arXiv subjects

Andrea Giorgieri

Publications and source records attributed to Andrea Giorgieri.

7 recordsLinked to original sources

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

The large-$N$ Yang--Mills $Λ$-parameter from step scaling

We use the step-scaling method and results obtained at $N = 3, 5$ and $8$ to determine the $N$-dependence of the dynamically generated scale $Λ$ of $\mathrm{SU}(N)$ Yang--Mills theories. We implement the step-scaling method in a suitable finite-volume renormalization scheme based on twisted boundary conditions, introduced to effectively achieve large-$N$ volume independence, and on a coupling defined through the gradient flow. In the $\overline{\mathrm{MS}}$ scheme, we obtain the following values in terms of the gradient flow scale $t_0$: $\sqrt{8t_0}Λ_{\scriptscriptstyle{\overline{\mathrm{MS}}}} = 0.577(23)$, $0.632(32)$, and $0.611(43)$ for $N=3,5$ and $8$, respectively. They extrapolate to a large-$N$ value of: $\sqrt{8t_0}Λ_{\scriptscriptstyle{\overline{\mathrm{MS}}}} (N=\infty) = 0.639(36)$, and the $N$-dependence is given by $\sqrt{8t_0}Λ_{\scriptscriptstyle{\overline{\mathrm{MS}}}}(N)=0.639(36)[1-0.85(62)/N^2+\mathcal{O}(1/N^4)]$. This work represents the first calculation of the Yang--Mills $Λ$-parameter in the large-$N$ limit that does not rely on asymptotic scaling strategies.

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↗

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 $\mathrm{SU}(3)$ 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.

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arXiv2023

The Twisted Gradient Flow strong coupling with Parallel Tempering on Boundary Conditions

We present a proposal for calculating the running of the coupling constant of the $\mathrm{SU}(3)$ pure-gauge theory, which combines the Twisted Gradient Flow (TGF) renormalization scheme with Parallel Tempering on Boundary Conditions (PTBC). The TGF is a gradient flow-based renormalization scheme formulated in an asymmetric lattice with twisted boundary conditions. Combined with step scaling, it has been successfully used to calculate the $\mathrm{SU}(3)$ $Λ$ parameter. As with all gradient flow-based schemes, the coupling constant is highly correlated with the topological charge and affected by topology freezing, an issue addressed by projecting the determination of the coupling onto the zero topological sector. As an alternative to the zero-charge projection, we combine TGF with PTBC, by replicating multiple copies of the same lattice, interpolating between periodic and open boundary conditions in a parallel-tempered manner. We present a first exploration of these ideas by analyzing specific ensembles of $\mathrm{SU}(3)$ lattices with and without PTBC.

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