In lattice QCD, the Maximum Entropy Method can be used to reconstruct spectral functions from euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and give a modification that avoids this. We demonstrate this approach using the vector currentcurrent correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.PACS numbers: 12.38.Gc Lattice QCD calculations, 12.38.Mh Quark-gluon plasmaIn the deconfined, high-temperature phase of Quantum Chromodynamics, the behaviour of spectral functions of conserved currents at small energies is of intrinsic interest due to its relation with transport properties of the quark-gluon plasma (QGP). According to the Kubo formulas [1], transport coefficients, such as the shear and bulk viscosities and the electrical conductivity, are proportional to the slope of appropriate spectral functions at vanishing energy. The success of e.g. ideal hydrodynamics in heavy ion phenomenology, assuming vanishing viscosities and requiring early thermalization [2], has lead to the notion [3] that the QGP created in relativistic heavy ion collisions at RHIC is strongly coupled and that the ratio of shear viscosity to entropy density in this sQGP may be close to the conjectured lower bound [4] reached in thermal field theories that admit a gravity dual [5].In order to put these ideas on firm footing, it is important to have a first-principle calculation of transport coefficients in the strongly coupled regime of hot QCD. As is well known [6,7], a nonperturbative calculation using lattice QCD is difficult due to the necessity to perform an analytic continuation from imaginary to real time. The most common approach used to obtain spectral functions from euclidean correlators is the Maximum Entropy Method [8], employing Bryan's algorithm [9]. Our first aim in this Letter is to discuss this method in some detail and point out a source of numerical instabilities present in most finite-temperature studies available to date. We show how the algorithm can be modified to avoid this problem. Our second aim is to apply the new method to the vector current-current correlator, obtained in quenched lattice QCD simulations at finite temperature, using staggered quarks. We study the behaviour at small energies and argue that it allows us to extract a value for electrical conductivity in the strongly coupled regime above the deconfinement transition.Maximum Entropy Method -The relation between the euclidean correlator G(τ ) = d 3 x J(τ, x)J † (0, 0) at zero momentum and the corresponding spectral function ρ(ω) readswhere the kernel is given byWe consider (local) meson operators of the form J(τ, x) =q(τ, x)Γq(τ, x), where Γ depends on the channel under consideration. The temperature T is related to the euclidean temporal extent N τ by 1/T = aN τ , where a is the (temporal) lattice spacing. Th...

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay B → D ν at nonzero recoil. We carry out numerical simulations on fourteen ensembles of gauge-field configurations generated with 2+1 flavors of asqtad-improved staggered sea quarks. The ensembles encompass a wide range of lattice spacings (approximately 0.045 to 0.12 fm) and ratios of light (up and down) to strange sea-quark masses ranging from 0.05 to 0.4.For the b and c valence quarks we use improved Wilson fermions with the Fermilab interpretation, while for the light valence quarks we use asqtad-improved staggered fermions. We extrapolate our results to the physical point using rooted staggered heavy-light meson chiral perturbation theory.We then parameterize the form factors and extend them to the full kinematic range using modelindependent functions based on analyticity and unitarity. We present our final results for f + (q 2 ) and f 0 (q 2 ), including statistical and systematic errors, as coefficients of a series in the variable z and the covariance matrix between these coefficients. We then fit the lattice form-factor data jointly with the experimentally measured differential decay rate from BaBar to determine the CKM matrix element, |V cb | = (39.6 ± 1.7 QCD+exp ± 0.2 QED ) × 10 −3 . As a byproduct of the joint fit we obtain the form factors with improved precision at large recoil. Finally, we use them to update our calculation of the ratio R(D) in the Standard Model, which yields R(D) = 0.299(11).

A new quark-field smearing algorithm is defined which enables efficient calculations of a broad range of hadron correlation functions. The technique applies a low-rank operator to define smooth fields that are to be used in hadron creation operators. The resulting space of smooth fields is small enough that all elements of the reduced quark propagator can be computed exactly at reasonable computational cost. Correlations between arbitrary sources, including multihadron operators can be computed a posteriori without requiring new lattice Dirac operator inversions. The method is tested on realistic lattice sizes with light dynamical quarks.

We report on a scale determination with gradient-flow techniques on the N f = 2 + 1 + 1 HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales √ t 0 /a and w 0 /a and their tree-level improvements, √ t 0,imp and w 0,imp , are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density E. Using a combination of continuum chiral perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales √ t 0 = 0.1416( systematic errors. The precision of w 0 and √ t 0 is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass-dependence of √ t 0 and w 0 , which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of E(t) . For long flow times, the autocorrelation length of E appears to be comparable to that of the topological charge.