Physical point simulation in2+1flavor lattice QCD

We generate $2+1$ flavor QCD configurations near the physical point on a $96^4$ lattice employing the 6-APE stout smeared Wilson clover action with a nonperturbative $c_{\rm SW}$ and the Iwasaki gauge action at $\beta=1.82$. The physical point is estimated based on the chiral perturbation theory using several data points generated by the reweighting technique from the simulation point, wherer $m_\pi$,$m_K$ and $m_\Omega$ are used as physical inputs. The physics results include the quark masses, the hadron spectrum, the pseudoscalar meson decay constants and nucleon sigma terms, using the nonperturbative renormalization factors evaluated with the Schrodinger functional method.

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 $m_{s}^{\bar{\rm MS}}(2 {\rm GeV}) = 107.3(4.4)_{\rm stat}(9.7)_{\rm ren}(4.9)_{\rm syst} {\rm MeV}$.

We present results for the static interquark potential, light meson and baryon masses, and light pseudoscalar meson decay constants obtained from simulations of domain wall QCD with one dynamical flavour approximating the s quark, and two degenerate dynamical flavours with input bare masses ranging from m{sub s} to m{sub s}/4 approximating the u and d quarks. We compare these quantities obtained using the Iwasaki and DBW2 improved gauge actions, and actions with larger rectangle coefficients, on 16{sup 3}x32 lattices. We seek parameter values at which both the chiral symmetry breaking residual mass due to the finite lattice extent in the fifth dimension and the Monte Carlo time history for topological charge are acceptable for this set of quark masses at lattice spacings above 0.1 fm. We find that the Iwasaki gauge action is best, demonstrating the feasibility of using QCDOC to generate ensembles which are good representations of the QCD path integral on lattices of up to 3 fm in spatial extent with lattice spacings in the range 0.09-0.13 fm. Despite large residual masses and a limited number of sea quark-mass values with which to perform chiral extrapolations, our results for light hadronic physics scale and agree with experimental measurementsmore » within our statistical uncertainties.« less

We present preliminary results for nucleon form factors including the axial charge and the isovector electric radius in 2+1 flavor QCD at almost the physical pion mass on a $96^4$ lattice with the lattice spacing of 0.085 fm. The configurations are generated with the stout-smeared $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\beta$=1.82. A large spatial volume of $(8.1 {\rm fm})^3$ allows us to investigate the form factors at small momentum transfer region. We discuss analyses of the momentum dependence of the form factors with the z-expansion.

O( a) improved Wilson quark action on anisotropic lattice

Precision Lattice Calculation of Kaon Decays with Mobius Domain Wall Fermions Hantao Yin We report our recent development in algorithms and progress in measurements in lattice QCD. The algorithmic development includes the forecasted force gradient integrator, and further theoretical development and implementation of the Mobius domain wall fermions. These new technologies make it practical to simulate large 48 × 96 and 64 × 128 lattice ensembles with (5.5fm) boxes and 140MeV pion. The calculation was performed using the Mobius domain wall fermions and the Iwasaki gauge action. Simulated directly at physical quark masses, these ensembles are of great value for our ongoing and future lattice measurement projects. With the help of measurement techniques such as the eigCG algorithm and the all mode averaging method, we perform a direct, precise lattice calculation of the semileptonic kaon decay K −→ πlν using these newly generated high quality lattice ensembles. Our main result is the form factor f± Kπ(q ) evaluated directly at zero momentum transfer q = 0. Free of various systematic errors, this new result can be used to determine the CKM matrix element Vus to a very high precision when combined with experimental input. The calculation also provides results for various low energy strong interaction constants such as the pseudoscalar decay constants fK and fπ, and the neutral kaon mixing matrix element BK . These calculations are naturally performed by reusing the propagators calculated for the kaon semileptonic decay mentioned above. So they come with no or very low additional cost. The results allow us to also determine these important low energy constants on the lattice to unprecedented accuracy.

The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU(3) flavour symmetry breaking expansion (or Gell-Mann–Okubo expansion) works very well. Simulations are performed for 2+1 flavours of clover fermions at four lattice spacings.

One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the flavor nonsinglet ($u\ensuremath{-}d$) unpolarized parton distribution function (PDF), utilizing the nonperturbative formulation of QCD on the lattice. We apply Radyushkin's pseudodistribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions from a matching procedure. The full Bjorken-$x$ dependence of PDFs is resolved using several reconstruction methods to tackle the ill-conditioned inverse problem encountered when using discrete lattice data. We consider both the valence distribution ${q}_{v}$ and the combination with antiquarks ${q}_{v}+2\overline{q}$, related to, respectively, the real and imaginary part of extracted matrix elements. Good agreement is found with PDFs from global fits already within statistical uncertainties and it is further improved by quantifying several systematic effects. The results presented here are the first ever ab initio determinations of PDFs fully consistent with global fits in the whole $x$ range. Thus, they pave the way to investigating a wider class of partonic distributions, such as e.g., singlet PDFs and generalized parton distributions. Therefore, essential and yet missing first-principle insights can be achieved, complementing the rich experimental programs dedicated to the structure of the nucleon.

We present results for the isovector nucleon form factors measured on a $96^4$ lattice at almost the physical pion mass with a lattice spacing of 0.085 fm in 2+1 flavor QCD. The configurations are generated with the stout-smeared $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\beta$=1.82. The pion mass at the simulation point is about 146 MeV. A large spatial volume of $(8.1~{\rm fm})^3$ allows us to investigate the form factors in the small momentum transfer region. We determine the isovector electric radius and magnetic moment from nucleon electric ($G_E$) and magnetic ($G_M$) form factors as well as the axial-vector coupling $g_A$. We also report on the results of the axial-vector ($F_A$), induced pseudoscalar ($F_P$) and pseudoscalar ($G_P$) form factors in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called the generalized Goldberger-Treiman relation.

Pseudoscalar-pole diagrams are an important component of estimates of the hadronic light-by-light (HLbL) contribution to the muon $g-2$. We report on our computation of the transition form factors $\mathcal{F}_{P \rightarrow \gamma^* \gamma^*}$ for the neutral pseudoscalar mesons $P=\pi^0$ and $\eta$. The calculation is performed using twisted-mass lattice QCD with physical quark masses. On the lattice, we have access to a broad range of (space-like) photon four-momenta and therefore produce form factor data complementary to the experimentally accessible single-virtual direction, which directly leads to an estimate of the pion- and $\eta$-pole components of the muon $g-2$. For the pion, our result for the $g-2$ contribution in the continuum is comparable with previous lattice and data-driven determinations, with combined relative uncertainties below $10\%$. For the $\eta$ meson, we report on a preliminary determination from a single lattice spacing.

We present a calculation of the electromagnetic form factor of the pion in N f = 2 + 1 flavor lattice QCD. Calculations are made on the PACS-CS gauge field configurations generated using Iwasaki gauge action and Wilson-clover quark action on a 323 × 64 lattice volume with the lattice spacing estimated as a = 0.0907(13) fm at the physical point. Measurements of the form factor are made using the technique of partially twisted boundary condition to reach small momentum transfer as well as periodic boundary condition with integer momenta. Additional improvements including random wall source techniques and a judicious choice of momenta carried by the incoming and outgoing quarks are employed for error reduction. Analyzing the form factor data for the pion mass at M π ≈ 411 MeV and 296 MeV, we find that the NNLO SU(2) chiral perturbation theory fit yields 〈r 2〉 = 0.441 ± 0.046 fm2 for the pion charge radius at the physical pion mass. Albeit the error is quite large, this is consistent with the experimental value of 0.452 ± 0.011 fm2. Below M π ≈ 300 MeV, we find that statistical fluctuations in the pion two-and three-point functions become too large to extract statistically meaningful averages on a 323 spatial volume. We carry out a sample calculation on a 644 lattice with the quark masses close to the physical point, which suggests that form factor calculations at the physical point become feasible by enlarging lattice sizes to M π L ≈ 4.

Partially quenched chiral perturbation theory and numerical simulations

We present an update on ongoing work to extract pseudoscalar and vector decay constants for $B^{(*)}$, $B^{(*)}_s$ and $B^{(*)}_c$ mesons and determine phenomenologically-interesting ratios such as $f_{B_s}/f_B$ or $f_{B^*}/f_B$. Our calculation is based on ${\rm N_f}=2+1$ dynamical flavour gauge field ensembles generated by the RBC/UKQCD collaborations using domain-wall fermions and the Iwasaki gauge action. Using domain-wall light, strange, and charm quarks and relativistic $b$ quarks, we obtain results at multiple lattice spacings and valence quark masses.

We update our determinations of f D + , f D s , f K , and quark mass ratios from simulations with four flavors of HISQ dynamical quarks.The availability of ensembles with light quarks near their physical mass means that we can extract physical results with only small corrections for valence-and sea-quark mass mistunings instead of a chiral extrapolation.The adjusted valencequark masses and lattice spacings may be determined from an ensemble-by-ensemble analysis, and the results for the quark mass ratios then extrapolated to the continuum limit.Our central values of the charmed meson decay constants, however, come from an alternative analysis, which uses staggered chiral perturbation theory for the heavy-light mesons, and allows us to incorporate data at unphysical quark masses where statistical errors are often smaller.A jackknife analysis propagated through all of these steps takes account of the correlations among all the quantities used in the analysis.Systematic errors from the finite spatial size and EM effects are estimated by varying the parameters in the analysis, and systematic errors from the assumptions in the continuum extrapolation are estimated from the spread of values from different extrapolations.

We calculate the decay constants of light and heavy-light pseudoscalar and vector mesons with improved soft-wall holographic wavefuntions, which take into account the effects of both quark masses and dynamical spins. We find that the predicted decay constants, especially for the ratio fV/fP, based on light-front holographic QCD, can be significantly improved, once the dynamical spin effects are taken into account by introducing the helicity-dependent wavefunctions. We also perform detailed χ2 analyses for the holographic parameters (i.e. the mass-scale parameter κ and the quark masses), by confronting our predictions with the data for the charged-meson decay constants and the meson spectra. The fitted values for these parameters are generally in agreement with those obtained by fitting to the Regge trajectories. At the same time, most of our results for the decay constants and their ratios agree with the data as well as the predictions based on lattice QCD and QCD sum rule approaches, with only a few exceptions observed.