QED Corrections to Hadronic Processes in Lattice QCD

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.

38 pages, 14 figures

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• $B\to D\ell {\nu }_{\ell }$ form factors beyond leading power and extraction of $|V_{cb}|$ and $R(D)$
• Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data
• Radiative corrections to semileptonic beta decays: Progress and challenges
• Flavour breaking effects in the pseudoscalar meson decay constants
• Future tests of parton distributions
• Hints and challenges in heavy flavor physics
• Notes on QED Corrections in Weak Decays
• The muon abundance in the primordial Universe
• Inclusion of isospin breaking effects in lattice simulations
• Isospin Breaking in Lattice QCD Computations of Decay Amplitudes
• Rotated twisted-mass: a convenient regularization scheme for isospin breaking QCD and QED lattice calculations