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Electroweak corrections to $B_{s, d} \to ℓ^{+} ℓ^{-}$

Christoph Bobeth^1,2,*, Martin Gorbahn^1,3,†, and Emmanuel Stamou^1,2,4,‡

¹Excellence Cluster Universe, Technische Universität München, D–85748 Garching, Germany
²Institute for Advanced Study, Lichtenbergstrasse 2a, Technische Universität München, D–85748 Garching, Germany
³Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom
⁴Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel

^*christoph.bobeth@ph.tum.de
^†martin.gorbahn@liverpool.ac.uk
^‡emmanuel.stamou@weizmann.ac.il

Phys. Rev. D 89, 034023 – Published 20 February, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.034023

Abstract

We calculate the full two-loop electroweak matching corrections to the operator governing the decay $B_{q} \to ℓ^{+} ℓ^{-}$ in the standard model. Their inclusion removes an electroweak scheme and scale uncertainty of about $\pm 7 %$ of the branching ratio. Using different renormalization schemes of the involved electroweak parameters, we estimate residual perturbative electroweak and QED uncertainties to be less than $\pm 1 %$ at the level of the branching ratio.

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