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arXiv · 1611.08497

Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD

V. Lubicz·G. Martinelli·C. T. Sachrajda·F. Sanfilippo·S. Simula·N. Tantalo
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Abstract

We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(\alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.\,\cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(\alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.

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V. Lubicz, G. Martinelli, C. T. Sachrajda, F. Sanfilippo, S. Simula, N. Tantalo. 2016-11-25. Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD. https://doi.org/10.1103/physrevd.95.034504

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