arXiv subjects

Haralambos Panagopoulos

Publications and source records attributed to Haralambos Panagopoulos.

At least 19 recordsLinked to original sources

arXiv2026

Lattice artifacts proportional to the quark mass in the QCD running coupling

Discretization artifacts proportional to the quark mass can limit the precision of strong-coupling determinations in lattice QCD, especially in the presence of heavy quarks. In this work, we perform a lattice perturbative analysis of such $\mathcal{O}(a m)$ effects in the running coupling by computing its two-loop renormalization factor $Z_g$. Using the background field method together with clover-improved Wilson fermions and Symanzik-improved gauge actions, we determine the mass-dependent components of the relevant two-point Green's functions and obtain the improvement coefficients needed to remove $\mathcal{O}(a m)$ artifacts in mass-independent renormalization schemes. Our results are presented for general values of the number of colors $N_c$, the number of quark flavors $N_f$, and the clover coefficient $c_{\mathrm sw}$, and satisfy all symmetry and consistency constraints. Numerical values are provided for widely used instances of the above gauge actions, allowing improved control of mass-related cutoff effects in high-precision determinations of the strong coupling constant from lattice QCD. Full derivations and extended numerical results can be found in Ref. [arXiv:2503.00463].

hep-lat↗

arXiv2026

Fine-tunings and renormalization of gluino bilinear operators in lattice SYM with Stout-Smeared links

In this paper, we compute the renormalization factors for the gluino and gluon fields, the gauge parameter, the coupling constant, as well as the scalar, pseudoscalar, and axial-vector gluino bilinear operators in N=1 supersymmetric Yang-Mills (SYM) theory, using improved lattice actions. Our lattice formulation employs clover fermions, a Symanzik-improved gauge action, and stout-smeared links, which suppress ultraviolet fluctuations and thus enable more accurate determinations of renormalization factors. Our methodology involves computing gauge-variant two-point and three-point Green's functions at one-loop order in lattice perturbation theory, in order to extract the multiplicative renormalization factors and the critical gluino mass. By analyzing lattice discretization effects on the axial current and their dependence on the stout-smearing and clover parameters, we identify a value of the smearing parameter that ensures axial-current conservation at one loop. The results presented in this work provide practical guidance for the fine-tuning procedures required to set up and calibrate lattice simulations of SYM.

hep-lat↗

arXiv2025

Perturbative determination of $\mathcal{O}(am)$ improvement on the QCD running coupling

We present the perturbative results of the discretization errors proportional to the quark mass ($\mathcal{O}(a m)$) on the QCD running coupling within lattice perturbation theory. Our analysis involves calculating the 2-loop renormalization factor $Z_g$ using improved lattice actions for the $SU(N_c)$ gauge group and $N_f$ multiplets of fermions with a finite quark mass. We employ the background field method to compute $Z_g$, by calculating quantum corrections on both the background and quantum gluon propagator, respecting the $\mathcal{O}(a)$ improvement. This allows us to evaluate the perturbative $\mathcal{O}(a m)$ lattice errors which affect the determination of the running coupling. Eliminating these $\mathcal{O}(a m)$ effects is crucial for the nonperturbative studies of precision determinations of the strong coupling constant using lattice field theory.

hep-lat↗

arXiv2025

Classification of four-quark operators with $ΔF\le 2$ under flavor symmetry and their renormalization in a gauge-invariant scheme

In this paper we study a complete set of scalar and pseudoscalar four-quark operators, with a particular emphasis on their renormalization within a Gauge-Invariant Renormalization Scheme (GIRS). We focus on operators that do not mix with lower-dimensional operators by virtue of their transformation properties under the flavor-symmetry group. This class includes all $ΔF = 2$ operators, as well as their partners that transform under the same irreducible representations of the flavor group. These encompass a substantial subset of $ΔF = 1$ and $ΔF = 0$ operators. The present analysis provides a detailed classification of all four-quark operators, exploring their Fierz identities, symmetry properties, and mixing patterns. Different variants of GIRS are explored, including a democratic version that treats all mixing operators uniformly. For selected variants, which exhibit smaller mixing effects, we present the conversion matrices from GIRS to the $\overline{\text{MS}}$ scheme at next-to-leading order.

hep-lat↗

arXiv2025

N=1 Supersymmetric QCD on the lattice using overlap fermions

Using N=1 Supersymmetric QCD (SQCD) as a prototype model, this work presents a formulation of overlap quarks and gluinos on the lattice, with particular emphasis on the construction of chirally symmetric Yukawa terms. By incorporating the Ginsparg-Wilson relation, chiral transformations, and the Majorana condition for gluinos, we construct a consistent framework that preserves a lattice-modified chiral symmetry and reduces the number of required counterterms compared to Wilson-type discretizations. The formulation introduces auxiliary fermionic fields to realize exact chiral symmetry in Yukawa interactions and enables a detailed analysis of the resulting matrix structures. Upon functionally integrating out the auxiliary fields, ultralocal interaction terms emerge as new contributions to the lattice action. This approach provides a robust foundation for nonperturbative lattice studies of supersymmetric gauge theories. Future work will focus on computing all perturbative fine-tunings required in this formulation to enable continuum matching and numerical simulations of SQCD.

hep-lat↗

arXiv2025

Critical dynamics of three-dimensional $Z_N$ gauge models and the inverted XY universality class

We investigate the critical relaxational dynamics of the three-dimensional (3D) lattice $Z_N$ gauge models with $N=6$ and $N=8$, whose equilibrium critical behavior at their topological transitions belongs to the inverted XY (IXY) universality class (this is also the universality class of the continuous transitions of the 3D lattice U(1) gauge Higgs models with a one-component complex scalar field), which is connected to the standard XY universality class by a nonlocal duality relation of the partition functions. Specifically, we consider the purely relaxational dynamics realized by a locally reversible Metropolis dynamics, as commonly used in Monte Carlo simulations. To determine the corresponding dynamic exponent $z$, we focus on the out-of-equilibrium critical relaxational flows arising from instantaneous quenches to the critical point, which are analyzed within an out-of-equilibrium finite-size scaling framework. We obtain the estimate $z=2.59(3)$. A numerical analysis of the equilibrium critical dynamics give consistent, but less accurate, results. This dynamic exponent is expected to characterize the critical slowing down of the purely relaxational dynamics of all topological transitions that belong to the 3D IXY universality class. We note that this result implies that the critical relaxational dynamics of the 3D IXY universality class is slower than that of the standard 3D XY universality class, whose relaxational dynamic exponent $z\approx 2.02$ is significantly smaller, although they share the same length-scale critical exponent $ν\approx 0.6717$.

cond-mat.stat-mech↗

arXiv2025

Out-of-equilibrium critical dynamics of the three-dimensional ${\mathbb Z}_2$ gauge model along critical relaxational flows

We address the out-of-equilibrium critical dynamics of the three-dimensional lattice ${\mathbb Z}_2$ gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link ${\mathbb Z}_2$ gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice ${\mathbb Z}_2$ gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent $z$ associated with the purely relaxational dynamics of the three-dimensional ${\mathbb Z}_2$ gauge universality class. We obtain $z=2.610(15)$, which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.

cond-mat.stat-mech↗

arXiv2025

Gluon nonlocal operator mixing in lattice QCD

In this study, we explore the renormalization of a comprehensive set of gauge-invariant gluon nonlocal operators on the lattice. We calculate the renormalization factors for these operators in the modified Minimal Subtraction $(\rm \overline{MS})$ scheme up to one-loop, using both dimensional and lattice regularizations in the Wilson gluon action. To facilitate a non-perturbative renormalization approach, we examine an appropriate version of the modified regularization-invariant (${\rm RI}'$) scheme and determine the conversion factors from this scheme to $\rm \overline{MS}$. As an integral part of this procedure, by employing symmetry arguments on the lattice, we identify the mixing pattern of these operators under renormalization.

hep-lat↗

arXiv2024

Supersymmetric QCD on the lattice: Fine-tuning and counterterms for the quartic couplings

In this work we calculate the renormalization of counterterms which arise in the lattice action of $N = 1$ Supersymmetric QCD (SQCD). In particular, the fine-tunings for quartic couplings are studied in detail through both continuum and lattice perturbation theory at one-loop level. For the lattice version of SQCD we make use of the Wilson gauge action for gluon fields and the Wilson fermion action for fermion fields (quarks, gluinos); for squark fields we use naïve discretization. On the lattice, different components of squark fields mix among themselves and a total of ten quartic terms arise at the quantum level. Consequently, the renormalization conditions must take into account these effects in order to appropriately fine-tune all quartic couplings. All our results for Green's functions and renormalization factors exhibit an explicit analytic dependence on the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $α$, which are left unspecified. Results for the specific case $N_f=1$ are also presented, where the symmetries allow only five linearly independent quartic terms. For the calculation of the Green's functions, we consider both one-particle reducible and one-particle irreducible Feynman diagrams. Knowledge of these renormalization factors is necessary in order to relate numerical results, coming from nonperturbative studies, to ``physical'' observables.

hep-lat↗

arXiv2024

Renormalization of nonlocal gluon operators on the lattice

We study the renormalization of a complete set of gauge-invariant gluon nonlocal operators in lattice perturbation theory. We determine the mixing pattern under renormalization of these operators using symmetry arguments, which extend beyond perturbation theory. Additionally, we derive the renormalization factors of the operators within the modified Minimal Subtraction $(\rm \overline{MS})$ scheme up to one-loop. To enable a non-perturbative renormalization procedure, we investigate a suitable version of the modified regularization-invariant (${\rm RI}'$) scheme, and we calculate the conversion factors from that scheme to $\rm\overline{MS}$. The computations are performed by employing both dimensional and lattice regularizations, using the Wilson gluon action. This work is relevant to nonperturbative studies of the gluon parton distribution functions (PDFs) on the lattice.

hep-lat↗

arXiv2024

Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory

In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the first-principle calculation of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD using the formulation of Large Momentum Effective Theory. We provide appropriate RI$'$-type conditions that address the power and logarithmic divergences, as well as the mixing among staple operators of different Dirac structures, using a number of different possible projectors. A variant of RI$'$, including calculations of rectangular Wilson loops, which cancel the pinch-pole singularities of the staple operators at infinite length and reduce residual power divergences, is also employed. We calculate at one-loop order the conversion matrix, which relates the quasi-TMDPDFs in the RI$'$-type schemes to the reference scheme $\overline{\rm MS}$ for arbitrary values of the renormalization momentum scale and of the dimensions of the staple.

hep-lat↗

arXiv2024

Out-of-equilibrium scaling of the energy density along the critical relaxational flow after a quench of the temperature

We study the out-of-equilibrium behavior of statistical systems along critical relaxational flows arising from instantaneous quenches of the temperature $T$ to the critical point $T_c$, starting from equilibrium conditions at time $t=0$. In the case of soft quenches, i.e. when the initial temperature $T$ is assumed sufficiently close to $T_c$ (to keep the system within the critical regime), the critical modes develop an out-of-equilibrium finite-size scaling (FSS) behavior in terms of the rescaled time variable $Θ=t/L^z$, where $t$ is the time interval after quenching, $L$ is the size of the system, and $z$ is the dynamic exponent associated with the dynamics. However, the realization of this picture is less clear when considering the energy density, whose equilibrium scaling behavior (corresponding to the starting point of the relaxational flow) is generally dominated by a temperature-dependent regular background term or mixing with the identity operator. These issues are investigated by numerical analyses within the three-dimensional lattice $N$-vector models, for $N=3$ and $N=4$, which provide examples of critical behaviors with negative values of the specific-heat critical exponent $α$, implying that also the critical behavior of the specific heat gets hidden by the background term. The results show that, after subtraction of its asymptotic critical value at $T_c$, the energy density develops an asymptotic out-of-equilibrium FSS in terms of $Θ$ as well, whose scaling function appears singular in the small-$Θ$ limit.

cond-mat.stat-mech↗

arXiv2023

Renormalization of non-local gluon operators in lattice perturbation theory

In this study, we investigate the renormalization of a complete set of gauge-invariant non-local gluon operators up to one-loop in lattice perturbation theory. Our computations have been performed in both dimensional and lattice regularizations, using the Wilson gluon action, leading to the renormalization functions in the modified Minimal Subtraction $(\overline{\text{MS}})$ scheme, as well as conversion factors from the modified regularization invariant $(RI')$ scheme to $\overline{\text{MS}}$.

hep-lat↗

arXiv2023

Perturbative study of renormalization and mixing for asymmetric staple-shaped Wilson-line operators on the lattice

We present one-loop perturbative results of the renormalization functions for a complete set of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line, using a family of improved lattice actions. This study is relevant for the nonperturbative investigations regarding the renormalization of the unpolarized, helicity and transversity transverse-momentum dependent parton distribution functions (TMDPDFs) in lattice QCD. We employ a number of different versions of regularization-independent (RI$'$) renormalization prescriptions which address the power and logarithmic divergences of such nonlocal operators, the pinch-pole singularities at infinite Wilson-line lengths, as well as the mixing among operators of different Dirac structures, as dictated by discrete symmetries. All cancelations of divergences and admixtures are confirmed by our results at one-loop level. We compare all the different prescriptions and we provide the conversion matrices at one-loop order which relate the matrix elements of the staple operators in RI$'$ to the reference scheme $\overline{\rm MS}$.

hep-lat↗

arXiv2023

Mass effects on the QCD $β$-function

In this study we present lattice results on the QCD $β$-function in the presence of quark masses. The $β$-function is calculated to three loops in perturbation theory and for improved lattice actions; it is extracted from the renormalization of the coupling constant $Z_g$. The background field method is used to compute $Z_g$, where it is simply related to the background gluon field renormalization constant $Z_A$. We focus on the quark mass effects in the background gluon propagator; the dependence of the QCD $β$-function on the number of colors $N_c$, the number of fermionic flavors $N_f$ and the quark masses, is shown explicitly. The perturbative results of the QCD $β$-function will be applied to the precise determination of the strong coupling constant, calculated by Monte Carlo simulations removing the mass effects from the nonperturbative Green's functions.

hep-lat↗

arXiv2022

Supercurrent renormalization of $\mathcal{N}=1$ supersymmetric Yang-Mills theory on the lattice

Supersymmetry on the lattice is explicitly broken by the gluino mass and lattice artifacts. However, it can be restored in the continuum limit by fine tuning the parameters based on the renormalized Ward identities. On the renormalization step not only the mass but also the renormalization of the supercurrent needs to be addressed. Here we present a lattice investigation to obtain the renormalization factors of the supercurrent for $\mathcal{N}$=1 Super-Yang Mills theory in a gauge invariant renormalization scheme. We also provide the conversion factors which are necessary in order to translate our results to the more standard $\overline{\text{MS}}$ scheme.

hep-lat↗

arXiv2022

Noether supercurrent operator mixing from lattice perturbation theory

In this work we present perturbative results for the renormalization of the supercurrent operator, $S_μ$, in ${\cal N} =1$ Supersymmetric Yang-Mills theory. At the quantum level, this operator mixes with both gauge invariant and noninvariant operators, which have the same global transformation properties. In total, there are 13 linearly independent mixing operators of the same and lower dimensionality. We determine, via lattice perturbation theory, the first two rows of the mixing matrix, which refer to the renormalization of $S_μ$, and of the gauge invariant mixing operator, $T_μ$. To extract these mixing coefficients in the ${\overline{\rm MS}}$ renormalization scheme and at one-loop order, we compute the relevant two-point and three-point Green's functions of $S_μ$ and $T_μ$ in two regularizations: dimensional and lattice. On the lattice, we employ the plaquette gluonic action and for the gluinos we use the fermionic Wilson action with clover improvement.

hep-lat↗

arXiv2022

Nonperturbative renormalization of the supercurrent in $\mathcal{N} = 1$ Supersymmetric Yang-Mills Theory

In this work, we study the nonperturbative renormalization of the supercurrent operator in $\mathcal{N} = 1$ Supersymmetric Yang-Mills (SYM) theory, using a gauge-invariant renormalization scheme (GIRS). The proposed prescription addresses successfully the unwanted mixing of the supercurrent with other operators of equal or lower dimension, which respect the same global symmetries. This mixing is introduced by the unavoidable breaking of supersymmetry on the lattice. In GIRS all gauge-noninvariant operators, which mix with the supercurrent, are excluded from the renormalization procedure. The one remaining mixing operator is accessible by numerical simulations. We present results for the renormalization of the supercurrent using a GIRS scheme. We also compute at one-loop order the conversion matrix which relates the nonperturbative renormalization factors in GIRS to the reference scheme $\bar{\rm MS}$.

hep-lat↗