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Register a new userHigh-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
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We extend our earlier lattice-QCD analysis of heavy-quark correlators to smaller lattice spacings and larger masses to obtain new values for the c mass and QCD coupling, and, for the first time, values for the b mass: m_c(3GeV,n_f=4)=0.986(6)GeV, alpha_msb(M_Z,n_f=5)=0.1183(7), and m_b(10GeV,n_f=5)=3.617(25)GeV. These are among the most accurate determinations by any method. We check our results using a nonperturbative determination of the mass ratio m_b(mu,n_f)/m_c(mu,n_f); the two methods agree to within our 1% errors and taken together imply m_b/m_c=4.51(4). We also update our previous analysis of alpha_msb from Wilson loops to account for revised values for r_1 and r_1/a, finding a new value alpha_msb(M_Z,n_f=5)=0.1184(6); and we update our recent values for light-quark masses from the ratio m_c/m_s. Finally, in the Appendix, we derive a procedure for simplifying and accelerating complicated least-squares fits.
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We use lattice QCD simulations, with MILC gluon configurations and HISQ c-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the MSbar mass of the charm quark and of the MSbar coupling. We find m_c(3GeV)=0.986(10)GeV, or, equivalently, m_c(m_c)=1.268(9)GeV, both for n_f=4 flavors; and alpha_msb(3GeV,n_f=4)=0.251(6), or, equivalently, alpha_msb(M_Z,n_f=5)=0.1174(12). The new mass agrees well with results from continuum analyses of the vector correlator using experimental data for e+e- annihilation (instead of using lattice QCD simulations). These lattice and continuum results are the most accurate determinations to date of this mass. Ours is also one of the most accurate determinations of the QCD coupling by any method.
We present a new lattice QCD analysis of heavy-quark pseudoscalar-pseudoscalar correlators, using gluon configurations from the MILC collaboration that include vacuum polarization from $u$, $d$, $s$ and $c$~quarks($n_f=4$). We extract new values for the QCD coupling and for the $c$ quarks $overline{mathrm{MS}}$ mass: $alpha_{overline{mathrm{MS}}}(M_Z,n_f=5) = 0.11822(74)$ and $m_c(3mathrm{GeV}, n_f=4) = 0.9851(63)$GeV. These agree well with our earlier simulations using $n_f=3$ sea quarks, vindicating the perturbative treatment of $c$ quarks in that analysis. We also obtain a new nonperturbative result for the ratio of $c$~and $s$~quark masses: $m_c/m_s=11.652(65)$. This ratio implies $m_s(2,mathrm{GeV}, n_f=3)=93.6(8)$MeV when it is combined with our new~$c$~mass. Combining $m_c/m_s$ with our earlier $m_b/m_c$ gives $m_b/m_s=52.55(55)$, which is several standard deviations (but only 4%) away from the Georgi-Jarlskop prediction from certain GUTs. Finally we obtain an $n_f=4$ estimate for $m_b/m_c=4.528(54)$ which agrees well with our earlier $n_f=3$ result. The new ratio implies~$m_b(m_b,n_f=5)=4.162(48)$GeV.
We propose a method to use lattice QCD to compute the Borel transform of the vacuum polarization function appearing in the Shifman-Vainshtein-Zakharov (SVZ) QCD sum rule. We construct the spectral sum corresponding to the Borel transform from two-point functions computed on the Euclidean lattice. As a proof of principle, we compute the $s bar{s}$ correlators at three lattice spacings and take the continuum limit. We confirm that the method yields results that are consistent with the operator product expansion in the large Borel mass region. The method provides a ground on which the OPE analyses can be directly compared with non-perturbative lattice computations.
In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), $alpha^{overline{mathrm{MS}}}_s(mu)$, for $overline{mathrm{MS}}$ renormalization scales $mu in (1,,2)$ GeV. The computation uses gauge field configuration ensembles with $mathcal{O}(a)$-improved Wilson-clover fermions generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach is based on current-current correlation functions and has never been applied before in this context. We convert the results perturbatively to the QCD $Lambda$-parameter and obtain $Lambda_{overline{mathrm{MS}}}^{N_f=3} = 342 pm 17$ MeV, which agrees with the world average published by the Particle Data Group and has competing precision. The latter was made possible by a unique combination of state-of-the-art CLS ensembles with very fine lattice spacings, further reduction of discretization effects from a dedicated numerical stochastic perturbation theory simulation, combining data from vector and axial-vector channels and matching to high-order perturbation theory.
We extract the pion valence quark distribution $q^pi_{rm v}(x)$ from lattice QCD (LQCD) calculated matrix elements of spacelike correlations of one vector and one axial vector current analyzed in terms of QCD collinear factorization, using a new short-distance matching coefficient calculated to one-loop accuracy. We derive the Ioffe time distribution of the two-current correlations in the physical limit by investigating the finite lattice spacing, volume, quark mass, and higher-twist dependencies in a simultaneous fit of matrix elements computed on four gauge ensembles. We find remarkable consistency between our extracted $q^pi_{rm v}(x)$ and that obtained from experimental data across the entire $x$-range. Further, we demonstrate that the one-loop matching coefficient relating the LQCD matrix computed in position space to the $q_{rm v}^{pi}(x)$ in momentum space has well-controlled behavior with Ioffe time. This justifies that LQCD calculated current-current correlations are good observables for extracting partonic structures by using QCD factorization, which complements to the global effort to extract partonic structure from experimental data.
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