Ginsparg-Wilson Pions Scattering in a Sea of Staggered Quarks

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, C_Mix, that appears in the chiral Lagrangian of the mixed theory. In addition, the contributions which nominally arise from operators appearing in the mixed action O(a^2 m_q) 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.

27 pages, 3 figures. Mistakes corrected in Eqs. (37), (42). Improved discussion in section 4 and related results in Eqs. (33), (37), (40) and (42). Added references. Version to be published in PRD

References in corpus (15)

• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD
• Chiral Perturbation Theory for Staggered Sea Quarks and Ginsparg-Wilson Valence Quarks
• I=2 Pion Scattering Length from Two-Pion Wave Functions
• Twisted valence quarks and hadron interactions on the lattice
• Hadronic physics with domain-wall valence and improved staggered sea quarks
• Lattice Computations of the Pion Form Factor
• Staggered Chiral Perturbation Theory at Next-to-Leading Order
• Baryons with Ginsparg-Wilson quarks in a staggered sea
• The role of the double pole in lattice QCD with mixed actions
• Algorithms for Lattice QCD with Dynamical Fermions
• B_K in Staggered Chiral Perturbation Theory
• Baryon masses at O(a^2) in chiral perturbation theory
• Pseudo scalar meson masses in Wilson Chiral Perturbation Theory for 2+1 flavors

Cited by in corpus (41)

• FLAG Review 2019
• FLAG Review 2021
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Nucleon Generalized Parton Distributions from Full Lattice QCD
• The Scalar Strange Content of the Nucleon from Lattice QCD
• Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea
• Nuclear Physics from Lattice QCD
• Nucleon-Nucleon Scattering From Fully-Dynamical Lattice QCD
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• Heavy physics contributions to neutrinoless double beta decay from QCD
• Pi-K Scattering in Full QCD with Domain-Wall Valence Quarks
• The K+K+ Scattering Length from Lattice QCD
• Two Meson Systems with Ginsparg-Wilson Valence Quarks
• Meson-Baryon Scattering Lengths from Mixed-Action Lattice QCD
• f_K/f_pi in Full QCD with Domain Wall Valence Quarks
• Hadronic Interactions from Lattice QCD
• Universality of Mixed Action Extrapolation Formulae
• Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions
• $F_K/F_{\pi }$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles
• Discretization effects and the scalar meson correlator in mixed-action lattice simulations
• SU(2) Low-Energy Constants from Mixed-Action Lattice QCD
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• Evidence for non-analytic light quark mass dependence in the baryon spectrum
• Mixed Action Effective Field Theory: an Addendum
• Nuclear Reactions from Lattice QCD
• Chiral effective theory with a light scalar and lattice QCD
• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length
• Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
• Connected and Disconnected Contractions in Pion-Pion Scattering
• The Kaon B-parameter in Mixed Action Chiral Perturbation Theory
• pi-pi Scattering in Twisted Mass Chiral Perturbation Theory
• Nucleon Mass with Highly Improved Staggered Quarks
• Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory
• Effective Field Theory for the Anisotropic Wilson Lattice Action
• $\pi \pi$ scattering in partially-quenched twisted-mass chiral perturbation theory
• Topics in Effective Field Theory for Lattice QCD
• Constraints on Disconnected Contributions in $\pi \pi$ Scattering
• Bubble contributions to scalar correlators with mixed actions
• Baryon-Baryon Interactions from the Lattice