arXiv subjects

Tim Harris

Publications and source records attributed to Tim Harris.

At least 55 records · Page 3Linked to original sources

arXiv2021

A novel computational paradigm for a precise determination of the hadronic contribution to $(g_μ-2)$ from lattice QCD

The hadronic contribution to the muon anomalous magnetic moment $a_μ=(g_μ-2)/2$ has to be determined at the per-mille level for the Standard Model prediction to match the expected final uncertainty of the ongoing E989 experiment. That is 3 times better than the current precision from the dispersive approach, and 5-15 times smaller than the uncertainty based on the purely theoretical determinations from lattice QCD. So far the stumbling-block is the large statistical error in the Monte Carlo evaluation of the required correlation functions which can hardly be tamed by brute force. In this talk we present our proposal to solve this problem by multi-level Monte Carlo integration, a technique which reduces the variance of correlators exponentially in the distance of the fields. We report the results of our feasibility tests for the computation of the Hadronic Vacuum Polarization on a lattice with a linear extension of 3~fm, a spacing of 0.065 fm, and a pion mass of 270 MeV. Indeed the two-level integration makes the contribution to the statistical error from long-distances de-facto negligible by accelerating its inverse scaling with the cost of the simulation. These findings establish multi-level Monte Carlo as a solid and efficient method for a precise lattice determination of the hadronic contribution to $a_μ$.

hep-lat↗

arXiv2020

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 to set in. Finally, we provide the parton-model interpretation of the structure functions in the Bjorken limit and test its consistency. As in DIS on the proton, the kinematic variable $x$ is proportional to the longitudinal momentum carried by the partons, however $x$ ranges from zero to infinity. Choosing the parton momentum parametrization to be $ x T u$ where $u$ is the fluid four-velocity and $T$ its temperature in the rest frame, the parton distribution function for a plasma of non-interacting quarks is proportional to $ x \log(1+e^{-x/2}) $.

hep-ph↗

arXiv2020

Frequency-splitting estimators for single-propagator traces

In these proceedings we address the computation of quark-line disconnected diagrams in lattice QCD. The evaluation of these diagrams is required for many phenomenologically interesting observables, but suffers from large statistical errors due to the vacuum and random-noise contributions to their variances. Motivated by a theoretical analysis of the variances, we introduce a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 MeV. The use of these estimators reduces the cost of the computation by one to two orders of magnitude over standard estimators depending on the fermion bilinear. As a concrete application, we show the impact of these findings on the computation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

hep-lat↗

arXiv2020

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 momenta $ 1.0\leq k[{\rm GeV}]\leq 1.4$, our non-perturbative results constrain the rate to be no larger than twice the weak-coupling prediction. We also provide a physics interpretation of the electromagnetic spectral functions valid for all frequencies and momenta.

hep-lat↗

arXiv2019

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 Padé 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 lattice analysis.

hep-lat↗

arXiv2019

Nucleon isovector charges and twist-2 matrix elements with $N_f=2+1$ 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 non-perturbatively improved $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_π\approx200$MeV. Several source-sink separations (typically ~1.0fm to ~1.5fm) 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 non-perturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the $\overline{MS}$ scheme at a scale of $μ=2$GeV and are obtained from a combined chiral, continuum and finite-size extrapolation. For the nucleon isovector axial, scalar and tensor charges we find physical values of $g_A^{u-d}=1.242(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+00}{-31})_\text{sys}$, $g_S^{u-d}=1.13(11)_\text{stat}(\genfrac{}{}{0pt}{2}{+07}{-06})_\text{sys}$ and $g_T^{u-d}=0.965(38)_\text{stat}(\genfrac{}{}{0pt}{2}{+13}{-41})_\text{sys}$, respectively, where individual systematic errors in each direction from the chiral, continuum and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by $\langle x\rangle_{u-d}=0.180(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+14}{-06})_\text{sys}$, $\langle x\rangle_{Δu-Δd}=0.221(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+10}{-00})_\text{sys}$ and $\langle x\rangle_{δu-δd}=0.212(32)_\text{stat}(\genfrac{}{}{0pt}{2}{+20}{-10})_\text{sys}$, respectively.

hep-lat↗

arXiv2019

Testing the strength of the $\text{U}_A(1)$ 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 matrix elements and iso-singlet correlation functions. Furthermore, we present results on larger volumes, including first results at the physical pion mass.

hep-lat↗

arXiv2019

Frequency-splitting estimators of single-propagator traces

Single-propagator traces are the most elementary fermion Wick contractions which occur in numerical lattice QCD, and are usually computed by introducing random-noise estimators to profit from volume averaging. The additional contribution to the variance induced by the random noise is typically orders of magnitude larger than the one due to the gauge field. We propose a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 MeV. Depending on the fermion bilinear considered, the cost of computing these diagrams is reduced by one to two orders of magnitude or more with respect to standard random-noise estimators. As two concrete examples of physics applications, we compute the disconnected contributions to correlation functions of two vector currents in the isosinglet omega channel and to the hadronic vacuum polarization relevant for the muon anomalous magnetic moment. In both cases, estimators with variances dominated by the gauge noise are computed with a modest numerical effort. Theory suggests large gains for disconnected three and higher point correlation functions as well. The frequency-splitting estimators and their split-even components are directly applicable to the newly proposed multi-level integration in the presence of fermions.

hep-lat↗

arXiv2019

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 renormalization constants needed for the local and the conserved electromagnetic current in QCD with $N_{\mathrm{f}}=2+1$ O($a$)-improved Wilson fermions and tree-level Symanzik improved gauge action, with the exception of one coefficient, which we show to be order $g_0^6$ in lattice perturbation theory. The method is based on the vector and axial Ward identities imposed at finite lattice spacing and in the chiral limit. We make use of lattice ensembles generated as part of the Coordinated Lattice Simulations (CLS) initiative.

hep-lat↗

arXiv2018

The hadronic vacuum polarization contribution to $(g-2)_μ$ from $2+1$ flavours of O($a$) improved Wilson quarks

We report on our ongoing project to determine the leading-order hadronic vacuum polarisation contribution to the muon $g-2$, using ensembles with $N_f=2+1$ flavours of O($a$) improved Wilson quarks generated by the CLS effort, with pion masses down to the physical value. We employ O($a$) improved versions of the local and conserved vector currents to compute the contributions of the light, strange and charm quarks to $(g-2)_μ$, using the time-momentum representation. We perform a detailed investigation of the systematic effects arising from constraining the long-distance regime of the vector correlator. To this end we make use of auxiliary calculations in the iso-vector channel using distillation and the Lüscher formalism. Our results are corrected for finite-volume effects by computing the timelike pion form factor in finite and infinite volume. For certain parameter choices, the corrections computed in this way can also be confronted with results determined on different volumes. Currently, the overall precision of our results is limited by the uncertainties in the lattice scale.

hep-lat↗

arXiv2018

Multi-level integration for meson propagators

The computation of many correlation functions in lattice QCD is severely hindered by a signal-to-noise problem. Recent developments in the factorization of both the fermion propagator and determinant pave the way for the implementation of multi-level Monte Carlo integration techniques for lattice QCD. In these proceedings we introduce new strategies for the estimation of the factorized contribution to the connected and disconnected diagrams for meson two-point functions. An estimator for the factorized connected diagram is constructed sequentially for a two-level integration scheme. For the disconnected diagram, we introduce an improved estimator by performing a frequency-splitting of traces, applicable with or without multi-level integration. Preliminary results in the quenched theory with a two-level integration scheme are presented.

hep-lat↗

arXiv2018

Nucleon charges and quark momentum fraction with $N_f=2+1$ Wilson fermions

We present a nucleon structure analysis including local isovector charges as well as twist-2 operator insertions. Computations are performed on CLS ensembles with $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_π\approx 200\,\mathrm{MeV}$. Several source-sink separations (typically $\sim 1.0\,\mathrm{fm}$ to $\sim 1.5\,\mathrm{fm}$) allow us to assess excited-state contaminations. Results on each ensemble are obtained from simultaneous two-state fits including all observables and all available source-sink separations with the mass gap as a free fit parameter. Finally, the chiral, continuum and finite size extrapolation is performed to extract physical results.

hep-lat↗

arXiv2018

Persistent Memory Transactions

This paper presents a comprehensive analysis of performance trade offs between implementation choices for transaction runtime systems on persistent memory. We compare three implementations of transaction runtimes: undo logging, redo logging, and copy-on-write. We also present a memory allocator that plugs into these runtimes. Our microbenchmark based evaluation focuses on understanding the interplay between various factors that contribute to performance differences between the three runtimes -- read/write access patterns of workloads, size of the persistence domain (portion of the memory hierarchy where the data is effectively persistent), cache locality, and transaction runtime bookkeeping overheads. No single runtime emerges as a clear winner. We confirm our analysis in more realistic settings of three "real world" applications we developed with our transactional API: (i) a key-value store we implemented from scratch, (ii) a SQLite port, and (iii) a persistified version of memcached, a popular key-value store. These findings are not only consistent with our microbenchmark analysis, but also provide additional interesting insights into other factors (e.g. effects of multithreading and synchronization) that affect application performance.

cs.DC↗

arXiv2017

Nucleon average quark momentum fraction with $N_\mathrm{f}=2+1$ Wilson fermions

We report on an analysis of the average quark momentum fraction of the nucleon and related quantities using $N_\mathrm{f}=2+1$ Wilson fermions. Computations are performed on four CLS ensembles covering three values of the lattice spacing at pion masses down to $M_π\approx 200\,\mathrm{MeV}$. Several source-sink separations ($\sim 1.0\,\mathrm{fm}$ to $\sim 1.4\,\mathrm{fm}$) 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.

hep-lat↗

arXiv2017

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 πT/2 to 2πT. 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 photon rate.

hep-lat↗

arXiv2017

Nucleon form factors and couplings with $N_\mathrm{f} = 2 + 1$ Wilson fermions

We present updated results on the nucleon electromagnetic form factors and axial coupling calculated using CLS ensembles with $N_\mathrm{f}=2+1$ dynamical flavours of Wilson fermions. The measurements are performed on large, fine lattices with a pseudoscalar mass reaching down to 200 MeV. The truncated-solver method is employed to reduce the variance of the measurements. Estimation of the matrix elements is challenging due to large contamination from excited states and further investigation is necessary to bring these effects under control.

hep-lat↗

arXiv2016

The End of a Myth: Distributed Transactions Can Scale

The common wisdom is that distributed transactions do not scale. But what if distributed transactions could be made scalable using the next generation of networks and a redesign of distributed databases? There would be no need for developers anymore to worry about co-partitioning schemes to achieve decent performance. Application development would become easier as data placement would no longer determine how scalable an application is. Hardware provisioning would be simplified as the system administrator can expect a linear scale-out when adding more machines rather than some complex sub-linear function, which is highly application specific. In this paper, we present the design of our novel scalable database system NAM-DB and show that distributed transactions with the very common Snapshot Isolation guarantee can indeed scale using the next generation of RDMA-enabled network technology without any inherent bottlenecks. Our experiments with the TPC-C benchmark show that our system scales linearly to over 6.5 million new-order (14.5 million total) distributed transactions per second on 56 machines.

cs.DB↗

arXiv2016

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. This approach can be interesting both for vacuum physics as well as for finite-temperature problems.

hep-lat↗