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Register a new userInfinite temperature limit of meson spectral functions calculated on the lattice
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F. Karsch
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We analyze the cut-off dependence of mesonic spectral functions calculated at finite temperature on Euclidean lattices with finite temporal extent. In the infinite temperature limit we present analytic results for lattice spectral functions calculated with standard Wilson fermions as well as a truncated perfect action. We explicitly determine the influence of `Wilson doublers on the high momentum structure of the mesonic spectral functions and show that this cut-off effect is strongly suppressed when using an improved fermion action.
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First principle calculation of the QCD spectral functions (SPFs) based on the lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian inference theory and the Maximum Entropy Method (MEM), which is a useful tool to extract SPFs from the imaginary-time correlation functions numerically obtained by the Monte Carlo method. Three important aspects of MEM are (i) it does not require a priori assumptions or parametrizations of SPFs, (ii) for given data, a unique solution is obtained if it exists, and (iii) the statistical significance of the solution can be quantitatively analyzed. The ability of MEM is explicitly demonstrated by using mock data as well as lattice QCD data. When applied to lattice data, MEM correctly reproduces the low-energy resonances and shows the existence of high-energy continuum in hadronic correlation functions. This opens up various possibilities for studying hadronic properties in QCD beyond the conventional way of analyzing the lattice data. Future problems to be studied by MEM in lattice QCD are also summarized.
It is shown that the Greens function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
We present results for the mass of the eta-prime meson in the continuum limit for two-flavor lattice QCD, calculated on the CP-PACS computer, using a renormalization-group improved gauge action, and Sheikholeslami and Wohlerts fermion action with tadpole-improved csw. Correlation functions are measured at three values of the coupling constant beta corresponding to the lattice spacing a approx. 0.22, 0.16, 0.11 fm and for four values of the quark mass parameter kappa corresponding to mpi over mrho approx. 0.8, 0.75, 0.7 and 0.6. For each beta, kappa pair, 400-800 gauge configurations are used. The two-loop diagrams are evaluated using a noisy source method. We calculate eta-prime propagators using local sources, and find that excited state contributions are much reduced by smearing. A full analysis for the smeared propagators gives metaprime=0.960(87)+0.036-0.248 GeV, in the continuum limit, where the second error represents the systematic uncertainty coming from varying the functional form for chiral and continuum extrapolations.
By exploiting the similarity between Blochs theorem for electrons in crystalline solids and the problem of Landau gauge-fixing in Yang-Mills theory on a replicated lattice, one is able to obtain essentially infinite-volume results from numerical simulations performed on a relatively small lattice. This approach, proposed by D. Zwanziger in cite{Zwanziger:1993dh}, corresponds to taking the infinite-volume limit for Landau-gauge field configurations in two steps: firstly for the gauge transformation alone, while keeping the lattice volume finite, and secondly for the gauge-field configuration itself. The solutions to the gauge-fixing condition are then given in terms of Bloch waves. Applying the method to data from Monte Carlo simulations of pure SU(2) gauge theory in two and three space-time dimensions, we are able to evaluate the Landau-gauge gluon propagator for lattices of linear extent up to sixteen times larger than that of the simulated lattice. The approach is reminiscent of Fisher and Ruelles construction of the thermodynamic limit in classical statistical mechanics.
We propose a method to non-perturbatively calculate the forward-scattering matrix elements relevant to inclusive semi-leptonic B meson decays. Corresponding hadronic structure functions at unphysical kinematics are accessible through lattice QCD calculation of four-point correlation functions. The unphysical kinematical point may be reached by analytic continuation from the physical differential decay rate. A numerical test is performed for the B_s -> X_c l nu mode in the zero-recoil limit. We use lattice ensembles generated with 2+1 dynamical quark flavors. The valence charm quark mass is tuned to its physical value, while the bottom quark mass is varied in the range (1.56-2.44)m_c. From the numerical results we can identify the contributions of the ground state D_s^(*) meson as well as those of excited states or continuum states.
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