Unphysical operators in partially quenched QCD

Sharpe, Stephen R.; Water, Ruth S. Van de

doi:10.1103/physrevd.69.054027

Cited by 29 publications

(30 citation statements)

References 18 publications

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“…18 17 We note that the vector hairpin is poorly determined from the MILC data, and that effects of the vector and axial vector hairpins are, in practice, difficult to disentangle in SχPT fits. 18 The explicit expression for B K in terms of B K is given in Eq.…”

Section: Guide For Lattice Determination Of B Kmentioning

confidence: 99%

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BKin staggered chiral perturbation theory

Water

Sharpe

2006

Phys. Rev. D

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We calculate the kaon B-parameter, B K , to next-to-leading order in staggered chiral perturbation theory. We find expressions for partially quenched QCD with three sea quarks, quenched QCD, and full QCD with m u = m d = m s . We extend the usual power counting to include the effects of using perturbative (rather than non-perturbative) matching factors. Taste breaking enters through the O(a 2 ) terms in the effective action, through O(a 2 ) terms from the discretization of operators, and through the truncation of matching factors. These effects cause mixing with several additional operators, complicating the chiral and continuum extrapolations. In addition to the staggered expressions, we present B K at next-to-leading order in continuum PQχPT for N f = 3 sea quarks with m u = m d = m s .

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Section: Guide For Lattice Determination Of B Kmentioning

confidence: 99%

“…This is relatively straightforward; we follow the graded group-theory method of Refs. [10,17] to insure that we include all possible linearly-independent operators. This results in two operators, Eqs.…”

mentioning

confidence: 99%

BKin staggered chiral perturbation theory

Water

Sharpe

2006

Phys. Rev. D

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“…Second, some of the mesons have more complicated propagators due to hairpin diagrams at the quark level [51,55]. Third, there are additional terms in the NLO Lagrangian which arise from partial quenching [52], and lattice spacing effects [10,38].…”

Section: B Mixed Gw-staggered Theory With Two Sea Quarksmentioning

confidence: 99%

“…[41,42] to MAPT. A mixed action simulation necessarily involves partially quenched QCD (PQQCD) [47][48][49][50][51][52], in which the valence and sea quarks are treated differently. Consequently, we provide the PQPT scattering amplitude by taking an appropriate limit of our MAPT expressions.…”

Section: Introductionmentioning

confidence: 99%

Ginsparg-Wilson pions scattering in a sea of staggered quarks

O’Connell²,

et al. 2006

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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 Oa 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.

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“…For example, the O p 4 Lagrangian has one additional operator as compared to the Gasser-Leutwyler Lagrangian. However, we do not need to consider the effects of this operator in our analysis as it has been shown that it can be constructed such that it does not contribute to valence quantities until O p 6 [60]. This is not generally the case, as is demonstrated by various examples in the baryon sector [61][62][63][64][65][66][67][68][69][70].…”

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confidence: 99%

Two meson systems with Ginsparg-Wilson valence quarks

2007

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Unphysical effects associated with finite lattice spacing and partial quenching may lead to the presence of unphysical terms in chiral extrapolation formulas. These unphysical terms must then be removed during data analysis before physical predictions can be made. In this work, we show that through next-to-leading order, there are no unphysical counterterms in the extrapolation formulas, expressed in lattice-physical parameters, for meson scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work applies to most sea quark discretizations, provided that chiral perturbation theory is a valid approximation. We demonstrate our results with explicit computations and show that, in favorable circumstances, the extrapolation formulas do not depend on the unknown constant C Mix appearing at lowest order in the mixed action chiral Lagrangian. We show that the I 1 KK scattering length does not depend on C Mix in contrast to the I 3=2 K scattering length. In addition, we show that these observables combined with f K =f and the I 2 scattering length share only two linearly independent sets of counterterms, providing a means to test the mixed action theory at one lattice spacing. We therefore make a prediction for the I 1 KK scattering length.

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Unphysical operators in partially quenched QCD

Cited by 29 publications

References 18 publications

BKin staggered chiral perturbation theory

BKin staggered chiral perturbation theory

Ginsparg-Wilson pions scattering in a sea of staggered quarks

Two meson systems with Ginsparg-Wilson valence quarks

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