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Ginsparg-Wilson pions scattering in a sea of staggered quarks

Chen, Jiunn-Wei and O'Connell, Donal and Van de Water, Ruth and Walker-Loud, André (2006) Ginsparg-Wilson pions scattering in a sea of staggered quarks. Physical Review D, 73 (7). Art. No. 074510. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:CHEprd06

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Abstract

We calculate isospin 2 pion-pion scattering in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We point out that for some scattering channels, the power-law volume dependence of two-pion states in nonunitary theories such as partially quenched or mixed action QCD is identical to that of QCD. Thus one can extract infinite-volume scattering parameters from mixed action simulations. We then determine the scattering length for both 2 and 2+1 sea quarks in the isospin limit. The scattering length, when expressed in terms of the pion mass and the decay constant measured on the lattice, has no contributions from mixed valence-sea mesons, thus it does not depend upon the parameter, CMix, that appears in the chiral Lagrangian of the mixed theory. In addition, the contributions which nominally arise from operators appearing in the mixed action [script O](a^2mq) Lagrangian exactly cancel when the scattering length is written in this form. This is in contrast to the scattering length expressed in terms of the bare parameters of the chiral Lagrangian, which explicitly exhibits all the sicknesses and lattice spacing dependence allowed by a partially quenched mixed action theory. These results hold for both 2 and 2+1 flavors of sea quarks.


Item Type:Article
Additional Information:©2006 The American Physical Society. (Received 6 January 2006; revised 20 March 2006; published 24 April 2006) We would like to thank Maarten Golterman, Martin Savage, and Steve Sharpe for many useful discussions and helpful comments on the manuscript. We would also like to thank the referee for helpful comments regarding the manuscript. R.V. would also like to thank Jack Laiho for a helpful discussion and for pointing out a relevant reference. J.W.C. and A.W.L. would like to thank the ECT* and the organizers of Effective theories in Nuclear physics and Lattice QCD, Paulo Bedaque, Elisabetta Pallante, and Assumpta Parreno for organizing a wonderful conference and providing a stimulating atmosphere where we formulated the idea for this project. J.W.C. thanks the INT at the University of Washington for hospitality. D.O'C. thanks the nuclear theory group at the University of Washington for hospitality during the completion of this work. J.W.C. is supported by the National Science Council of R.O.C. D.O'C. is supported in part by the U.S. DOE under the grant No. DE-FG03-9ER40701. R.V. was supported under DOE grant No. DE-FG02-96ER40956. A.W. L. is supported under DOE grant No. DE-FG03-97ER41014.
Subject Keywords:pion-pion scattering; isotopic spin (elementary particles); chiral symmetries; perturbation theory; lattice field theory; quantum chromodynamics; pion decay; meson mass; pions; Lagrangian field theory
Issue or Number:7
Record Number:CaltechAUTHORS:CHEprd06
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:CHEprd06
Alternative URL:http://dx.doi.org/10.1103/PhysRevD.73.074510
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10748
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:06 Jun 2008
Last Modified:26 Dec 2012 10:04

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