Radiative corrections in weak semi-leptonic processes at low energy: a two-step matching determination

• Published in: The European physical journal. C, Particles and fields Vol. 42; no. 4; pp. 403 - 417
• Main Authors: Descotes-Genon, S., Moussallam, B.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.08.2005; Springer Verlag (Germany)
• Subjects: Correlators; Couplings; Fermi theory; High Energy Physics - Phenomenology; Leptons; Mathematical analysis; Physics
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s2005-02316-8

We focus on the chiral Lagrangian couplings describing radiative corrections to weak semi-leptonic decays and relate them to the decay amplitude of a lepton, computed by Braaten and Li at one loop in the standard model. For this purpose, we follow a two-step procedure. A first matching, from the standard model to Fermi theory, yields a relevant set of counterterms. The latter are related to chiral couplings thanks to a second matching, from Fermi theory to the chiral Lagrangian, which is performed using the spurion method. We show that the chiral couplings of physical relevance obey integral representations in a closed form, expressed in terms of QCD chiral correlators and vertex functions. We deduce exact relations among the couplings, as well as numerical estimates which go beyond the usual \(\log(M_Z/M_\rho)\) approximation.