Numerical experiments using deflation with the HISQ 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 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

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 the first lattice-QCD x-dependent pion valence-quark generalized parton distribution (GPD) calculated directly at physical pion mass using the Large-Momentum Effective Theory (LaMET) with next-to-next-to-leading order perturbative matching correction. We use clover fermions for the valence action on 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, with lattice spacing a≈0.09 fm and box size L≈5.5 fm; the pion two-point measurements number up to O(106) with boost momentum 1.73 GeV. The pion valence distribution is renormalized in hybrid scheme with Wilson-line mass subtraction at large distances in coordinate space, followed by a procedure to match it to the MS‾ scheme. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken x and the transverse impact-parameter distributions. We take the integral of our GPD functions to generate leading moment so that we can make comparisons with past lattice-QCD and experimental determinations of the pion form factors and found consistent agreement among them. We predict the higher GPD moments and reveal x-dependent tomography of the pion for the first time using lattice QCD.

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 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.

The study of neutrino oscillation physics is a major research goal of the worldwide particle physics program over the upcoming decade. Many new experiments are being built to study the properties of neutrinos and to answer questions about the phenomenon of neutrino oscillation. These experiments need precise theoretical cross sections in order to access fundamental neutrino properties. Neutrino oscillation experiments often use large atomic nuclei as scattering targets, which are challenging for theorists to model. Nuclear models rely on free-nucleon amplitudes as inputs. These amplitudes are constrained by scattering experiments with large nuclear targets that rely on the very same nuclear models. The work in this dissertation is the rst step of a new initiative to isolate and compute elementary amplitudes with theoretical calculations to support the neutrino oscillation experimental program. Here, the eort focuses on computing the axial form factor, which is the largest contributor of systematic error in the primary signal measurement process for neutrino oscillation studies, quasielastic scattering. Two approaches are taken. First, neutrino scattering data on a deuterium target are reanalyzed with a model-independent parametrization of the axial form factor to quantify the present uncertainty in the free-nucleon amplitudes. The uncertainties on the free-nucleon cross section are found to be underestimated by about an order of magnitude compared to the ubiquitous dipole model parametrization. The second approach uses lattice QCD to perform a rst-principles computation of the nucleon axial form factor. The Highly Improved Staggered Quark (HISQ) action is employed for both valence and sea quarks. The results presented in this dissertation are computed at physical pion mass for one lattice spacing. This work presents a computation of the axial form factor at zero momentum transfer, and forms the basis for a computation of the axial form factor momentum dependence with an extrapolation to the continuum limit and a full systematic error budget.

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 lattice QCD results for mesonic screening masses in the temperature range 140 MeV ≲ T ≲ 2500 MeV. Our calculations were carried out using (2+1) flavors of the Highly Improved Staggered Quark (HISQ) action, with a physical value for the strange quark mass and two values of the light quark mass corresponding to pion masses of 160 MeV and 140 MeV. Continuum extrapolated results were obtained using calculations with a variety of lattice spacings corresponding to temporal lattice extents N<sub>τ</sub> = 6 16. We discuss the implications of these results for the e effective restoration of various symmetries in the high temperature phase of QCD, as well as the approach toward the perturbative limit.

We present the most precise results for the ground state mass of the triply-charmed spin- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>3</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:math> baryon using lattice quantum chromodynamics. The calculations are performed on six <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>N</c:mi> <c:mi>f</c:mi> </c:msub> <c:mo>=</c:mo> <c:mn>2</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:math> highly improved staggered quark (HISQ) lattice ensembles generated by the MILC collaboration. Two different lattice setups are employed: in the first one, a fully dynamical calculation with HISQ action is performed, while in the second calculation, an overlap action is utilized for the valence charm quark dynamics. Following the continuum extrapolation of our results, obtained at five different lattice spacings, two different volumes, and two different actions, our prediction for the mass of the lowest triply charmed spin- <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mn>3</e:mn> <e:mo>/</e:mo> <e:mn>2</e:mn> </e:mrow> </e:math> baryon, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:msub> <g:mrow> <g:mi mathvariant="normal">Ω</g:mi> </g:mrow> <g:mrow> <g:mi>c</g:mi> <g:mi>c</g:mi> <g:mi>c</g:mi> </g:mrow> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mn>3</g:mn> <g:mo>/</g:mo> <g:msup> <g:mrow> <g:mn>2</g:mn> </g:mrow> <g:mrow> <g:mo>+</g:mo> </g:mrow> </g:msup> <g:mo stretchy="false">)</g:mo> </g:mrow> </g:math> , is <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mrow> <l:mn>4793</l:mn> <l:mo stretchy="false">(</l:mo> <l:mn>5</l:mn> <l:mo stretchy="false">)</l:mo> <l:msubsup> <l:mrow> <l:mo stretchy="false">(</l:mo> </l:mrow> <l:mrow> <l:mo>−</l:mo> <l:mn>8</l:mn> </l:mrow> <l:mrow> <l:mo>+</l:mo> <l:mn>11</l:mn> </l:mrow> </l:msubsup> <l:mo stretchy="false">)</l:mo> <l:mtext> </l:mtext> <l:mtext> </l:mtext> <l:mi>MeV</l:mi> </l:mrow> </l:math> . This is the most precise determination to date, fully addressing the systematic uncertainties. We also predict the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:msub> <r:mrow> <r:mi mathvariant="normal">Ω</r:mi> </r:mrow> <r:mrow> <r:mi>c</r:mi> <r:mi>c</r:mi> <r:mi>c</r:mi> </r:mrow> </r:msub> <r:mo stretchy="false">(</r:mo> <r:mn>3</r:mn> <r:mo>/</r:mo> <r:msup> <r:mrow> <r:mn>2</r:mn> </r:mrow> <r:mrow> <r:mo>−</r:mo> </r:mrow> </r:msup> <r:mo stretchy="false">)</r:mo> </r:mrow> </r:math> mass to be <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:mn>5094</w:mn> <w:mo stretchy="false">(</w:mo> <w:mn>12</w:mn> <w:mo stretchy="false">)</w:mo> <w:msubsup> <w:mrow> <w:mo stretchy="false">(</w:mo> </w:mrow> <w:mrow> <w:mo>−</w:mo> <w:mn>17</w:mn> </w:mrow> <w:mrow> <w:mo>+</w:mo> <w:mn>19</w:mn> </w:mrow> </w:msubsup> <w:mo stretchy="false">)</w:mo> <w:mtext> </w:mtext> <w:mtext> </w:mtext> <w:mi>MeV</w:mi> </w:mrow> </w:math> .

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.

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 present a lattice QCD determination of the $B_c \rightarrow J/\psi$ vector and axial-vector form factors over the full physical $q^2$ range with non-perturbatively renormalised lattice currents. Our calculation uses the Highly Improved Staggered Quark (HISQ) action on the second generation MILC gluon ensembles including light, strange and charm sea quarks. We use HISQ heavy quarks, with a range of masses going up to the $b$ on our finest lattices. Finally we use these form factors to compute the differential decay rates and construct the ratio of decay rates $R(J/\psi) = \Gamma(B_c \rightarrow J/\psi \tau^-\overline{\nu}_\tau)/\Gamma(B_c \rightarrow J/\psi \ell^-\overline{\nu}_\ell)$ where $\ell$ is either a muon or electron.

We study correlation functions of spatially separated static quark-antiquark pairs in $2+1$ flavor QCD in order to investigate the nature of color screening at high temperatures. We perform lattice calculations in a wide temperature range, $116~\text{MeV} \leq T \leq 5814~\text{MeV}$, using the highly improved staggered quark (HISQ) action and several lattice spacings to control discretization effects. We alleviate the UV noise problem through the use of four dimensional hypercubic (HYP) smearing, which enables the reconstruction of correlators and determination of screening properties even at low temperatures and at large distances.