Interpolation between the epsilon and p regimes

Details Interpolation between the epsilon and p regimes Interpolation between the epsilon and p regimes

2011-05-09

arxiv.org/abs/1105.1606v3

Phys.Rev.D84:014501,2011

Physics

High Energy Physics

High Energy Physics - Lattice

49 pages, 6 figures, minor corrections, references added, version to appear in PRD

Scientific paper

10.1103/PhysRevD.84.014501

We reconsider chiral perturbation theory in a finite volume and develop a new computational scheme which smoothly interpolates the conventional epsilon and p regimes. The counting rule is kept essentially the same as in the p expansion. The zero-momentum modes of Nambu-Goldstone bosons are, however, treated separately and partly integrated out to all orders as in the epsilon expansion. In this new scheme, the theory remains infra-red finite even in the chiral limit, while the chiral-logarithmic effects are kept present. We calculate the two-point function in the pseudoscalar channel and show that the correlator has a constant contribution in addition to the conventional hyperbolic cosine function of time t. This constant term rapidly disappears in the p regime but it is indispensable for a smooth convergence of the formula to the epsilon regime result. Our calculation is useful to precisely estimate the finite volume effects in lattice QCD simulations on the pion mass Mpi and kaon mass MK, as well as their decay constants Fpi and FK.

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