An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator

This paper considers a new class of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. The estimators considered are prewhitened kernel estimators with vetor autoregressions employed in the prewhitening stage. The paper establishes consistency, rate of convergence, and asymptotic truncated mean squared error (MSE) results for the estimators when a fixed or automatic bandwidth procedure is employed. Conditions are obtained under which prewhitening improves asymptotic truncated MSE. Monte Carlo results show that prewhitening is very effective in reducing bias, improving confidence interval coverage probabilities, and rescuing over-rejection of t -statistics constructed using kernel-HAC estimators. On the other hand, prewhitening is found to inflate variance and MSE of the kernel estimators. Since confidence interval coverage probabilities and over-rejection of t-statistics are usually of primary concern, prewhitened kernel estimators provide a significant improvement over the standard non-prewhitened kernel estimators

A model-independent framework for determining finite-volume effects of spatially nonlocal operators

We present a model-independent framework to determine finite-volume corrections of matrix elements of spatially-separated current-current operators. We define these matrix elements in terms of Compton-like amplitudes, i.e. amplitudes coupling single-particle states via two current insertions. We show that the infrared behavior of these matrix elements is dominated by the single-particle pole, which is approximated by the elastic form factors of the lowest-lying hadron. Therefore, given lattice data on the relevant elastic form factors, the finite-volume effects can be estimated non-perturbatively and without recourse to effective field theories. For illustration purposes, we investigate the implications of the proposed formalism for a class of scalar theories in two and four dimensions.Comment: 15 pages, 5 figure

Consistency Checks For Two-Body Finite-Volume Matrix Elements: Conserved Currents and Bound States

We present a model-independent framework to determine finite-volume corrections of matrix elements of spatially separated current-current operators. We define these matrix elements in terms of Compton-like amplitudes, i.e., amplitudes coupling single-particle states via two current insertions. We show that the infrared behavior of these matrix elements is dominated by the single-particle pole, which is approximated by the elastic form factors of the lowest-lying hadron. Therefore, given lattice data on the relevant elastic form factors, the finite-volume effects can be estimated nonperturbatively and without recourse to effective field theories. For illustration purposes, we investigate the implications of the proposed formalism for a class of scalar theories in two and four dimensions

Bs→DsℓνB_s \to D_s \ell \nu Form Factors and the Fragmentation Fraction Ratio fs/fdf_s/f_d

We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the $B_s \rightarrow D_s \ell \nu$ decay over the full physical range of momentum transfer. In conjunction with future experimental data, our results will provide a new method to extract $|V_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of this parameter. Combining the form factor results at non-zero recoil with recent HPQCD results for the $B \rightarrow D \ell \nu$ form factors, we determine the ratios $f^{B_s \rightarrow D_s}_0(M_\pi^2) / f^{B \rightarrow D}_0(M_K^2) = 1.000(62)$ and $f^{B_s \rightarrow D_s}_0(M_\pi^2) / f^{B \rightarrow D}_0(M_\pi^2) = 1.006(62)$. These results give the fragmentation fraction ratios $f_s/f_d = 0.310(30)_{\mathrm{stat.}}(21)_{\mathrm{syst.}}(6)_{\mathrm{theor.}}(38)_{\mathrm{latt.}}$ and $f_s/f_d = 0.307(16)_{\mathrm{stat.}}(21)_{\mathrm{syst.}}(23)_{\mathrm{theor.}}(44)_{\mathrm{latt.}}$, respectively. The fragmentation fraction ratio is an important ingredient in experimental determinations of $B_s$ meson branching fractions at hadron colliders, in particular for the rare decay ${\cal B}(B_s \rightarrow \mu^+ \mu^-)$. In addition to the form factor results, we make the first prediction of the branching fraction ratio $R(D_s) = {\cal B}(B_s\to D_s\tau\nu)/{\cal B}(B_s\to D_s\ell\nu) = 0.301(6)$, where $\ell$ is an electron or muon. Current experimental measurements of the corresponding ratio for the semileptonic decays of $B$ mesons disagree with Standard Model expectations at the level of nearly four standard deviations. Future experimental measurements of $R(D_s)$ may help understand this discrepancy.Comment: 21 pages, 15 figure

Notes on lattice observables for parton distributions:nongauge theories

We review recent theoretical developments concerning the definition and the renormalization of equal-time correlators that can be computed on the lattice and related to Parton Distribution Functions (PDFs) through a factorization formula. We show how these objects can be studied and analyzed within the framework of a nongauge theory, gaining insight through a one-loop computation. We use scalar field theory as a playground to revise, analyze and present the main features of these ideas, to explore their potential, and to understand their limitations for extracting PDFs. We then propose a framework that would allow to include the available lattice QCD data in a global analysis to extract PDFs.Comment: 20 pages, 2 figure

Role of the Euclidean Signature in Lattice Calculations of Quasidistributions and Other Nonlocal Matrix Elements

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate that the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Finally we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory

PDFs in small boxes

PDFs can be studied directly using lattice QCD by evaluating matrix elements of non-local operators. A number of groups are pursuing numerical calculations and investigating possible systematic uncertainties. One systematic that has received less attention is the effect of calculating in a finite spacetime volume. Here we present first attempts to assess the role of the finite volume for spatially non-local operators. We find that these matrix elements may suffer from large finite-volume artifacts and more careful investigation is needed.Comment: 6 pages, 3 figures, Conference: The 36th Annual International Symposium on Lattice Field Theory - LATTICE2018, 22-28 July, 2018, Michigan State University, East Lansing, Michigan, US

One-loop matching for quark dipole operators in a gradient-flow scheme

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromo-magnetic dipole operator (qCMDM), which contributes for example to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators