Chronological Inversion Method for the Dirac Matrix in Hybrid Monte Carlo

In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve smoothly as a function of Molecular Dynamics time. Here we investigate improved methods of estimating the trial or starting solutions for the Dirac matrix inversion as superpositions of a chronological sequence of solutions in the recent past. By taking as the trial solution the vector which minimizes the residual in the linear space spanned by the past solutions, the number of conjugate gradient iterations per unit MD time is decreased by at least a factor of 2. Extensions of this basic approach to precondition the conjugate gradient iterations are also discussed.Comment: 35 pages, 18 EPS figures A new "preconditioning" method, derived from the Chronological Inversion, is described. Some new figures are appended. Some reorganization of the material has taken plac

Non-perturbative improvement of bilinears in unquenched QCD

We describe how the improvement of quark bilinears generalizes from quenched to unquenched QCD, and discuss which of the additional improvement constants can be determined using Ward Identities.Comment: LATTICE99 (Improvement and Renormalization). 3 pages, no figures. Corrected error (improvement coefficient $g_T$ is not needed

Entropy of Horizons, Complex Paths and Quantum Tunneling

In any spacetime, it is possible to have a family of observers following a congruence of timelike curves such that they do not have access to part of the spacetime. This lack of information suggests associating a (congruence dependent) notion of entropy with the horizon that blocks the information from these observers. While the blockage of information is absolute in classical physics, quantum mechanics will allow tunneling across the horizon. This process can be analysed in a simple, yet general, manner and we show that the probability for a system with energy $E$ to tunnel across the horizon is $P(E)\propto\exp[-(2\pi/\kappa)E)$ where $\kappa$ is the surface gravity of the horizon. If the surface gravity changes due to the leakage of energy through the horizon, then one can associate an entropy $S(M)$ with the horizon where $dS = [ 2\pi / \kappa (M) ] dM$ and $M$ is the active gravitational mass of the system. Using this result, we discuss the conditions under which, a small patch of area $\Delta A$ of the horizon contributes an entropy $(\Delta A/4L_P^2)$, where $L_P^2$ is the Planck area.Comment: published versio

Light Quark Masses and the CP violation parameter ϵ′/ϵ\epsilon'/\epsilon

We present estimates of light quarks masses using lattice data. Our main results are based on a global analysis of all the published data for Wilson and Staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. The Wilson and Staggered results agree after extrapolation to the continuum limit for both the $n_f=0,2$ theories. Our best estimates, in the MSbar scheme at scale $2 GeV$, are $mbar=3.2(4) MeV$ and $m_s = 90(20) MeV$ in the quenched approximation, and $mbar ~ 2.7 MeV$ and $m_s ~ 70 MeV$ for the $n_f=2$ theory. These estimates are significantly smaller than phenomenological estimates based on sum rules, but maintain the ratios predicted by chiral perturbation theory. Along with the new estimates of 4-fermion operators, lower quark masses have a significant impact on the extraction of $\epsilon'/\epsilon$ from the Standard Model.Comment: 3 Pages LaTex. Axis files of figures included. Talk presented at LATTICE96 (phenomenology

Heavy Quarkonium Potential Model and the 1P1{}^1P_1 State of Charmonium

A theoretical explanation of the observed splittings among the P~states of charmonium is given with the use of a nonsingular potential model for heavy quarkonia. We also show that the recently observed mass difference between the center of gravity of the ${}^3P_J$ states and the ${}^1P_1$ state of $c\bar{c}$ does not provide a direct test of the color hyperfine interaction in heavy quarkonia. Our theoretical value for the mass of the ${}^1P_1$ state is in agreement with the experimental result, and its E1 transition width is 341.8~keV. The mass of the $\eta_c'$ state is predicted to be 3622.3~MeV.Comment: 15 page REVTEX documen

Understanding the effects of geometry and rotation on pulsar intensity profiles

We have developed a method to compute the possible distribution of radio emission regions in a typical pulsar magnetosphere, taking into account the viewing geometry and rotational effects of the neutron star. Our method can estimate the emission altitude and the radius of curvature of particle trajectory as a function of rotation phase for a given inclination angle, impact angle, spin-period, Lorentz factor, field line constant and the observation frequency. Further, using curvature radiation as the basic emission mechanism, we simulate the radio intensity profiles that would be observed from a given distribution of emission regions, for different values of radio frequency and Lorentz factor. We show clearly that rotation effects can introduce significant asymmetries into the observed radio profiles. We investigate the dependency of profile features on various pulsar parameters. We find that the radiation from a given ring of field lines can be seen over a large range of pulse longitudes, originating at different altitudes, with varying spectral intensity. Preferred heights of emission along discrete sets of field lines are required to reproduce realistic pulsar profiles, and we illustrate this for a known pulsar. Finally, we show how our model provides feasible explanations for the origin of core emission, and also for one-sided cones which have been observed in some pulsars.Comment: 21 pages, 11 figures, accepted for publication in MNRA