Abstract
In this paper, for the first time a method is proposed to compute electromagnetic effects in hadronic processes using lattice simulations. The method can be applied, for example, to the leptonic and semileptonic decays of light or heavy pseudoscalar mesons. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure much more complicated than is the case for the hadronic spectrum, for which calculations already exist. In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to the emission of real photons. Only in this way do the infrared divergences cancel as first understood by Bloch and Nordsieck in 1937. We present a detailed analysis of the method for the leptonic decays of a pseudoscalar meson. The implementation of our method, although challenging, is within reach of the present lattice technology.
Highlights
Precision flavor physics is a powerful tool for exploring the limits of the Standard Model of particle physics and in searching for inconsistencies which would signal the existence of new physics
In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to the emission of real photons
In this paper we propose a strategy to include electromagnetic effects in processes for which infrared divergences are present but which cancel in the standard way between diagrams containing different numbers of real and virtual photons [11]
Summary
Precision flavor physics is a powerful tool for exploring the limits of the Standard Model of particle physics and in searching for inconsistencies which would signal the existence of new physics. In this paper we propose a strategy to include electromagnetic effects in processes for which infrared divergences are present but which cancel in the standard way between diagrams containing different numbers of real and virtual photons [11]. Γ1ðΔEÞ can be evaluated in lattice simulations by computing the amplitudes for a range of photon momenta and using the results to perform the integral over phase space Such calculations would be very challenging . When including the OðαÞ corrections, the ultraviolet contributions to the matrix element of the local operator are different from those in the Standard Model, and we discuss the matching factors which must be computed to determine the OðαÞ corrections to the πþ → lþνl decay from lattice computations of correlation functions containing the local operator in (7). Other electroweak corrections not explicitly mentioned above are all absorbed into GF
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