arXiv subjects

M. Constantinou

Publications and source records attributed to M. Constantinou.

71 records · Page 4Linked to original sources

arXiv2012

Perturbative subtraction of lattice artifacts in the computation of renormalization constants

The determination of renormalization factors is of crucial importance. They relate the observables obtained on finite, discrete lattices to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. They are always present because simulations are done at lattice spacings $a$ and momenta $p$ with $ap$ not necessarily small. In this paper we try to suppress these artifacts by subtraction of one-loop contributions in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of $O(a^2)$.

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arXiv2012

Renormalization constants of local operators for Wilson type improved fermions

Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level and up to second order in the lattice spacing, is performed for a fermion action, which includes the clover term and the twisted mass parameter yielding results that are applicable for unimproved Wilson fermions, as well as for improved clover and twisted mass fermions. We consider ten variants of the Symanzik improved gauge action corresponding to ten different values of the plaquette coefficients. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations are performed for pion masses in the range of 480 MeV to 260 MeV and at three values of the lattice spacing, a, corresponding to beta=3.9, 4.05, 4.20. For each renormalization factor computed non-perturbatively we subtract its perturbative O(a^2) terms so that we eliminate part of the cut-off artifacts. The renormalization constants are converted to MS-bar at a scale of mu=2 GeV. The perturbative results depend on a large number of parameters and are made easily accessible to the reader by including them in the distribution package of this paper, as a Mathematica input file.

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arXiv2011

Nucleon form factors and moments of parton distributions in twisted mass lattice QCD

We present results on the electroweak form factors and on the lower moments of parton distributions of the nucleon, within lattice QCD using two dynamical flavors of degenerate twisted mass fermions. Results are obtained on lattices with three different values of the lattice spacings, namely a=0.089 fm, a=0.070 fm and a=0.056 fm, allowing the investigation of cut-off effects. The volume dependence is examined by comparing results on two lattices of spatial length L=2.1 fm and L=2.8 fm. The simulations span pion masses in the range of 260-470 MeV. Our results are renormalized non-perturbatively and the values are given in the MS-scheme at a scale mu=2 GeV.

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arXiv2011

Moments of nucleon generalized parton distributions from lattice QCD

We present results on the lower moments of the nucleon generalized parton distri butions within lattice QCD using two dynamical flavors of degenerate twisted mass fermions. Our simulations are performed on lattices with three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm, allowing the investigation of cut-off effects. The volume dependence is examined using simulations on two lattices of spatial length $L=2.1$ fm and $L=2.8$ fm. The simulations span pion masses in the range of 260-470 MeV. Our results are renormalized non-perturbatively and the values are given in the $\bar{\rm MS}$ scheme at a scale $ μ=2$ GeV. They are chirally extrapolated to the physical point in order to compare with experiment. The consequences of these results on the spin carried by the quarks in the nucleon are investigated.

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arXiv2011

Renormalization constants for 2-twist operators in twisted mass QCD

Perturbative and non-perturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the non-perturbative evaluation of the one-derivative twist-2 vector and axial vector operators. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing $a$ corresponding to $β=3.9, 4.05, 4.20$. Subtraction of ${\cal O}(a^2)$ terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to ${\cal O}(a^2)$. The renormalization conditions are defined in the RI$'$-MOM scheme, for both perturbative and non-perturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to ${\bar{\rm MS}}$ at 2 GeV using 3-loop perturbative results for the conversion factors.

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arXiv2011

Nucleon electromagnetic form factors in twisted mass lattice QCD

We present results on the nucleon electromagnetic form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length L=2.1 fm and L=2.8 fm. Cut-off effects are investigated using three different values of the lattice spacings, namely a=0.089 fm, a=0.070 and a=0.056 fm. The nucleon magnetic moment, Dirac and Pauli radii are obtained in the continuum limit and chirally extrapolated to the physical pion mass allowing for a comparison with experiment.

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arXiv2011

BK-parameter from Nf = 2 twisted mass lattice QCD

We present an unquenched $N_f=2$ lattice computation of the $B_{K}$ parameter which controls $K^0-\bar K^0$ oscillations. A partially quenched setup is employed with two maximally twisted dynamical (sea) light Wilson quarks, and valence quarks of both the maximally twisted and the Osterwalder--Seiler variety. Suitable combinations of these two kinds of valence quarks lead to a lattice definition of the $B_{K}$ parameter which is both multiplicatively renormalizable and O($a$) improved. Employing the non-perturbative RI-MOM scheme, in the continuum limit and at the physical value of the pion mass we get $B^{\rm RGI}_K=0.729\pm 0.030$, a number well in line with the existing quenched and unquenched determinations.

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arXiv2010

Renormalization constants for one-derivative fermion operators in twisted mass QCD

We present perturbative and non-perturbative results on the renormalization constants of the local and one-derivative vector and axial vector operators. Non-perturbative results are obtained using the twistedmassWilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action for pion masses in the range of about 450-260 MeV and at there values of the lattice spacing, namely 0.055 fm, 0.070 fm and 0.089 fm. Subtraction of O(a^2) terms is carried out by performing the perturbative evaluation of these operators at 1- loop and up to O(a^2). The renormalization conditions are defined in the RI'-MOM scheme, for both perturbative and non-perturbative results. The Z-factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS-bar at 2 GeV using 3-loop perturbative results for the conversion factors.

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arXiv2010

Axial Nucleon form factors from lattice QCD

We present results on the nucleon axial form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm. Cut-off effects are investigated using three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial charge is obtained in the continuum limit and chirally extrapolated to the physical pion mass enabling comparison with experiment.

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arXiv2010

Nucleon Structure in Lattice QCD using twisted mass fermions

We present results on the nucleon form factors and moments of generalized parton distributions obtained within the twisted mass formulation of lattice QCD. We include a discussion of lattice artifacts by examining results at different volumes and lattice spacings. We compare our results with those obtained using different discretization schemes and to experiment.

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arXiv2010

Non-perturbative renormalization of quark bilinear operators with Nf=2 (tmQCD) Wilson fermions and the tree-level improved gauge action

We present results for the renormalization constants of bilinear quark operators obtained by using the tree-level Symanzik improved gauge action and the Nf=2 twisted mass fermion action at maximal twist, which guarantees automatic O(a)-improvement. Our results are also relevant for the corresponding standard (un-twisted) Wilson fermionic action since the two actions only differ, in the massless limit, by a chiral rotation of the quark fields. The scale-independent renormalization constants ZV, ZA and the ratio ZP/ZS have been computed using the RI-MOM approach, as well as other alternative methods. For ZA and ZP/ZS, the latter are based on both standard twisted mass and Osterwalder-Seiler fermions, while for ZV a Ward Identity has been used. The quark field renormalization constant Zq and the scale dependent renormalization constants ZS, ZP and ZT are determined in the RI-MOM scheme. Leading discretization effects of O(g^2 a^2), evaluated in one-loop perturbation theory, are explicitly subtracted from the RI-MOM estimates.

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arXiv2009

O(a^2) 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 $\barΨΓΨ$, to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and a family of Symanzik improved actions for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, $O(a^2)$. 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 $O(a^1)$ improvement calculations; there, IR divergent terms are seen to have the same structure as in the $O(a^0)$ 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 $O(a^2)$ dependence; in fact, our method is generalizable to any order in $a$. The $O(a^2)$ 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.

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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.

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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.

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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.

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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.

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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.

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