The pion mass in finite volume

Abstract

We determine the relative pion mass shift $M_{\pi }(L)/M_{\pi }-1$ 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 $\pi \pi$ 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.

Comments: 16 pages, 7 figures, 3 tables