Isospin Breaking Effects in Lattice QCD

Abstract

Isospin symmetry is not exact and the corrections to the isosymmetric limit are, in general, at the percent level. For gold plated quantities, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the errors quoted in nowadays lattice calculations and cannot be neglected any longer. In this talk I discuss the methods that have been developed in the last few years to calculate isospin breaking corrections by starting from first principles lattice simulations. In particular, I discuss how to perform a combined QCD+QED lattice simulation and a renormalization prescription to be used in order to separate QCD from QED isospin breaking effects. A brief review of recent lattice results of isospin breaking effects on the hadron spectrum is also included.

Finite-volume QED corrections to decay amplitudes in lattice QCD

“…Equation (14) is particularly useful in controlling the finite-volume effects in the mass shift. The Oð1=LÞ and Oð1=L 2 Þ terms can be subtracted explicitly and the remaining extrapolation of the Oð1=L 3 Þ and smaller terms to the infinite volume limit is substantially milder, resulting in smaller extrapolation uncertainties.…”

“…The leading, Oð1=LÞ, and next-toleading, Oð1=L 2 Þ, FV corrections can therefore be calculated explicitly and for a (pseudo)scalar meson of charge q give the result in Eq. (14).…”

“…Indeed, using a variety of different methods, several collaborations have recently obtained remarkably accurate results for the hadron spectrum, for example in the determination of the charged-neutral mass splittings of light pseudoscalar mesons and baryons [3][4][5][6][7][8][9][10][11][12][13] (see [14][15][16] for reviews on the subject).…”

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

“…[1], particularly in the past few years, leading to recent determinations of the electromagnetic mass splitting of light pseudoscalar mesons and light baryons, see refs. [2][3][4][5][6][7][8][9] for recent works on the subject. All these works rely on finite-volume formulations of QED obtained by quenching some Fourier modes of the gauge field.…”

“…In eq. (D.7) Pf K CD J is the Pfaffian of CD J that, by using the algebraic identities 8) can be related to the determinant of D J . Algorithms for the lattice simulation of theories involving Pfaffians have been discussed in the context of C boundary conditions or the closely-related G-parity boundary conditions and also in the context of lattice supersymmetric models (see [39][40][41][42] for a list of references on this subject).…”