T. S. Eliot

Sharpe, Tony

doi:10.1007/978-1-349-21667-3

Cited by 47 publications

(82 citation statements)

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“…For discussion of these issues see Refs. [17,18,20,[25][26][27][28][29][30][31]. All that matters here, however, is that a consistent criterion exists in which m c is fixed, such as the one based on the PCAC mass used in practice in present simulations [18][19][20].…”

Section: Using Partial Quenching To Select Quark-connected Correlmentioning

confidence: 99%

Constraint on the low energy constants of Wilson chiral perturbation theory

Hansen

Sharpe

2012

Phys. Rev. D

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Wilson chiral perturbation theory (WChPT) is the effective field theory describing the longdistance properties of lattice QCD with Wilson or twisted-mass fermions. We consider here WChPT for the theory with two light flavors of Wilson fermions or a single light twisted-mass fermion. Discretization errors introduce three low energy constants (LECs) into partially quenched WChPT at O(a 2 ), conventionally called W ′ 6 , W ′ 7 and W ′ 8 . The phase structure of the theory at non-zero a depends on the sign of the combination 2W ′ 6 + W ′ 8 , while the spectrum of the lattice Hermitian Wilson-Dirac operator depends on all three constants. It has been argued, based on the positivity of partition functions of fixed topological charge, and on the convergence of graded group integrals that arise in the ǫ-regime of ChPT, that there is a constraint on the LECs arising from the underlying lattice theory. In particular, for W ′ 6 = W ′ 7 = 0, the constraint found is W ′ 8 ≤ 0. Here we provide an alternative line of argument, based on mass inequalities for the underlying partially quenched theory. We find that W ′ 8 ≤ 0, irrespective of the values of W ′ 6 and W ′ 7 . Our constraint implies that 2W ′ 6 > |W ′ 8 | if the phase diagram is to be described by the first-order scenario, as recent simulations suggest is the case for some choices of action.

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Section: Using Partial Quenching To Select Quark-connected Correlmentioning

confidence: 99%

Constraint on the low energy constants of Wilson chiral perturbation theory

Hansen

Sharpe

2012

Phys. Rev. D

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“…7 Thus we give no further details. (13) 1.018(32) Ratio UN/SM π/a 1.044(11) 1.021 (14) 0.991(34) Table 2: Results for B K (NDR, 2 GeV) at the physical kaon mass, using the α scales. "UN" and "SM" refer to unsmeared and smeared operators, respectively.…”

Section: Numerical Detailsmentioning

confidence: 99%

Staggered fermion matrix elements using smeared operators

1998

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We investigate the use of two kinds of staggered fermion operators, smeared and unsmeared. The smeared operators extend over a 4 4 hypercube, and tend to have smaller perturbative corrections than the corresponding unsmeared operators. We use these operators to calculate kaon weak matrix elements on quenched ensembles at β = 6.0, 6.2 and 6.4. Extrapolating to the continuum limit, we find B K (N DR, 2 GeV) = 0.62 ± 0.02(stat) ± 0.02(syst). The systematic error is dominated by the uncertainty in the matching between lattice and continuum operators due to the truncation of perturbation theory at one-loop. We do not include any estimate of the errors due to quenching or to the use of degenerate s and d quarks. For the ∆I = 3/2 electromagnetic penguin operators we find B (3/2) 7 = 0.62 ± 0.03 ± 0.06 and B (3/2) 8 = 0.77 ± 0.04 ± 0.04. We also use the ratio of unsmeared to smeared operators to make a partially non-perturbative estimate of the renormalization of the quark mass for staggered fermions. We find that tadpole improved perturbation theory works well if the coupling is chosen to be α MS (q * = 1/a).

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“…To this one must add uncertainties due to quenching and the fact that the down and strange quarks are degenerate in the calculation. Sharpe [49], on the basis of qχPT and the preliminary "N f = 3" OSU results [44], suggests an enhancement factor of 1.05 ± 0.15 to "unquench" quenched results for B K . He advocates an additional factor 1.05±0.05 to compensate for the effect of working with degenerate quark masses.…”

Section: B K Summarymentioning

confidence: 89%