Finite-volume QED corrections to decay amplitudes in lattice QCD

Abstract

We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at OðαÞ 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 nonuniversal, structuredependent terms are of Oð1=L 2 Þ [compared to the Oð1=L 3 Þ leading nonuniversal 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. [N. Carrasco et al., Phys. Rev. D 91, 074506 (2015).] for using lattice simulations to compute the decay widths at OðαÞ, with the remaining finite-volume effects starting at order Oð1=L 2 Þ. The methods developed in this paper can be generalized to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavor physics.

Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

“…[8], which was developed and extended in Ref. [20], is the universality of the O( 1 L ) and O( 1 L 2 ) finite-volume corrections to the mass. The statement goes as follows: even in the case where the particle is not elementary, but rather a composite bound state of the strong interaction, the O( 1 L ) and O( 1 L 2 ) electromagnetic finite-size corrections to the mass are identical to the case of a point particle.…”

“…First efforts in this direction date back over two decades [2], and interest in this field has picked up considerably over the last few years. First results are now available, in particular, for spectral quantities [3][4][5][6][7][8][9][10][11][12][13][14][15][16], and progress is being made in matrix elements and scattering and decay amplitudes [17][18][19][20][21][22][23][24].…”

“…All approaches introduced above suffer from large finite-volume effects induced by the absence of a mass gap (or the small photon mass in the case of QED M ). Understanding these effects analytically has been the subject of a series of articles [8,20,27,31,37]. These finite-volume effects are power suppressed in L for massless photons, where L denotes the extent of the finite cubic volume, and their precise form depends on which formulation of QED in a finite volume is implemented.…”

Toward a First-Principles Calculation of Electroweak Box Diagrams

“…With lattice QCD simulations having reached an impressive level of precision for tree-level parameters of the electroweak interaction, it becomes timely and important to study higher-order electroweak corrections. The examples of such lattice applications include the QED corrections to hadron masses [8][9][10][11][12][13][14][15] and leptonic decay rates [16][17][18][19] and a series of higher-order electroweak effects, such as K L -K S mass difference [20][21][22], K [23], rare kaon decays [24][25][26][27][28][29] and double beta decays [30][31][32][33][34][35]. As for the γW -box contribution, which is a QED correction to semileptonic decays, it still remains a new horizon for lattice QCD.…”

Numerical investigation of finite-volume effects for the HVP

“…Leading FV effects can therefore be studied using low-energy effective field theories in which hadrons are treated as point particles. FV corrections have been calculated analytically for hadron masses [10,11] and leptonic decay rates [12], within the QED L zero-mode subtraction scheme [13].…”