Towards $$ \overline{B}\to {X}_s\gamma $$ at the NNLO in QCD without interpolation in mc
Miko-laj Misiak, Abdur Rehman, Matthias Steinhauser
Abstract
A bstract Strengthening constraints on new physics from the $$ \overline{B}\to {X}_s\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>γ</mml:mi> </mml:math> 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 m c . 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 ℬ sγ = (3 . 40 ± 0 . 17) × 10 − 4 and R γ ≡ $$ {\mathrm{\mathcal{B}}}_{\left(s+d\right)\gamma }/{\mathrm{\mathcal{B}}}_{c\mathrm{\ell}\overline{v}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℬ</mml:mi> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:mfenced> <mml:mi>γ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>ℬ</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mi>ℓ</mml:mi> <mml:mover> <mml:mi>v</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:msub> </mml:math> = (3 . 35 ± 0 . 16) × 10 − 3 for E γ > 1 . 6 GeV in the decaying meson rest frame.