arXiv subjects

Massimo D'Elia

Publications and source records attributed to Massimo D'Elia.

At least 19 recordsLinked to original sources

arXiv2026

Topological properties around the Roberge-Weiss transition in $N_f = 2 + 1 + 1$ QCD

We investigate the topological properties of QCD across the finite temperature Roberge-Weiss transition, which is found for particular values of the imaginary baryon chemical potential. Our study is conducted for $N_f = 2+1+1$ QCD with physical quark masses, discretized via stout improved staggered fermions and considering mostly two different values of the compactifed dimension, $N_t = 8$ and $N_t = 10$. Results for $T_{RW}$ and for the associated universality class are consistent with those found in the $N_f = 2 + 1$ case with a slightly different discretization. The topological susceptibility appears to be practically constant for $T \lesssim T_{RW}$, then rapidly decaying for higher temperatures. The analysis of the fourth order cumulant of the topological charge distribution, $b_2$, reveals that it is compatible with the prediction of the Dilute Instanton Gas Approximation right after $T_{RW}$, showing thus a sharp transition, which is more similar to what observed in pure gauge theories rather than to full QCD along the standard thermal line, where instead a slower transition was observed in previous studies.

hep-lat↗

arXiv2026

Real-time topological rate at non-zero momentum in quenched QCD

We present a proof-of-concept numerical study of the real-time topological rate at non-zero momentum in quenched lattice QCD at a temperature $T\simeq 1.24 \, T_c \simeq 360$ MeV, as an important step toward the determination of this quantity in full QCD. Our strategy, already applied to compute the sphaleron rate in pure Yang--Mills and in full QCD, extracts the rate from the resolution of an appropriate inverse problem, solved applying the Hansen--Lupo--Tantalo (HLT) method to the thermal Euclidean time-correlator of the topological charge density. This method requires to control three different limits: continuum limit, limit of vanishing smearing width used in the HLT inverse problem resolution, and limit of vanishing smoothing radius used in the topological charge density correlator computation. Our lattice calculation is based on the standard Wilson discretization for the gauge action, and on three gauge ensembles with up to $N_τ=16$ temporal points to achieve a controlled continuum limit. In all cases we employed an aspect ratio $LT=4$, which allowed us to compute the topological rate up to momenta as large as $p/T \sim 10$.

hep-lat↗

arXiv2026

Topological Susceptibility and QCD at Finite Theta Angle

In this chapter we provide a pedagogical introduction to the main theoretical aspects related to topology and $θ$-dependence in Quantum Chromo-Dynamics (QCD), and to their phenomenological relevance in the Standard Model ($η^\prime$ physics, neutron electric dipole moment) and beyond (strong CP problem and the axion solution). We then provide an overview of the main analytic predictions for $θ$-dependence obtained using several different approaches (chiral effective theories, large-$N$ arguments, semiclassical methods) and their regimes of validity, as well as a selection of the most recent numerical results about QCD topology obtained via Monte Carlo simulations of the lattice-discretized theory.

hep-lat↗

arXiv2026

The Roberge-Weiss transition as a probe for conformality in many-flavor QCD

We consider the problem of identifying the onset of the conformal window for QCD with $N_f$ massless flavors in the fundamental representation, and propose a new effective method to determine it from lattice simulations. This method is based on the investigation of the so-called Roberge-Weiss transition temperature $T_{RW}$, which is encountered at specific values of the imaginary baryon chemical potential, and can also be interpreted as the inverse of the critical spatial size at which charge conjugation is spontaneously broken in a finite box. Since $T_{RW}$ corresponds to a genuine phase transition for any value of the quark masses, it is a well-defined quantity; we argue that the critical $N_f$ at which $T_{RW}$ vanishes in the chiral limit coincides with the onset of the conformal window. We implement our proposal by investigating QCD with $N_f = 8$ flavors, discretized via stout improved staggered fermions and the tree-level improved Symanzik pure gauge action, at Euclidean temporal extents $N_t = 8, 10, 12, 16, 24$. In this case, we find evidence that $T_{RW}$ already vanishes in the chiral limit, indicating that $N_f = 8$ is already in the conformal window.

hep-lat↗

arXiv2026

Lattice determination of the QCD low-energy constant $\ell_{\scriptscriptstyle{7}}$

We provide a non-perturbative determination of the scheme- and scale-independent low-energy constant $\ell_{\scriptscriptstyle{7}}$, appearing in the QCD effective chiral Lagrangian at next-to-leading order, by means of lattice QCD simulations with $N_{\scriptscriptstyle{\rm f}}=2+1$ quark flavors. We adopt staggered fermions and extract $\ell_{\scriptscriptstyle{7}}$ from the pion mass splitting by suitably generalizing the method introduced in [Phys. Rev. D 104 (2021) 074513] for the Wilson discretization. Adopting 12 gauge ensembles with 3 different values of the pion mass, and 4 different values of the lattice spacing, we are able to achieve controlled extrapolations towards the continuum, infinite volume, and chiral limits. Our final result $\ell_{\scriptscriptstyle{7}} \,\times \, 10^3 = 2.79(58)_{\scriptscriptstyle{\rm stat}}(19)_{\scriptscriptstyle{\rm syst}} = 2.79(61)_{\scriptscriptstyle{\rm tot}}$ agrees with and substantially improves on previous determinations.

hep-lat↗

arXiv2026

Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence

We set the scale of SU($N$) Yang--Mills theories for $N=3,5,8$ and in the large-$N$ limit via gradient flow, as a first step towards the computation of the large-$N$ $Λ$-parameter using step scaling. We adopt twisted boundary conditions to achieve large-$N$ volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as $\sim 0.025$ fm for all the explored values of $N$, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-$N$ twisted volume reduction.

hep-lat↗

arXiv2026

Strong CP problem, theta term and QCD topological properties

In this chapter we introduce the $θ$-dependence and the topological properties of QCD, features of the strongly interacting sector which give rise to the strong CP problem in the more general context of the Standard Model of particle physics. We discuss the analytical approaches that can be used to obtain qualitative, or in some cases quantitative, information on the $θ$-dependence of QCD and QCD-like models, discussing their range of validity and comparing their predictions with the numerical results obtained by means of lattice simulations.

hep-lat↗

arXiv2026

Yang--Mills topology on four-dimensional triangulations

We consider 4D $SU(N)$ gauge theories coupled to gravity in the Causal Dynamical Triangulations (CDT) approach, focusing on the topological classification of the gauge path integral over fixed triangulations. We discretize the topological charge and, after checking the emergence of topology and the continuum scaling on flat triangulations, we show that topology emerges on thermalized triangulations only in the so-called $C$-phase of CDT, thus enforcing the link between such phase and semiclassical spacetime. We also provide a tool to visualize the topological structures.

hep-lat↗

arXiv2025

The Roberge-Weiss transition for QCD in a magnetic background

We investigate how a magnetic background field influences the location and the nature of the Roberge-Weiss (RW) finite temperature transition for $N_f = 2+1$ QCD with physical quark masses. To that purpose, we perform numerical simulations of the finite temperature theory, discretized through stout staggered quarks and the tree-level improved Symanzik pure gauge action, considering two different values of the Euclidean temporal extent in lattice units, $N_t = 6, 8$. The RW transition temperature $T_{RW}$ decreases with $eB$, in particular it follows closely the behavior of the pseudo-critical QCD crossover temperature $T_{pc}$, so that $T_{RW} (eB) - T_{pc}(eB)$ is practically constant, within errors, for magnetic fields up to $eB \sim 1$ GeV$^2$; consistent results are found from the drop of the chiral condensate, which signals chiral symmetry restoration, leading also to the phenomenon of inverse magnetic catalysis above the transition. Moreover, we find that the magnetic field turns the RW transition from second order to first order, with a tri-critical magnetic field in-between 1 and 2.4 GeV$^2$, i.e. for magnetic fields substantially lower than those for which the standard QCD transition turns to first order.

hep-lat↗

arXiv2025

Scale setting of $\mathrm{SU}(N)$ Yang-Mills theories via Twisted Gradient Flow

We present preliminary results for the scale setting of $\mathrm{SU}(N)$ Yang-Mills theories using twisted boundary conditions and the gradient-flow scale $\sqrt{t_0}$. The end goal of this study is to determine the $\mathrm{SU(N)}$ $Λ$-parameter through the step-scaling method. The scale $\sqrt{t_0}$, being defined from the flowed action density of the gauge fields, is correlated with their topological charge and thus could be affected by topological freezing. We deal with this problem with the Parallel Tempering on Boundary Conditions algorithm, which we found to be effective for the same numerical setup in a previous work.

hep-lat↗

arXiv2024

An update on the determination of the sphaleron rate in finite temperature QCD

The sphaleron rate is a key phenomenological quantity both for the axion thermal production in the Early Universe and the Chiral Magnetic Effect occurring in the Quark-Gluon Plasma in presence of a background magnetic field. In this talk we present an extension of our recent determination of the sphaleron rate, in the SU(3) gauge theory, based on the determination of the two-point function of the topological charge density at finite temperature.

hep-lat↗

arXiv2024

The Roberge-Weiss endpoint in $(2+1)$-flavor QCD with background magnetic fields

In this work we discuss our preliminary results regarding the so-called Roberge-Weiss (RW) transition, which is found for imaginary values of the baryon chemical potential, in the presence of a background magnetic field. We perform lattice QCD simulations on $N_t = 6, 8$ lattices with $2+1$ flavors of stout-staggered fermions at physical quark masses and the tree-level Symanzik improved gauge action. We determine the location the RW endpoint at finite magnetic fields and we study the order of the transition.

hep-lat↗

arXiv2024

Distributing Quantum Computations, Shot-wise

NISQ (Noisy Intermediate-Scale Quantum) era constraints, high sensitivity to noise and limited qubit count, impose significant barriers on the usability of QPUs (Quantum Process Units) capabilities. To overcome these challenges, researchers are exploring methods to maximize the utility of existing QPUs despite their limitations. Building upon the idea that the execution of a quantum circuit's shots needs not to be treated as a singular monolithic unit, we propose a methodological framework, termed shot-wise, which enables the distribution of shots for a single circuit across multiple QPUs. Our framework features customizable policies to adapt to various scenarios. Additionally, it introduces a calibration method to pre-evaluate the accuracy and reliability of each QPU's output before the actual distribution process and an incremental execution mechanism for dynamically managing the shot allocation and policy updates. Such an approach enables flexible and fine-grained management of the distribution process, taking into account various user-defined constraints and (contrasting) objectives. Experimental findings show that while these strategies generally do not exceed the best individual QPU results, they maintain robustness and align closely with average outcomes. Overall, the shot-wise methodology improves result stability and often outperforms single QPU runs, offering a flexible approach to managing variability in quantum computing.

quant-ph↗

arXiv2024

Dirac Spectral Density in N$_f$=2+1 QCD at T=230 MeV

We compute the renormalized Dirac spectral density in $N_f = 2+1$ QCD at physical quark masses, temperature $T = 230$ MeV and system size $L_s = 3.4$ fm. To that end, we perform a point-wise continuum limit of the staggered density in lattice QCD with staggered quarks. We find, for the first time, that a clear infrared structure (IR peak) emerges in the density of Dirac operator describing dynamical quarks. We also provide numerical evidence that a component of this peak, which becomes dominant in the thermodynamic limit, is due to a non-trivial accumulation of near-zero modes. Features of this structure are consistent with those previously attributed to the recently-proposed IR phase of thermal QCD. Our results (i) provide the only complete first-principles evidence that these IR features exist and are physical; (ii) improve the upper bound for IR-phase transition temperature $T_{\mathrm{IR}}$ so that the new window is $200 < T_{\mathrm{IR}} < 230\,$MeV; (iii) are consistent with non-restoration of anomalous U$_{\mathrm A}$(1) symmetry (chiral limit) below $T = 230$ MeV.

hep-lat↗

arXiv2024

The $\mathrm{SU}(3)$ twisted gradient flow strong coupling without topological freezing

We investigate the role of topology on the lattice determination of the $\mathrm{SU}(3)$ strong coupling renormalized via gradient flow. To deal with the topological freezing of standard local algorithms, the definition of the coupling is usually projected onto the zero topological sector. However, it is not obvious that this definition is not biased by the loss of ergodicity. We instead avoid the topological freezing using a novel algorithm, the Parallel Tempering on Boundary Conditions. The comparison with a standard algorithm shows that, even in the case where the latter is severely frozen, one obtains the same projected coupling. Moreover, we show that the two definitions of the coupling, projected and non-projected, lead to the same flow of the renormalization scale. Our results imply that projecting the coupling does not affect the determination of the dynamically-generated scale of the theory $Λ$, as obtained through the step-scaling method.

hep-lat↗

arXiv2024

Full QCD with milder topological freezing

We simulate $N_f=2+1$ QCD at the physical point combining open and periodic boundary conditions in a parallel tempering framework, following the original proposal by M. Hasenbusch for $2d$ $\mathrm{CP}^{N-1}$ models, which has been recently implemented and widely employed in $4d$ $\mathrm{SU}(N)$ pure Yang-Mills theories too. We show that using this algorithm it is possible to achieve a sizable reduction of the auto-correlation time of the topological charge in dynamical fermions simulations both at zero and finite temperature, allowing to avoid topology freezing down to lattice spacings as fine as $a \sim 0.02$ fm. Therefore, this implementation of the Parallel Tempering on Boundary Conditions algorithm has the potential to substantially push forward the investigation of the QCD vacuum properties by means of lattice simulations.

hep-lat↗

arXiv2024

Electrical conductivity of the Quark-Gluon Plasma in the presence of strong magnetic fields

We compute the electrical conductivity of the strongly interacting medium in the presence of strong magnetic background fields, $eB=4,9~GeV^2$, and for different values of the temperature, both in the confined and in the deconfined Quark-Gluon Plasma (QGP) phase. The conductivity is obtained from the Euclidean lattice time correlator of the electrical current, computed on gauge configurations sampled from Monte-Carlo simulations of an improved staggered discretization of $N_f = 2+1$ QCD. We perform the inverse Laplace transform of the correlator adopting a recently-proposed version of the standard Backus--Gilbert procedure for the inversion. The results obtained in the QGP phase show a sizable enhancement of the conductivity in the direction parallel to the magnetic field, as well as a suppression in the direction orthogonal to it. Such enhancement could be attributed to the manifestation of the Chiral Magnetic Effect (CME): following this guess, we extract the behaviour of the relaxation time of this process, extrapolate it to the continuum limit and compare it to previous results, finding it lower than expected in the explored range of temperatures.

hep-lat↗

arXiv2024

Non-perturbative determination of the $N_f=2+1$ QCD sphaleron rate

The strong sphaleron rate, i.e., the rate of real time QCD topological transitions, is a key phenomenological quantity, playing a fundamental role in several physical contexts. In heavy-ion collisions, a non-vanishing rate can lead to the so-called Chiral Magnetic Effect. In early-Universe cosmology, instead, it can be related to the rate of thermal production of QCD axions. In this talk, we present the first reliable fully non-perturbative computation of the strong sphaleron rate in $N_f=2+1$ QCD at the physical point by means of lattice simulations, in a range of temperatures going from 200 MeV to 600 MeV. Our strategy is based on the inversion of lattice correlators via a recently-proposed modified version of the Backus-Gilbert method.

hep-lat↗