> e gamma)
             6     9.20566951E-17   # Br(mu -> e gamma)
             7     5.43318338E-16   # Br(tau -> mu mu mu)
             8     8.82689326E-17   # Br(tau -> e e e)
             9     6.80189300E-19   # Br(mu -> e e e)
    #
    BLOCK FINETUNE  #
             1     1.75230800E+02   # delta mZ^2/mZ^2 (mu^2)
             2     8.76436259E+01   # delta mt/mt (mu^2)

The program prints BLOCK SELMIX in the SLHA output, which contains the
elements of the tree level $6\times 6$ slepton mixing matrix. The notation and
the method of diagonalization is explained in more detail in the A.

####  7.1.2 Non-SLHA Interface

The source file for non-SLHA input is runonce.f. To use the traditional
SuSeFLAV interface the user should execute suseflav by modifying the
corresponding input file. This executable takes the following input files,
sinputs.in for mSUGRA/CMSSM models, sinputs-gmsb.in for GMSB models, sinputs-
nuhm.in for non-universal higgs model (NUHM2) models and sinputs-cnum.in for
complete non-universal models. For example, to run the program with complete
non-universal boundary conditions type the following command in the terminal
./suseflav <sinputs-cnum.in
The sample input/output below corresponds to 10.4.4 of [101] with Type-I see-
saw mechanism with minimal mixing in the context of mSUGRA/CMSSM scenario. To
execute the program for the sample point type the following command in the
terminal

./suseflav <sinputs.in

      mSUG           # MODEL name
      1              # prinstat (1 for printing output on terminal, 0 otherwise)
      1.00000E+01    # tanbeta
      5.00000E+02    # m0
      0.00000E+00    # a0
      1.05000E+03    # M1/2
      1.00000E+00    # sgn(mu)
      1.16639E-05    # G_fermi
      1.27934E+02    # alpha_em^(-1)
      1.17200E-01    # alpha_strong
      9.11876E+01    # mz_pole
      2              # one loop or two loops
      1              # quark mixing
      1              # 1= rhn on; 0 = rhn off
      CKM            # case: CKM/MNS/USD
      1.00000E-03    # spectrum tolerance
      1.72700E+02    # Mtpole
      4.23000E+00    # Mbpole
      1.77000E+00    # Mtaupole
      1.00000E+06    # MR1
      1.00000E+09    # MR2
      1.00000E+14    # MR3
      0.00000E+00    # Ynu(1,1)
      0.00000E+00    # Ynu(1,2)
      0.00000E+00    # Ynu(1,3)
      0.00000E+00    # Ynu(2,1)
      0.00000E+00    # Ynu(2,2)
      0.00000E+00    # Ynu(2,3)
      0.00000E+00    # Ynu(3,1)
      0.00000E+00    # Ynu(3,2)
      0.00000E+00    # Ynu(3,3)
      ------------------------------------------------

The Output in SuSeFLAV format is contained in the file suseflav.out.

     ******** Begin Program SuSeFLAV ************
               model =    mSUG
                loop =    2
             tanbeta =    1.0000E+01
                 m0  =    5.0000E+02
                 a0  =    0.0000E+00
                 M12 =    1.0500E+03
                 m10 =    5.0000E+02
                 m20 =    5.0000E+02
             sign mu =    1.0000E+00
                qmix =    1
       top pole mass =    1.7270E+02
                 rhn =    1
                case =    CKM
                 MR1 =    1.0000E+06
                 MR2 =    1.0000E+09
                 MR3 =    1.0000E+14
     ********************************************

      up-type yukawa at high energy:
         2.6401E-06    6.1056E-07    1.2205E-08
        -6.1068E-04    2.6401E-03    1.1119E-04
         3.8672E-03   -1.8624E-02    4.5212E-01

      down-type yukawa at high energy:
         7.9987E-05   -3.1319E-09    7.4082E-08
        -6.2638E-08    1.6000E-03   -7.1355E-06
         3.7936E-05   -1.8270E-04    4.5575E-02

      lepton-type yukawa at high energy:
         1.7539E-05   -1.3061E-10    3.1014E-09
        -2.7282E-08    3.6638E-03   -3.1200E-06
         1.1175E-05   -5.3817E-05    6.4558E-02

      neutrino yukawa at high energy:
         3.1809E-06    7.3564E-07    1.4835E-08
        -7.3579E-04    3.1810E-03    1.3396E-04
         4.7106E-03   -2.2686E-02    5.5081E-01

      up-type yukawa at msusy :
         6.3637E-06    1.4719E-06    2.3911E-08
        -1.4720E-03    6.3637E-03    2.6931E-04
         7.1199E-03   -3.4289E-02    8.3124E-01

      down-type yukawa at msusy :
         2.4935E-04   -1.2210E-09    2.8477E-08
        -2.4420E-08    4.9870E-03   -2.7429E-06
         1.4571E-05   -7.0171E-05    1.2939E-01

      lepton-type yukawa at msusy :
         2.7626E-05   -1.0563E-11    3.7615E-10
        -2.2066E-09    5.7706E-03   -3.7838E-07
         1.3609E-06   -6.5535E-06    9.9328E-02

      Spectrum at msusy, q =   1.7679E+03
                  alpha_1  =   3.6366E-01
                  alpha_2  =   6.4050E-01
                  alpha_3  =   1.0297E+00
                   vev1    =   2.5253E+01
                   vev2    =   2.4230E+02
               newtbeta    =   9.5948E+00
                      \mu  =   1.2105E+03
                  ~gluino  =   2.3009E+03
                   ~stop_1 =   1.6702E+03
                   ~stop_2 =   1.9889E+03
                 ~scharm_R =   2.0550E+03
                 ~scharm_L =   2.1380E+03
                    ~sup_R =   2.0550E+03
                    ~sup_L =   2.1383E+03
               ~sbottom_1  =   1.9606E+03
               ~sbottom_2  =   2.0368E+03
               ~sstrange_R =   2.0460E+03
               ~sstrange_L =   2.1394E+03
                 ~sdown_R  =   2.0461E+03
                 ~sdown_L  =   2.1396E+03
                   ~stau_1 =   6.3321E+02
                   ~stau_2 =   8.5289E+02
                   ~smu_R  =   6.4202E+02
                   ~smu_L  =   8.6003E+02
                  ~sel_R   =   6.4206E+02
                  ~sel_L   =   8.6012E+02
                  ~tausnu  =   8.4727E+02
                    ~musnu =   8.5526E+02
                    ~elsnu =   8.5520E+02

     Higgs Spectrum
                     mA0   =   1.4726E+03
                mh_charged =   1.4754E+03
                     mh0   =   1.1866E+02
                      mH   =   1.4730E+03
                \alpha_h   =  -1.0481E-01

     Neutralino spectrum
                      N1   =   4.4421E+02
                      N2   =   8.3081E+02
                      N3   =   1.2193E+03
                      N4   =   1.2280E+03

     Chargino spectrum
                      C1   =   8.1458E+02
                      C2   =   1.2179E+03

      Low Energy Observables
       Fine tuning, Cmz^2mu^2   =    3.5356E+02
       Fine tuning, Cmt^2mu^2   =    1.7680E+02
            Br(B  => s,gamma)   =    3.8430E-04
           Br(mu  => e,gamma)   =    3.1044E-06 X 10^(-11)
           Br(tau => mu,gamma)  =    5.9654E-06 X 10^(-08)
           Br(tau => e,gamma)   =    2.5629E-08 X 10^(-07)
             Br(tau => e,e,e)   =    3.0580E-10 X 10^(-07)
          Br(tau => mu,mu,mu)   =    1.8321E-09 X 10^(-07)
              Br(mu => e,e,e)   =    2.2577E-07 X 10^(-12)
            Br(mu => e in Ti)   =    2.0425E-06 X 10^(-12)
                (g_mu - 2)      =    1.8491E+00 X 10^(-10)

     -----------------------------

     flag for the point is  AOK
     --------------------------------------------------
     FLAGS AND THEIR MEANINGS
     AOK = Everything is fine.
     BMUNEG = B_mu is negative at Msusy.
     REWSB = |\mu|^2 < 0 at Msusy.
     MUNOC = Non-convergent |\mu| at Msusy.
     SW2NOC = Non-convergent Sin^2_thetaw at Mz.
     TACSPEC = Spectrum is tachyonic at Msusy.
     NPERTYUK = Non-perturbative yukawa.
     TACSPECMZ = Spectrum is tachyonic at Mz.
     FSNC = Final spectrum non-convergent.
     TACMh = Lightest CP-even neutral higgs tachyonic.
     TACMH = Heaviest CP-even neutral higgs tachyonic.
     TACMA = CP-odd neutral higgs tachyonic.
     TACMHCH = Charged higgs tachyonic.
     VARUNDER = Stepsize is zero while integrating the RGEs.
     TACSUP = SUP sector tachyonic.
     TACSDN = SDOWN sector tachyonic.
     TACSLP = SLEPTON sector tachyonic.
     TACSNU = SNEUTRINO sector tachyonic.
     LEPH = Lightest higgs mass below LEP limit.
     LEPC = Lightest chargino mass < 103.5 GeV.
     LSPSTAU = Lightest stau is LSP.
     --------------------------------------------------

##  8 Outlook

The MEG experiment has recently reported the latest limits on the rare
leptonic decay $\mu\to e+\gamma$ [89]. Simultaneously, there are results from
LHC as well as direct detection dark matter experiments. SuSeFLAV is designed
to compute supersymmetric spectrum with full flavor violation and further to
compute most of the leptonic flavor violating observables. The program can be
coupled to Dark Matter routines such as MicrOMEGAs [102], DarkSUSY [103] and
SuperIso [31] to compute the relic density and direct detection rates. The
program is free under the GNU Public License and can be downloaded from the
following websites:

  * 1.

http://cts.iisc.ernet.in/Suseflav/main.html

  * 2.

http://projects.hepforge.org/suseflav/

In the present version of the program only Type-I seesaw mechanism is
implemented. Future versions will include other seesaw mechanisms as well as
other improvements like inclusion new flavor violating decays rates in the
quark sector.

## Acknowledgments

We appreciate discussions with and acknowledge suggestions from L. Calibbi, S.
Kraml, W. Porod and O. Vives. We thank D. Grellscheid, T. Hahn and P. Slavich
for important inputs. We thank U. Chattopadhyaya, Aseshkrishna Dutta and M.
Guchait for encouragement. SKV thanks M. Ciuchini, A. Faccia, A. Masiero, P.
Paradisi and L. Silvestrini for collaborations during which parts of this
program were written. We thank Ketan Patel, Brandon Murakami for reporting
bugs. SKV acknowledges support from DST project “Complementarity between
direct and indirect searches for Supersymmetry” and also support from DST
Ramanujan Fellowship SR/S2/RJN-25/2008. RG acknowledges support from
SR/S2/RJN-25/2008. DC acknowledges partial support from SR/S2/RJN-25/2008.

##  Appendix A Tree-Level Masses

Here we suppress any gauge indices and follow the notation of BPMZ111111Except
in our case the sign of $\mu$ parameter is opposite of BPMZ. [70] closely. The
Lagrangian contains the neutralino mass matrix as

${-\frac{1}{2}{\tilde{\psi}^{0\,T}}{\cal
M}_{\tilde{\psi}^{0}}\tilde{\psi}^{0}+h.c.\,,}$ (52)

where $\tilde{\psi}^{0}=$ $(\widetilde{B},$ $\widetilde{W}^{0},$
$\widetilde{H}_{d},$ $\widetilde{H}_{u})^{T}$ and

${\cal M}_{\tilde{\psi}^{0}}\ =\
\left(\begin{array}[]{cccc}M_{1}&0&-M_{Z}c_{\beta}s_{W}&M_{Z}s_{\beta}s_{W}\\\
0&M_{2}&M_{Z}c_{\beta}c_{W}&-M_{Z}s_{\beta}c_{W}\\\
-M_{Z}c_{\beta}s_{W}&M_{Z}c_{\beta}c_{W}&0&-\mu\\\
M_{Z}s_{\beta}s_{W}&-M_{Z}s_{\beta}c_{W}&-\mu&0\end{array}\right).$ (53)

We use the letter $s$ and $c$ for sine and cosine, so that
$s_{\beta}\equiv\sin\beta,\ c_{\beta}\equiv\cos\beta$ and $s_{W}(c_{W})$ is
the sine (cosine) of the weak mixing angle. The $4\times 4$ neutralino mixing
matrix is an orthogonal matrix $O$ with real entries, such that $O^{T}{\cal
M}_{\widetilde{\psi}^{0}}O$ is diagonal. The neutralinos $\chi^{0}_{i}$ are
defined such that their absolute masses increase with increasing $i$. Some of
their mass values can be negative.

We make the identification ${\widetilde{W}}^{\pm}=({\widetilde{W}^{1}}\mp
i{\widetilde{W}^{2}})/\sqrt{2}$ for the charged winos and
${\widetilde{H}_{u}^{+}},{\widetilde{H}_{d}^{-}}$ for the charged higgsinos.
The Lagrangian contains the chargino mass matrix as

$-\frac{1}{2}{\widetilde{\psi}^{-\,T}}{\cal
M}_{\widetilde{\psi}^{+}}\widetilde{\psi}^{+}+h.c.,$ (54)

where $\widetilde{\psi}^{+}=(\widetilde{W}^{+},\ \widetilde{H}_{u}^{+})^{T},\
\widetilde{\psi}^{-}=(\widetilde{W}^{-},\ \widetilde{H}_{d}^{-})^{T}$ and

${\cal M}_{\tilde{\psi}^{+}}\ =\
\left(\begin{array}[]{cc}M_{2}&\sqrt{2}\,M_{W}s_{\beta}\\\
\sqrt{2}\,M_{W}c_{\beta}&\mu\end{array}\right).$ (55)

The chargino masses are found by acting on the matrix ${\cal
M}_{\tilde{\psi}^{+}}$ with a bi-unitary transformation, so that $U^{*}{\cal
M}_{\tilde{\psi}^{+}}V^{\dagger}$ is a diagonal matrix containing the two
chargino mass eigenvalues, $m_{\tilde{\chi}_{i}^{+}}$. The matrices $U$ and
$V$ are easily found, as they diagonalize, respectively, the matrices ${\cal
M}_{\tilde{\psi}^{+}}^{*}{\cal M}_{\tilde{\psi}^{+}}^{\rm T}$ and ${\cal
M}_{\tilde{\psi}^{+}}^{\dagger}{\cal M}_{\tilde{\psi}^{+}}$. And we have taken
the $U$ and $V$ matrices to be real.

The tree-level squark and slepton mass squared values for the family $i$ are
found by diagonalizing the following mass matrices
${\mathcal{M}}_{\tilde{f}}^{2}$ defined in the
$({\tilde{f}}_{iL},{\tilde{f}}_{iR})^{T}$ basis:

$\left(\begin{array}[]{cc}(m_{\tilde{Q}}^{2})_{ii}+m_{u_{i}}^{2}+\left(\frac{1}{2}-\frac{2}{3}s_{W}^{2}\right)M_{Z}^{2}c_{2\beta}&m_{u_{i}}\left(({\tilde{A}}_{\tilde{u}})_{ii}-\mu\cot\beta\right)\\\
m_{u_{i}}\left(({\tilde{A}}_{\tilde{u}})_{ii}-\mu\cot\beta\right)&(m^{2}_{\tilde{u}})_{ii}+m_{u_{i}}^{2}+\frac{2}{3}s_{W}^{2}M_{Z}^{2}c_{2\beta}\end{array}\right)\
,$ (56)
$\left(\begin{array}[]{cc}(m_{\tilde{Q}}^{2})_{ii}+m_{d_{i}}^{2}-\left(\frac{1}{2}-\frac{1}{3}s_{W}^{2}\right)M_{Z}^{2}c_{2\beta}&m_{d_{i}}\left(({\tilde{A}}_{\tilde{d}})_{ii}-\mu\tan\beta\right)\\\
m_{d_{i}}\left(({\tilde{A}}_{\tilde{d}})_{ii}-\mu\tan\beta\right)&(m^{2}_{\tilde{d}})_{ii}+m_{d_{i}}^{2}-\frac{1}{3}s_{W}^{2}M_{Z}^{2}c_{2\beta}\end{array}\right)\
,$ (57)
$\Biggl{(}\begin{array}[]{cc}(m_{\tilde{L}}^{2})_{ii}+m_{e_{i}}^{2}-\left(\frac{1}{2}-s_{W}^{2}\right)M_{Z}^{2}c_{2\beta}&m_{e_{i}}\left(({\tilde{A}}_{\tilde{e}})_{ii}-\mu\tan\beta\right)\\\
m_{e_{i}}\left(({\tilde{A}}_{\tilde{e}})_{ii}-\mu\tan\beta\right)&(m^{2}_{\tilde{e}})_{ii}+m_{e_{i}}^{2}-s_{W}^{2}M_{Z}^{2}c_{2\beta}\end{array}\Biggr{)}\
,$ (58)

where, $m_{f},e_{f}$ are the mass and electric charge of fermion $f$
respectively. The mixing of the first two families is suppressed by a small
fermion mass, which we approximate to zero. The sfermion mass eigenstates are
given by

$\left(\begin{array}[]{cc}m^{2}_{\tilde{f}_{1}}&0\\\
0&m^{2}_{\tilde{f}_{2}}\end{array}\right)=\left(\begin{array}[]{cc}c_{f}&s_{f}\\\
-s_{f}&c_{f}\end{array}\right){\mathcal{M}}_{\tilde{f}}^{2}\left(\begin{array}[]{cc}c_{f}&-s_{f}\\\
s_{f}&c_{f}\end{array}\right)$ (59)

where $c_{f}$ is the cosine of the sfermion mixing angle, $\cos\theta_{f}$,
and $s_{f}$ is $\sin\theta_{f}$. These angles are given by

$\displaystyle\tan(2\theta_{u})$ $\displaystyle=$
$\displaystyle\frac{2\,m_{u}\left({\tilde{A}}_{\tilde{u}}-\mu\cot\beta\right)}{m_{\tilde{Q}}^{2}-m_{\tilde{u}}^{2}+\left({\frac{1}{2}}-2\,e_{u}\,s_{W}^{2}\right)M_{Z}^{2}c_{2\beta}}\
,$ (60) $\displaystyle\tan(2\theta_{d})$ $\displaystyle=$
$\displaystyle\frac{2\,m_{d}\left({\tilde{A}}_{\tilde{d}}-\mu\tan\beta\right)}{m_{\tilde{Q}}^{2}-m_{\tilde{d}}^{2}+\left(-{\frac{1}{2}}-2\,e_{d}\,s_{W}^{2}\right)M_{Z}^{2}c_{2\beta}}\
.$ (61)

To calculate the lepton flavor violating decays, we diagonalize the full
$6\times 6$ sleptonic mass matrix (${\cal M}^{2}_{\tilde{l}}$) by $U^{T}\
{\cal M}^{2}_{\tilde{l}}\ U$, where $U$ is the sleptonic mixing matrix with
real entries. In the gauge basis of
$\left\\{\tilde{e}_{L},\tilde{\mu}_{L},\tilde{\tau}_{L},\tilde{e}_{R},\tilde{\mu}_{R},\tilde{\tau}_{R}\right\\}^{T}$
the sleptonic mass matrix is defined as

${\cal M}^{2}_{\tilde{l}}\ =\ \begin{pmatrix}{\bf
m}_{\tilde{L}}^{2}+\left[m_{e_{i}}^{2}-\left(\frac{1}{2}-s_{W}^{2}\right)M_{Z}^{2}c_{2\beta}\right]{\bf
1}&m_{e_{i}}\left({\tilde{\bf A}}_{\tilde{e}}-\mu\tan\beta\;{\bf 1}\right)\\\
m_{e_{i}}\left({\tilde{\bf A}}^{T}_{\tilde{e}}-\mu\tan\beta\ {\bf
1}\right)&{\bf
m}^{2}_{\tilde{e}}+\left[m_{e_{i}}^{2}-s_{W}^{2}M_{Z}^{2}c_{2\beta}\right]{\bf
1}\end{pmatrix}\ ,$ (62)

where ${\bf m}_{\tilde{L}}^{2}$, ${\bf m}^{2}_{\tilde{e}}$ and ${\tilde{\bf
A}}_{\tilde{e}}$ are the scalar mass matrices and tri-linear coupling matrix
respectively. Using the full $6\times 6$ sleptonic mixing matrix we define the
lepton flavor violating couplings following Hisano et al. [14]. With these
couplings we calculate the rare lepton flavor violating decays as described in
section 6.

Given values for $\tan\beta$ one can write the CP-odd Higgs-boson mass,
$m_{A}$, and the other Higgs masses at tree level by

$m_{A}^{2}=\frac{2B_{\mu}}{\sin
2\beta}=2|\mu|^{2}+m^{2}_{H_{u}}+m^{2}_{H_{d}}\ ,$ (63) $m_{H,h}^{2}\ =\
\frac{1}{2}\Biggl{(}m_{A}^{2}+M_{Z}^{2}\pm\sqrt{\left(m_{A}^{2}+M_{Z}^{2}\right)^{2}-4m_{A}^{2}M_{Z}^{2}c_{2\beta}^{2}}\Biggr{)}\
,$ (64)

and

$m_{H^{\pm}}^{2}\ =\ m_{A}^{2}\ +\ M_{W}^{2}\ .$ (65)

The CP-even gauge eigenstates $(H^{0}_{d},\,H^{0}_{u})$ are rotated by the
angle $\alpha$ into the mass eigenstates $(H,\,h)$ as follows,

$\frac{1}{\sqrt{2}}\left(\begin{array}[]{c}H\\\\[5.69054pt]
h\end{array}\right)\ =\
\left(\begin{array}[]{cc}c_{\alpha}&s_{\alpha}\\\\[5.69054pt]
-s_{\alpha}&c_{\alpha}\end{array}\right)\left(\begin{array}[]{c}\mathfrak{Re}H^{0}_{d}\\\\[5.69054pt]
\mathfrak{Re}H^{0}_{u}\end{array}\right)~{}.$ (66)

At tree level, the angle $\alpha$ is given by

$\tan 2\alpha\ =\ \frac{m_{A}^{2}+M_{Z}^{2}}{m_{A}^{2}-M_{Z}^{2}}\tan 2\beta\
.$ (67)

##  Appendix B One Loop Threshold Corrections

We compute flavor conserving complete one-loop corrections to masses and
couplings in MSSM following BPMZ [70]. In this appendix we present the summary
of one-loop corrections implemented in SuSeFLAV.

  * 1.

Quarks and Leptons

The corrections to fermions are evaluated at the weak scale. The running
masses $m_{\hat{f}}$ are related to the corresponding $\overline{DR}$ masses
by the expression

$m_{f}=m_{\hat{f}}-\Sigma_{f}^{BPMZ}(m^{2}_{f})$ (68)

Where, $\Sigma_{f}^{BPMZ}(m^{2}_{f})$ is the one loop self-energy of the
fermion $f$. We follow equation D.18 of BPMZ [70]. At the present version of
SuSeFLAV we add the correction only to the third generation fermions.

  * 2.

W and Z Bosons

Corrections to W and Z bosons are evaluated at the weak scale as well as EWSB
scale. The $\overline{DR}$ running W and Z boson mass squared at the scale $Q$
($\hat{M}_{Z}^{2}(Q)$ and $\hat{M}_{W}^{2}(Q)$) are related to the physical
pole mass of gauge bosons as follows

$\displaystyle M_{Z}^{2}$ $\displaystyle=$ $\displaystyle\hat{M}_{Z}^{2}(Q)\
-\ \Pi^{T}_{ZZ}(M_{Z}^{2})$ (69) $\displaystyle M_{W}^{2}$ $\displaystyle=$
$\displaystyle\hat{M}_{W}^{2}(Q)\ -\ \Pi^{T}_{WW}(M_{W}^{2})$ (70)

Where, $\Pi^{T}_{ZZ}(M_{Z}^{2})$ and $\Pi^{T}_{WW}(M_{W}^{2})$ are the
transverse part of self energy terms. Consult appendix D of BPMZ [70] for
detailed discussion and the complete expression of the self energy terms.

  * 3.

sQuarks and sLeptons

Flavor conserving one-loop masses and mixings for squarks and sleptons are
evaluated by diagonalizing ${\cal M}_{\tilde{f}}^{2}(p^{2})$ for eigenvalues
at the EWSB scale.

${\cal M}_{\tilde{f}}^{2}(p^{2})\ =\
\left(\begin{array}[]{cc}M_{\tilde{f}_{L}\tilde{f}_{L}}^{2}-\Pi_{\tilde{f}_{L}\tilde{f}_{L}}(p^{2})&\qquad
M_{\tilde{f}_{L}\tilde{f}_{R}}^{2}-\Pi_{\tilde{f}_{L}\tilde{f}_{R}}(p^{2})\\\\[5.69054pt]
M_{\tilde{f}_{R}\tilde{f}_{L}}^{2}-\Pi_{\tilde{f}_{R}\tilde{f}_{L}}(p^{2})&\qquad
M_{\tilde{f}_{R}\tilde{f}_{R}}^{2}-\Pi_{\tilde{f}_{R}\tilde{f}_{R}}(p^{2})\end{array}\right)~{}$
(71)

$M^{2}_{\tilde{f}\tilde{f}}$ is the $2\times 2$ tree level mass matrix defined
in equations 56, 57 and 58. The self-energy terms of the above matrix
($\Pi_{\tilde{f}_{L}\tilde{f}_{L}}$, $\Pi_{\tilde{f}_{L}\tilde{f}_{R}}$,
$\Pi_{\tilde{f}_{R}\tilde{f}_{L}}$, $\Pi_{\tilde{f}_{R}\tilde{f}_{R}}$) are
defined in appendix D of BPMZ [70].

  * 4.

Higgs Bosons

The mass of the two loop CP-even higges are obtained by diagonalizing ${\cal
M}^{2}_{s}(p^{2})$ at the EWSB scale. Where the matrix ${\cal
M}^{2}_{s}(p^{2})$ is given by,

${\cal M}^{2}_{s}(p^{2})\ =\
\left(\begin{array}[]{cc}\hat{M}_{Z}^{2}c_{\beta}^{2}+\hat{m}_{A}^{2}s_{\beta}^{2}-\,\Pi_{s_{1}s_{1}}(p^{2})+t_{1}/v_{1}&-(\hat{M}_{Z}^{2}+\hat{m}_{A}^{2})s_{\beta}c_{\beta}-\,\Pi_{s_{1}s_{2}}(p^{2})\\\\[5.69054pt]
-(\hat{M}_{Z}^{2}+\hat{m}_{A}^{2})s_{\beta}c_{\beta}-\,\Pi_{s_{2}s_{1}}(p^{2})&\hat{M}_{Z}^{2}s_{\beta}^{2}+\hat{m}_{A}^{2}c_{\beta}^{2}-\,\Pi_{s_{2}s_{2}}(p^{2})+t_{2}/v_{2}\end{array}\right)\
$ (72)

The self energy terms $\Pi_{s_{1}s_{1}},\,\Pi_{s_{1}s_{2}},\,\Pi_{s_{2}s_{1}}$
and $\Pi_{s_{2}s_{2}}$ are presented in appendix D of BPMZ [70]. Whereas, one
loop tadpole contributions $t_{1}/v_{1}$ and $t_{2}/v_{2}$ are presented in
appendix E of BPMZ [70]. Besides the complete one loop correction to $m_{h}$
and $m_{H}$, we evaluate the top mass enhanced dominant two loop corrections
provided in [71]. From version 1.2 onwards, we have implemented the full two
loop Higgs corrections due to Slavich et. al [72].

The tree level mass of CP-odd higgs boson, $m_{A}$ and charged higgs boson
$m_{H^{\pm}}$ is given by equations 63 and 65 respectively. The one loop
correction to masses is evaluated at EWSB scale and given by

$\displaystyle\hat{m}^{2}_{A}$ $\displaystyle=$ $\displaystyle
m^{2}_{A}+\Pi_{AA}(m_{A}^{2})-b_{A}$ (73) $\displaystyle\hat{m}_{H^{\pm}}$
$\displaystyle=$ $\displaystyle
m^{2}_{A}+M^{2}_{W}+\Pi_{AA}(m_{A}^{2})+\Pi^{T}_{WW}(M_{W}^{2})-\Pi_{H^{+}H^{-}}(m^{2}_{H^{\pm}})$
(74)

Where, $b_{A}=s^{2}_{\beta}\ t_{1}/v_{1}+c^{2}_{\beta}\ t_{2}/v_{2}$.

  * 5.

Neutralino and Chargino

The one loop corrected neutralino mass matrix has the following form,

${\cal M}_{\tilde{\psi}^{0}}\ +\ \frac{1}{2}\left(\delta{\cal
M}_{\tilde{\psi}^{0}}(p^{2})+\delta{\cal
M}_{\tilde{\psi}^{0}}^{T}(p^{2})\right)~{}$ (75)

where

$\delta{\cal M}_{\tilde{\psi}^{0}}(p^{2})\ =\ -\ \Sigma_{R}^{0}(p^{2}){\cal
M}_{\tilde{\psi}^{0}}\ -\ {\cal M}_{\tilde{\psi}^{0}}\Sigma_{L}^{0}(p^{2})\ -\
\Sigma_{S}^{0}(p^{2})\ $ (76)

Where, ${\cal M}_{\tilde{\psi}^{0}}$ is the tree level neutralino mass matrix
defined in 53. And the matrix $\delta{\cal M}_{\tilde{\psi}^{0}}(p^{2})$ is
the one loop correction to the neutralino mass matrix.

The one-loop chargino mass matrix is as follows,

${\cal M}_{\tilde{\psi}^{+}}\ -\ \Sigma_{R}^{+}(p^{2})\,{\cal
M}_{\tilde{\psi}^{+}}\ -\ {\cal M}_{\tilde{\psi}^{+}}\,\Sigma_{L}^{+}(p^{2})\
-\ \Sigma_{S}^{+}(p^{2})~{}$ (77)

Where, ${\cal M}_{\tilde{\psi}^{+}}$ is the tree level chargino mass matrix
defined in 55. We evaluate the self energies $\Sigma^{+,0}_{L,R,S}$ with
$p^{2}=Q$(EWSB scale). See appendix D of BPMZ for the complete expressions of
these self-energies. One loop neutralino and chargino mass matrices are then
diagonalized to obtain the eigenvalues and eigenvectors at EWSB scale.

  * 6.

Gauge Couplings and $\sin^{2}\theta_{W}$

The correction to $\overline{DR}$ electromagnetic coupling at the weak scale
is given by,

$\hat{\alpha}=\frac{\alpha_{em}}{1-\Delta\hat{\alpha}}\qquad{\rm
and}\qquad\alpha_{em}=\frac{1}{127.934}$ (78)

Where $\Delta\hat{\alpha}$ contains contribution from SM particles as well as
SUSY particles. Similarly, the correction to strong coupling $\alpha_{s}$ at
the weak scale is given by,

$\hat{\alpha}_{s}=\frac{\alpha_{s}}{1-\Delta\alpha_{s}}$ (79)

$\Delta\alpha_{s}$ receives contribution from top quark, gluino and squarks.
The exact expression given by equation 3 of BPMZ [70]. The correction to
$\overline{DR}$ weak mixing angle is given by,

$\sin^{2}2\hat{\theta}_{W}=\frac{4\pi\hat{\alpha}}{\sqrt{2}M_{Z}^{2}G_{\mu}(1-\Delta\hat{r})}$
(80)

The exact expression of $\Delta\hat{\alpha}$ and $\Delta\hat{r}$ is presented
in the appendix C of BPMZ [70].

  * 7.

Gluino

One loop corrected gluino mass $m_{\tilde{g}}$ at scale Q is given by,

$m_{\tilde{g}}=M_{3}(Q)-\Sigma_{\tilde{g}}(m_{\tilde{g}})$ (81)

where $M_{3}(Q)$ is the tree level gluino mass generated by the RGEs and
$\Sigma_{\tilde{g}}(m_{\tilde{g}})$ is the one loop self-energy contribution
to the gluino mass. See equation D.44 of BPMZ [70] for the complete
expression.

##  Appendix C Program File Structure

Figure 3: File structure and program flow

In this appendix we briefly list the subroutines of interest in the program
and its purpose (for more details see the technical manual provided with the
program). Fig. (3) depicts the program structure and the flow of variables in
the program. The subroutine name is printed first followed by the respective
file which contains the subroutine.

The program begins by reading inputs from the main program contained in the
files ‘runonce.f’, ‘runslha.f’ (for SLHA input format), ‘scanning.f’. The
convention followed in the program is such that all the input parameters which
do not receive one-loop susy threshold correction such as the masses of the
first two generation of quarks and leptons are contained in the file
‘stdinputs.h’. Whereas, parameters such as $\sin^{2}\theta_{W}$, gauge
couplings and the third generation quark and lepton masses which receive one-
loop SUSY threshold correction are contained in the file ‘SuSemain.f’.
Moreover, the complete $3\times 3$ structure of the Yukawas and soft terms are
defined in ‘SuSemain.f’.

  * 1.

rgeiterate.f: The heart of the program. The iterative algorithm is contained
here.

  * 2.

softspectrum.f: Given the RGE output at low scale, this routine computes the
complete tree level SUSY spectrum by diagonalizing the mass matrices.

  * 3.

slha.f: Contains the ingredients for SLHA input/output interface.

  * 4.

mueconvernew.f: Contains routines which calculate the decay rates and
branching fractions of rare lepton flavor violating decays.

  * 5.

mssmrge.f: The complete MSSM two loop RGEs are contained in this file.

  * 6.

oneloopparticle.f: A set of several files which contain the one loop
corrections to the corresponding particle, which could be gauge, neutralino,
charging, sfermion etc.

  * 7.

oneloopPV.f: The analytical form of all scalar one loop Passarino-Veltman
functions are contained in this file.

  * 8.

math.f: Routines for matrix manipulations, integration routine for ordinary
differential equations using Runge-Kutta with adaptive step size and other
general purpose functions such as random number generator.

##  Appendix D Spectrum Comparison with Other Codes

In this section we compare the spectrum of SuSeFLAV with other codes for two
different parameter space points form [101]. For both the points we have set
RHN equals to zero.

Table 2: Spectrum comparison for point 10.1.5 of [101] 10.1.5 |  $m_{0}=175$, $M_{\frac{1}{2}}=700$, $\tan\beta=10$, $A_{0}=0$, sign$(\mu)>0$
---|---
Parameters | SuSeFLAV | SOFTSUSY | SuSpect | SPheno
$W^{+}$ | 8.05096462E+01 | 8.03860774e+01 | 8.04813477E+01 | 8.03115948E+01
$h$ | 1.16294107E+02 | 1.16694326e+02 | 1.16799828E+02 | 1.16829168E+02
$H$ | 9.66133037E+02 | 9.74430227e+02 | 9.68302501E+02 | 9.79779724E+02
$A$ | 9.65805171E+02 | 9.74206243e+02 | 9.68101504E+02 | 9.79577186E+02
$H^{+}$ | 9.69592528E+02 | 9.77728714e+02 | 9.71660981E+02 | 9.83266787E+02
$\tilde{q}_{L}$ | 1.43474627E+03 | 1.43580606e+03 | 1.43214020E+03 | 1.43992830E+03
$\tilde{q}_{R}$ | 1.37749634E+03 | 1.37825389e+03 | 1.37724979E+03 | 1.38138749E+03
$\tilde{t}_{1}$ | 1.11659996E+03 | 1.11105612e+03 | 1.11462082E+03 | 1.10949455E+03
$\tilde{t}_{2}$ | 1.35668185E+03 | 1.35225046e+03 | 1.35767238E+03 | 1.35426026E+03
$\tilde{b}_{1}$ | 1.31765879E+03 | 1.31707770e+03 | 1.32640786E+03 | 1.31861062E+03
$\tilde{b}_{2}$ | 1.36683066E+03 | 1.36729669e+03 | 1.36701474E+03 | 1.37028335E+03
$\tilde{l}_{L}$ | 5.01303257E+02 | 5.01757612e+02 | 4.94643201E+02 | 5.01101877E+02
$\tilde{l}_{R}$ | 3.23056643E+02 | 3.18458635e+02 | 3.13310890E+02 | 3.18342964E+02
$\tilde{\tau}_{1}$ | 3.15781781E+02 | 3.11269901e+02 | 3.06660771E+02 | 3.11160940E+02
$\tilde{\tau}_{2}$ | 5.01464374E+02 | 5.01745556e+02 | 4.94979107E+02 | 5.01126010E+02
$\tilde{\nu}_{l}$ | 4.94057805E+02 | 4.95324112e+02 | 4.88544346E+02 | 4.94578335E+02
$\tilde{\nu}_{\tau}$ | 4.92669260E+02 | 4.93751173e+02 | 4.87265068E+02 | 4.92997226E+02
$\tilde{g}$ | 1.56391437E+03 | 1.56476030e+03 | 1.56495608E+03 | 1.57232851E+03
$\tilde{\chi}^{0}_{1}$ | 2.95219584E+02 | 2.91289971e+02 | 2.92926561E+02 | 2.92509855E+02
$\tilde{\chi}^{0}_{2}$ | 5.45858411E+02 | 5.51079728e+02 | 5.52119478E+02 | 5.52386977E+02
$\tilde{\chi}^{0}_{3}$ | 8.44975403E+02 | 8.50445968e+02 | 8.60389258E+02 | 8.56133860E+02
$\tilde{\chi}^{0}_{4}$ | 8.56487466E+02 | 8.62039492e+02 | 8.72046145E+02 | 8.67579765E+02
$\tilde{\chi}^{\pm}_{1}$ | 5.35344839E+02 | 5.51280182e+02 | 5.52043599E+02 | 5.52530182E+02
$\tilde{\chi}^{\pm}_{2}$ | 8.49067665E+02 | 8.61668017e+02 | 8.71711677E+02 | 8.67856046E+02
$\mu$ | 8.37298648E+02 | 8.44864881e+02 | 8.55544693E+02 | 8.50798325E+02
$M_{\rm SUSY}$ | 1.19242602E+03 | 1.19031414e+03 | 1.19174751E+03 | 1.22578828E+03
$M_{\rm GUT}$ | 1.26703749E+16 | 1.67323027e+16 | $-$ | 1.53713886E+16
Table 3: Spectrum comparison for point 40.2.3 of [101] 40.2.3 |  $m_{0}=650$, $M_{\frac{1}{2}}=550$, $\tan\beta=40$, $A_{0}=-500$, sign$(\mu)>0$
---|---
Parameters | SuSeFLAV | SOFTSUSY | SuSpect | SPheno
$W^{+}$ | 8.05066107E+01 | 8.03827802e+01 | 8.04773725E+01 | 8.03087734E+01
$h$ | 1.16958052E+02 | 1.17297317e+02 | 1.17322254E+02 | 1.17682268E+02
$H$ | 7.30962046E+02 | 7.47689856e+02 | 7.18511292E+02 | 7.72497154E+02
$A$ | 7.31051866E+02 | 7.47643928e+02 | 7.18551942E+02 | 7.72499188E+02
$H^{+}$ | 7.35889065E+02 | 7.52307728e+02 | 7.23362920E+02 | 7.77278228E+02
$\tilde{u}_{L}$ | 1.30348659E+03 | 1.28439273e+03 | 1.30388612E+03 | 1.31020706E+03
$\tilde{u}_{R}$ | 1.26813307E+03 | 1.24781930e+03 | 1.27013696E+03 | 1.27389691E+03
$\tilde{d}_{L}$ | 1.30579237E+03 | 1.28668811e+03 | 1.30621620E+03 | 1.31246645E+03
$\tilde{d}_{R}$ | 1.26498184E+03 | 1.24450694e+03 | 1.26672885E+03 | 1.27054542E+03
$\tilde{t}_{1}$ | 9.24983971E+02 | 9.21498284e+02 | 9.69783691E+02 | 9.19586596E+02
$\tilde{t}_{2}$ | 1.14470194E+03 | 1.14136271e+03 | 1.17704096E+03 | 1.14412090E+03
$\tilde{b}_{1}$ | 1.08597531E+03 | 1.08516841e+03 | 1.11715522E+03 | 1.09021482E+03
$\tilde{b}_{2}$ | 1.15972419E+03 | 1.16046164e+03 | 1.19253887E+03 | 1.16721088E+03
$\tilde{l}_{L}$ | 7.46153736E+02 | 7.46218781e+02 | 7.43808878E+02 | 7.46077658E+02
$\tilde{l}_{R}$ | 6.83925820E+02 | 6.82393714e+02 | 6.80821036E+02 | 6.82370617E+02
$\tilde{\tau}_{1}$ | 5.23418984E+02 | 5.18531351e+02 | 5.54473085E+02 | 5.18371511E+02
$\tilde{\tau}_{2}$ | 6.95666250E+02 | 6.94111081e+02 | 7.16257580E+02 | 6.94363534E+02
$\tilde{\nu}_{l}$ | 7.40378630E+02 | 7.41675551e+02 | 7.39679081E+02 | 7.41481196E+02
$\tilde{\nu}_{\tau}$ | 6.79971865E+02 | 6.77798789e+02 | 6.94510135E+02 | 6.77596601E+02
$\tilde{g}$ | 1.27460200E+03 | 1.27746572e+03 | 1.28080280E+03 | 1.28539752E+03
$\tilde{\chi}^{0}_{1}$ | 2.33065416E+02 | 2.29995196e+02 | 2.31351813E+02 | 2.30719919E+02
$\tilde{\chi}^{0}_{2}$ | 4.32028446E+02 | 4.38269965e+02 | 4.43044390E+02 | 4.39375323E+02
$\tilde{\chi}^{0}_{3}$ | 7.36025983E+02 | 7.45547839e+02 | 9.13965835E+02 | 7.54411085E+02
$\tilde{\chi}^{0}_{4}$ | 7.44572370E+02 | 7.54116707e+02 | 9.19380416E+02 | 7.62689372E+02
$\tilde{\chi}^{\pm}_{1}$ | 4.22498882E+02 | 4.38347771e+02 | 4.43031333E+02 | 4.39557714E+02
$\tilde{\chi}^{\pm}_{2}$ | 7.40879408E+02 | 7.54555638e+02 | 9.20007967E+02 | 7.63794652E+02
$\mu$ | 7.29597776E+02 | 7.41004045e+02 | 9.12311446E+02 | 7.50392113E+02
$M_{\rm SUSY}$ | 9.97283261E+02 | 9.96175665e+02 | 1.03350532E+03 | 1.02572777E+03
$M_{\rm GUT}$ | 1.23171917E+16 | 1.88768830e+16 | $-$ | 1.75795520E+16

## References

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