NNLL QCD Corrections to the Decay $B \to X_s \ell^+ \ell^-$

TL;DR

This paper discusses recent NNLL QCD calculations for the inclusive rare B decay $B o X_s \, ext{l}^+ ext{l}^-$, highlighting improvements in theoretical precision and implications for testing new physics.

Contribution

It presents the completion of two-loop matrix elements and bremsstrahlung contributions, enhancing the accuracy of theoretical predictions for the decay.

Findings

Two-loop matrix elements of ${\cal O}_2$ finalized

Bremsstrahlung contributions calculated, shifting asymmetry zero

Low-scale uncertainty reduced by half

Abstract

We briefly discuss the status of the NNLL QCD calculations in the inclusive rare B decay $B \to X_s \ell^+ \ell^-$. Two important ingredients, the two-loop matrix elements of the four quark operator ${\cal O}_2$ and the bremsstrahlung contributions, were quite recently finalised. The new contributions significantly improve the sensitivity of the inclusive decay $B \to X_s l^+ l^-$ decay in testing extensions of the standard model in the sector of flavour dynamics; for instance the two-loop calculation cuts the low- scale uncertainty in half and the bremsstrahlung calculation leads to a 10% shift of the position of the zero of the forward- backward asymmetry.