[Paper Review] The MSSM with a softly broken U(2)^3 flavor symmetry

Andreas Crivellin, Lars Hofer+1 more|arXiv (Cornell University)|Nov 1, 2011

Particle physics theoretical and experimental studies9 references8 citations

TL;DR

This paper proposes a radiative flavor violation (RFV) scenario in the MSSM where the U(2)^3 flavor symmetry—broken only by soft trilinear A-terms—is used to generate the CKM matrix and quark masses via loop corrections. Unlike minimal flavor violation (MFV), this model allows for non-decoupling Higgs penguin contributions to $B_s \to \mu^+\mu^-$ and $B_s$-$\bar{B}_s$ mixing, enabling a new CP-violating phase in $B_s$ mixing even at moderate $\tan\beta$, while remaining compatible with current experimental bounds on $B_s \to \mu^+\mu^-$.

ABSTRACT

In this article we review the phenomenological consequences of radiative flavor-violation (RFV) in the MSSM. In the model under consideration the U(3)^3 flavor symmetry of the gauge sector is broken in a first step to U(2)^3 by the top and bottom Yukawa couplings of the superpotential (and possibly also by the bilinear SUSY-breaking terms). In a second step the remaining U(2)^3 flavor symmetry is softly broken by the trilinear A-terms in order to obtain the measured quark masses and the CKM matrix of the Standard Model (SM) at low energies. The phenomenological implications of this model depend on the actual choice of the SUSY breaking A-terms. If the CKM matrix is generated in the down sector (by A^d), Bs->mu^+mu^- receives non-decoupling contributions from Higgs penguins which become important already for moderate values of tan(beta). Also the Bs mixing amplitude can be significantly modified compared to the SM prediction including a potential induction of a new CP-violating phase (which is not possible in the MSSM with MFV).

Motivation & Objective

• To address tensions between minimal flavor violation (MFV) and hints of new CP violation in $B_d$ and $B_s$ mixing.
• To resolve the conflict between the $U(3)^3$ flavor symmetry and stringent constraints from $K$- and $D$-physics.
• To explain the smallness of light quark masses via loop suppression in a framework where $A$-terms break $U(2)^3$ symmetry.
• To explore phenomenological consequences of $U(2)^3$-breaking $A$-terms, particularly in $B_s \to \mu^+\mu^-$ and $B_s$-$\bar{B}_s$ mixing.
• To demonstrate that this model can generate a new CP-violating phase in $B_s$-$\bar{B}_s$ mixing, unlike standard MFV.

Proposed method

• Assumes the superpotential Yukawa couplings $Y^{u(0)}$ and $Y^{d(0)}$ preserve $U(2)^3$ symmetry, with $A$-terms as the sole source of $U(2)^3$ breaking.
• Performs $U(2)$ rotations to diagonalize $A^{u,d}$ matrices, fixing a non-weak-basis where $A$-terms have specific non-diagonal structures.
• Derives effective quark masses and CKM matrix elements via one-loop radiative corrections, with $m_q \propto A^{q}_{ii}/\mu_A$ and $V_{cb} \propto A^{d}_{23}/\mu_A$.
• Computes Higgs double-penguin amplitudes $\Gamma^{LR}_{sb}$ and $\Gamma^{LR}_{bs}$, showing they are not suppressed by $m_s/m_b$ in RFV, unlike in MFV.
• Introduces $V^R_{32} \propto A^{d*}_{32}/\mu_A$ to parametrize the effective coupling, allowing direct comparison with $V_{ts}$.
• Uses experimental bounds on $\text{Br}(B_s \to \mu^+\mu^-)$ to constrain parameter space and correlate with $B_s$-$\bar{B}_s$ mixing.

Experimental results

Research questions

• RQ1 Can a $U(2)^3$-symmetric MSSM with $A$-terms as the sole source of flavor violation generate the observed CKM matrix and quark masses via radiative corrections?
• RQ2 Does this model allow for a new CP-violating phase in $B_s$-$\bar{B}_s$ mixing, absent in standard MFV scenarios?
• RQ3 Can the $B_s \to \mu^+\mu^-$ decay rate be enhanced beyond MFV predictions without violating current experimental bounds?
• RQ4 How do the Higgs penguin contributions to $B_s$-$\bar{B}_s$ mixing scale with $\tan\beta$ in this RFV framework compared to MFV?
• RQ5 What is the correlation between $B_s \to \mu^+\mu^-$ and $B_s$-$\bar{B}_s$ mixing in the $m_H$–$\tan\beta$ plane under this model?

Key findings

• The model generates the CKM matrix and quark masses via loop corrections from $A$-terms, explaining the smallness of light quark masses through loop suppression.
• When the CKM matrix is generated in the down sector via $A^{d}_{23}$, $\Gamma^{LR}_{sb}$ is proportional to $A^{d}_{23}/\mu_A$, leading to non-decoupling effects in $B_s \to \mu^+\mu^-$ at moderate $\tan\beta$.
• The $B_s$-$\bar{B}_s$ mixing amplitude can be significantly modified due to non-suppressed $\Gamma^{LR}_{bs}$, which is not related to $\Gamma^{LR}_{sb}$ by quark mass ratios in this framework.
• A new CP-violating phase in $B_s$-$\bar{B}_s$ mixing is possible, unlike in MFV, due to the $A$-term-induced $V^R_{32}$ coupling not being constrained by $V_{ts}$.
• For $m_H = 400\,\text{GeV}$, $\tan\beta = 11$, and $\epsilon_b = 0.0075$, a region exists where the model explains a new phase in $B_s$-$\bar{B}_s$ mixing while remaining compatible with the current bound on $\text{Br}(B_s \to \mu^+\mu^-) \leq 1.08 \times 10^{-8}$.
• The correlation between $B_s \to \mu^+\mu^-$ and $B_s$-$\bar{B}_s$ mixing is probed by LHCb, and a potential signal in $B_s$-$\bar{B}_s$ mixing would imply a measurable enhancement in $B_s \to \mu^+\mu^-$.