Gluino Contribution to Radiative B Decays: Organization of QCD Corrections and Leading Order Results

TL;DR

This work develops a comprehensive LO QCD framework for gluino-induced contributions to the radiative decay $b\to s\gamma$ in generic SUSY with flavour violation. It shows that gluino loops demand a substantially enlarged operator basis, including magnetic, chromomagnetic, and multiple four-quark operators, and that the LO running must treat gluino-induced operators with dedicated anomalous-dimension matrices. By employing a mass-eigenstate formalism, the authors derive the Wilson coefficients at the electroweak scale and evolve them down to the decay scale $\mu_b$, providing a simple LO expression for the branching ratio in terms of both SM and gluino contributions. Numerical results illustrate that LO QCD corrections are crucial for reliable bounds on flavour-violating squark mass terms, with the strongest constraints typically arising from chirality-flipping LR-type insertions; the analysis highlights the need for full NLO studies and inclusion of all SUSY contributions for robust model discrimination.

Abstract

The gluino-induced contributions to the decay b-> s gamma are investigated in supersymmetric frameworks with generic sources of flavour violation. It is shown that, when QCD corrections are taken into account, the relevant operator basis of the Standard Model effective Hamiltonian gets enlarged to contain: i) magnetic and chromomagnetic operators with a factor of alpha_s and weighted by a quark mass m_b or m_c; ii) magnetic and chromomagnetic operators of lower dimensionality, also containing alpha_s; iii) four-quark operators weighted by a factor alpha_s^2. Numerical results are given, showing the effects of the leading order QCD corrections on the inclusive branching ratio for b-> s gamma. Constraints on supersymmetric sources of flavour violation are derived.

Figures (8)

• Figure 1: Diagram mediating the $b \to s \gamma$ decay through gluino exchange and contributing to the operator ${\cal O}_{7b,\tilde{g}}$. A contribution to the primed operator ${\cal O}_{7b,\tilde{g}}^{\prime}$ is obtained by exchanging $L\leftrightarrow R$.
• Figure 2: Contribution to ${\cal O}_{7\tilde{g},\tilde{g}}$ from the insertion of the gluino mass and of a scalar mass term simultaneously violating chirality and flavour. A contribution to ${\cal O}_{7\tilde{g},\tilde{g}}^{\prime}$ is obtained through the interchange $L\leftrightarrow R$.
• Figure 4: Penguin diagram contributing to the operators (\ref{['penguinboxop']}).
• Figure 5: Diagrams contributing to the operators (\ref{['boxop']}). In the two upper diagrams, the quark (squark) $q$ ($\widetilde{q}$) can be of up- or down-type and the flavour violation on the lower squark line, not explicitly indicated, can be realized through a direct flavour--chiral transition (see Fig. \ref{['glopgoneins']}) or through distinct chirality and flavour transitions (see Fig. \ref{['glopgtwoins']}). In the lower diagrams, the down-type quark $d_i$ is a $b$- or an $s$-quark if a single flavour violation is allowed in the squark lines.
• Figure 6: Gluino-induced branching ratio ${\rm BR}(\bar{B}\to X_s\gamma)$ as a function of $x= m^2_{\tilde{g}}/m^2_{\tilde{q}}$, obtained when the only source of flavour violation is $\delta_{LR,23}$ (see text), fixed to the value $0.01$, for $m_{\tilde{q}}=500\,$GeV. The solid line shows the branching ratio at the LO in QCD, for $\mu_b =4.8\,$GeV and $\mu_W = M_W$; the two dotted lines indicate the range of variation of the branching ratio when $\mu_b$ spans the interval $2.4$--$9.6\,$GeV. Also shown are the values of ${\rm BR}(\bar{B}\to X_s\gamma)$ when no QCD corrections are included and the explicit factor $\alpha_s(\mu)$ in the gluino-induced operators is evaluated at $4.8\,$GeV (dashed line) or at $M_W$ (dot-dashed line).