Meson screening masses in ( 2+1 )-flavor QCD

We present our methods to fit the two point correlators for light, strange, and charmed pseudoscalar meson physics with the highly improved staggered quark (HISQ) action. We make use of the least-squares fit including the full covariance matrix of the correlators and including Gaussian constraints on some parameters. We fit the correlators on a variety of the HISQ ensembles. The lattice spacing ranges from 0.15 fm down to 0.06 fm. The light sea quark mass ranges from 0.2 times the strange quark mass down to the physical light quark mass. The HISQ ensembles also include lattices with different volumes and with unphysical values of the strange quark mass. We use the results from this work to obtain our preliminary results of fD, fDs , fDs = fD, and ratios

We report on numerical experiments using deflation to compute quark propagators for the highly improved staggered quark (HISQ) action. The method is tested on HISQ gauge configurations, generated by the MILC collaboration, with lattice spacings of 0.15 fm, with a range of volumes, and sea quark masses down to the physical quark mass.

We present recent results on the QCD equation of state with 2+1+1 flavors of highly improved staggered quarks (HISQ). We focus on three sets of ensembles with temporal extent 6, 8 and 10, that reach up to temperatures of 967, 725 and 580 MeV, respectively. The strange and charm quark masses are tuned to the physical values and the light quarks mass is set to one fifth of the strange. This corresponds to a Goldstone pion of about 300 MeV.

We present results from our simulations of quantum chromodynamics with four flavors of quarks: u, d, s, and c. These simulations are performed with a one-loop Symanzik improved gauge action and the highly improved staggered quark action. We are generating gauge configurations with four values of the lattice spacing ranging from 0.06 to 0.15 fm, and three values of the light quark mass, including the value for which the Goldstone pion mass is equal to the physical pion mass. We discuss simulation algorithms, scale setting, taste symmetry breaking, and the autocorrelations of various quantities. We also present results for the topological susceptibility that demonstrate the improvement of the highly improved staggered quark configurations relative to those generated earlier with the asqtad improved staggered action.

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\to\eta_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f = 2 + 1 + 1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays.

We present the first lattice QCD determination of the $B_c \rightarrow J/\psi$ vector and axial-vector form factors. These will enable experimental information on the rate for $B_c$ semileptonic decays to $J/\psi$ to be converted into a value for $V_{cb}$. Our calculation covers the full physical $q^2$ range of the decay and uses non-perturbatively renormalised lattice currents. We use the Highly Improved Staggered Quark (HISQ) action for all valence quarks on the second generation MILC ensembles of gluon field configurations including $u$, $d$, $s$ and $c$ HISQ sea quarks. Our HISQ heavy quarks have masses ranging upwards from that of $c$; we are able to reach that of the $b$ on our finest lattices. This enables us to map out the dependence on heavy quark mass and determine results in the continuum limit at the $b$. We use our form factors to construct the differential rates for $B_c^- \rightarrow J/\psi \mu^- \bar{\nu}_\mu$ and obtain a total rate with $7\%$ uncertainty: $\Gamma(B_c^-\rightarrow J/\psi \mu^-\bar{\nu}_{\mu})/|\eta_{\mathrm{EW}}V_{cb}|^2 = 1.73(12)\times 10^{13} ~\mathrm{s}^{-1}$. Including values for $V_{cb}$, $\eta_{\mathrm{EW}}$ and $\tau_{B_c}$ yields a branching fraction for this decay mode of 0.0150(11)(10)(3) ~with uncertainties from lattice QCD, $\eta_\mathrm{EW}V_{cb}$ and $\tau_{B_c}$ respectively.

We calculate the one loop renormalisation parameters for the heavy-light axial-vector and vector currents using lattice perturbation theory. We use NonRelativistic QCD (NRQCD) heavy quarks and the Highly Improved Staggered Quark (HISQ) action for the light quarks. We present results for heavy-light currents with massless HISQ quarks and briefly discuss the extension to heavyheavy currents with massive HISQ quarks.

Typically, the conjugate gradient (CG) algorithm employs mixed precision and even-odd preconditioning to compute propagators for highly improved staggered quarks (HISQ). This approach suffers from critical slowing down as the light quark mass is decreased to its physical value. Multigrid is one alternative to combat critical slowing down; however, it involves setup costs that are not always easy to amortize. We consider deflation, which can also remove critical slowing down, but incurs its own setup cost to compute eigenvectors. Results using the MILC and QUDA software libraries to generate eigenvectors and to perform deflated solves on lattices up to $144^3 \times 288$ (with lattice spacing 0.04 fm) and with a range of quark masses from the physical strange down to the physical light quark values will be presented. We compare with CG and comment on deflation versus multigrid.

Light and strange quark masses with dynamical Wilson Fermions

A key search mode for axionlike particles (ALPs) that couple to charm quarks is J/ψ→γa. Here we calculate the form factor that allows the rate of this process to be determined using lattice QCD for the first time. Our calculations use the relativistic highly improved staggered quark (HISQ) action for the valence charm quarks on gluon field configurations generated by the MILC collaboration that include u, d, s and c HISQ quarks in the sea at four values of the lattice spacing and both unphysical and physical sea quark masses. We determine the form factor as a function of ALP mass with an uncertainty of less than 2% across our full range of ALP masses from zero up to 95% of the J/ψ mass. This represents a substantial improvement in accuracy of the theoretical picture of this decay compared to the previously used tree-level and O(αs) perturbation theory. We use our form factor to determine constraints on ALP masses and couplings to charm quarks and photons in several different scenarios using recent experimental data from BESIII. Our calculation paves the way for further lattice QCD input on new physics constraints from radiative decays.

We present a lattice QCD determination of the $B_s \\to D_s \\ell\\nu$ scalar\nand vector form factors over the full physical range of momentum transfer. The\nresult is derived from correlation functions computed using the Highly Improved\nStaggered Quark (HISQ) formalism, on the second generation MILC gluon ensembles\naccounting for up, down, strange and charm contributions from the sea. We\ncalculate correlation functions for three lattice spacing values and an array\nof unphysically light $b$-quark masses, and extrapolate to the physical value.\nUsing the HISQ formalism for all quarks means that the lattice current coupling\nto the $W$ can be renormalized non-perturbatively, giving a result free from\nperturbative matching errors for the first time. Our results are in agreement\nwith, and more accurate than, previous determinations of these form factors.\nFrom the form factors we also determine the ratio of branching fractions that\nis sensitive to violation of lepton universality: $R(D_s) = \\mathcal{B}(B_s\\to\nD_s \\tau \\nu_{\\tau})/\\mathcal{B}(B_s\\to D_s \\ell \\nu_{l})$, where $\\ell$ is an\nelectron or a muon. We find $R(D_s) = 0.2987(46)$, which is also more accurate\nthan previous lattice QCD results. Combined with a future measurement of\n$R(D_s)$, this could supply a new test of the Standard Model. We also compare\nthe dependence on heavy quark mass of our form factors to expectations from\nHeavy Quark Effective Theory.\n

We report on our study of QCD thermodynamics with 2 ¡ 1 flavors of dynamical quarks.In this proceeding we present several thermodynamic quantities and our recent calculation of the critical temperature.In order to investigate the thermodynamic properties of QCD near the continuum limit we adopt improved staggered (p4) quarks coupled with tree-level Symanzik improved glue on N t ¢ 4 and 6 lattices.The simulations are performed with a physical value of the strange quark mass and light quark masses which are in the range of m q £ m s ¢ 0¤ 05 ¥ 0¤ 4. The lightest quark mass corresponds to a pion mass of about 150 MeV.

We present a systematic study of the effectiveness of light quark mass reweighting. This method allows a single lattice QCD ensemble, generated with a specific value of the dynamical light quark mass, to be used to determine results for other, nearby light dynamical quark masses. We study two gauge field ensembles generated with 2+1 flavors of dynamical domain wall fermions with light quark masses m_l=0.02 (m_\pi=620 MeV) and m_l=0.01 (m_\pi=420 MeV). We reweight each ensemble to determine results which could be computed directly from the other and check the consistency of the reweighted results with the direct results. The large difference between the 0.02 and 0.01 light quark masses suggests that this is an aggressive application of reweighting as can be seen from fluctuations in the magnitude of the reweighting factor by four orders of magnitude. Never-the-less, a comparison of the reweighed topological charge, average plaquette, residual mass, pion mass, pion decay constant, and scalar correlator between these two ensembles shows agreement well described by the statistical errors. The issues of the effective number of configurations and finite sample size bias are discussed. An examination of the topological charge distribution implies that it is more favorable to reweight from heavier mass to lighter quark mass.

Since gluons in QCD are interacting fundamental constituents just as quarks are, we expect that in addition to mesons made from a quark and an antiquark, there should also be glueballs and hybrids (bound states of quarks, antiquarks and gluons). In general, these states would mix strongly with the conventional q-bar-q mesons. However, they can also have exotic quantum numbers inaccessible to q-bar-q mesons. Confirmation of such states would give information on the role of "dynamical" color in low energy QCD. In the quenched approximation we present a lattice calculation of the masses of mesons with exotic quantum numbers. These hybrid mesons can mix with four quark (q-bar-q-bar-q-q) states. The quenched approximation partially suppresses this mixing. Nonetheless, our hybrid interpolating fields also couple to four quark states. Using a four quark source operator, we demonstrate this mixing for the 1-+ meson. Using the conventional Wilson quark action, we calculate both at reasonably light quark masses, intending to extrapolate to small quark mass, and near the charmed quark mass, where we calculate the masses of some c-bar-c-g hybrid mesons. The hybrid meson masses are large --- over 4 GeV for charmonium and more than twice the vector meson mass at our smallest quark mass, which is near the strange quark mass.

We have simulated QCD using 2+1 flavors of domain wall quarks on a $(2.74 {\rm fm})^3$ volume with an inverse lattice scale of $a^{-1} = 1.729(28)$ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter $B_K$ and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the $\Omega$ baryon, and the $\pi$ and $K$ mesons to set the lattice scale and determine the quark masses. We then find $f_\pi = 124.1(3.6)_{\rm stat}(6.9)_{\rm syst} {\rm MeV}$, $f_K = 149.6(3.6)_{\rm stat}(6.3)_{\rm syst} {\rm MeV}$ and $f_K/f_\pi = 1.205(0.018)_{\rm stat}(0.062)_{\rm syst}$. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to $\bar{\rm MS}$ we find $ m_{ud}^{\bar{\rm MS}}(2 {\rm GeV}) = 3.72(0.16)_{\rm stat}(0.33)_{\rm ren}(0.18)_{\rm syst} {\rm MeV}$ and $m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}$.