Interpolation between the epsilon and p regimes

Abstract

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.

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

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Cited by in corpus (8)

• FLAG Review 2019
• Lattice Study on quantum-mechanical dynamics of two-color QCD with six light flavors
• Computation of the electromagnetic pion form factor from lattice QCD in the epsilon regime
• Low-Energy QCD in the Delta Regime
• Nontrivial Thermodynamics in 't Hooft's Large-$N$ Limit
• Extracting the electro-magnetic pion form factor from QCD in a finite volume
• Chiral interpolation in a finite volume
• Pion form factors in the epsilon regime