Towards overline{B}to {X}_sgamma at the NNLO in QCD without interpolation in mc

Miko-Laj Misiak,Matthias Steinhauser,Abdur Rehman

doi:10.1007/jhep06(2020)175

Abstract

Strengthening constraints on new physics from the overline{B}to {X}_sgamma branching ratio requires improving accuracy in the measurements and the Standard Model predictions. To match the expected Belle-II accuracy, Next-to-Next-to-Leading Order (NNLO) QCD corrections must be calculated without the so-far employed interpolation in the charm- quark mass mc. In the process of evaluating such corrections at the physical value of mc, we have finalized the part coming from diagrams with closed fermion loops on the gluon lines that contribute to the interference of the current-current and photonic dipole operators. We confirm several published results for corrections of this type, and supplement them with a previously uncalculated piece. Taking into account the recently improved estimates of non-perturbative contributions, we find ℬsγ = (3.40±0.17)×10−4 and Rγ≡ {mathrm{mathcal{B}}}_{left(s+dright)gamma }/{mathrm{mathcal{B}}}_{cmathrm{ell}overline{v}} = (3.35 ± 0.16) × 10−3 for Eγ> 1.6 GeV in the decaying meson rest frame.

Highlights

To match the expected Belle-II accuracy, Next-to-Next-to-Leading Order (NNLO) QCD corrections must be calculated without the so-far employed interpolation in the charmquark mass mc
In the process of evaluating such corrections at the physical value of mc, we have finalized the part coming from diagrams with closed fermion loops on the gluon lines that contribute to the interference of the current-current and photonic dipole operators
The dominant NNLO effects come from G17, G27 and G77 that originate from the operators

Summary

Introduction

In the process of evaluating such corrections at the physical value of mc, we have finalized the part coming from diagrams with closed fermion loops on the gluon lines that contribute to the interference of the current-current and photonic dipole operators. Final results are presented for contributions originating from diagrams with closed fermion loops on the gluon lines, like those in the first row of figure 1. As far as the new contribution (the third plot in figure 3) is concerned, it has so far been included in the interpolated part of the NNLO correction, and resulted in a tiny effect, around one per-mille of the decay rate only.

Results

Conclusion