Next-to-Leading QCD Corrections to B\to X_s γin Supersymmetry

TL;DR

This work addresses the decay $B\to X_s \gamma$ in supersymmetric models with minimal flavour violation by computing QCD next-to-leading order matching conditions for the (chromo-)magnetic operators. Using an effective theory with a hierarchy $\mu_{\tilde g} \gg \mu_W$, the authors integrate out heavy squarks and gluinos and determine the SUSY contributions to the Wilson coefficients $C_i^{eff}(\mu_W)$, including large non-decoupling logarithms in the chargino-stop sector. They find sizeable NLO corrections to $C_7^{eff}$ and $C_8^{eff}$ that significantly modify interference with a light charged Higgs, thereby tightening or relaxing charged-Higgs bounds depending on the parameter region. The results show that NLO effects are essential for robust constraints on SUSY parameter space in MFV scenarios with light charginos and stops, and they provide a framework for applying these corrections to precise phenomenology of $BR(B\to X_s \gamma)$.

Abstract

We compute the QCD next-to-leading order matching conditions of the (chromo)-magnetic operators relevant for B\to X_s γin supersymmetric models with minimal flavour violation. The calculation is performed under the assumption that the charginos and one stop are lighter than all other squarks and the gluino. In the parameter region where a light charged Higgs boson is consistent with measurements of BR(B\to X_s γ), we find sizeable corrections to the Wilson coefficients. As a consequence, there is a significant reduction of the stop-chargino mass region where the supersymmetric contribution has a large destructive interference with the charged-Higgs boson contribution.

Figures (2)

• Figure 1: Dependence of the prediction for the $B\to X_s \gamma$ branching ratio on the heavy mass scale $\mu_{\tilde{g}}$ for the following choice of parameters: $\tan\beta=1$, $M_{{ H}^\pm}=m_{\tilde{t}_{2}}=m_{{\chi}_2}= 100$ GeV, $m_{{\chi}_1}=300$ GeV, $\theta_{\tilde{t}}=-\pi/10$, $A_b=A_t$, all heavy particle masses equal to $\mu_{\tilde{g}}$; the lighter chargino is predominantly higgsino. The value corresponding to "LOdecoupled" is the result of the LO calculation in the limit in which the heavy masses decouple. The two upper lines are the LO and NLO predictions in the two-Higgs doublet model (2HDM).
• Figure 2: Upper bounds on the lighter chargino and stop masses from the CLEO 95% CL limit on ${\rm BR}(B\to X_s \gamma )$ in the case $M_{{ H}^\pm}=100$ GeV. We have taken $|\theta_{\tilde{t}}|<\pi/10$, $|\mu|<500$ GeV, $A_b=A_t$, and set all heavy masses to 1 TeV. For $\tan\beta=2$ and $4$ we show the results of the LO and NLO calculations. The result of neglecting the new NLO supersymmetric contributions to the Wilson coefficients is labelled as "NLO running".