B -> X_s gamma in supersymmetry: large contributions beyond the leading order

TL;DR

The paper addresses potentially large next-to-leading-order contributions to $B\to X_s\gamma$ in supersymmetric models, focusing on terms that are enhanced by $\tan\beta$ and by $\ln(\mu_{SUSY}/\mu_W)$ when SUSY scales are heavy. It develops compact analytic formulae to capture these effects, including both bottom- and top-Yukawa sector corrections, and demonstrates how resummation and renormalization-group running modify the Wilson coefficients $C_7$ and $C_8$. A key finding is that $\tan\beta$-enhanced terms persist in the charged-Higgs sector beyond the decoupling limit, and that log-enhanced and RG-induced corrections can substantially alter the predicted branching ratio, particularly at large $\tan\beta$. Practically, these results relax lower bounds on the charged-Higgs mass and improve the reliability of SUSY parameter analyses even when colored superpartners are heavy.

Abstract

We discuss possible large contributions to B -> X_s gamma, which can occur at the next-to-leading order in supersymmetric models. They can originate from terms enhanced by tan(beta) factors, when the ratio between the two Higgs vacuum expectation values is large, or by logarithm of M_{susy}/M_W, when the supersymmetric particles are considerably heavier than the W boson. We give compact formulae which include all potentially large higher-order contributions. We find that tan(beta) terms at the next-to-leading order do not only appear from the Hall-Rattazzi-Sarid effect (the modified relation between the bottom mass and Yukawa coupling), but also from an analogous effect in the top-quark Yukawa coupling. Finally, we show how next-to-leading order corrections, in the large tan(beta) region, can significantly reduce the limit on the charged-Higgs mass, even if supersymmetric particles are very heavy.

Figures (5)

• Figure 1: Feynman diagrams (for current squark eigenstates) representing the QCD (a) and Yukawa (b) contributions to $\epsilon_b^\prime (t)$ and the QCD (c) and Yukawa (d) contribution to $\epsilon_t^\prime (b)$.
• Figure 2: Branching ratio for $B\to X_s \gamma$ in a minimal supergravity scenario with $m_0=600$ GeV, $m_{1/2}=$ 400GeV, $A_0=0$, and $\mu>0$ as a function of $\tan\beta$. The solid and dashed lines represent our improved framework for $\mu_{SUSY}=$ 600 GeV and 1.2 TeV, while the dotted line represents the results of the calculation with LO supersymmetric contributions.
• Figure 3: Same as Fig.2 but with $\mu<0$.
• Figure 4: Branching ratio for $B\to X_s \gamma$ in a two-Higgs doublet model with the charged-Higgs mass $M_H=150$ GeV, for different values of $\epsilon \equiv \epsilon_{b,t}=\epsilon_{b,t}^\prime$.
• Figure 5: Lower bounds on the charged Higgs boson mass obtained from the experimental measurement of the branching ratio for $B\to X_s \gamma$ in a two-Higgs doublet model, for different values of $\epsilon\equiv\epsilon_{b,t}=\epsilon_{b,t}^\prime$ and as a function of $\tan\beta$.