arXiv subjects
Publications and source records attributed to Ph. de Forcrand.
The matter and the pseudoscalar densities inside a hadron are calculated via gauge-invariant equal-time correlation functions. A comparison is made between the charge charge and the matter density distributions for the pion, the rho, the nucleon and the $Δ^+$ within the quenched theory, and with two flavours of dynamical quarks.
The magnetic dipole, the electric quadrupole and the Coulomb quadrupole amplitudes for the transition $γN\to Δ$ are evaluated both in quenched lattice QCD at $β=6.0$ and using two dynamical Wilson fermions simulated at $β=5.6$. The dipole transition form factor is accurately determined at several values of momentum transfer. On the lattices studied in this work, the electric quadrupole amplitude is found to be non-zero yielding a negative value for the ratio, $ R_{EM}$, of electric quadrupole to magnetic dipole amplitudes at three values of momentum transfer.
We present results for the phase diagram of three flavor QCD for μ_B ~ 500 MeV. Our simulations are performed with imaginary chemical potential μ_I for which the fermion determinant is positive. Physical observables are then fitted by truncated Taylor series and continued to real chemical potential. We map out the location of the critical line T_c(μ_B) with an accuracy up to terms of order (μ_B/T)^6. We also give first results on a determination of the critical endpoint of the transition and its quark mass dependence. Our results for the endpoint differ significantly from those obtained by other methods, and we discuss possible reasons for this.
We demonstrate how to locate the critical endpoint of the QCD phase transition by means of simulations at imaginary μ. For the three flavor theory, we present numerical results for the pseudo-critical line as a function of chemical potential and bare quark mass, as well as the bare quark mass dependence of the endpoint.
The matter density distribution inside a hadron is evaluated using gauge-invariant correlation functions within the quenched and the unquenched theory. Comparison with the charge density distribution suggests that hadron deformation is a consequence of the relativistic motion of the quarks.
Calculations of the magnetic dipole, electric quadrupole and Coulomb quadrupole amplitudes for the transition $γN\to Δ$ are presented both in quenched QCD and with two flavours of degenerate dynamical quarks.
We present results on the ratio of electric quadrupole to magnetic dipole amplitudes, $R_{EM}={\cal G}_{E2}/{\cal G}_{M1}$, for the transition $γN to Δ$ from lattice QCD. We consider both the quenched and the 2-flavor theory.
Gauge-invariant spatial correlations between two and three quarks inside a hadron are measured within quenched and unquenched QCD. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $Δ$.
Using gauge invariant hadronic two- and three- density correlators we extract information on the spatial distributions of quarks in hadrons, and on hadron shape and multipole moments within quenched lattice QCD. Combined with the calculation of N to Delta transition amplitudes the issue of nucleon deformation can be addressed.
We study charmonium using the standard relativistic formalism in the quenched approximation, on a set of lattices with isotropic lattice spacings ranging from 0.1 to 0.04 fm. We concentrate on the calculation of the hyperfine splitting between eta_c and J/psi, aiming for a controlled continuum extrapolation of this quantity. The splitting extracted from the non-perturbatively improved clover Dirac operator shows very little dependence on the lattice spacing for $a \leq 0.1$ fm. The dependence is much stronger for Wilson and tree-level improved clover operators, but they still yield consistent extrapolations if sufficiently fine lattices, $a \leq 0.07$ fm ($a M(η_c) \leq 1$), are used. Our result for the hyperfine splitting is 77(2)(6) MeV (where Sommer's parameter, r_0, is used to fix the scale). This value remains about 30% below experiment. Dynamical fermions and OZI-forbidden diagrams both contribute to the remainder. Results for the eta_c and J/psi wave functions are also presented.
We review our results for the QCD phase diagram at baryonic chemical potential mu_B \leq pi T. Our simulations are performed with an imaginary chemical potential mu_I for which the fermion determinant is positive. For 2 flavors of staggered quarks, we map out the phase diagram and identify the pseudo-critical temperature T_c(mu_I). For mu_I/T \leq pi/3, this is an analytic function, whose Taylor expansion is found to converge rapidly, with truncation errors far smaller than statistical ones. The truncated series may then be continued to real mu, yielding the corresponding phase diagram for mu_B \lsim 500 MeV. This approach provides control over systematics and avoids reweighting. We outline our strategy to find the (2+1)-flavor critical point.
Gauge-invariant equal-time correlation functions are calculated in lattice QCD within the quenched approximation and with two dynamical quark species. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $Δ$.
Within the reweighting approach, one has the freedom to choose the Monte Carlo action so that it provides a good overlap with the finite-μmeasure but remains simple to simulate. We explore several choices of action in the regime of small μ. Simulating with a finite isospin chemical potential μ_I=μgives a better overlap than the standard choice μ=0, with no computational overhead.
We measure the static three-quark potential in SU(3) lattice gauge theory with improved accuracy, by using all available technical refinements, including Luscher-Weisz exponential variance reduction. Together with insight gained from 3-state Potts model simulations, our results allow us to sort out the merits of the Delta- and Y-ansaetze.
We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings $β_{11}$ and $β_{12}$ corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive numerical calculations of the RG flow are made in the fourth quadrant of this coupling space, i.e., $β_{11}>0$ and $β_{12}<0$. Swendsen's factor two blocking and the Schwinger-Dyson method are used to find an effective action for the blocked gauge field. The resulting renormalization group flow runs quickly towards an attractive stream which has an approximate line shape. This is numerical evidence of a renormalized trajectory which locates close to the two coupling space. A model flow equation which incorporates a marginal coupling (asymptotic scaling term), an irrelevant coupling and a non-perturbative attraction towards the strong coupling limit reproduces qualitatively the observed features. We further examine the scaling properties of an action which is closer to the attractive stream than the currently used improved actions. It is found that this action shows excellent restoration of rotational symmetry even for coarse lattices with $a \sim 0.3$ fm.
We present results on the QCD phase diagram for mu_B <= pi T. Our simulations are performed with an imaginary chemical potential mu_I for which the fermion determinant is positive. On an 8^3 x 4 lattice with 2 flavors of staggered quarks, we map out the phase diagram and identify the pseudo-critical temperature T_c(mu_I). For mu_I/T <= pi/3, this is an analytic function, whose Taylor expansion is found to converge rapidly, with truncation errors far smaller than statistical ones. The truncated series may then be continued to real mu, yielding the corresponding phase diagram for mu_B <~ 500 MeV. This approach provides control over systematics and avoids reweighting. We compare it with other recent work.
We consider the SO(3) lattice gauge theory at weak coupling, in the Villain action. We exhibit an analytic path in coupling space showing the equivalence of the SO(3) theory with SU(2) summed over all twist sectors. This clarifies the ``mysterious phase'' of SO(3). As order parameter, we consider the dual string tension or center vortex free energy, which we measure in SO(3) using multicanonical Monte Carlo. This allows us to set the scale, indicating that ${\cal O}(700)^4$ lattices are necessary to probe the confined phase. We consider the relevance of our findings for confinement in other gauge groups with trivial center.
We examine the gluon propagator in the Laplacian gauge in quenched lattice QCD as a function of the number of colours. We observe a weak dependence on $N_c$ over the whole momentum range. This implies an almost $N_c$-independent gluon pole mass in units of the string tension.