Eur. Phys. J. C (2004) 33: 543-553
https://doi.org/10.1140/epjc/s2004-01593-y

theoretical physics

The pion mass in finite volume

¹ Institute for Theoretical Physics, University of Bern, 3012, Bern, Switzerland
² DESY Zeuthen, 15738, Zeuthen, Germany

Abstract

We determine the relative pion mass shift due to the finite spatial extent L of the box by means of two-flavor chiral perturbation theory and the one-particle Lüscher formula. We use as input the expression for the infinite volume forward scattering amplitude up to next-to-next-to-leading order and can therefore control the convergence of the chiral series. A comparison to the full leading order chiral expression for the pion mass in finite volume allows us to check the size of subleading terms in the large-L expansion.