Exploring MSSM for Charge and Color Breaking and Other Constraints in the Context of Higgs@125 GeV

Exploring MSSM parameter space after the discovery of Higgs Boson with mass 125 GeV naturally demands large top-squark mixing or large trilinear coupling parameter $A_t$ in particular, so as to avoid excessively heavy squark, specially for the universal models like CMSSM. We study stability of electroweak symmetry breaking vacua in possible presence of deeper charge-color symmetry breaking minima within MSSM. Besides stable vacua, we consider scenarios characterized by the presence of global CCB minima, with SM like charge and color conserving vacuum, having stability over cosmologically large lifetime {(\it long-lived states)}. We allow vacuum expectation values for both stop as well as sbottom fields, since these belong to the third generation of sfermions with larger Yukawa couplings that have immediate effect on the tunneling time. Moreover, for large $\mu$ regions, radiative corrections to Higgs boson mass from bottom-squark loop is quite significant. Regions of MSSM parameters space become viable for large $A_t$ and large $\mu$ zones which are generically excluded via the traditional analytical CCB constraints. For a large value of $\tan\beta$, safe vacua associated with large values of $|\mu|$ and $|A_t|$ are predominantly long-lived and may be associated with relatively light stop masses. We also identify low $\mu$ regions associated with long-lived states. Both the above zones can be friendly to muon $g-2$ constraint. We also impose constraints from ${\rm Br}(B \rightarrow X_s \gamma)$ and ${\rm Br}(B_s \rightarrow \mu^+ \mu^-)$. We do the analysis for a moderate and a large $\tan\beta$. Results are compatible with dark matter related constraints, as expected.


Outline Introduction
Aspects of CCB minima, Decay of False Vacuum and MSSM Results Conclusion Higgs@125 GeV ! radiative corrections to Higgs mass important In SUSY models, this demands exessively heavy scalar sparticles(in CMSSM), stops(in MSSM)

Stop loop is most important,
In large µ region, for large tan , sbottom and stau loop significant.
However large radiative correction possible for relatively lighter stops by enhancing contribution from mixing terms.
Here,¯ is a particular configuration of the field for which S=0. Analytical calculation for the simplest case of a single scalar field under certain approximations namely, thin wall and thick wall scenario. [Coleman (1977), Langacker(1994)

Analytic CCB constraints
Obtained under di↵erent simplifying relations between the vevs of the concerned fields. [Casas et. al. 1996] Outline Introduction Aspects of CCB minima, Decay of False Vacuum and MSSM Results Conclusion Considering the existence of long-lived states the above constraints modified to [Kusenko et. al.(1994), Cohen et. al. (2000)] Outline Introduction Aspects of CCB minima, Decay of False Vacuum and MSSM Results Conclusion CCB constraints not unique and may be too stringent. Relaxed constraints found to be neither necessary nor su cient. Numerical investigation of vacuum stability in CCB scenario using Vevacious. Large µ significant contribution to m h from the sbottom loop. Violation of CCB constraints for large A t and µ non-zero vevs for stops and sbottom fields and scan over A t and A b and µ, while investigating the large µ regions. Vevacious is a new publicly available code [Staub et. al.(2012)] that

Takes a model file
Takes an SLHA file Prepares and run the code HOM4PS2 to find all the tree level extrema.

Prepares and run the code PyMinuit
If the global minima is not an SM like vacuum, then calculates the tunneling time using (CosmoTransition) to identify the SM like vacuua associated with a point in the multi-dimensional parameter space as "long-lived" or "short-lived" Outline Introduction Aspects of CCB minima, Decay of False Vacuum and MSSM Results Conclusion Study of generic region of pMSSM parameter space for the stability Scan over wide range of µ and At for tan = 20 Scan over wide range of µ and At for tan = 40

Results
Vacuum stability for low values of µ.
Wide range of values of µ and A t for a moderate and a large value of tan considering non-zero vevs for stop and sbottom.
Br(B s ! µ + µ ), Br(B s ! µ + µ ), direct detection cross section and relic abundance for neutralino dark matter Outline Introduction Aspects of CCB minima, Decay of False Vacuum and MSSM Results Conclusion Study of generic region of pMSSM parameter space for the stability Scan over wide range of µ and At for tan = 20 Scan over wide range of µ and At for tan = 40

Study of generic region of pMSSM parameter space for the stability of vacuum
The parameter space spans a broad range of tan Third generation of up-type squark masses varied A t and µ upto a TeV.
Only stop fields (t L andt R ) non-zero vevs.
Outline Introduction Aspects of CCB minima, Decay of False Vacuum and MSSM Results Conclusion Study of generic region of pMSSM parameter space for the stability Scan over wide range of µ and At for tan = 20 Scan over wide range of µ and At for tan = 40 Figure: The variation of m h against A 2 . Blue, green, grey dots correspond to stable, long-lived and short-lived vacua respectively. The first two type will comprise "safe" vacuum. Scan over wide range of µ and A t for tan = 40 A larger value (3 TeV) for the third generation of squark mass parameter. The combined sbottom and stau loop contributions typically amounts to 10-15 percent within the range of Higgs boson mass. We choose the following ranges for µ, A t and A b .

Conclusion
The Higgs boson has been discovered at LHC with its mass around 125 GeV,relatively heavy, not friendly to Hierarchy problem. Very large A t ! lighter stop but heavier Higgs for low µ.
Large µ ! negative contribution to m h for sbottom and stau loops, for large tan Large µ, sensitive to CCB minima For large µ and large A t , there exist region characterized by long-lived SM like vacuum, that are otherwise excluded by traditional CCB constraints. These region are characterized by lighter stops.
The above region compatible with low energy constraints and dark matter direct detection results and give adequate relic abundance.