Abstract
We present a model-independent and relativistic approach to analytically derive electromagnetic finite-size effects beyond the point-like approximation. The key element is the use of electromagnetic Ward identities to constrain vertex functions, and structure-dependence appears via physical form-factors and their derivatives. We apply our general method to study the leading finitesize structure-dependence in the pseudoscalar mass (at order 1/L3) as well as in the leptonic decay amplitudes of pions and kaons (at order 1/L2). Knowledge of the latter is essential for Standard Model precision tests in the flavour physics sector from lattice simulations.
Highlights
Lattice quantum chromodynamics (QCD) allows for systematically improvable StandardModel (SM) precision tests from numerical simulations performed in a finite-volume (FV), discretised Euclidean spacetime
In order to reachpercent precision in lattice predictions, strong and electromagnetic isospin breaking corrections have to be included. The latter are encoded via quantum electrodynamics (QED), but the inclusion of QED in a FV spacetime is complicated because of Gauss’ law [1]
Several prescriptions of how to include QED in a finite volume have been formulated and the one used here is QEDL where the spatial zero-modes are removed on each time-slice
Summary
Lattice quantum chromodynamics (QCD) allows for systematically improvable Standard. Model (SM) precision tests from numerical simulations performed in a finite-volume (FV), discretised Euclidean spacetime. In order to reach (sub-)percent precision in lattice predictions, strong and electromagnetic isospin breaking corrections have to be included. The latter are encoded via quantum electrodynamics (QED), but the inclusion of QED in a FV spacetime is complicated because of Gauss’ law [1]. This problem is related to zeromomentum modes of photons and the absence of a QED mass-gap. Several prescriptions of how to include QED in a finite volume have been formulated and the one used here is QEDL where the spatial zero-modes are removed on each time-slice. The discussion is based on the results in Ref. [2], and the reader is referred there for further technical details
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