arXiv subjects

Michele Pepe

Publications and source records attributed to Michele Pepe.

At least 19 recordsLinked to original sources

arXiv2026

The QCD energy-momentum tensor on the lattice: non-perturbative renormalization with $N_f=3$

We construct the traceless components of the energy-momentum tensor on the lattice for QCD with $N_f=3$ flavours, such that their correlation functions satisfy the appropriate Ward identities in the continuum limit. To carry out this program, we define the theory on the lattice by the Wilson-plaquette and the $O(a)$-improved Wilson actions for gluons and quarks respectively. The discretization of the space-time entails that (i) the irreducible nonet representation of the SO($4$) group splits into a triplet and a sextet irreducible representations of the hypercubic group, and (ii) for each multiplet non-perturbative determinations of the the gluonic and fermionic renormalization constants are required. The bare gluonic components of the energy-momentum tensor are defined via the clover discretization of the field strength tensor, while the fermionic ones are discretized by appropriate combinations of symmetric covariant derivatives. Either for the triplet or the sextet representations, the two independent renormalization constants are then fixed non-perturbatively by imposing discretized versions of continuum Ward identities for one-point correlation functions in the presence of shifted boundary conditions and an imaginary chemical potential. The non-perturbative calculation is then carried out by Monte Carlo simulations, and the resulting renormalization constants are determined with a final accuracy of a few percent for values of the bare coupling constant squared in the range $0 \leq g_0^2\leq 0.96$.

hep-lat↗

arXiv2026

Hadronic screening masses in thermal QCD up to the electroweak scale

Novel theoretical and computational strategies have opened the possibility of exploring thermal QCD at the non-perturbative level at unprecedented temperatures, reaching from the GeV scale up to the electroweak scale. A number of observable quantities are now being investigated in this regime. Key ones are the hadronic screening masses, which encode the correlation length of the medium and thus the extent to which strong interactions are screened in a thermal environment. In these proceedings we present recent lattice results for hadronic screening masses, including baryonic modes and preliminary non-static mesonic modes. These results can be compared with predictions from the perturbative expansion in the three-dimensional effective theory valid at asymptotically large temperatures. The comparison reveals persistent higher-order effects including those of non-perturbative origin, up to the electroweak scale, shedding new light on the microscopic structure of QCD at extreme temperatures.

hep-lat↗

arXiv2026

Non-perturbative determination of the QCD Equation of State up to the electroweak scale

The QCD Equation of State with $N_f=3$ massless quark flavours is determined non-perturbatively over a broad range of temperatures, extending from the electroweak scale down to 3 GeV, and smoothly connecting to the low-temperature regime. The comparison with perturbative predictions shows that, even at temperatures approaching the electroweak scale, the Equation of State can be accurately described only by adding terms beyond the known perturbative series, including non-perturbative contributions. The strategy that allows this investigation in the previously unexplored high-temperature regime combines shifted boundary conditions with a determination of the lines of constant physics based on the running of a non-perturbatively defined renormalized coupling. This methodology is general and can be applied to QCD with four or five massive quark flavours.

hep-lat↗

arXiv2026

QCD Equation of State at very high temperature: computational strategy, simulations and data analysis

We present a detailed account of the theoretical progress and the computational strategy that led to the non-perturbative determination of the QCD Equation of State at temperatures up to the electroweak scale reported in [Phys. Rev. Lett. 134, 201904 (2025)]. The two key ingredients that make such a calculation feasible with controlled uncertainties are: (i) the definition of lines of constant physics through the running of a non-perturbatively defined finite-volume coupling across a wide range of energy scales, and (ii) the use of shifted boundary conditions which allow a direct determination of the entropy density thus without the need for a zero-temperature subtraction. Considering the case of QCD with $N_f =3$ massless flavours in the temperature interval between 3 GeV and 165 GeV, we describe the numerical strategy based on integrating in the bare coupling and quark mass, the perturbative improvement of lattice observables, the optimization of numerical simulations, and the continuum extrapolation. Extensive consistency checks, including finite-volume and topological-freezing effects, confirm the robustness of the method. The final results have a relative accuracy of about $1\%$ or better, and the errors are dominated by the statistical fluctuations of the Monte Carlo ensembles. We also compare our non-perturbative results with predictions from standard and hard thermal loop perturbation theory showing that at the level of $\%$-precision contributions beyond those known, including non-perturbative ones due to ultrasoft modes, are relevant up to the highest temperatures explored. The methodological framework is general and readily applicable to QCD with four and five massive quark flavours and to other thermal observables, paving the way for systematic non-perturbative studies of thermal QCD at very high temperatures.

hep-lat↗

arXiv2025

Equation of State of QCD with $N_f=3$ flavours up to the electroweak scale

The Equation of State of Quantum Chromodynamics with $N_f=3$ flavours is determined non-perturbatively with a precision of about $0.5\%-1.0\%$ in the range of temperatures between 3 GeV and 165 GeV. The computation is carried out by numerical simulations of the gauge theory discretized on the lattice. At each given temperature the entropy density is computed at several lattice spacings in order to extrapolate the results to the continuum limit. The pressure and energy density are then determined by integrating the entropy density with respect to the temperature. The numerical data show a linear behaviour in the strong coupling constant squared, which points to the Stefan-Boltzmann limit at infinite temperature. They are also compatible with the known perturbative formula supplemented by higher order terms in the coupling constant, containing non-perturbative contributions. This parametrization describes well our data together with those present in the literature down to 500 MeV.

hep-lat↗

arXiv2025

QCD Equation of State with $N_f=3$ Flavors up to the Electroweak Scale

The equation of state of Quantum Chromodynamics with $N_f=3$ flavors is determined non-perturbatively in the range of temperatures between $3$ and $165$~GeV with a precision of about $0.5$-$1.0$\%. The calculation is carried out by numerical simulations of lattice gauge theory discretized à la Wilson with shifted boundary conditions in the compact direction. At each given temperature the entropy density is computed at several lattice spacings in order to extrapolate the results to the continuum limit. Taken at face value, data point straight to the Stefan-Boltzmann value by following a linear behavior in the strong coupling constant squared. They are also compatible with the known perturbative formula supplemented by higher order terms in the coupling constant, a parametrization which describes well our data together with those present in the literature down to $500$ MeV.

hep-lat↗

arXiv2025

The hyperfine splitting in QCD mesonic screening masses at asymptotically large temperatures

We determine the hyperfine splitting in the QCD flavour non-singlet mesonic screening masses at asymptotically large temperatures. The analytic calculation is carried out in the dimensionally-reduced effective theory where the first non-zero contribution is of $O(g^4)$ in the QCD coupling constant $g$. Apart for its own theoretical interest, this result provides instrumental information to interpret and to parameterize non-perturbative data that are being produced at very high temperatures by numerical simulations of lattice QCD. Indeed, the comparison with existing non-perturbative results shows that higher order (non-perturbative) contributions in $g$ are needed to explain the data up to the highest temperatures explored, which is of the order of the electroweak scale.

hep-lat↗

arXiv2025

Computation of the latent heat of the deconfinement phase transition of SU(3) Yang-Mills theory

We investigate the thermal properties of $\mathrm{SU}(3)$ Yang-Mills theory across the deconfinement phase transition considering the framework of shifted boundary conditions in the temporal direction. By measuring the entropy density $s(T_c)/T_c^3$ on both sides of the phase transition at the critical temperature $T_c$, we can retrieve the latent heat $h$. Additionally, we compute $h$ from the discontinuity in the trace anomaly of the energy-momentum tensor. Simulations are performed at five different values of the lattice spacing, allowing us to extrapolate the results to the continuum limit. The two observables produce compatible results, giving the combined estimate $h = 1.175(10)$ in the continuum limit, achieving a precision of about 1 %. Moreover, we determine the critical temperature in physical units with permille accuracy, yielding $T_c \sqrt{t_0} = 0.24915(29)$. These results allow us to connect the confined and the deconfined phases with precision, and we present an improved computation of the Equation of State across the phase transition for temperatures between $0$ and $3.4 T_c$.

hep-lat↗

arXiv2025

The Equation of State of QCD up to very high temperatures

We present the non-perturbative computation of the entropy density in QCD for temperatures ranging from 3 GeV up to the electro-weak scale, using $N_f=3$ flavours of massless O$(a)$-improved Wilson fermions. We adopt a new strategy designed to be computationally efficient and based on formulating thermal QCD in a moving reference frame, where the fields satisfy shifted boundary conditions in the temporal direction and periodic boundary conditions along the spatial ones. In this setup the entropy density can be computed as the derivative of the free-energy density with respect to the shift parameter. For each physical temperature, we perform Monte Carlo simulations at four values of the lattice spacing in order to extrapolate the numerical data of the entropy density to the continuum limit. We achieve a final accuracy of approximatively $0.5$-$1.0\%$ and our results are compared with predictions from high-temperature perturbation theory.

hep-lat↗

arXiv2025

A precise study of the SU(3) Yang-Mills theory across the deconfinement transition

We perform a detailed computation of key quantities across the first-order deconfinement phase transition of the SU(3) Yang-Mills theory. Specifically, we calculate the entropy density, $s(T_c)/T_c^3$, on both sides of the transition and determine the latent heat $h$. The calculations are carried out in the lattice regularization with the Wilson action, employing shifted boundary conditions in the temporal direction. Our simulations are performed at five different values of the lattice spacing in order to extrapolate the results to the continuum limit. The latent heat can be measured also as the discontinuity in the trace anomaly of the energy-momentum tensor: our result using the entropy density is compatible with the one obtained from the trace anomaly, giving a combined estimate $h=1.175(10)$. Additionally, we determine the critical temperature $T_c$ in physical units with permille accuracy, yielding $T_c \sqrt{t_0} = 0.24915(29)$. These results allow to connect with precision the confined and the deconfined phases and we present an improved computation of the Equation of State across the deconfinement transition for $T$ between 0 and $3.4 T_c$.

hep-lat↗

arXiv2024

Non-perturbative thermal QCD at very high temperatures: computational strategy and hadronic screening masses

We discuss a recently introduced strategy to study non-perturbatively thermal QCD up to temperatures of the order of the electro-weak scale, combining step scaling techniques and shifted boundary conditions. The former allow to renormalize the theory for a range of scales which spans several orders of magnitude with a moderate computational cost. Shifted boundary conditions remove the need for the zero temperature subtraction in the Equation of State. As a consequence, the simulated lattices do not have to accommodate two very different scales, the pion mass and the temperature, at the very same spacing. Effective field theory arguments guarantee that finite volume effects can be kept under control safely. With this strategy the first computation of the hadronic screening spectrum has been carried out over more than two orders of magnitude in the temperature, from $T\sim 1$ GeV up to $\sim 160$ GeV. This study is complemented with the first quantitative computation of the baryonic screening mass at next-to-leading order in the three-dimensional effective theory describing QCD at high temperatures. Both for the mesonic and the baryonic screening masses, the known leading behaviour in the coupling constant is found to be not sufficient to explain the non-perturbative data over the entire range of temperatures. These findings shed further light on the limited applicability of the perturbative approach at finite temperature, even at the electro-weak scale.

hep-lat↗

arXiv2024

Non-perturbative thermal QCD at very high temperatures

We present a recently introduced strategy to study non-perturbatively thermal QCD up to temperatures of the order of the electro-weak scale, combining step scaling techniques and shifted boundary conditions. The former allow to renormalize the theory for a range of scales which spans several orders of magnitude with a moderate computational cost. Shifted boundary conditions avoid the need for the zero temperature subtraction in the Equation of State. As a consequence, the simulated lattices do not have to accommodate two very different scales, the pion mass and the temperature. Effective field theory arguments guarantee that finite volume effects can be kept under control safely. As a first application of this strategy, we present the results of the computation of the hadronic screening spectrum in QCD with $N_f=3$ flavours of massless quarks for temperatures from $T\sim 1$ GeV up to $\sim 160$ GeV.

hep-lat↗

arXiv2024

Baryonic thermal screening mass at NLO

We determine the resummed 1-loop correction to a baryonic thermal screening mass. The calculation is carried out in the framework of a dimensionally reduced effective theory, where quarks are heavy fields due to their non-zero Matsubara frequencies. The correction due to interactions is computed at O($g^2_{ }$) in the coupling constant. In order to solve a 3-body Schrödinger equation, we exploit a two-dimensional generalization of the hyperspherical harmonics method. At electroweak scale temperatures, the NLO correction represents a $\sim 4.6 \%$ increase of the free-theory value $3πT$ of the screening mass.

hep-ph↗

arXiv2023

Progresses on high-temperature QCD: Equation of State and energy-momentum tensor

We present first non-perturbative results for the renormalization constants of the QCD energy-momentum tensor, based on the framework of thermal QCD with shifted and twisted (for quarks only) boundary conditions in the compact direction. We also show preliminary results for the entropy density obtained with the very same numerical strategy. This opens the way to the determination of the QCD Equation of State up to very high temperatures.

hep-lat↗

arXiv2023

Baryonic Screening Masses in High Temperature QCD

We compute the screening masses of fields with nucleon quantum numbers for a wide range of temperatures between $T \sim 1$ GeV and $T\sim 160$ GeV. The computation has been performed by means of Monte Carlo simulations of lattice QCD with $N_f=3$ flavors of $O(a)$-improved Wilson fermions: we exploit a novel strategy which has recently allowed to determine for the first time non-singlet mesonic screening masses up to extremely high temperatures. The baryonic screening masses are measured with a few per-mille precision in the continuum limit, and percent deviations from the free theory result $3πT$ are clearly visible even at the highest temperatures. The observed degeneracy of the positive and negative parity state's screening mass, expected from Ward identities associated to non-singlet axial transformations, provides further evidence for the restoration of chiral symmetry in the high temperature regime of QCD.

hep-lat↗

arXiv2022

QCD mesonic screening masses and restoration of chiral symmetry at high T

We present a strategy to study QCD non-perturbatively on the lattice at very high temperatures. This strategy exploits a non-perturbative, finite-volume, definition of the strong coupling constant to renormalize the theory. As a first application we compute the flavor non-singlet mesonic screening masses in a wide range of temperature, from $T\sim 1 $ GeV up to $\sim 160 $ GeV with three flavors in the chiral limit of QCD. Our results show very interesting features of the screening spectrum at very high temperatures. On one hand the mass splitting between the vector and the pseudoscalar screening masses is clearly visible up to the electroweak scale and cannot be explained by the known 1-loop perturbative result. On the other hand the restoration of chiral symmetry manifests itself through the degeneracy of the pseudoscalar and the scalar channels and of the vector and the axial-vector ones. This degeneracy pattern is the one expected by Ward identities associated to the presence of chiral symmetry.

hep-lat↗

arXiv2022

Thermal QCD for non-perturbative renormalization of composite operators

We present our progresses in the use of the non-perturbative renormalization framework based on considering QCD at finite temperature with shifted and twisted (for quarks only) boundary conditions in the compact direction. We report our final results in the application of this method for the non-perturbative renormalization of the flavor-singlet local vector current. We then discuss the more challenging case of the renormalization of the energy-momentum tensor, and show preliminary results on the relevant one-point functions for the computation of the renormalization constants of its non-singlet components.

hep-lat↗

arXiv2022

QCD mesonic screening masses up to high temperatures

We discuss a strategy to study non-perturbatively QCD up to very high temperatures by Monte Carlo simulations on the lattice. It allows not only the thermodynamic properties of the theory but also other interesting thermal features to be investigated. As a first concrete application, we compute the flavour non-singlet mesonic screening masses and we present the results of Monte Carlo simulations at 12 temperatures covering the range from T $\sim$ 1 GeV up to $\sim$ 160 GeV in the theory with three massless quarks. On the one side, chiral symmetry restoration manifests itself in our results through the degeneracy of the vector and the axial vector channels and of the scalar and the pseudoscalar ones, and, on the other side, we observe a clear splitting between the vector and the pseudoscalar screening masses up to the highest investigated temperature. A comparison with the high-temperature effective theory shows that the known one-loop order in the perturbative expansion does not provide a satisfactory description of the non-perturbative data up to the highest temperature considered.

hep-lat↗