Abstract

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow technique. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.

Highlights

  • Partial analytical results can be found in the appendices

  • We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged pseudoscalar mesons

  • The corresponding effective theory for partially quenched QCD (PQQCD) is given by Partially Quenched Chiral Perturbation Theory (PQChPT) [8]

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Summary

Partially Quenched Chiral Perturbation Theory

This section is very similar to the description of PQChPT given in [13] since our work is the extension to finite volume of that paper. The lowest order and p4-Lagrangian can be found in [4]. We use the standard renormalization scheme in ChPT. The expansion in ChPT is in momenta p and quark-masses. We count the latter as two powers of p. We refer to lowest order (LO) as order p2, next-to-leading order (NLO) as order p4 or one-loop order and next-to-nextto-leading order (NNLO) as order p6 or two-loop order and include in the terminology oneor two-loop order the diagrams with fewer loops but the same order in p-counting

The Lagrangian Three massless quark flavours QCD has a chiral symmetry
The propagator and notation for masses and residues
The quark flow case
The finite volume integrals
Analytical results
Numerical examples
The pion mass
The pion decay constant
The kaon mass and decay constant
Conclusions
A Expressions for the mass
B Expressions for the decay constant
Full Text
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