Finite Supersymmetric Threshold Corrections to CKM Matrix Elements in the Large $tanβ$ Regime

TL;DR

The paper addresses finite SUSY threshold corrections at large $\tan\beta$ that modify down-type quark masses and CKM matrix elements, potentially altering low-energy predictions in SUSY GUTs. It develops analytical expressions for the mass-matrix corrections, parameterized by $\boldsymbol{\Gamma}_d$ and $\boldsymbol{\Gamma}_u$, and provides both exact forms and practical approximations, validated by a numerical RG study. The main findings show significant corrections to $V_{cb}$, $V_{ub}$, $V_{ts}$, $V_{td}$ and to the Jarlskog invariant $J$, while the unitarity-triangle angles $\alpha$, $\beta$, $\gamma$ and the ratio $|V_{ub}/V_{cb}|$ remain unchanged at this order; the corrections depend on the SUSY spectrum and the sign of $\mu M_{\tilde{g}}$, with implications for fermion-mass models and parameter constraints. Overall, these finite threshold effects are essential for accurate modeling of quark masses and CP violation in high-$\tan\beta$ SUSY frameworks and offer a route to discriminate among fermion-mass models via their sensitivity to SUSY parameters.

Abstract

We evaluate the finite 1-loop threshold corrections, proportional to $tanβ$, to the down quark mass matrix. These result in corrections to down quark masses and to Cabibbo-Kobayashi-Maskawa [CKM] matrix elements. The corrections to CKM matrix elements are the novel feature of this paper. For grand unified theories with large $\tanβ$ these corrections may significantly alter the low energy predictions of four of the CKM matrix elements and the Jarlskog parameter J, a measure of CP violation. The angles $α,\: β$ and $γ$ of the unitarity triangle and the ratio $|{V_{ub} \over V_{cb}}|$, however, are not corrected to this order. We also discuss these corrections in the light of recent models for fermion masses. Here the corrections may be useful in selecting among the various models. Moreover, if one model fits the data, it will only do so for a particular range of SUSY parameters.