Chiral perturbation theory with virtual photons and leptons

M. Knecht; H. Neufeld; H. Rupertsberger; P. Talavera

doi:doi:10.1007/s100529900265

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C 12, 469-478
DOI 10.1007/s100529900265

Chiral perturbation theory with virtual photons and leptons

M. Knecht¹ - H. Neufeld² - H. Rupertsberger² - P. Talavera³

¹ Centre de Physique Théorique, CNRS Luminy, Case 907, 13288 Marseille Cedex 9, France
² Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
³ Department of Theoretical Physics 2, Lund University, Sölvegatan 14A, 22362 Lund, Sweden

Received: 9 September 1999 / Published online: 10 December 1999

Abstract
We construct a low-energy effective field theory which allows for a full treatment of the isospin-breaking effects in semileptonic weak interactions. To this end, we enlarge the particle spectrum of chiral perturbation theory with virtual photons by including also the light leptons as dynamical degrees of freedom. Using super-heat-kernel techniques, we determine the additional one-loop divergences generated by the presence of virtual leptons and give the full list of associated local counterterms. We illustrate the use of our effective theory by applying it to the decays $\pi \rightarrow\ell \nu_{\ell}$ and $K \rightarrow\ell \nu_{\ell}$ .