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Title: Kaon B-parameter in mixed action chiral perturbation theory

Abstract

We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed-action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At 1-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of O(a{sup 2}). This term, however, is not strictly due to taste breaking, and is therefore also present in the expression for B{sub K} for pure Ginsparg-Wilson lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.

Authors:
 [1]; ;  [2]
  1. Department of Physics, Columbia University, New York, New York 10027 (United States)
  2. Theoretical Physics Department, Fermilab, Batavia, Illinois 60510 (United States)
Publication Date:
OSTI Identifier:
21010998
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevD.75.034502; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; CHIRALITY; ERRORS; FLAVOR MODEL; KAONS; LATTICE FIELD THEORY; NUMERICAL ANALYSIS; PERTURBATION THEORY; QUARKS; REST MASS; SYMMETRY BREAKING; VALENCE

Citation Formats

Aubin, C., Laiho, Jack, and Water, Ruth S. van de. Kaon B-parameter in mixed action chiral perturbation theory. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.034502.
Aubin, C., Laiho, Jack, & Water, Ruth S. van de. Kaon B-parameter in mixed action chiral perturbation theory. United States. doi:10.1103/PHYSREVD.75.034502.
Aubin, C., Laiho, Jack, and Water, Ruth S. van de. Thu . "Kaon B-parameter in mixed action chiral perturbation theory". United States. doi:10.1103/PHYSREVD.75.034502.
@article{osti_21010998,
title = {Kaon B-parameter in mixed action chiral perturbation theory},
author = {Aubin, C. and Laiho, Jack and Water, Ruth S. van de},
abstractNote = {We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed-action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At 1-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an O(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of O(a{sup 2}). This term, however, is not strictly due to taste breaking, and is therefore also present in the expression for B{sub K} for pure Ginsparg-Wilson lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.},
doi = {10.1103/PHYSREVD.75.034502},
journal = {Physical Review. D, Particles Fields},
number = 3,
volume = 75,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 2007},
month = {Thu Feb 01 00:00:00 EST 2007}
}
  • We calculate the kaon B-parameter, B{sub K}, in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We find that the resulting expression is similar to that in the continuum, and in fact has only two additional unknown parameters. At one-loop order, taste-symmetry violations in the staggered sea sector only contribute to flavor-disconnected diagrams by generating an {Omicron}(a{sup 2}) shift to the masses of taste-singlet sea-sea mesons. Lattice discretization errors also give rise to an analytic term which shifts the tree-level value of B{sub K} by an amount of {Omicron}(a{sup 2}).more » This term, however, is not strictly due to taste-breaking, and is therefore also present in the expression for B{sub K} for pure G-W lattice fermions. We also present a numerical study of the mixed B{sub K} expression in order to demonstrate that both discretization errors and finite volume effects are small and under control on the MILC improved staggered lattices.« less
  • No abstract prepared.
  • We calculate the neutral kaon mixing parameter B_K in unquenched lattice QCD using asqtad-improved staggered sea quarks and domain-wall valence quarks. We use the "2+1" flavor gauge configurations generated by the MILC Collaboration, and simulate with multiple valence and sea quark masses at two lattice spacings of a ~ 0.12 fm and a ~ 0.09 fm. We match the lattice determination of B_K to the continuum value using the nonperturbative method of Rome-Southampton, and extrapolate B_K to the continuum and physical quark masses using mixed action chiral perturbation theory. The "mixed-action" method enables us to control all sources of systematicmore » uncertainty and therefore to precisely determine B_K; we find a value of B_K^{MSbar, NDR}(2 GeV) = 0.527(6)(20), where the first error is statistical and the second is systematic.« less
  • We calculate the neutral kaon mixing parameter B{sub K} in unquenched lattice QCD using asqtad-improved staggered sea quarks and domain-wall valence quarks. We use the '2+1' flavor gauge configurations generated by the MILC Collaboration, and simulate with multiple valence and sea quark masses at two lattice spacings of a {approx} 0.12 fm and a {approx} 0.09 fm. We match the lattice determination of B{sub K} to the continuum value using the nonperturbative method of Rome-Southampton, and extrapolate B{sub K} to the continuum and physical quark masses using mixed action chiral perturbation theory. The 'mixed-action' method enables us to control allmore » sources of systematic uncertainty and therefore to precisely determine B{sub K}; we find a value of B{sub K}{sup {ovr MS},NDR} (2 GeV) = 0.527(6)(21), where the first error is statistical and the second is systematic.« less
  • We calculate the neutral kaon mixing parameter B{sub K} in unquenched lattice QCD using asqtad-improved staggered sea quarks and domain-wall valence quarks. We use the ''2+1'' flavor gauge configurations generated by the MILC Collaboration, and simulate with multiple valence and sea-quark masses at two lattice spacings of a{approx_equal}0.12 fm and a{approx_equal}0.09 fm. We match the lattice determination of B{sub K} to the continuum value using the nonperturbative method of Rome-Southampton, and extrapolate B{sub K} to the continuum and physical quark masses using mixed-action chiral perturbation theory. The ''mixed-action'' method enables us to control all sources of systematic uncertainty and thereforemore » to precisely determine B{sub K}; we find a value of B{sub K}{sup MS,NDR}(2 GeV)=0.527(6)(21), where the first error is statistical and the second is systematic.« less