We present the corrections to the fermion propagator, to second order in the lattice spacing, O(a^2), in 1-loop perturbation theory. The fermions are described by the clover action and for the gluons we use a 3-parameter family of Symanzik improved actions. Our calculation has been carried out in a general covariant gauge. The results are provided as a polynomial of the clover parameter, and are tabulated for 10 popular sets of the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action).
We also study the O(a^2) corrections to matrix elements of fermion bilinear operators that have the form $\barΨΓΨ$, where $Γ$ denotes all possible distinct products of Dirac matrices. These correction terms are essential ingredients for improving, to O(a^2), the matrix elements of the fermion operators.
Our results are applicable also to the case of twisted mass fermions.
A longer write-up of this work, including non-perturbative results, is in preparation together with V. Gimenez, V. Lubicz and D. Palao.
We study properties of the finite temperature quark propagator by using the SU(3) quenched lattice simulation in the Landau gauge and report numerical results of the standard Wilson quark case as well as the improved clover one. The mass function in the deconfinement phase is different from that of the confinement phase, especially at low momentum regions.
We calculate corrections to the fermion propagator and to the Green's functions of all fermion bilinear operators of the form $\barΨΓΨ$, to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and a family of Symanzik improved actions for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, $O(a^2)$. Consequently, they have addressed a number of new issues, most notably the appearance of loop integrands with strong IR divergences (convergent only beyond 6 dimensions). Such integrands are not present in $O(…
This is the first part of a study of the quark propagator and the vertex function of the vector current on the lattice in the Landau gauge and using both Wilson-clover and overlap actions. In order to be able to identify lattice artifacts and to reach large momenta we use a range of lattice spacings. The lattice artifacts turn out to be exceedingly large in this study. We present a new and very efficient method to eliminate the hypercubic (anisotropy) artifacts based on a systematic expansion on hypercubic invariants which are not SO(4) invariant. A simpler version of this method has been used…
We compute the difference in the renormalization of flavor singlet and nonsinglet fermion bilinear operators, to two loops in perturbation theory. Our results are applicable to a rather wide class of lattice actions with Symanzik improved gluons, stout links and clover fermions, including the Twisted Mass and SLiNC actions. A more detailed presentation of our results, along with relevant references, will appear in a forthcoming publication.
In this work we examine the Fat-Link Irrelevant Clover (FLIC) overlap quark propagator and the gluon propagator on both dynamical and quenched lattices. The tadpole-improved Luscher-Weisz gauge action is used in both cases. The dynamical gauge fields use the FLIC fermion action for the sea quark contribution. We observe that the presence of sea quarks causes a suppression of the mass function, quark renormalization function and gluon dressing function in the infrared. The ultraviolet physics is unaffected.
We compute the renormalization functions on the lattice, in the RI' scheme, of local bilinear quark operators $\barψΓψ$, where $Γ= 1, γ_5, γ_μ, γ_5γ_μ, γ_5σ_{μν}$. This calculation is carried out to two loops for the first time. We consider both the flavor non-singlet and singlet operators. As a prerequisite for the above, we compute the quark field renormalization, $Z_ψ$, up to two loops. We also compute the 1-loop renormalization functions for the gluon field, $Z_A$, ghost field, $Z_c$, gauge parameter, $Z_α$, and coupling constant $Z_g$. We use the clover action for fermions and the Wilson …
We present preliminary results for the contributions to the neutron EDM arising from the QCD $θ$-term, the Weinberg three-gluon and the quark chromo-EDM operators from our ongoing lattice calculations using clover valence quarks on the MILC HISQ lattices. We use the gradient-flow technique to smooth the lattices and renormalize the gluonic operators, and use the Schwinger source method to incorporate the quark chromo-EDM interactions in the quark propagator. For the QCD $θ$-term and the Weinberg three-gluon operator, we report results in the gradient-flow scheme from 8 ensembles at four lattic…
FLIC overlap fermions are a variant of the standard (Wilson) overlap action, with the FLIC (Fat Link Irrelevant Clover) action as the overlap kernel rather than the Wilson action. The structure of the FLIC overlap fermion propagator in momentum space is studied, and a comparison against previous studies of the Wilson overlap propagator in quenched QCD is performed. To explore the scaling properties of the propagator for the two actions, numerical calculations are performed in Landau Gauge across three lattices with different lattice spacing $a$ and similar physical volumes. We find that at lig…
We present preliminary results for the spectrum and decay matrix elements for heavy-light and heavy-heavy mesons, obtained on the 64-node Meiko Computing Surface at the University of Edinburgh. Quark propagators are computed with an O(a)-improved fermion action on 24^3x48 lattices at beta = 6.2, using three values of the quark mass up to around the strange quark mass, and four values of the quark mass in the region of the charm quark mass. We compare results for the hyperfine splitting in charmonium with those obtained using the conventional Wilson fermion action and find that the splitting is…
We present high-statistics estimates of the isovector charges of the nucleon from four 2+1-flavor ensembles generated using Wilson-clover fermions with stout smearing and tree-level tadpole improved Symanzik gauge action at lattice spacings $a=0.114$ and $0.080$ fm and with $M_π\approx 315$ and 200 MeV. The truncated solver method with bias correction and the coherent source sequential propagator construction are used to cost-effectively achieve $O(10^5)$ measurements on each ensemble. Using these data, the analysis of two-point correlation functions is extended to include four states in the f…
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\barψΓψ$, where $Γ$ corresponds to the Vector, Axial-Vector and Tensor Dirac operators, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. Finally, we present our results in the MSbar scheme, for easier comparison with calculatio…
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\barψΓψ$, where $Γ$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_ψ$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW…
The clover coefficient $\csw$ is computed at one loop order of perturbation theory for improved gluon actions including six-link loops. The O(a) improvement coefficients for the dimension three isovector composite operators bilinear in the quark fields are also calculated.
We calculate one-loop renormalization factors of bilinear quark operators for gluon action including six-link loops and $O(a)$-improved quark action in the limit of massless quark. We find that finite parts of one-loop coefficients of renormalization factors diminish monotonically as either of the coefficients $c_1$ or $c_2+c_3$ of the six-link terms are decreased below zero. Detailed numerical results are given, for general values of the clover coefficient, for the tree-level improved gluon action in the Symanzik approach $(c_1=-1/12, c_2=c_3=0)$ and for the choices suggested by Wilson $(c_1=…
We investigate the Symanzik improvement of the Wilson quark action on anisotropic lattices. Taking first a general action with nearest-neighbor and clover interactions, we study the mass dependence of the ratio of the hopping parameters, the clover coefficients, and an improvement coefficient for heavy-light vector and axial vector currents. We show how tree-level improvement can be achieved. For a particular choice of the spatial Wilson coupling, the results simplify, and $O(m_0a_τ)$ improvement is possible. (Here $m_0$ is the bare quark mass and $a_τ$ the temporal lattice spacing.) With this…
We present results for matching factors for bilinear operators composed of HYP-smeared staggered fermions and constructed using HYP-smeared fat links. The matching factors are calculated perturbatively at one-loop order. The new feature of our calculation compared to previous work on HYP-smeared staggered fermions is the use of the Symanzik-improved gluon propagator, which allows our results to be applied to our ongoing simulations based on configurations generated by the MILC collaboration. We address the issue of the relative efficiency of various improvement schemes in reducing one-loop cor…
We compute the two-loop renormalization functions, in the RI $^\prime$ scheme, of local bilinear quark operators $\barψΓψ$, where $Γ$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_ψ$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial …
We study the possible significance of four-quark states in the iso-singlet scalar mesons ($J^{PC}=0^{++}$, $I=0$) by performing two-flavor full lattice QCD simulations on an $8^3 \times 16$ lattice using the improved gauge action and the clover-improved Wilson quark action. In particular, we evaluate the propagators of molecular and tetra-quark operators together with singly disconnected diagrams. In the computation of the singly disconnected diagrams we employ the $Z_2$-noise method with the truncated eigenmode approach. We show that the quark loops given by the disconnected diagrams play an …
We present a 1-loop perturbative calculation of the fermion propagator, up to O(a^2) (a: lattice spacing). The fermions are described by Wilson, clover and twisted-mass actions; for gluons we use Symanzik improved actions (Plaquette, Tree-level Symanzik, Iwasaki, TILW, DBW2). Our results are given in a general covariant gauge, and their dependence on the coupling constant, the external momentum, the masses and the clover parameter is shown explicitly. We also study the O(a^2) corrections to matrix elements of unpolarized/polarized fermion bilinear operators, which include up to one derivative.…
We apply non-perturbative renormalization to bilinears composed of improved staggered fermions. We explain how to generalize the method to staggered fermions in a way which is consistent with the lattice symmetries, and introduce a new type of lattice bilinear which transforms covariantly and avoids mixing. We derive the consequences of lattice symmetries for the propagator and vertices. We implement the method numerically for hypercubic-smeared (HYP) and asqtad valence fermion actions, using lattices with asqtad sea quarks generated by the MILC collaboration. We compare the non-perturbative r…
FermiQCD is a C++ library for fast development of parallel Lattice Quantum Field Theory computations. It has been developed following a top-down fully Object Oriented design approach with focus on simplicity of use. FermiQCD includes: a heatbath algorithm for Wilson and $O(a^2)$ improved SU(n) gauge actions; inversion algorithms for Wilson, Clover, Kogut-Susskind, Asqtad, and Domain Wall fermionic actions; example programs for various types of meson propagators; and converters for the most common gauge file formats.
We extend an earlier study of the Landau gauge quark propagator in quenched QCD where we used two forms of the O(a)-improved propagator with the Sheikholeslami-Wohlert quark action. In the present study we use the nonperturbative value for the clover coefficient c_sw and mean-field improvement coefficients in our improved quark propagators. We compare this to our earlier results which used the mean-field c_sw and tree-level improvement coefficients for the propagator. We also compare three different implementations of tree-level correction: additive, multiplicative, and hybrid. We show that th…
We present results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched QCD at two values of lattice spacing, beta = 5.7 and 5.9, with clover-improved Wilson fermions. The study of the chiral limit is facilitated by the pole-shifting ansatz of the modified quenched approximation. Pseudoscalar masses and decay constants are determined as a function of quark mass and quenched chiral log effects are estimated. A study of the flavor singlet eta prime hairpin diagram yields a precise determination of the eta prime mass insertion. The corresponding value of the quenche…
Flavor singlet and non-singlet axial Ward identities are investigated using the Wilson formulation of lattice QCD with Clover O(a)-improvement, which breaks explicitly chiral symmetry. The matching at one-loop order of all the relevant renormalization constants with the continuum \bar{MS} scheme is presented. Our calculations include: 1) the contributions arising from the Clover term of the action; 2) the complete mixing of the gluon operator G \tilde{G} with the divergence of the singlet axial current; 3) the use of both local and extended definitions of the fermionic bilinear operators. A de…
This talk provides an update on the calculation of matrix elements of flavor diagonal axial, scalar and tensor quark bilinear operators between the nucleon ground state. The simulations are done using Wilson-clover fermions on a sea of eight 2+1+1-flavor HISQ ensembles generated by the MILC collaboration. We discuss the signal in the connected and disconnected contributions, calculation of the renormalization constants and mixing in the RI-sMOM scheme, and control over the simultaneous chiral-continuum-finite-volume fit used to extract the final charges.
This talk provides an update on the calculation of matrix elements of flavor diagonal axial, scalar and tensor quark bilinear operators between the nucleon ground state. The simulations are done using Wilson-clover fermions on a sea of eight 2+1+1-flavor HISQ ensembles generated by the MILC collaboration. We discuss the signal in the sum of the connected and disconnected contributions for the up, down and strange quarks, control over fits to remove excited state contamination, and the simultaneous chiral-continuum fit used to extract the charges.
The renormalization factors of local quark-bilinear operators are computed non-perturbatively for $N_f=3$ flavors of SLiNC fermions, with emphasis on the various procedures for the chiral and continuum extrapolations. The simulations are performed at a lattice spacing $a=0.074$ fm, and for five values of the pion mass in the range of 290-465 MeV, allowing a safe and stable chiral extrapolation. Emphasis is given in the subtraction of the well-known pion pole which affects the renormalization factor of the pseudoscalar current. We also compute the inverse propagator and the Green's functions of…
The B-$\bar B$ mixing, B-meson lifetimes, the $B_{s}$-$\bar{B}_{s}$ lifetime difference and SUSY FCNC effects in $ΔB=2$ processes are very important measurable quantities in B-meson phenomenology whose theoretical predictions depend on unknown matrix elements of several four-fermion operators. We present preliminary results for the matrix elements of the relevant four-fermion operators computed on a sample of 600 lattices of size $24^3\times 40$ at $β=6.0$, using the SW--Clover action for light quarks with rotated light quark propagators and the lattice version of the HQET for heavy quarks. As…
Single-propagator traces are the most elementary fermion Wick contractions which occur in numerical lattice QCD, and are usually computed by introducing random-noise estimators to profit from volume averaging. The additional contribution to the variance induced by the random noise is typically orders of magnitude larger than the one due to the gauge field. We propose a new family of stochastic estimators of single-propagator traces built upon a frequency splitting combined with a hopping expansion of the quark propagator, and test their efficiency in two-flavour QCD with pions as light as 190 …
We calculate the fermion propagator and the quark-antiquark Green's functions for a complete set of ultralocal fermion bilinears, ${{\cal O}_Γ}$ [$Γ$: scalar (S), pseudoscalar (P), vector (V), axial (A) and tensor (T)], using perturbation theory up to one-loop and to lowest order in the lattice spacing. We employ the staggered action for fermions and the Symanzik Improved action for gluons. From our calculations we determine the renormalization functions for the quark field and for all ultralocal taste-singlet bilinear operators. The novel aspect of our calculations is that the gluon links whi…
We present an update on Numerical Stochastic Perturbation Theory projects for Lattice QCD, which are by now run on apeNEXT. As a first issue, we discuss a strategy to tackle finite size effects which can be quite sizeable in the computation of logarithmically divergent renormalization constants. Our first high loop determination of quark bilinears for Wilson fermions was limited to finite constants and finite ratios. A precise determination of Z_P and Z_S (and hence of Z_m) now becomes possible. We also give an account of computations for actions different from the standard regularization we h…
We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge-invariant by considered the compact gauge transporters and localized within a $7\times 7$ lattice centered around one of the fermions. We then simulate the model at various values of $β$ and compare with results obtai…
Lattice QCD calculations of radiative transitions between hadrons have in the past been limited to processes of hadrons stable under the strong interaction. Recently developed methods for $1\to2$ transition matrix elements in a finite volume now enable the determination of radiative decay rates of strongly unstable particles. Our lattice QCD study focuses on the process $ππ\to πγ^{*}$, where the $ρ$ meson is present as an enhancement in the cross-section. We use $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV and a lattice size of approximately $3.6$ fm. The required…
We motivate undertaking precision analyses of neutron decays to look for signatures of new scalar and tensor interactions that can arise in extensions of the Standard Model at the TeV scale. The key ingrediant needed to connect experimental data with theoretical analysis are high-precision calculations of matrix elements of isovector bilinear operators between the decaying neutron and final state proton. We describe the status of our Lattice QCD program of using valence clover fermions on dynamical N_f=2+1+1 HISQ configurations generated by the MILC Collaboration. On the theoretical side we us…
We present results on the renormalization functions of the quark field and fermion bilinears with up to one covariant derivative. For the fermion part of the action we employ the twisted mass formulation with $N_f{=}2$ and $N_f{=}4$ degenerate dynamical quarks, while in the gluon sector we use the Iwasaki improved action. The simulations for $N_f{=}4$ have been performed for pion masses in the range of 390MeV - 760MeV and at three values of the lattice spacing, $a$, corresponding to $β{=}1.90,\,1.95,\,2.10$. The $N_f{=}2$ action includes a clover term with $c_{\rm sw}{=}1.57551$ at $β{=}2.10$,…
We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size $32^3 \times 64$ generated using the rational hybrid Monte Carlo algorithm at $a=0.081$~fm and with $M_π=312$ MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple valu…
