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H. Panagopoulos

Publications and source records attributed to H. Panagopoulos.

At least 55 records · Page 3Linked to original sources
arXiv2009

Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice

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 calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, together with some special features of superficially divergent integrals, are included in the Appendices.

hep-lat↗
arXiv2008

Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice

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 in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. Finally, we present our results in the $\bar{MS}$ scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, are included in an Appendix.

hep-lat↗
arXiv2008

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

We calculate the critical value of the hopping parameter, $κ_c$, 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 $c_{SW}$ (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 non perturbative evaluations of $κ_c$ coming from Monte Carlo simulations, we employ an improved perturbation theory method for improved actions.

hep-lat↗
arXiv2007

Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3-loop beta-function

This work presents the calculation of the relation between the bare coupling constant g_0 and the MSbar-renormalized coupling g_MS, g_0 = Z_g(g_0,aμ) g_MS, to 2 loops in perturbation theory, with fermions in an arbitrary representation of the gauge group SU(N). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. The corresponding results in the fundamental representation appear in our longer publication [arXiv:0709.4368]. The 3-loop coefficient of the bare beta-function, b_2^L, is extracted using the 2-loop expression for Z_g, and it is presented as a function of the overlap parameter rho, the number of fermion flavors (N_f) and the number of colors (N). We also provide the expression for the ratio Lambda_L/Lambda_MS, in an arbitrary representation. A plot of Lambda_L/Lambda_MS is given in the adjoint representation.

hep-lat↗
arXiv2007

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 - Wolhert (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 lattice, with subsequent extrapolation to infinite size. The results are presented as a function of the fermion mass m, for any SU(N_c) 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.

hep-lat↗
arXiv2007

QCD with overlap fermions: Running coupling and the 3-loop beta-function

We calculate the relation between the bare coupling constant g_0 and the MSbar-renormalized coupling g_MS: g_0 = Z_g(g_0,a μ) g_MS, to 2 loops in perturbation theory. We employ the standard Wilson action for gluons and the overlap action for fermions. For convenience, we have worked with the background field technique, which only requires evaluation of 2-point Green's function for the problem at hand. Our results depend explicitly on the number of fermion flavors (N_f) and colors (N). Since the dependence of Z_g on the overlap parameter rho cannot be extracted analytically, we tabulate our results for different values in the allowed range of rho (0 < rho < 2), focusing on values which are being used most frequently in simulations. Knowledge of Z_g allows us to derive the 3-loop coefficient of the bare beta-function (beta_L(g_0)) which, unlike the 1- and 2-loop coefficients, is regularization-dependent. The nontrivial dependence of Z_g and of beta_L(g_0) on rho is plotted for various choices of N, N_f.

hep-lat↗
arXiv2007

Lambda-parameter of lattice QCD with Symanzik improved gluon actions

We compute the ratio Lambda_L/Lambda_MS, where the scale parameter Lambda_L is associated with a lattice formulation of QCD. We consider a 3-parameter family of gluon actions, which are most frequently used for O(a) improvement a` la Symanzik. The gluon action is put togeter with standard discretizations for fermions (Wilson/clover, overlap), to provide Lambda_L for several possible combinations of fermion and gluon actions. We employ the background field technique in order to calculate the 1PI 2-point function of the background field; this leads to the coupling constant renormalization function, Z_g, at 1-loop level. Our results are obtained for an extensive range of values for the Symanzik coefficients.

hep-lat↗
arXiv2007

Higher loop renormalization of fermion bilinear operators

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 $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. A longer write-up of the present work, including the conversion of our results to the MSbar scheme and a generalization to arbitrary fermion representations, can be found in arXiv:0707.2906 .

hep-lat↗
arXiv2006

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

We calculate the critical value of the hopping parameter, kappa_c, in Lattice QCD, up to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions and the Symanzik improved gluon action for 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_{SW} (clover parameter) and cover a wide range of values for the Symanzik coefficients c_i. Furthermore, the dependence on the number of colors N and the number of fermionic flavors N_f is shown explicitly. In order to compare our results to non perturbative evaluations of kappa_c coming from Monte Carlo simulations, we employ an improved perturbation theory method applied to improved actions.

hep-lat↗
arXiv2006

Improved Perturbation Theory for Improved Lattice Actions

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.

hep-lat↗
arXiv2006

Perturbative renormalization in parton distribution functions using Overlap fermions and Symanzik improved gluons

We calculate the 1-loop renormalization of the fermion self-energy, all local fermion bilinears, as well as a set of extended bilinears which form a basis corresponding to moments of the parton distribution functions. We use the overlap action for fermions and Symanzik improved action for gluons. Our results are presented as a function of the overlap parameter rho and the parameters entering the Symanzik action.

hep-lat↗
arXiv2006

Free Energy and Plaquette expectation value for gluons on the lattice, in three dimensions

We calculate the perturbative value of the Free Energy in Lattice QCD in three dimensions, up to three loops. Our calculation is performed using the Wilson formulation for gluons in SU(N) gauge theories. The Free Energy is directly related to the average plaquette. To carry out the calculation, we compute the coefficients involved in the perturbative expansion of the Free Energy up to three loops, using an automated set of procedures developed by us in Mathematica. The dependence on N is shown explicitly in our results. For purposes of comparison, we also present the individual contributions from every diagram. These have been obtained by means of two independent calculations, in order to cross check our results.

hep-lat↗
arXiv2006

Additive and multiplicative renormalization of topological charge with improved gluon/fermion actions: A test case for 3-loop vacuum calculations, using overlap or clover fermions

We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power divergent additive renormalization of the topological susceptibility is calculated to 3 loops. Our work serves also as a test case of the techniques and limitations of lattice perturbation theory, it being the first 3-loop computation in the literature involving overlap fermions.

hep-lat↗
arXiv2005

Perturbative renormalization in parton distribution functions using improved actions

We calculate the 1-loop renormalization of a set of extended fermionic bilinears which form a basis corresponding to moments of the parton distribution functions. We use the overlap action for fermions and Luescher-Weisz (LW) action for gluons. Our results are presented as a function of the overlap parameter rho and the parameters entering the LW action.

hep-lat↗
arXiv2005

Two-loop evaluation of large Wilson loops with overlap fermions: the b-quark mass shift, and the quark-antiquark potential

We compute, to two loops in pertubation theory, the fermionic contribution to rectangular RxT 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 -> Infinity our results lead to the shift in the b-quark mass. We also evaluate the perturbative static potential as T -> Infinity.

hep-lat↗
arXiv2005

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 pertubation theory, the fermionic contribution to rectangular RxT 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 -> Infinity our results lead to the shift in the b-quark mass. We also evaluate the perturbative static potential as T -> Infinity.

hep-lat↗
arXiv2005

Topological charge renormalization: A test case for 3-loop vacuum calculations using overlap fermions and Symanzik improved gluons

We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power divergent additive renormalization of the topological susceptibility is calculated to 3 loops.

hep-lat↗
arXiv2005

Optimized interpolations and nonlinearity in numerical studies of woodwind instruments

We study the impedance spectra of woodwind instruments with arbitrary axisymmetric geometry. We perform piecewise interpolations of the instruments' profile, using interpolating functions amenable to analytic solutions of the Webster equation. Our algorithm optimizes on the choice of such functions, while ensuring compatibility of wavefronts at the joining points. Employing a standard mathematical model of a single-reed mouthpiece as well as the time-domain reflection function, which we derive from our impedance results, we solve the Schumacher equation for the pressure evolution in time. We make analytic checks that, despite the nonlinearity in the reed model and in the evolution equation, solutions are unique and singularity-free.

physics.comp-ph↗