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 $\Delta m_0 \sim a^3$ 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.Comment: 22 pages, LaTeX, 5 figures (added several references and a comment

Lattice QCD and Hydro/Cascade Model of Heavy Ion Collisions

We report here on a recent lattice study of the QCD transition region at finite temperature and zero chemical potential using domain wall fermions (DWF). We also present a parameterization of the QCD equation of state obtained from lattice QCD that is suitable for use in hydrodynamics studies of heavy ion collisions. Finally, we show preliminary results from a multi-stage hydrodynamics/hadron cascade model of a heavy ion collision, in an attempt to understand how well the experimental data (e.g. particle spectra, elliptic flow, and HBT radii) can constrain the inputs (e.g. initial temperature, freezeout temperature, shear viscosity, equation of state) of the theoretical model.Comment: 10 pages, 12 figures. Proceedings for the 26th Winter Workshop on Nuclear Dynamics, Ocho Rios, Jamaica, Jan 2-9, 201

Baryon-Baryon Interactions from Lattice QCD

We report on new attempt to investigate baryon-baryon interactions in lattice QCD. From the Bethe-Salpeter (BS) wave function, we have successfully extracted the nucleon-nucleon ($NN$) potentials in quenched QCD simulations, which reproduce qualitative features of modern $NN$ potentials. The method has been extended to obtain the tensor potential as well as the central potential and also applied to the hyperon-nucleon ($YN$) interactions, in both quenched and full QCD.Comment: 6 pages, 10 figures, A plenary talk given at the 5-th International Conference on Quark and Nuclear Physics, Beijing, September 21-26, 200

Domain Wall Fermions in Quenched Lattice QCD

We study the chiral properties and the validity of perturbation theory for domain wall fermions in quenched lattice QCD at beta=6.0. The explicit chiral symmetry breaking term in the axial Ward-Takahashi identity is found to be very small already at Ns=10, where Ns is the size of the fifth dimension, and its behavior seems consistent with an exponential decay in Ns within the limited range of Ns we explore. From the fact that the critical quark mass, at which the pion mass vanishes as in the case of the ordinary Wilson-type fermion, exists at finite Ns, we point out that this may be a signal of the parity broken phase and investigate the possible existence of such a phase in this model at finite Ns. The rho and pi meson decay constants obtained from the four-dimensional local currents with the one-loop renormalization factor show a good agreement with those obtained from the conserved currents

The Weakly Coupled Gross-Neveu Model with Wilson Fermions

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.Comment: 15 pages including 1 figur

1++1^{++} Nonet Singlet-Octet Mixing Angle, Strange Quark Mass, and Strange Quark Condensate

Two strategies are taken into account to determine the $f_1(1420)$-$f_1(1285)$ mixing angle $\theta$. (i) First, using the Gell-Mann-Okubo mass formula together with the $K_1(1270)$-$K_1(1400)$ mixing angle $\theta_{K_1}=(-34\pm 13)^\circ$ extracted from the data for ${\cal B}(B\to K_1(1270) \gamma), {\cal B}(B\to K_1(1400) \gamma), {\cal B}(\tau\to K_1(1270) \nu_\tau)$, and ${\cal B}(\tau\to K_1(1420) \nu_\tau)$, gave $\theta = (23^{+17}_{-23})^\circ$. (ii) Second, from the study of the ratio for $f_1(1285) \to \phi\gamma$ and $f_1(1285) \to \rho^0\gamma$ branching fractions, we have two-fold solution $\theta=(19.4^{+4.5}_{-4.6})^\circ$ or $(51.1^{+4.5}_{-4.6})^\circ$. Combining these two analyses, we thus obtain $\theta=(19.4^{+4.5}_{-4.6})^\circ$. We further compute the strange quark mass and strange quark condensate from the analysis of the $f_1(1420)-f_1(1285)$ mass difference QCD sum rule, where the operator-product-expansion series is up to dimension six and to ${\cal O}(\alpha_s^3, m_s^2 \alpha_s^2)$ accuracy. Using the average of the recent lattice results and the $\theta$ value that we have obtained as inputs, we get $/ =0.41 \pm 0.09$.Comment: 10 pages, 1 table, published versio

Domain-Wall Fermions at Strong Coupling

The DWF formulation becomes increasingly problematic at gauge couplings for which $a^{-1}<2$ GeV, where the roughness of the gauge field leads to increased explicit chiral symmetry breaking (\mres). This problem becomes especially severe for sufficiently strong coupling where the underlying 4-dimensional Wilson theory is in the Aoki phase. We review our attempts to find a suitable modification of the gauge and/or the fermion action which would allow the DWF method to work reliably at stronger coupling.Comment: 4 pages, 4 figures, Lattice2004(chiral

Pion scattering in Wilson ChPT

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) a\Lambda_QCD^2 and (ii) a^2\Lambda_QCD^3. Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the O(a^2) terms the I=0 and I=2 scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a^2\ln M_{\pi}^2 are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.Comment: 20 pages, 4 figures. V3: Comments on finite size effects and the axial vector current added, one more reference. To be published in PR

A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\bar{\psi} i \gamma_{5} \tau^{3}\psi$ was added to the fermion action. The order parameter $$ was computed with the Hybrid Monte Carlo algorithm at several values of $(\beta,\kappa,h)$ on lattices of sizes $4^4$ to $12^4$ and extrapolated to $h=0$. The existence of a parity-flavor breaking phase can be confirmed at $\beta=4.0$ and 4.3, while we do not find parity-flavor breaking at $\beta=4.6$ and 5.0.Comment: 8 pages, 5 figures, Revised version as to be published in Phys.Rev.

The s process in massive stars at low metallicity. Effect of primary N14 from fast rotating stars

The goal of this paper is to analyze the impact of a primary neutron source on the s-process nucleosynthesis in massive stars at halo metallicity. Recent stellar models including rotation at very low metallicity predict a strong production of primary N14. Part of the nitrogen produced in the H-burning shell diffuses by rotational mixing into the He core where it is converted to Ne22 providing additional neutrons for the s process. We present nucleosynthesis calculations for a 25 Msun star at [Fe/H] = -3, -4, where in the convective core He-burning about 0.8 % in mass is made of primary Ne22. The usual weak s-process shape is changed by the additional neutron source with a peak between Sr and Ba, where the s-process yields increase by orders of magnitude with respect to the yields obtained without rotation. Iron seeds are fully consumed and the maximum production of Sr, Y and Zr is reached. On the other hand, the s-process efficiency beyond Sr and the ratio Sr/Ba are strongly affected by the amount of Ne22 and by nuclear uncertainties, first of all by the Ne22(alpha,n)Mg25 reaction. Finally, assuming that Ne22 is primary in the considered metallicity range, the s-process efficiency decreases with metallicity due to the effect of the major neutron poisons Mg25 and Ne22. This work represents a first step towards the study of primary neutron source effect in fast rotating massive stars, and its implications are discussed in the light of spectroscopic observations of heavy elements at halo metallicity.Comment: Accepted for publication in ApJ Letters, 11 pages, 2 figures, 1 tabl