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Stephen Sharpe

Publications and source records attributed to Stephen Sharpe.

At least 19 recordsLinked to original sources
arXiv2008

't Hooft vertices, partial quenching, and rooted staggered QCD

We discuss the properties of 't Hooft vertices in partially quenched and rooted versions of QCD in the continuum. These theories have a physical subspace, equivalent to ordinary QCD, that is contained within a larger space that includes many unphysical correlation functions. We find that the 't Hooft vertices in the physical subspace have the expected form, despite the presence of unphysical 't Hooft vertices appearing in correlation functions that have an excess of valence quarks (or ghost quarks). We resolve an apparent paradox that arises when one uses rooted staggered fermions to study one-flavor QCD, by showing how, in partially quenched theories, it is possible to have spontaneous symmetry breaking of a non-anomalous symmetry in finite volume. Using these results, we demonstrate that arguments recently given by Creutz--claiming to disprove the validity of rooted staggered QCD--are incorrect. In particular, the unphysical 't Hooft vertices do not present an obstacle to the recovery of taste symmetry in the continuum limit.

hep-lat↗
arXiv2007

Comment on "Chiral anomalies and rooted staggered fermions"

In hep-lat/0701018, Creutz claims that the rooting trick used in simulations of staggered fermions to reduce the number of tastes misses key physics whenever the desired theory has an odd number of continuum flavors, and uses this argument to call into question the rooting trick in general. Here we show that his argument fails as the continuum limit is approached, and therefore does not imply any problem for staggered simulations. We also show that the cancellations necessary to restore unitarity in physical correlators in the continuum limit are a straightforward consequence of the restoration of taste symmetry.

hep-lat↗
arXiv2005

Effective theory for quenched lattice QCD and the Aoki phase

We discuss the symmetries of quenched QCD with Wilson fermions, starting from its lagrangian formulation, taking into account the constraints needed for convergence of the ghost-quark functional integral. We construct the corresponding chiral effective lagrangian, including terms linear and quadratic in the lattice spacing. This allows us to study the phase structure of the quenched theory, and compare it to that in the unquenched theory. In particular we study whether there may be an Aoki phase (with parity and flavor spontaneously broken) or a first order transition line (with no symmetry breaking but meson masses proportional to the lattice spacing), which are the two possibilities in the unquenched theory. The presence of such phase structure, and the concomitant long-range correlations, has important implications for numerical studies using both quenched and dynamical overlap and domain-wall fermions. We argue that the phase structure is qualitatively the same as in the unquenched theory, with the choice between the two possibilities depending on the sign of a parameter in the low-energy effective theory.

hep-lat↗
arXiv2004

Is there an Aoki phase in quenched QCD?

We argue that quenched QCD has non-trivial phase structure for negative quark mass, including the possibility of a parity-flavor breaking Aoki phase. This has implications for simulations with domain-wall or overlap fermions.

hep-lat↗
arXiv2003

Perturbative matching of staggered four-fermion operators with hypercubic fat links

We calculate the one-loop matching coefficients between continuum and lattice four-fermion operators for lattice operators constructed using staggered fermions and improved by the use of fattened links. In particular, we consider hypercubic fat links and SU(3) projected Fat-7 links, and their mean-field improved versions. We calculate only current-current diagrams, so that our results apply for operators whose flavor structure does not allow ``eye-diagrams''. We present general formulae, based on two independent approaches, and give numerical results for the cases in which the operators have the taste (staggered flavor) of the pseudo-Goldstone pion. We find that the one-loop corrections are reduced down to the 10-20% level, resolving the problem of large perturbative corrections for staggered fermion calculations of matrix elements.

hep-lat↗
arXiv2001

Scaling behavior of improvement and renormalization constants

This talk summarizes results for all the scale independent renormalization constants for bilinear currents ($Z_A$, $Z_V$, and $Z_S/Z_P$), the improvement constants ($c_A$, $c_V$, and $c_T$), the quark mass dependence of $Z_O$, and the coefficients of the equation of motion operators for $O(a)$ improved lattice QCD. Using data at $β=6.0$, 6.2 and 6.4 we study the scaling behavior of these quantities and quantify residual discretization errors.

hep-lat↗
arXiv2001

Partially quenched chiral perturbation theory without $Φ_0$

This paper completes the argument that lattice simulations of partially quenched QCD can provide quantitative information about QCD itself, with the aid of partially quenched chiral perturbation theory. A barrier to doing this has been the inclusion of $Φ_0$, the partially quenched generalization of the $η'$, in previous calculations in the partially quenched effective theory. This invalidates the low energy perturbative expansion, gives rise to many new unknown parameters, and makes it impossible to reliably calculate the relation between the partially quenched theory and low energy QCD. We show that it is straightforward and natural to formulate partially quenched chiral perturbation theory without $Φ_0$, and that the resulting theory contains the effective theory for QCD without the $η'$. We also show that previous results, obtained including $Φ_0$, can be reinterpreted as applying to the theory without $Φ_0$. We contrast the situation with that in the quenched effective theory, where we explain why it is necessary to include $Φ_0$. We also compare the derivation of chiral perturbation theory in partially quenched QCD with the standard derivation in unquenched QCD. We find that the former cannot be justified as rigorously as the latter, because of the absence of a physical Hilbert space. Finally, we present an encouraging result: unphysical double poles in certain correlation functions in partially quenched chiral perturbation theory can be shown to be a property of the underlying theory, given only the symmetries and some plausible assumptions.

hep-lat↗
arXiv2001

Order a improved renormalization constants

We present non-perturbative results for the constants needed for on-shell $O(a)$ improvement of bilinear operators composed of Wilson fermions. We work at $β=6.0$ and 6.2 in the quenched approximation. The calculation is done by imposing axial and vector Ward identities on correlators similar to those used in standard hadron mass calculations. A crucial feature of the calculation is the use of non-degenerate quarks. We also obtain results for the constants needed for off-shell $O(a)$ improvement of bilinears, and for the scale and scheme independent renormalization constants, (Z_A), (Z_V) and (Z_S/Z_P). Several of the constants are determined using a variety of different Ward identities, and we compare their relative efficacies. In this way, we find a method for calculating $c_V$ that gives smaller errors than that used previously. Wherever possible, we compare our results with those of the ALPHA collaboration (who use the Schrödinger functional) and with 1-loop tadpole-improved perturbation theory.

hep-lat↗
arXiv2001

Improvement and Renormalization Constants in O(a) Improved Lattice QCD

We present results at beta=6.0 and 6.2 for the O(a) improvement and renormalization constants for bilinear operators using axial and vector Ward identities. We discuss the extraction of the mass dependence of the renormalization constants and the coefficients of the equation of motion operators.

hep-lat↗
arXiv2000

Physical Results from Unphysical Simulations

We calculate various properties of pseudoscalar mesons in partially quenched QCD using chiral perturbation theory through next-to-leading order. Our results can be used to extrapolate to QCD from partially quenched simulations, as long as the latter use three light dynamical quarks. In other words, one can use unphysical simulations to extract physical quantities - in this case the quark masses, meson decay constants, and the Gasser-Leutwyler parameters L_4-L_8. Our proposal for determining L_7 makes explicit use of an unphysical (yet measurable) effect of partially quenched theories, namely the double-pole that appears in certain two-point correlation functions. Most of our calculations are done for sea quarks having up to three different masses, except for our result for L_7, which is derived for degenerate sea quarks.

hep-lat↗
arXiv1999

Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a^2), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a^2) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. These predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how it is possible that, for physical quark masses of O(a^2), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki-phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action.

hep-lat↗
arXiv1999

Non-perturbative Renormalization Constants using Ward Identities

We extend the application of axial Ward identities to calculate $b_A, b_P$ and $b_T$, coefficients that give the mass dependence of the renormalization constants of the corresponding bilinear operators in the quenched theory. The extension relies on using operators with non-degenerate quark masses. It allows a complete determination of the O(a) improvement coefficients for bilinears in the quenched approximation using Ward Identities alone. Only the scale dependent normalization constants $Z_P^0$ (or $Z_S^0$) and $Z_T$ are undetermined. We present results of a pilot numerical study using hadronic correlators.

hep-lat↗
arXiv1998

Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions

We presents results for the matrix elements of a variety of four-fermion operators calculated using quenched Wilson fermions. Our simulations are done on 170 lattices of size $32^3 x 64$ at $β= 6.0$. We find $B_K=0.74 +- 0.04 +- 0.05$, $B_D= 0.78 +- 0.01$, $B_7^{3/2}= 0.58 +- 0.02 {+0.07 \atop -0.03}$, $B_8^{3/2}= 0.81 +- 0.03 {+.03 \atop -0.02}$, with all results being in the NDR scheme at $μ=2 GeV$. We also calculate the B-parameter for the operator $\CQ_s$, which is needed in the study of the difference of B-meson lifetimes. Our best estimate is $B_s(NDR,μ=1/a)=0.80 +- 0.01$. This is given at the lattice scale since the required 2-loop anomalous dimension matrix is not known. In all these estimates, the first error is statistical, while the second is due to the use of truncated perturbation theory to match continuum and lattice operators. Errors due to quenching and lattice discretization are not included. We also present new results for the perturbative matching coefficients, extending the calculation to all Lorentz scalar four-fermion operators, and using NDR as the continuum scheme.

hep-lat↗
arXiv1998

Partial Restoration of Flavor Symmetry for Chiral Staggered Fermions

At non-zero lattice spacing the flavor symmetry of staggered fermions is broken to a discrete subgroup. We show that in the chiral limit the flavor symmetry of the pion effective Lagrangian enlarges to an SO(4) subgroup of the continuum SU(4) symmetry. This provides an explanation for observed degeneracies in the pion spectrum.

hep-lat↗
arXiv1998

Predicting the Aoki Phase using the Chiral Lagrangian

This work is concerned with the phase diagram of Wilson fermions in the mass and coupling constant plane for two-flavor (unquenched) QCD. We show that as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian, supplemented by additional terms proportional to powers of the lattice spacing. We find two possible phase structures at non-zero lattice spacing: (1) There is an Aoki phase of spontaneously broken flavor and parity, with two massless Goldstone-pions, and a width $Δm_0 \sim a^3$; (2) There is no spontaneous symmetry breaking, and all three pions have equal mass of order $a$. Present numerical simulations suggest that the former option is realized.

hep-lat↗
arXiv1998

Spontaneous Flavor and Parity Breaking with Wilson Fermions

We discuss the phase diagram of Wilson fermions in the $m_0$--$g^2$ plane for two-flavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken ``Aoki phase''. We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional terms proportional to powers of the lattice spacing. We find that there are two possible phase structures at non-zero lattice spacing: (1) there is an Aoki phase of width $Δm_0 \sim a^3$ with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal non-vanishing mass of order $a$. Present numerical evidence suggests that the former option is realized for Wilson fermions. Our analysis then predicts the form of the pion masses and the flavor-parity breaking condensate within the Aoki phase. Our analysis also applies for non-perturbatively improved Wilson fermions.

hep-lat↗