Restoration Of Flavor Symmetry Research Articles

Dynamical fermions with fat links

We present and test a new method for simulating dynamical fermions with fat links. Our construction is based on the introduction of auxiliary but dynamical gauge fields and works with any fermionic action and can be combined with any fermionic updating. In our simulation we use an over-relaxation step which makes it effective. For four flavors of staggered fermions first results indicate that flavor symmetry at a lattice spacing a~0.2 fm is restored to a few percent. With the standard action this amount of flavor symmetry restoration is achieved at a~0.07 fm. We estimate that the overall computational cost is reduced by at least a factor 10.

Improved flavor symmetry in Kogut-Susskind fermion actions

We study improved Kogut-Susskind fermion actions focusing on flavor symmetry restoration. Several variants of fat actions suitable for dynamical simulations are considered, including an action with no tree level O( a 2) errors. The spectrum of all the pions is computed and used as a measure of flavor symmetry violation. Finally, the Naik term is introduced to restore rotational symmetry.

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{sup 2}), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a{sup 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{sup 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.) or to higher order in a{sup 2}. We show how it is possible that, for physical quark masses of O(a{sup 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.more » (c) 1999 The American Physical Society.« less

Variants of fattening and flavor symmetry restoration

We study the effects of different "fat link" actions for Kogut-Susskind quarks on flavor symmetry breaking. Our method is mostly empirical - we compute the pion spectrum with different valence quark actions on common sets of sample lattices. Different actions are compared, as best we can, at equivalent physical points. We find significant reductions in flavor symmetry breaking relative to the conventional or to the "link plus staple" actions, with a reasonable cost in computer time. We also develop and test a scheme for approximate unitarization of the fat links. While our tests have concentrated on the valence quark action, our results will be useful in designing simulations with dynamical quarks.

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.

Tests of improved Kogut-Susskind fermion actions

Improved Kogut-Susskind quark actions containing repeatedly smeared links are studied to address the issue of flavor symmetry restoration. As a measure of the flavor symmetry restoration the mass spectrum of all the pions is computed. We present results for several variants of the “fat” actions that are suitable for full QCD simulations.

Flavor-symmetry restoration and Symanzik improvement for staggered quarks

We resolve contradictions in the literature concerning the origins and size of unphysical flavor-changing strong interactions generated by the staggered-quark discretization of QCD. We show that the leading contributions are tree-level in $\order(a^2)$ and that they can be removed by adding three correction terms to the link operator in the standard action. These corrections are part of the systematic Symanzik improvement of the staggered-quark action. We present a new improved action for staggered quarks that is accurate up to errors of $\order(a^4,a^2\alpha_s)$ --- more accurate than most, if not all, other discretizations of light-quark dynamics.

Light quark spectrum with improved gauge and fermion actions

We report on a study of the light quark spectrum using an improved gauge action and both Kogut-Susskind and Naik quark actions. We have studied six different lattice spacings, corresponding to plaquette couplings ranging from 6.8 to 7.9, with five to six quark masses per coupling. We compare the two quark actions in terms of the spectrum and restoration of flavor symmetry. We also compare these results with those from the conventional action.

Color dipole phenomenology of diffractive electroproduction of light vector mesons at HERA

We develop the color dipole phenomenology of diffractive photo- and electroproduction γ* N → V(V′)N of light vector mesons (V(1S) = ϕ0, ω0, ρ0) and their radial excitations (V′(2S) ϕ′, ω′, ρ′). The node of the radial wave function of the 2S states in conjunction with the energy dependence of the color dipole cross section is shown to lead to a strikingly different Q 2 and ν dependence of diffractive production of the V(1S) and V′(2S) vector mesons. We discuss the restoration of flavor symmetry and universality properties of production of different vector mesons as a function of Q 2 + m V 2 . The color dipole model predictions for the ρ 0 and ϕ 0 production are in good agreement with the experimental data from the EMC, NMC, ZEUS and H1 collaborations. We present the first direct evaluation of the dipole cross section from these data.

Hard diffractive electroproduction of vector mesons in QCD.

Hard diffractive electroproduction of longitudinally polarized vector mesons is calculated within the leading $\alpha_s\ln{Q^2\over\Lambda_{QCD}^2}$ approximation of QCD using the leading order parton densities within the nucleon. Novel QCD features of the production of excited states and of the restoration of flavor symmetry are analyzed. At the onset of the asymptotic regime, our analysis finds an important role of quark Fermi motion within the diffractively produced vector mesons, and we suggest to use this effect to measure the high momentum tail of the wave function of the vector mesons. We deduce a kinematical boundary for the region of applicability of the decomposition of the hard amplitudes over powers of $Q^2$ and/or a limit on the increase of the cross sections of hard processes at small $x$, and briefly analyze its consequences. We also estimate the nuclear attenuation of the diffractive electroproduction of vector mesons and compare with estimates of the shadowing of the longitudinal structure function.

Effects of spatial size, lattice doubling, and source operators on the hadron spectrum with dynamical staggered quarks at 6/g2=5.6.

We have extended our previous study of the lattice QCD spectrum with 2 flavors of staggered dynamical quarks at $6/g^2=5.6$ and $am_q=0.025$ and 0.01 to larger lattices, with better statistics and with additional sources for the propagators. The additional sources allowed us to estimate the $\Delta$ mass and to measure the masses of all mesons whose operators are local in time. These mesons show good evidence for flavor symmetry restoration, except for the masses of the Goldstone and non-Goldstone pions. PCAC is observed in that $m_\pi^2 \propto m_q$, and $f_\pi$ is estimated. Use of undoubled lattices removes problems with the pion propagator found in our earlier work. Previously we found a large change in the nucleon mass at a quark mass of $am_q=0.01$ when we increased the spatial size from 12 to 16. No such effect is observed at the larger quark mass, $am_q=0.025$. Two kinds of wall source were used, and we have found difficulties in getting consistent results for the nucleon mass between the two sources.

Hadron masses in 2-flavor QCD at β = 5.7

High statistics hadron mass calculations of full QCD with 2-flavor staggered fermions are performed on the Columbia 16GFLOP parallel supercomputer. At β = 5.7 with ma = 0.01 and 0.025 on a 16 3 × 32 lattice using the hybrid algorithm, the restoration of flavor symmetry is easily recognized. However, the mass ratio of the nucleon to the rho is still found to be too high, even when the valence quark mass is reduced to m v a = 0.004. The results at ma = 0.025 with various quenched strange quark masses indicate that better mass ratios of strange hadrons to the nucleon are possible at m s a = 0.1. We also find a factor of two reduction in the errors for the ϱ and nucleon masses by averaging over many time slices in each configuration.

Study of the hadron mass spectrum with dynamical kogut-susskind fermions

Status report is made of a hadron mass calculation with two flavors of dynamical Kogut-Susskind quarks on a lattice of sizes 8 4 – 20 4 and β = 5.5 – 5.7 at m q a = 0.01 and 0.02. Size effects in hadron masses are appreciable at least up to a 16 4 lattice at β = 5.7 and m q a = 0.01. Restoration of flavor symmetry with an increasing β is observed in the pion channel. Various ϱ and nucleon operators give consistent values for their masses. Signal for the Δ baryon is observed, whose mass is larger than that of nucleon by about 10% at β = 5.7 and m q a = 0.01.

Hadron masses from the MTc collaboration

Preliminary results of the MT c collaboration on the hadron spectrum in full QCD with four flavors of staggered fermions are presented. The calculation is being carried out on a 16 3 × 24 lattice at β = 5.15 and 5.35 for a quark mass ma = 0.01, using a Hybrid Monte Carlo algorithm. Some emphasis is put on the investigation of flavor symmetry restoration. The results are compared with a quenched analysis at β values between 5.7 and 6.0, a range where the lattice spacing roughly corresponds to the unquenched simulation.