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]
Summary
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
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