The Ademollo-Gatto theorem for lattice semileptonic decays

TL;DR

This paper calculates the Kl3 semileptonic form factor at zero momentum transfer using one-loop partially quenched Chiral Perturbation Theory, providing formulas to aid lattice QCD mass extrapolations.

Contribution

It extends the Ademollo-Gatto theorem to lattice semileptonic decays, offering new analytical results for form factor corrections in different quark mass regimes.

Findings

Correction is of order (MK^2 - Mpi^2)^3 for Nf=2 with equal valence and sea quark masses.

Derived formulae facilitate mass extrapolation in lattice simulations.

Results applicable to Nf=2 and Nf=3 scenarios.

Abstract

We present the results of the calculation of the Kl3 semileptonic form factor at zero momentum transfer, f(0), obtained at one-loop in partially quenched Chiral Perturbation Theory (with either Nf=2, or Nf=3, and with generic valence and sea quark masses). We show that for Nf=2, when the masses of the valence and sea light quarks are equal, the correction is of the order (MK^2-Mpi^2)^3. The formulae presented here can be useful for the mass extrapolation of the results obtained in lattice simulations to the physical point.