Nonperturbative renormalization and O(a) -improvement of the nonsinglet vector current with Nf=2+1 Wilson fermions and tree-level Symanzik improved gauge action

In calculating hadronic contributions to precision observables for tests of the Standard Model in lattice QCD, the electromagnetic current plays a central role. Using a Wilson action with $\mathrm{O}(a)$ improvement in QCD with ${N}_{\mathrm{f}}$ flavors, a counterterm must be added to the vector current in order for its on-shell matrix elements to be $\mathrm{O}(a)$ improved. In addition, the local vector current, which has support on one lattice site, must be renormalized. At $\mathrm{O}(a)$, the breaking of the $\mathrm{SU}({N}_{\mathrm{f}})$ symmetry by the quark mass matrix leads to a mixing between the local currents of different quark flavors. We present a nonperturbative calculation…

Nucleon isovector charges and twist-2 matrix elements with Nf=2+1 dynamical Wilson quarks

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with nonperturbatively improved ${N}_{f}=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to ${M}_{\ensuremath{\pi}}\ensuremath{\approx}200\text{ }\text{ }\mathrm{MeV}$. Several source-sink separations (typically $\ensuremath{\sim}1.0$ to $\ensuremath{\sim}1.5\text{ }\text{ }\mathrm{fm}$) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available sou…

Nucleon average quark momentum fraction with Nf = 2+1 Wilson fermions

We report on an analysis of the average quark momentum fraction of the nucleon and related quantities using Nf = 2 + 1 Wilson fermions. Computations are performed on four CLS ensembles covering three values of the lattice spacing at pion masses down to Mπ ≈ 200 MeV. Several source-sink separations (~ 1:0 fm to ~ 1:4 fm) are used to assess the excited-state contamination. To gain further insight, the generalized pencil-of-functions approach has been implemented to reduce the excited-state contamination in the relevant two-and three-point functions. Preliminary results are shown for the isovector nucleon charges from vector, axial vector and tensor derivative (twist-2) operators.

Nonperturbative renormalization and O(a)-improvement of the nonsinglet vector current with Nf=2+1 Wilson fermions and tree-level Symanzik improved gauge action

In calculating hadronic contributions to precision observables for tests of the Standard Model in lattice QCD, the electromagnetic current plays a central role. Using a Wilson action with O(a) improvement in QCD with Nf flavors, a counterterm must be added to the vector current in order for its on-shell matrix elements to be O(a) improved. In addition, the local vector current, which has support on one lattice site, must be renormalized. At O(a), the breaking of the SU(Nf) symmetry by the quark mass matrix leads to a mixing between the local currents of different quark flavors. We present a nonperturbative calculation of all the required improvement and renormalization constants needed for …

Nucleon isovector charges and twist-2 matrix elements with Nf=2+1 dynamical Wilson quarks

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with nonperturbatively improved Nf=2+1 Wilson fermions, covering four values of the lattice spacing and pion masses down to Mπ≈200 MeV. Several source-sink separations (typically ∼1.0 to ∼1.5 fm) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed nonperturbatively using the R…

Non-perturbative renormalization and O$(a)$-improvement of the non-singlet vector current with $N_{\mathrm{f}}=2+1$ Wilson fermions and tree-level Symanzik improved gauge action

In calculating hadronic contributions to precision observables for tests of the Standard Model in lattice QCD, the electromagnetic current plays a central role. Using a Wilson action with O($a$) improvement in QCD with $N_{\mathrm{f}}$ flavors, a counterterm must be added to the vector current in order for its on-shell matrix elements to be O($a$) improved. In addition, the local vector current, which has support on one lattice site, must be renormalized. At O($a$), the breaking of the SU($N_{\mathrm{f}}$) symmetry by the quark mass matrix leads to a mixing between the local currents of different quark flavors. We present a non-perturbative calculation of all the required improvement and re…

Aspects of chiral symmetry in QCD at T = 128 MeV

We investigate several aspects of chiral symmetry in QCD at a temperature of $T = 128\,\text{MeV}$. The study is based on a $24\times 96^3$ lattice-QCD ensemble with O($a$)-improved Wilson quarks and physical up, down and strange quark masses. The pion quasiparticle turns out to be significantly lighter than the zero-temperature pion mass, even though the corresponding static correlation length is shorter. We perform a quantitative comparison of our findings to predictions of chiral perturbation theory. Among several order parameters for chiral symmetry restoration, we compute the difference of the vector- and axial-vector time-dependent correlators and find it to be reduced by a factor $\s…

Genome-wide Analyses Identify KIF5A as a Novel ALS Gene

© 2018 Elsevier Inc.

Testing the strength of the UA(1) anomaly at the chiral phase transition in two-flavour QCD

We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $\mathcal{O}(a)$-improved Wilson quarks. Particular emphasis lies on the pattern of chiral symmetry restoration, which we probe via the static screening correlators. On $32^3$ volumes we observe that the screening masses in transverse iso-vector vector and axial-vector channels become degenerate at the transition temperature. The splitting between the screening masses in iso-vector scalar and pseudoscalar channels is strongly reduced compared to the splitting at zero temperature and is actually consistent with zero within uncertainties. In this proceedings article we extend our studies to …

Estimation of the photon production rate using imaginary momentum correlators

The thermal photon emission rate is determined by the spatially transverse, in-medium spectral function of the electromagnetic current. Accessing the spectral function using Euclidean data is, however, a challenging problem due to the ill-posed nature of inverting the Laplace transform. In this contribution, we present the first results on implementing the proposal of directly computing the analytic continuation of the retarded correlator at fixed, vanishing virtuality of the photon via the calculation of the appropriate Euclidean correlator at imaginary spatial momentum. We employ two dynamical O(a)-improved Wilson fermions at a temperature of 250 MeV.

Photon and dilepton production rate in the quark-gluon plasma from lattice QCD

The photon emissivity of the quark-gluon plasma (QGP) is an important input to predict the photon yield in heavy-ion collisions, particularly for transverse momenta in the range of 1 to 2 GeV. Photon production in the QGP can be probed non-perturbatively in lattice QCD via (Euclidean) time-dependent correlators. Analyzing the spatially transverse channel, as well as the difference of the transverse and longitudinal channels as a consistency check, we determine the photon emissivity based on continuum-extrapolated correlators in two-flavour QCD. Estimates of the lepton-pair production rate can be derived by combining the two aforementioned channels. © Copyright owned by the author(s) under t…

Photon emissivity of the quark-gluon plasma: A lattice QCD analysis of the transverse channel

We present results for the thermal photon emissivity of the quark-gluon plasma derived from spatially transverse vector correlators computed in lattice QCD at a temperature of 250 MeV. The analysis of the spectral functions, performed at fixed spatial momentum, is based on continuum-extrapolated correlators obtained with two flavours of dynamical Wilson fermions. We compare the next-to-leading order perturbative QCD correlators, as well as the ${\cal N}=4$ supersymmetric Yang-Mills correlators at infinite coupling, to the correlators from lattice QCD and find them to lie within $\sim10\%$ of each other. We then refine the comparison, performing it at the level of filtered spectral functions…

Deep inelastic scattering off quark-gluon plasma and its photon emissivity

The photon emissivity of quark-gluon plasma probes the interactions in the medium and differs qualitatively between a weakly coupled and a strongly coupled plasma in the soft-photon regime. The photon emissivity is given by the product of kinematic factors and a spectral function associated with the two-point correlator of the electromagnetic current at lightlike kinematics. A certain Euclidean correlator at imaginary spatial momentum can be calculated in lattice QCD and is given by an integral over the relevant spectral function at lightlike kinematics. I present a first exploratory lattice calculation of this correlator. Secondly, I show how Euclidean correlators at imaginary spatial mome…

Vacuum correlators at short distances from lattice QCD

Non-perturbatively computing the hadronic vacuum polarization at large photon virtualities and making contact with perturbation theory enables a precision determination of the electromagnetic coupling at the $Z$ pole, which enters global electroweak fits. In order to achieve this goal ab initio using lattice QCD, one faces the challenge that, at the short distances which dominate the observable, discretization errors are hard to control. Here we address challenges of this type with the help of static screening correlators in the high-temperature phase of QCD, yet without incurring any bias. The idea is motivated by the observations that (a) the cost of high-temperature simulations is typica…

Estimating the thermal photon production rate using lattice QCD

We present results for the photon emission rate determined from the transverse channel vector correlator at fixed spatial momentum using two flavors of dynamical Wilson fermions at $T\sim$250 MeV. We estimate the transverse channel spectral function using the continuum extrapolated correlator by applying various fit ans\"atze with a smooth matching to the NLO perturbative result. We confront our estimate based on this channel with the latest results of our collaboration based on the difference of the transverse and longitudinal channels.

An estimate for the thermal photon rate from lattice QCD

We estimate the production rate of photons by the quark-gluon plasma in lattice QCD. We propose a new correlation function which provides better control over the systematic uncertainty in estimating the photon production rate at photon momenta in the range {\pi}T/2 to 2{\pi}T. The relevant Euclidean vector current correlation functions are computed with $N_{\mathrm f}$ = 2 Wilson clover fermions in the chirally-symmetric phase. In order to estimate the photon rate, an ill-posed problem for the vector-channel spectral function must be regularized. We use both a direct model for the spectral function and a model-independent estimate from the Backus-Gilbert method to give an estimate for the p…

Deep inelastic scattering on the quark-gluon plasma

We provide an interpretation of the structure functions of a thermal medium such as the quark-gluon plasma in terms of the scattering of an incoming electron on the medium via the exchange of a spacelike photon. We then focus on the deep-inelastic scattering (DIS) regime, and formulate the corresponding moment sum rules obeyed by the structure functions. Accordingly, these moments are given by the thermal expectation value of twist-two operators, which is computable from first principles in lattice QCD for the first few moments. We also show how lattice QCD calculations can be used to probe how large the photon virtuality needs to be in order for the Bjorken scaling of structure functions t…

The rate of photon production in the quark-gluon plasma from lattice QCD

We calculate the thermal rate of real-photon production in the quark-gluon plasma at a temperature of $T=254$ MeV using lattice QCD. The calculation is based on the difference between the spatially transverse and longitudinal parts of the polarization tensor, which has the advantage of falling off rapidly at large frequencies. We obtain this linear combination in the time-momentum representation from lattice QCD with two flavors of quarks in the continuum limit with a precision of about two parts per mille. Applying a theoretically motivated fit ansatz for the associated spectral function, we obtain values for the photon rate that are in line with QCD weak-coupling calculations; for photon …

Nonperturbative renormalization and O ( a ) -improvement of the nonsinglet vector current with N

Nonperturbative renormalization and $O(a )$-improvement of the nonsinglet vector current with $N_f = 2 + 1$ Wilson fermions and tree-level Symanzik improved gauge action

Physical review / D 99(1), 014519 (2019). doi:10.1103/PhysRevD.99.014519

A variational method for spectral functions

The Generalized Eigenvalue Problem (GEVP) has been used extensively in the past in order to reliably extract energy levels from time-dependent Euclidean correlators calculated in Lattice QCD. We propose a formulation of the GEVP in frequency space. Our approach consists of applying the model-independent Backus-Gilbert method to a set of Euclidean two-point functions with common quantum numbers. A GEVP analysis in frequency space is then applied to a matrix of estimators that allows us, among other things, to obtain particular linear combinations of the initial set of operators that optimally overlap to different local regions in frequency. We apply this method to lattice data from NRQCD. Th…

Electromagnetic form factors and axial charge of the nucleon from Nf = 2 + 1 Wilson fermions

We present an update on our determination of the electromagnetic form factors and axial charge of the nucleon from theNf= 2 + 1 CLS ensembles with increased statistics and an additional finer lattice spacing. We also investigate the impact ofO(a)-improvement of the currents.

Lattice QCD estimate of the quark-gluon plasma photon emission rate

We present a computation of the photon emission rate of the quark-gluon plasma from two-flavor lattice QCD at a temperature of 254 MeV, which follows up on the work presented in [1]. We perform a continuum extrapolation of the vector-current correlator, and consider a linear combination of the Lorentz indices corresponding to a UV-finite spectral function. To extract the spectral function from the lattice correlators, an ill-posed inverse problem, we model the spectral function with a Pad\'e ansatz. We further constrain our analysis by simultaneously fitting data with different momenta. We present results for a multi-momentum fit including the three smallest momenta available from our latti…

Non-perturbative improvement of the vector current in Wilson lattice QCD

Many observables of interest in lattice QCD are extracted from correlation functions involving the vector current. If Wilson fermions are used, it is therefore of practical importance that, besides the action, the current be O($a$) improved in order to remove the leading discretization errors from the observables. Here we introduce and apply a new method to determine the improvement coefficient for the two most widely used discretizations of the current.