Clover Fermions Research Articles

Study of QCD critical point using canonical ensemble method

The existence of the QCD critical point at non-zero baryon density is not only of great interest for experimental physics but also a challenge for the theory. We use lattice simulations based on the canonical ensemble method to explore the finite baryon density region and look for the critical point. We scan the phase diagram of QCD with three degenerate quark flavors using clover fermions with m π ≈ 700 MeV on 6 3 × 4 lattices. We measure the baryon chemical potential as we increase the density and we see the characteristic “S-shape” that signals the first order phase transition. We determine the phase boundary by Maxwell construction and report our preliminary results for the location of critical point.

𝒪(a2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons

We calculate corrections to the fermion propagator and to the Green's functions of all fermion bilinear operators of the form , to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and the Symanzik improved action for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, (a2). 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 (a1) improvement calculations; there, IR divergent terms are seen to have the same structure as in the (a0) case, by virtue of parity under integration, and they can thus be handled by well-known techniques. We explain how to correctly extract the full (a2) dependence; in fact, our method is generalizable to any order in a. The (a2) corrections to the quark propagator and Green's functions computed in this paper are useful to improve the nonperturbative RI-MOM determination of renormalization constants for quark bilinear operators. Our results depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: Oa2results.m; the file is best perused as Mathematica input.

Electromagnetic structure of decuplet baryons towards the chiral regime

The electromagnetic properties of the baryon decuplet are calculated in quenched QCD on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm using the fat-link irrelevant clover (FLIC) fermion action with quark masses providing a pion mass as low as 300 MeV. Magnetic moments and charge radii are extracted from the electric and magnetic form factors for each individual quark sector. From these, the corresponding baryon properties are constructed. We present results for the higher order moments of the spin-3/2 baryons, including the electric quadrupole moment E2 and the magnetic octupole moment M3. The world's first determination of a non-zero M3 form factor for the Delta baryon is presented. With these results we provide a conclusive analysis which shows that decuplet baryons are deformed. We compare the decuplet baryon results from a similar lattice calculation of the octet baryons. We establish that the environment sensitivity is far less pronounced in the case of the decuplet baryons compared to that in the octet baryons. A surprising result is that the charge radii of the decuplet baryons are generally smaller than that of the octet baryons. The magnetic moment of the Delta^+ reveals a turn over in the low quark mass region, making it smaller than the proton magnetic moment. These results are consistent with the expectations of quenched chiral perturbation theory. A similar turn over is also noticed in the magnetic moment of the Sigma^*0, but not for Xi^* where only kaon loops can appear in quenched QCD. The electric quadrupole moment of the Omega^- baryon is positive when the negative charge factor is included, and is equal to 0.86 +- 0.12 x 10^-2 fm^2, indicating an oblate shape.

High statistics analysis using anisotropic clover lattices: Single hadron correlation functions

We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total of 292,500 sets of measurements are made using 1194 gauge configurations of size 20^3 x 128 with an anisotropy parameter \xi= b_s/b_t = 3.5, a spatial lattice spacing of b_s=0.1227\pm 0.0008 fm, and pion mass of m_\pi ~ 390 MeV. Ground state baryon masses are extracted with fully quantified uncertainties that are at or below the ~0.2%-level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the N\pi threshold and, therefore, the isospin-1/2 \pi N s-wave scattering phase-shift can be extracted using Luescher's method. The disconnected contributions to this process are included indirectly in the gauge-field configurations and do not require additional calculations. The signal-to-noise ratio in the various correlation functions is explored and is found to degrade exponentially faster than naive expectations on many time-slices. This is due to backward propagating states arising from the anti-periodic boundary conditions imposed on the quark-propagators in the time-direction. We explore how best to distribute computational resources between configuration generation and propagator measurements in order to optimize the extraction of single baryon observables.

Nonperturbative improvement of stout-smeared three-flavor clover fermions

We discuss a three-flavor lattice QCD action with clover improvement in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree-level) Symanzik improved gluon action this constitutes the stout link nonperturbative clover or SLiNC action. To cancel $O(a)$ terms the clover term coefficient has to be tuned. We present here results of a nonperturbative determination of this coefficient using the Schr\odinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the results are made with lowest order perturbation theory.

Extracting electric polarizabilities from lattice QCD

Charged and neutral, pion and kaon electric polarizabilities are extracted from lattice QCD using an ensemble of anisotropic gauge configurations with dynamical clover fermions. We utilize classical background fields to access the polarizabilities from two-point correlation functions. Uniform background fields are achieved by quantizing the electric field strength with the proper treatment of boundary flux. These external fields, however, are implemented only in the valence quark sector. A novel method to extract charge particle polarizabilities is successfully demonstrated for the first time.

Lattice calculation of the magnetic moments ofΔandΩ−baryons with dynamical clover fermions

We calculate the magnetic dipole moment of the $\ensuremath{\Delta}(1232)$ and ${\ensuremath{\Omega}}^{\ensuremath{-}}$ baryons with $2+1$ flavors of clover fermions on anisotropic lattices using a background magnetic field. This is the first dynamical calculation of these magnetic moments using a background field technique. The calculation for ${\ensuremath{\Omega}}^{\ensuremath{-}}$ is done at the physical strange quark mass, with the result in units of the physical nuclear magneton ${\ensuremath{\mu}}_{{\ensuremath{\Omega}}^{\ensuremath{-}}}=\ensuremath{-}1.93\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.12$ (where the first error is statistical and the second is systematic) compared to the experimental number: $\ensuremath{-}2.02\ifmmode\pm\else\textpm\fi{}0.05$. The $\ensuremath{\Delta}$ has been studied at three unphysical quark masses, corresponding to pion mass ${m}_{\ensuremath{\pi}}=366$, 438, and 548 MeV. The pion mass dependence is compared with the behavior obtained from chiral effective field theory.

Logarithmic link smearing for full QCD

A Lie-algebra based recipe for smoothing gauge links in lattice field theory is presented, building on the matrix logarithm. With or without hypercubic nesting, this LOG/HYL smearing yields fat links which are differentiable with respect to the original ones. This is essential for defining UV-filtered (“fat link”) fermion actions which may be simulated with a HMC-type algorithm. The effect of this smearing on the distribution of plaquettes and on the residual mass of tree-level O ( a ) -improved clover fermions in quenched QCD is studied.

Nucleon distribution amplitudes and proton decay matrix elements on the lattice

Baryon distribution amplitudes (DAs) are crucial for the theory of hard exclusive reactions. We present a calculation of the first few moments of the leading-twist nucleon DA within lattice QCD. In addition we deal with the normalization of the next-to-leading (twist-four) DAs. The matrix elements determining the latter quantities are also responsible for proton decay in Grand Unified Theories. Our lattice evaluation makes use of gauge field configurations generated with two flavors of clover fermions. The relevant operators are renormalized nonperturbatively with the final results given in the MSbar scheme. We find that the deviation of the leading-twist nucleon DA from its asymptotic form is less pronounced than sometimes claimed in the literature.

Nucleon Distribution Amplitudes from Lattice QCD

We calculate low moments of the leading-twist and next-to-leading-twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MS[over ] scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature.

Perturbative determination ofcSWfor plaquette and Symanzik gauge action and stout link clover fermions

Using plaquette and Symanzik improved gauge action and stout link clover fermions we determine the improvement coefficient c{sub SW} in one-loop lattice perturbation theory from the off-shell quark-quark-gluon three-point function. In addition, we compute the coefficients needed for the most general form of quark field improvement and present the one-loop result for the critical hopping parameter {kappa}{sub c}. We discuss mean field improvement for c{sub SW} and {kappa}{sub c} and the choice of the mean field coupling for the actions we have considered.

Tuning for three flavors of anisotropic clover fermions with stout-link smearing

In this work we perform the parameter tuning of three flavors of dynamical clover quarks on anisotropic lattices. The fermion action uses three-dimensional spatial stout-link smearing. The gauge anisotropy is determined in a small box with Schr\"odinger background using Wilson-loop ratios. The fermion anisotropy is obtained from studying the meson dispersion relation with antiperiodic boundary conditions in the time direction. The spatial and temporal clover coefficients are fixed to the tree-level tadpole-improved values, and we demonstrate that they satisfy the nonperturbative conditions as determined by the Schr\"odinger-functional method. For the desired lattice spacing ${a}_{s}\ensuremath{\approx}0.12\text{ }\text{ }\mathrm{fm}$ and renormalized anisotropy $\ensuremath{\xi}=3.5$, we find the gauge and fermionic anisotropies can be fixed to quark mass independent values up through the strange quark mass. This work lays the foundation needed for further studies of the excited-state hadron spectrum.

Relation between bare lattice coupling andMS¯coupling at one loop with general lattice fermions

A compact general integral formula is derived from which the fermionic contribution to the one-loop coefficient in the perturbative expansion of the MS coupling in powers of the bare lattice coupling can be extracted. It is seen to reproduce the known results for unimproved naive, staggered and Wilson fermions, and has advantageous features which facilitate the evaluation in the case of improved lattice fermion formulations. This is illustrated in the case of Wilson clover fermions, and an expression in terms of known lattice integrals is obtained in this case which gives the coefficient to much greater numerical accuracy than in the previous literature.

Renormalisation of composite operators in lattice perturbation theory with clover fermions: Non-forward matrix elements

We consider the renormalisation of lattice QCD operators with one and two covariant derivatives related to the first and second moments of generalised parton distributions and meson distribution amplitudes. Employing the clover fermion action we calculate their non-forward quark matrix elements in one-loop lattice perturbation theory. For some representations of the hypercubic group commonly used in simulations we determine the sets of all possible mixing operators and compute the matrices of renormalisation factors in one-loop approximation. We describe how tadpole improvement is applied to the results.

Large Wilson loops with overlap and clover fermions: Two-loop evaluation of the b-quark mass shift and the quark–antiquark potential

We compute, to two loops in perturbation theory, the fermionic contribution to rectangular R × T Wilson loops, for different values of R and T. We use the overlap fermionic action. We also employ the clover action, for comparison with existing results in the literature. In the limit R , T → ∞ our results lead to the shift in the static quark energy, which can be used to determine the b-quark mass. We also evaluate the perturbative static potential as T → ∞ .

Two-loop additive mass renormalization with clover fermions and Symanzik improved gluons

We calculate the critical value of the hopping parameter, ${\ensuremath{\kappa}}_{c}$, in lattice QCD, up to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for fermions and the Symanzik improved gluon action with 4- and 6-link loops. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. Our results are polynomial in ${c}_{\mathrm{SW}}$ (clover parameter) and cover a wide range of values for the Symanzik coefficients ${c}_{i}$. The dependence on the number of colors $N$ and the number of fermion flavors ${N}_{f}$ is shown explicitly. In order to compare our results to nonperturbative evaluations of ${\ensuremath{\kappa}}_{c}$ coming from Monte Carlo simulations, we employ an improved perturbation theory method for improved actions.

Scaling analysis of fat-link irrelevant clover fermion actions

The fat-link irrelevant clover fermion action is a variant of the O(a)-improved Wilson action where the irrelevant operators are constructed using smeared links. While the use of such smearing allows for the use of highly improved definitions of the field strength tensor F{sub {mu}}{sub {nu}}, we show that the standard 1-loop clover term with a mean field improved coefficient c{sub sw} is sufficient to remove the O(a) errors, avoiding the need for nonperturbative tuning. This result enables efficient dynamical simulations in QCD with the fat-link irrelevant clover fermion action.

The lattice free energy of QCD with clover fermions, up to three-loops

We calculate the perturbative value of the free energy in Lattice QCD, up to three loops. Our calculation is performed using Wilson gluons and the Sheikholeslami–Wohlert (clover) improved action for fermions. The free energy is directly related to the average plaquette. To carry out the calculation, we compute all relevant Feynman diagrams up to 3 loops, using a set of automated procedures in Mathematica; numerical evaluation of the resulting loop integrals is performed on finite lattices, with subsequent extrapolation to infinite size. The results are presented as a function of the fermion mass m, for any SU(Nc) gauge group, and for an arbitrary number of fermion flavors. In order to enable independent comparisons, we also provide the results on a per diagram basis, for a specific mass value.

H-Dibaryon from Lattice QCD with Improved Anisotropic Actions

The six quark state(uuddss) called H dibaryon(JP = 0+,S = -2) has been calculated to study its existence and stability. The simulations are performed in quenched QCD on 83 × 24 and 163 × 48 anisotropic lattices with Symanzik improved gauge action and Clover fermion action. The gauge coupling is β = 2.0 and aspect ratio ξ = as/at = 3.0. Preliminary results indicate that mass of H dibaryon is 2134(100)Mev on 83 × 24 lattice and 2167(59)Mev on 163 × 48 respectively. It seems that the radius of H dibaryon is very large and the finite size effect is very obvious.

Neutron electric dipole moment with external electric field method in lattice QCD

We discuss a possibility that the neutron electric dipole moment (NEDM) can be calculated in lattice QCD simulations in the presence of the $CP$-violating $\ensuremath{\theta}$ term. In this paper we measure the energy difference between spin-up and spin-down states of the neutron in the presence of a uniform and static external electric field. We first test this method in quenched QCD with the renormalization group improved gauge action on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at ${a}^{\ensuremath{-}1}\ensuremath{\simeq}2\text{ }\text{ }\mathrm{GeV}$, employing two different lattice fermion formulations, the domain-wall fermion and the clover fermion for quarks, at relatively heavy quark mass $({m}_{PS}/{m}_{V}\ensuremath{\simeq}0.85)$. We obtain nonzero values of the NEDM from calculations with both fermion formulations. We next consider some systematic uncertainties of our method for the NEDM, using ${24}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at the same lattice spacing only with the clover fermion. We finally investigate the quark mass dependence of the NEDM and observe a nonvanishing behavior of the NEDM toward the chiral limit. We interpret this behavior as a manifestation of the pathology in the quenched approximation.