An asymptotic formula for the pion decay constant in a large volume

Abstract

We derive an asymptotic formula a la Luscher for the finite volume correction to the pion decay constant: this is expressed as an integral over the < 3 \pi | A_\mu|0 > amplitude after proper subtraction of the pion pole contribution. We analyze the formula numerically at leading and next-to-leading order in the chiral expansion.

Comments: 10 pages, 2 figures, v2: two references and a comment on the corresponding lattice results added