Improved Wilson Fermions Research Articles

Lattice cutoff effects forFDswith improved Wilson fermions — a final lesson from the quenched case

Lattice cutoff effects for<i>F</i>_{D_s}with improved Wilson fermions — a final lesson from the quenched case

Search for the charmonia dissociation in lattice QCD

Dissociation of charmonia in hot QCD is studied on a quenched anisotropic lattice using standard plaquette gauge action and O(a) improved Wilson fermion action. Simulations are carried out at temperatures in the range 0.88 TC to 2.3 TC. We calculate effective masses and Bethe–Salpeter wavefunctions for the ground state (1S, 1P) and some excited states (2S, 2P) with variational analysis. To distinguish between bound states and scattering states, we apply two methods: first, we compare effective masses for charmonium correlation functions under different spatial boundary conditions. Because the scattering states are sensitive to the boundary conditions, finite volume effects are expected when a charmonium dissociates. Second, we study if the wavefunctions show a sign of scattering states which will be characterized by a broad wavefunction. We find no clear evidence of dissociation for the charmonium states up to 2.3 TC so far.

Spatial string tension in N f = 2 lattice QCD at finite temperature

The spatial string tension across a crossover from the low temperature phase to the high temperature phase is computed in QCD with two flavors of non-perturbatively improved Wilson fermions at small lattice spacing a \sim 0.12fm. We find that in the low temperature phase spatial string tension agrees well with zero temperature string tension. Furthermore, it does not show increasing for temperatures up to T = 1.36 T_{pc}, the highest temperature considered. Our results agree with some theoretical predictions.

Low energy chiral constants from epsilon-regime simulations with improved Wilson fermions

We present a lattice QCD calculation of the low-energy constants of the leading order chiral Lagrangian. In these simulations the epsilon regime is reached by using tree-level improved nHYP Wilson fermions combined with reweighting in the quark mass. We analyze two point functions on two ensembles with lattices of size $(1.85\text{ }\text{ }\mathrm{fm}{)}^{4}$ and $(2.8\text{ }\text{ }\mathrm{fm}{)}^{4}$, and at several quark mass values between 4 and 20 MeV. The data are well fitted with next-to-leading order chiral perturbative formulas and predict $F=90(4)\text{ }\text{ }\mathrm{MeV}$ and ${\ensuremath{\Sigma}}^{1/3}=248(6)\text{ }\text{ }\mathrm{MeV}$ in the $\overline{\mathrm{MS}}$ scheme at 2 GeV.

Spin Structure of the Pion

We present the first calculation of the transverse spin structure of the pion in lattice QCD. Our simulations are based on two flavors of nonperturbatively improved Wilson fermions, with pion masses as low as 400 MeV in volumes up to (2.1 fm)(3) and lattice spacings below 0.1 fm. We find a characteristic asymmetry in the spatial distribution of transversely polarized quarks. This asymmetry is very similar in magnitude to the analogous asymmetry we previously obtained for quarks in the nucleon. Our results support the hypothesis that all Boer-Mulders functions are alike.

Lattice QCD study of the heavy-heavy-light quark potential

We study the heavy-heavy-light quark ($QQq$) potential in SU(3) quenched lattice QCD, and discuss one of the roles of the finite-mass valence quark in the interquark potential. Monte Carlo simulations are performed with the standard gauge action on the ${16}^{4}$ lattice at $\ensuremath{\beta}=6.0$ and the $O(a)$-improved Wilson fermion action at four hopping parameters. For statistical improvement, the gauge configuration is fixed with the Coulomb gauge. We calculate the potential energy of $QQq$ systems as a function of the inter-heavy-quark distance $R$ in the range of $R\ensuremath{\le}0.8\text{ }\text{ }\mathrm{fm}$. The $QQq$ potential is well described with a Coulomb plus linear potential, and the effective string tension between the two heavy quarks is significantly smaller than the string tension $\ensuremath{\sigma}\ensuremath{\simeq}0.89\text{ }\text{ }\mathrm{GeV}/\mathrm{fm}$. It would generally hold that the effect of the finite-mass valence quark reduces the inter-two-quark confinement force in baryons.

Heavy–heavy–light quark potential in [formula omitted] lattice QCD

We perform the first study for the heavy–heavy–light quark (QQq) potential in SU(3) quenched lattice QCD with the Coulomb gauge. The calculations are done with the standard gauge and O(a)-improved Wilson fermion action on the 164 lattice at β=6.0. We calculate the energy of QQq systems as the function of the distance R between the two heavy quarks, and find that the QQq potential is well described with a Coulomb plus linear potential form up to the intermediate distance R⩽0.8 fm. Compared to the static three-quark case, the effective string tension between the heavy quarks is significantly reduced by the finite-mass valence quark effect. This reduction is considered to be a general property for baryons.

Effective field theory for the anisotropic Wilson lattice action

We construct the effective field theory appropriate for describing the low-energy behavior of anisotropic Wilson lattice actions and the $\mathcal{O}(a)$ improved variant thereof. We then apply this effective field theory to the hadron spectrum and dispersion relations, focussing on the corrections due to the anisotropy. We point out an important feature of anisotropic lattices regarding the Aoki regime; for a given set of fermion masses and spatial lattice spacing, if an isotropic action is in the QCD-phase, this does not guarantee that the anisotropic action is outside the Aoki regime. This may be important in the tuning of bare parameters for anisotropic lattices using domain-wall and overlap fermions as well as Wilson and $\mathcal{O}(a)$-improved Wilson fermions.

Lattice QCD calculation of theρmeson decay width

We present a lattice QCD calculation of the $\rho$ meson decay width via the $P$-wave scattering phase shift for the I=1 two-pion system. Our calculation uses full QCD gauge configurations for $N_f=2$ flavors generated using a renormalization group improved gauge action and an improved Wilson fermion action on a $12^3\times24$ lattice at $m_\pi/m_\rho=0.41$ and the lattice spacing $1/a=0.92 {\rm GeV}$. The phase shift calculated with the use of the finite size formula for the two-pion system in the moving frame shows a behavior consistent with the existence of a resonance at a mass close to the vector meson mass obtained in spectroscopy. The decay width estimated from the phase shift is consistent with the experiment, when the quark mass is scaled to the realistic value.

Spectral properties of quarks above [formula omitted] in quenched lattice QCD

We analyze the quark spectral function above the critical temperature for deconfinement in quenched lattice QCD using clover improved Wilson fermions in Landau gauge. We show that the temporal quark correlator is well reproduced by a two-pole approximation for the spectral function and analyze the bare quark mass dependence of both poles as well as their residues. In the chiral limit we find that the quark spectral function has two collective modes which correspond to the normal and plasmino excitations. At large values of the bare quark mass the spectral function is dominated by a single pole.

Decay constants of charm and beauty pseudoscalar heavy–light mesons on fine lattices

We compute decay constants of heavy–light mesons in quenched lattice QCD with a lattice spacing of a≃0.04 fm using non-perturbatively O(a) improved Wilson fermions and O(a) improved currents. We obtain fDs=220(6)(5)(11) MeV, fD=206(6)(3)(22) MeV, fBs=205(7)(26)(17) MeV and fB=190(8)(23)(25) MeV, using the Sommer parameter r0=0.5 fm to set the scale. The first error is statistical, the second systematic and the third from assuming a ±10% uncertainty in the experimental value of r0. A detailed discussion is given in the text. We also present results for the meson decay constants fK and fπ and the ρ meson mass.

Probing nucleon structure on the lattice

The QCDSF/UKQCD collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction and the first three moments of the nucleon's spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320 MeV.

The pion form factor from lattice QCD with two dynamical flavours

We compute the electromagnetic form factor of the pion using non-perturbatively O(a) improved Wilson fermions. The calculations are done for a wide range of pion masses and lattice spacings. We check for finite size effects by repeating some of the measurements on smaller lattices. The large number of lattice parameters we use allows us to extrapolate to the physical point. For the square of the charge radius we find =0.441(20) fm^2, in good agreement with experiment.

Moments of pseudoscalar meson distribution amplitudes from the lattice

Based on lattice simulations with two flavors of dynamical, $\mathcal{O}(a)$-improved Wilson fermions we present results for the first two moments of the distribution amplitudes of pseudoscalar mesons at several values of the valence quark masses. By extrapolating our results to the physical masses of up/down and strange quarks, we find the first two moments of the ${K}^{+}$ distribution amplitude and the second moment of the ${\ensuremath{\pi}}^{+}$ distribution amplitude. We use nonperturbatively determined renormalization coefficients to obtain results in the $\overline{\mathrm{MS}}$ scheme. At a scale of $4\text{ }\text{ }{\mathrm{GeV}}^{2}$ we find ${a}_{2}^{\ensuremath{\pi}}=0.201(114)$ for the second Gegenbauer moment of the pion's distribution amplitude, while for the kaon, ${a}_{1}^{K}=0.0453(9)(29)$ and ${a}_{2}^{K}=0.175(18)(47)$.

Estimating the unquenched strange quark mass from the lattice axial Ward identity

We present a determination of the strange quark mass for two flavors (${n}_{f}=2$) of light dynamical quarks using the axial Ward identity. The calculations are performed on the lattice using $O(a)$ improved Wilson fermions and include a fully nonperturbative determination of the renormalization constant. In the continuum limit we find ${m}_{s}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=111(6)(4)(6)\text{ }\text{ }\mathrm{MeV}$, using the force scale ${r}_{0}=0.467\text{ }\text{ }\mathrm{fm}$, where the first error is statistical, the second and third are systematic due to the fit and scale uncertainties, respectively. Results are also presented for the light quark mass and the chiral condensate. The corresponding results are also given for ${r}_{0}=0.5\text{ }\text{ }\mathrm{fm}$.

Nucleon structure from generalized parton distributions in lattice QCD

This talk presents results from the QCDSF-UKQCD collaboration for moments of leading twist generalized parton distributions in two-flavor lattice QCD based on O(a) improved Wilson Fermions. We study helicity independent and helicity flip GPDs with a focus on densities of quarks in the transverse plane.

Determination of the Lambda parameter from full lattice QCD

We present a determination of the QCD parameter $\ensuremath{\Lambda}$ in the quenched approximation (${n}_{f}=0$) and for two flavors (${n}_{f}=2$) of light dynamical quarks. The calculations are performed on the lattice using $O(a)$ improved Wilson fermions and include taking the continuum limit. We find ${\ensuremath{\Lambda}}_{{n}_{f}=0}^{\overline{MS}}=259(1)(19)\text{ }\text{ }\mathrm{MeV}$ and ${\ensuremath{\Lambda}}_{{n}_{f}=2}^{\overline{MS}}=261(17)(26)\text{ }\text{ }\mathrm{MeV}$, using ${r}_{0}=0.467\text{ }\text{ }\mathrm{fm}$ to set the scale. Extrapolating our results to five flavors, we obtain for the running coupling constant at the mass of the $Z$ boson ${\ensuremath{\alpha}}_{s}^{\overline{MS}}({m}_{Z})=0.112(1)(2)$.

Bulk first-order phase transition in three-flavor lattice QCD withO(a)-improved Wilson fermion action at zero temperature

Three-flavor QCD simulation with the $O(a)$-improved Wilson fermion action is made employing an exact fermion algorithm developed for odd number of quark flavors. For the plaquette gauge action, an unexpected first-order phase transition is found in the strong coupling regime ($\beta\lesssim$ 5.0) at relatively heavy quark masses ($m_{\mathrm{PS}}/m_{\mathrm{V}}\sim$ 0.74--0.87). Strong metastability persists on a large lattice of size $12^3\times 32$, which indicates that the transition has a bulk nature. The phase gap becomes smaller toward weaker couplings and vanishes at $\beta\simeq 5.0$, which corresponds to a lattice spacing $a\simeq$ 0.1 fm. The phase transition is not found if the improved gauge actions are employed. Our results imply that realistic simulations of QCD with three flavors of dynamical Wilson-type fermions at lattice spacings in the range $a=$ 0.1--0.2 fm require use of improved gauge actions. Possible origins of the phase transition is discussed.

Chiral properties of dynamical Wilson fermions

We consider two-flavor QCD in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken at order a and hence the isovector axial currents require improvement as well as a finite renormalization if they are to satisfy continuum Ward--Takahashi identities up to small lattice corrections of O(a^2). Algorithmic difficulties at coarse lattice spacings, where HMC suffers from a distorted Dirac spectrum, are discussed. This is shown to be a cutoff effect, which disappears rapidly as the lattice spacing is decreased. An alternative algorithm, the polynomial hybrid Monte Carlo algorithm, is found to perform significantly better in the presence of exceptionally small eigenvalues. Extending previously used methods both the improvement and the renormalization of the axial current are implemented non--perturbatively in terms of correlation functions formulated in the framework of the Schroedinger functional. In both cases this is achieved by enforcing continuum Ward identities at finite lattice spacing. Together, this restores the isovector chiral symmetry to quadratic order in the lattice spacing. With little additional effort the normalization factor of the local vector current is also obtained.

Non-perturbative renormalization of the axial current with dynamical Wilson fermions

We present a new normalization condition for the axial current, derived from the PCAC relation with non-vanishing quark mass. This condition is expected to reduce mass effects in the chiral extrapolation of the results for the normalization factor Z_A. The application to the two-flavor theory with improved Wilson fermions shows that this expectation is indeed fulfilled. Using the Schroedinger functional setup we calculate Z_A(g_0^2) as well as the vector current normalization factor Z_V(g_0^2) for beta = 6/g_0^2 >= 5.2.