Finite-volume two-pion energies and scattering in the quenched approximation

Details Finite-volume two-pion energies and scattering in the quenched approximation Finite-volume two-pion energies and scattering in the quenched approximation

1995-07-06

arxiv.org/abs/hep-lat/9507004v1

Phys.Rev. D53 (1996) 476-484

Physics

High Energy Physics

High Energy Physics - Lattice

22 pages, uuencoded, compressed postscript file

Scientific paper

10.1103/PhysRevD.53.476

We investigate how L\"uscher's relation between the finite-volume energy of two pions at rest and pion scattering lengths has to be modified in quenched QCD. We find that this relation changes drastically, and in particular, that ``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$ occur at one loop ($L$ is the linear size of the box), due to the special properties of the $\eta'$ in the quenched approximation. We define quenched pion scattering lengths, and show that they are linearly divergent in the chiral limit. We estimate the size of these various effects in some numerical examples, and find that they can be substantial.

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