Chiral Perturbation Theory at Finite Volume and/or with Twisted Boundary Conditions

TL;DR

This paper discusses advanced Chiral Perturbation Theory calculations relevant for lattice QCD, including finite volume effects, hadronic vacuum polarization, and twisted boundary conditions, providing two-loop and one-loop estimates for various quantities.

Contribution

It presents new two-loop finite volume corrections for masses, decay constants, and vacuum polarization, as well as one-loop twisted boundary condition effects on form factors.

Findings

Two-loop finite volume corrections for masses and decay constants.

Two-loop estimates for hadronic vacuum polarization contributions.

One-loop finite volume effects on $f_+(q^2)$ and $K_{ ext{l}3}$ amplitudes.

Abstract

In this talk we discuss a number of ChPT calculations relevant for lattice QCD. These include the finite volume corrections at two-loop order for masses and decay constants. The second part is about hadronic vacuum polarization where we present the two-loop ChPT estimate for the disconnected and strange quark contributions. We also present the finite volume corrections at two-loop order. The final part is the one-loop finite volume with twisted boundary conditions contribution to $f_+(q^2)$ and the full $K_{\ell3}$ amplitude