arXiv subjects
Publications and source records attributed to H. Panagopoulos.
We present a scheme for the analytic computation of renormalization functions on the lattice, using a symbolic manipulation computer language. Our first nontrivial application is a new three-loop result for the topological susceptibility.
We calculate the free energy of SU(N) gauge theories on the lattice, to three loops. Our result, combined with Monte Carlo data for the average plaquette, gives a more precise estimate of the gluonic condensate.
We study the spectrum of confining strings in SU(3) pure gauge theory, in different representations of the gauge group. Our results provide direct evidence that the string spectrum agrees with predictions based on n-ality. We also investigate the large-N behavior of the topological susceptibility $χ$ in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at $T_c$. The results indicate that $χ$ has a nonvanishing large-N limit for $T T_c$.
We calculate the perturbative value of the free energy in QCD on the lattice. This quantity is directly related to the average plaquette. Our calculation is done to 3 loops using the clover action for fermions; the results are presented for arbitrary values of the clover coefficient, and for a wide range of fermion masses. In addition, we calculate the 2 loop result for the same quantity, using the overlap action.
We calculate the 2-loop partition function of QCD on the lattice, using the Wilson formulation for gluons and the overlap-Dirac operator for fermions. Direct by-products of our result are the 2-loop free energy and average plaquette. Our calculation serves also as a prototype for further higher loop calculations in the overlap formalism. We present our results as a function of a free parameter $M_0$ entering the overlap action; the dependence on the number of colors $N$ and fermionic flavors $N_f$ is shown explicitly.
We study the dependence of the free energy on the CP violating angle theta, in four-dimensional SU(N) gauge theories with N >= 3, and in the large-N limit. Using the Wilson lattice formulation for numerical simulations, we compute the first few terms of the expansion of the ground-state energy F(theta) around theta = 0, F(theta) - F(0) = A_2 theta^2 (1 + b_2 theta^2 + ...). Our results support Witten's conjecture: F(theta) - F(0) = A theta^2 + O(1/N) for theta < pi. We verify that the topological susceptibility has a nonzero large-N limit chi_infinity = 2A with corrections of O(1/N^2), in substantial agreement with the Witten-Veneziano formula which relates chi_infinity to the eta' mass. Furthermore, higher order terms in theta are suppressed; in particular, the O(theta^4) term b_2 (related to the eta' - eta' elastic scattering amplitude) turns out to be quite small: b_2 = -0.023(7) for N=3, and its absolute value decreases with increasing N, consistently with the expectation b_2 = O(1/N^2).
We calculate the critical value of the hopping parameter, $κ_c$, in O(a) improved Lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions. 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. The dependence of our results on the number of colors $N$, the number of fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown explicitly. We compare our results to non perturbative evaluations of $κ_c$ coming from Monte Carlo simulations.
We calculate the 3-loop bare $β$-function of QCD, formulated on the lattice with the clover fermionic action. The dependence of our result on the number of colors $N$, the number of fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown explicitly. A direct outcome of our calculation is the two-loop relation between the bare coupling constant $g_0$ and the one renormalized in the MS-bar scheme. Further, we can immediately derive the three-loop correction to the relation between the lattice $Λ$-parameter and $g_0$, which turns out to be very pronounced. We also calculate the critical value of the hopping parameter, $κ_c$, in the clover action, to two loops in perturbation theory. This quantity is an additive renormalization; as such, it exhibits a linear divergence in the lattice spacing. We compare our results to non perturbative evaluations of $κ_c$ coming from MC simulations.
We calculate, to 3 loops in perturbation theory, the bare $β$-function of QCD, formulated on the lattice with the clover fermionic action. The dependence of our result on the number of colors $N$, the number of fermionic flavors $N_f$, as well as the clover parameter $c_{SW}$, is shown explicitly. A direct outcome of our calculation is the two-loop relation between the bare coupling constant $g_0$ and the one renormalized in the MS-bar scheme. Further, we can immediately derive the three-loop correction to the relation between the lattice $Λ$-parameter and $g_0$, which is important in checks of asymptotic scaling. For typical values of $c_{SW}$, this correction is found to be very pronounced.
We compute, for the four-dimensional SU(4) and SU(6) gauge theories formulated on a lattice, the string tensions sigma_k related to sources with Z_N charge k, using Monte Carlo simulations. Our results are compatible with sigma_k \propto sin (k pi/N), and show sizeable deviations from Casimir scaling.
We calculate the third coefficient of the lattice beta function associated with the Wilson formulation for both gauge fields and fermions. This allows us to evaluate the three-loop correction (linear in $g_0^2$) to the relation between the lattice Lambda-parameter and the bare coupling $g_0$, which is important in order to verify asymptotic scaling predictions. Our calculation also leads to the two-loop relation between the coupling renormalized in the MSbar scheme and $g_0$. The original version of this paper contained a numerical error in one of the diagrams, which has now been corrected. The calculations, as well as the layout of the paper have remained identical, but there are some important changes in the numerical results.
We calculate the critical value of the hopping parameter, $κ_c$, in Lattice QCD with Wilson fermions, to two loops in perturbation theory. This quantity is an additive renormalization; as such, it is characterized not only by the standard caveats regarding the asymptotic nature of perturbative results, but also by a linear divergence in the lattice spacing. Consequently, our calculation tests rather stringently the limits of applicability of perturbation theory. We compare our results to non perturbative evaluations of $κ_c$ coming from Monte Carlo simulations. Finally, we apply a tadpole improvement technique on our results; this shifts them quite favourably towards the non perturbative values.
We compute the one-loop lattice renormalization of the two-quark operators $\barψ Γψ$, where $Γ$ denotes the generic Dirac matrix, for the lattice formulation of QCD using the overlap-Dirac operator. We also study the renormalization of quark bilinears which are more extended and have better chiral properties. Finally, we present improved estimates of these renormalization constants, coming from cactus resummation and from mean field perturbation theory.
We compute the ratio $Λ_L/Λ_{\bar{MS}}$ between the scale parameter $Λ_L$, associated with a lattice formulation of QCD using the overlap-Dirac operator, and $Λ_{\bar{MS}}$ of the $\bar{\rm MS}$ renormalization scheme. To this end, the necessary one-loop relation between the lattice coupling $g_0$ and the coupling renormalized in the $\bar{\rm MS}$ scheme is calculated, using the lattice background field technique.
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant tadpole-like diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, e.g. the lattice renormalization of some two-fermion operators, this expansion yields results remarkably close to corresponding nonperturbative estimates. We consider in our study both the Wilson and the clover action for fermions.
We compare the performance of an UV-filtered Multiboson algorithm, including a global quasi-heatbath update, to the standard Hybrid Monte Carlo algorithm in full QCD with two flavours of Wilson fermions.
We study the efficiency of an improved Multiboson algorithm with two flavours of Wilson fermions in a realistic physical situation ($β= 5.60$, $κ= 0.156$ on a $16^3 \times 24$ lattice). The performance of this exact algorithm is compared with that of a state-of-the-art HMC algorithm: a considerable improvement is obtained for the plaquette auto-correlation time, while the two algorithms appear similarly efficient at decorrelating the topological charge.
Gauge invariant correlators in QCD are studied on the lattice.A Systematic determination of the correlation lengths for gluon field strength correlators and quark correlators is made.The measurement of the gluon and quark condensates is discussed.