Higher-order Wilson coefficients for c → u transitions in the standard model

• Published in: The journal of high energy physics Vol. 2016; no. 8; p. 1
• Main Authors: de Boer, Stefan, Müller, Bastian, Seidel, Dirk
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2016; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Renormalization Group; Perturbative QCD; Effective field theories
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2016)091

A bstract The standard theoretical framework to deal with weak decays of heavy mesons is the so-called weak effective Hamiltonian. It involves the short-distance Wilson coefficients, which depend on the renormalisation scale μ . For specific calculations one has to evolve the Wilson coefficients down from the electroweak scale μ = M W to the typical mass scale of the decay under consideration. This is done by solving a renormalisation group equation for the effective operator basis. In this paper the results of a consistent two-step running of the c → u ℓ + ℓ − Wilson coefficients for dimension-6 operators are presented. This running involves the intermediate scale μ = m b (with M W > m b > m c ) where the bottom quark is integrated out. The matching coefficients and anomalous dimensions are taken to the required order by generalizing and extending results from b → s or s → d transitions available in the literature.