Finite volume two pion energies and scattering in the quenched approximation

Bernard, Claude W.; Golterman, Maarten F.L.

doi:10.1103/PhysRevD.53.476

Finite volume two pion energies and scattering in the quenched approximation

Jun, 1995

22 pages

Published in:

Phys.Rev.D 53 (1996) 476-484

e-Print:

hep-lat/9507004 [hep-lat]

DOI:

10.1103/PhysRevD.53.476

Report number:

WASH-U-HEP-95-61

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Abstract:

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.

lattice field theory
quantum chromodynamics
approximation: quenching
pi pi: interaction
interaction: pi pi
pi: scattering length
scattering length: pi
pi: energy
correlation function
perturbation theory: chiral

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