arXiv subjects

Mattia Dalla Brida

Publications and source records attributed to Mattia Dalla Brida.

At least 37 records · Page 2Linked to original sources

arXiv2022

Non-perturbative thermal QCD at all temperatures: the case of mesonic screening masses

We present a strategy based on the step-scaling technique to study non-perturbatively thermal QCD up to very high temperatures. As a first concrete application, we compute the flavour non-singlet meson screening masses at 12 temperatures covering the range from $T \sim 1$ GeV up to $\sim 160$ GeV in the theory with three massless quarks. The calculation is carried out by Monte Carlo simulations on the lattice by considering large spatial extensions in order to have negligible finite volume effects. For each temperature we have simulated 3 or 4 values of the lattice spacing, so as to perform the continuum limit extrapolation with confidence at a few permille accuracy. 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. In the entire range of temperatures explored, the meson screening masses deviate from the free theory result, $2 πT$, by at most a few percent. These deviations, however, cannot be explained by the known leading term in the QCD coupling constant $g$ up to the highest temperature, where other contributions are still very relevant. In particular the vector-pseudoscalar mass splitting turns out to be of $O(g^4)$ in the entire range explored, and it remains clearly visible up to the highest temperature, where the two screening masses are still significantly different within our numerical precision. The pattern of different contributions that we have found explains why it has been difficult in the past to match non-perturbative lattice results at $T \sim 1$ GeV with the analytic behaviour at asymptotically high temperatures.

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arXiv2021

Nonperturbative running of the quark mass for $N_f=3$ QCD from the chirally rotated Schrödinger Functional

We study the Renormalisation Group (RG) running of the quark mass, for $N_f=3$ QCD with Wilson fermions in a mixed action setup, with standard Schrödinger Functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger Functional ($χ$SF) boundary conditions for valence quarks. This necessitates the tuning of the boundary factor $z_f(g_0^2)$ of the $χ$SF valence action, in order to ensure that QCD symmetries are fully recovered in the continuum. The properties of this novel setup are monitored through the ratios $Z_S/Z_P$ and $Σ_S/Σ_P$ of the renormalisation parameters and step scaling functions of the scalar and pseudoscalar densities. Where comparison is possible, our $Z_S/Z_P$ results are found to agree with previous determinations, based on a mass ratio method arXiv:1906.03445 and Ward identities arXiv:2005.01352, arXiv:2101.10969, with Schrödinger Functional boundary conditions. The behaviour of $Σ_S/Σ_P$ confirms the theoretical expectations of $χ$SF QCD, related to the restoration of the theory's symmetries in the continuum limit. From the step scaling function of the pseudoscalar density we obtain the quark mass RG-running function from hadronic to perturbative energy scales. This is fully compatible with the earlier result obtained in a similar setup for Wilson quarks with Schrödinger Functional boundary conditions arXiv:1802.05243 and provides a strong universality test for the two lattice setups.

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arXiv2021

Quark mass RG-running for $N_f$ =3 QCD in a $χSF$ setup

We compute the nonperturbative quark mass RG-running in the range $Λ_{QCD}\lessapproxμ\lessapprox M_W$ for $N_f=3$ massless QCD with a mixed action approach: sea quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with Schrödinger functional (SF) boundary conditions, employing the configurations of 1802.05243, while valence quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with chirally rotated Schrödinger functional boundary conditions ($χ$SF). Our result is compatible with its SF counterpart of ref.1802.05243, confirming the universality of $χ$SF and SF in the continuum limit. We also establish the optimal tuning strategy for the critical hopping parameter $κ_c$ and the $χ$SF boundary counterterm coefficient $z_{\rm f}$. We work in two energy regimes with two different definitions of the coupling: SF-coupling for 2 GeV $\lessapproxμ\lessapprox M_W$ and GF-coupling for $Λ_{QCD} \lessapproxμ\lessapprox 2 GeV$.

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arXiv2021

Results for $α_s$ from the decoupling strategy

We present analysis details and new results for the strong coupling $α_s(m_Z)$, determined by the decoupling strategy. We measure a massive gradient flow (GF) coupling defined in finite volume with Schrödinger functional (SF) boundary conditions in a theory with $N_\text{f}=3$ degenerate heavy quarks of mass $M$. The massive couplings are matched to effective couplings in pure gauge. Using the running in the pure gauge theory and the perturbative relation of the Lambda parameters, the Lambda parameter of the three flavor theory is obtained by an extrapolation to infinite M. Our final result is compatible both with the FLAG average and with the previous ALPHA result, albeit with a slightly smaller, yet still statistics dominated, error. This constitutes a non-trivial check, as the decoupling strategy is conceptually very different from the 3-flavor QCD step-scaling method, and so are most of its systematic errors. These include the uncertainties of the decoupling and continuum limits, which we discuss in some detail. Furthermore, by relying on decoupling once again, we could estimate the small $O(a)$ and $O(1/M)$ contaminations to the massive GF coupling stemming from the SF boundaries by means of pure gauge simulations.

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arXiv2021

Renormalization $\&$ improvement of the tensor operator for $N_f=3$ QCD in a $χ$SF setup

We present preliminary results of the non-perturbative renormalization group (RG) running of the flavor non-singlet tensor operator. We employ the $χ$SF scheme for $N_f=3$ QCD using ensembles generated by the ALPHA collaboration for the computation of the quark mass running. The $χ$SF property of automatic $O(a)$ improvement prevents the $O(a)$ mixing of the correlation functions.

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arXiv2021

Computation of QCD meson screening masses at high temperature

We compute flavor non-singlet meson screening masses in the chiral limit of QCD with $N_f=3$ quarks. The calculation is carried out at 12 temperatures from $T\approx 1$ GeV up to the electroweak scale. For each temperature we simulated several lattice spacings, so as to be able to perform the continuum limit extrapolation with confidence at a few permille accuracy. In the entire range of temperatures explored, the meson screening masses deviate from the free theory result $2πT$ by at most a few percent. Their values, however, cannot be explained by one-loop perturbation theory up to the electroweak scale, where the pseudoscalar and the vector screening masses are still significantly different within our precision. Chiral symmetry restoration manifests itself through the degeneracy of the pseudoscalar and the scalar channels and of the vector and the axial ones.

hep-lat↗

arXiv2021

Multi-level computation of the hadronic vacuum polarization contribution to $(g_μ-2)$

The first results from the Fermilab E989 experiment have confirmed the long-standing tension between the experimental determination of the muon anomalous magnetic moment $a_μ=(g_μ-2)/2$ and its SM determination using the dispersive approach. In order to match the expected final precision from E989, the current uncertainty on ab initio determinations using lattice QCD must be decreased by a factor 5-15, a goal which is hampered by the signal-to-noise ratio problem of the electromagnetic current correlator. Multi-level Monte Carlo integration with fermions is a method which reduces the variance of correlators exponentially in the distance of the fields. Here we demonstrate that the variance reduction in a realistic two-level simulation with a pion mass of 270 MeV, linear size of 3 fm and lattice spacing around 0.065 fm is sufficient to compute the tail of the current correlator with the statistical accuracy required for the hadronic vacuum polarization contribution to $a_μ$. An efficient estimator is also employed for computing the disconnected contribution.

hep-lat↗

arXiv2021

Multi-level Monte Carlo computation of the hadronic vacuum polarization contribution to $(g_μ-2)$

The hadronic contribution to the muon anomalous magnetic moment $a_μ=(g_μ-2)/2$ has to be determined at the per-mille level for the Standard Model prediction to match the expected final uncertainty from the ongoing E989 experiment. This is 3 times better than the current precision from the dispersive approach, and 5-15 times smaller than the uncertainty on the purely theoretical determinations from lattice QCD. So far the stumbling-block is the large statistical error in the Monte Carlo evaluation of the required correlation functions which can hardly be tamed by brute force. Here we propose to solve this problem by multi-level Monte Carlo integration, a technique which reduces the variance of correlators exponentially in the distance of the fields. We test our strategy by computing the Hadronic Vacuum Polarization on a lattice with a linear extension of 3 fm, a spacing of 0.065 fm, and a pion mass of 270 MeV. Indeed the two-level integration makes the contribution to the statistical error from long-distances de-facto negligible by accelerating its inverse scaling with the cost of the simulation. These findings establish multi-level Monte Carlo as a solid and efficient method for a precise lattice determination of the hadronic contribution to $a_μ$. As the approach is applicable to other computations affected by a signal-to-noise ratio problem, it has the potential to unlock many open problems for the nuclear and particle physics community.

hep-lat↗

arXiv2021

Past, present, and future of precision determinations of the QCD coupling from lattice QCD

Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task. In this contribution we focus on the case of the QCD coupling. We critically address the common challenges that state-of-the-art lattice determinations have to face in order to be significantly improved. In addition, we review a novel strategy that has been recently put forward in order to solve this non-perturbative renormalization problem and discuss its implications for future precision determinations. The new ideas exploit the decoupling of heavy quarks to match $N_{\rm f}$-flavor QCD and the pure Yang-Mills theory. Through this matching the computation of the non-perturbative running of the coupling in QCD can be shifted to the computationally much easier to solve pure-gauge theory. We shall present results for the determination of the $Λ$-parameter of $N_{\rm f}=3$-flavor QCD where this strategy has been applied and proven successful. The results demonstrate that these techniques have the potential to unlock unprecedented precision determinations of the QCD coupling from the lattice. The ideas are moreover quite general and can be considered to solve other non-perturbative renormalization problems.

hep-lat↗

arXiv2021

A novel computational paradigm for a precise determination of the hadronic contribution to $(g_μ-2)$ from lattice QCD

The hadronic contribution to the muon anomalous magnetic moment $a_μ=(g_μ-2)/2$ has to be determined at the per-mille level for the Standard Model prediction to match the expected final uncertainty of the ongoing E989 experiment. That is 3 times better than the current precision from the dispersive approach, and 5-15 times smaller than the uncertainty based on the purely theoretical determinations from lattice QCD. So far the stumbling-block is the large statistical error in the Monte Carlo evaluation of the required correlation functions which can hardly be tamed by brute force. In this talk we present our proposal to solve this problem by multi-level Monte Carlo integration, a technique which reduces the variance of correlators exponentially in the distance of the fields. We report the results of our feasibility tests for the computation of the Hadronic Vacuum Polarization on a lattice with a linear extension of 3~fm, a spacing of 0.065 fm, and a pion mass of 270 MeV. Indeed the two-level integration makes the contribution to the statistical error from long-distances de-facto negligible by accelerating its inverse scaling with the cost of the simulation. These findings establish multi-level Monte Carlo as a solid and efficient method for a precise lattice determination of the hadronic contribution to $a_μ$.

hep-lat↗

arXiv2020

Non-perturbative definition of the QCD energy-momentum tensor on the lattice

We present a strategy to define non-perturbatively the energy-momentum tensor in Quantum Chromodynamics (QCD) which satisfies the appropriate Ward identities and has the right trace anomaly. The tensor is defined by regularizing the theory on a lattice, and by fixing its renormalization constants non-perturbatively by suitable Ward identities associated to the Poincare' invariance of the continuum theory. The latter are derived in thermal QCD with a non-zero imaginary chemical potential formulated in a moving reference frame. A renormalization group analysis leads to simple renormalization-group-invariant definitions of the gluonic and fermionic contributions to either the singlet or the non-singlet components of the tensor, and therefore of their form factors among physical states. The lattice discussion focuses on the Wilson discretization of quark fields but the strategy is general. Specific to that case, we also carry out the analysis for the on-shell O(a)-improvement of the energy-momentum tensor. The renormalization and improvement programs profit from the fact that, as shown here, the thermal theory enjoys de-facto automatic O(a)-improvement at finite temperature. The validity of the proposal is scrutinized analytically by a study to 1-loop order in lattice perturbation theory with shifted and twisted (for quarks only) boundary conditions. The latter provides also additional useful insight for a precise non-perturbative calculation of the renormalization constants. The strategy proposed here is accessible to Monte Carlo computations, and in this sense it provides a practical way to define non-perturbatively the energy-momentum tensor in QCD.

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arXiv2019

Non-perturbative renormalization by decoupling

We propose a new strategy for the determination of the QCD coupling. It relies on a coupling computed in QCD with $N_{\rm f} \geq 3$ degenerate heavy quarks at a low energy scale $μ_{\rm dec}$, together with a non-perturbative determination of the ratio $Λ/μ_{\rm dec}$ in the pure gauge theory. We explore this idea using a finite volume renormalization scheme for the case of $N_{\rm f} = 3$ QCD, demonstrating that a precise value of the strong coupling $α_s$ can be obtained. The idea is quite general and can be applied to solve other renormalization problems, using finite or infinite volume intermediate renormalization schemes.

hep-lat↗

arXiv2019

The energy-momentum tensor in lattice QCD and the Equation of State

We present a new theoretical and practical strategy to renormalize non-perturbatively the energy-momentum tensor in lattice QCD based on the framework of shifted boundary conditions. As a preparatory step for the fully non-perturbative calculation, we apply the strategy at 1-loop order in perturbation theory determining the renormalization constants of both the gluonic and the fermionic components of the energy-momentum tensor. Using shifted boundary conditions, the entropy density of QCD is directly related to the expectation value of the space-time components of the renormalized energy-momentum tensor. We then discuss its practical implementation by numerical simulations of QCD with 3 flavours of Wilson quarks for temperatures between 2.5 GeV and 80 GeV.

hep-lat↗

arXiv2019

$χ$SF near the electroweak scale

We employ the chirally rotated Schrödinger functional ($χ$SF) to study two-point fermion bilinear correlation functions used in the determination of $Z_{A,V,S,P,T}$ on a series of well-tuned ensembles. The gauge configurations, which span renormalisation scales from 4 to 70~GeV, are generated with $N_{\rm f}=3$ massless flavors and Schrödinger Functional (SF) boundary conditions. Valence quarks are computed with $χ$SF boundary conditions. We show preliminary results on the tuning of the $χ$SF Symanzik coefficient $z_f$ and the scaling of the axial current normalization $Z_{\rm A}$. Moreover we carry out a detailed comparison with the expectations from one-loop perturbation theory. Finally we outline how automatically $\mathrm{O}(a)$-improved $B_{\rm K}$ matrix elements, including BSM contributions, can be computed in a $χ$SF renormalization scheme.

hep-lat↗

arXiv2019

The gradient flow coupling at high-energy and the scale of SU(3) Yang-Mills theory

Using finite size scaling techniques and a renormalization scheme based on the Gradient Flow, we determine non-perturbatively the $β$-function of the $SU(3)$ Yang-Mills theory for a range of renormalized couplings $\bar g^2\sim 1-12$. We perform a detailed study of the matching with the asymptotic NNLO perturbative behavior at high-energy, with our non-perturbative data showing a significant deviation from the perturbative prediction down to $\bar{g}^2\sim1$. We conclude that schemes based on the Gradient Flow are not competitive to match with the asymptotic perturbative behavior, even when the NNLO expansion of the $β$-function is known. On the other hand, we show that matching non-perturbatively the Gradient Flow to the Schrödinger Functional scheme allows us to make safe contact with perturbation theory with full control on truncation errors. This strategy allows us to obtain a precise determination of the $Λ$-parameter of the $SU(3)$ Yang-Mills theory in units of a reference hadronic scale ($\sqrt{8t_0}\,Λ_{\overline{\rm MS}} = 0.6227(98)$), showing that a precision on the QCD coupling below 0.5\% per-cent can be achieved using these techniques.

hep-lat↗

arXiv2019

Towards a precise determination of the equation of state of QCD at high-temperature

We present preliminary results towards a fully non-perturbative determination of the equation of state of QCD at very high-temperatures, $T\approx 3-80\,{\rm GeV}$. The key ingredient is the lattice formulation of QCD in a moving reference frame, which allows us for a neat determination of the entropy density from simple expectation values of the momentum-components of the energy-momentum tensor. For the computation we employ $N_{\rm f}=3$ flavours of non-perturbatively O($a$)-improved Wilson-fermions. We present an analysis of the O($a$)-improvement of the expectation values entering the determination, and show how these can be accurately computed in simulations.

hep-lat↗

arXiv2019

High precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks

We determine the non-perturbatively renormalized axial current for O($a$) improved lattice QCD with Wilson quarks. Our strategy is based on the chirally rotated Schrödinger functional and can be generalized to other finite (ratios of) renormalization constants which are traditionally obtained by imposing continuum chiral Ward identities as normalization conditions. Compared to the latter we achieve an error reduction up to one order of magnitude. Our results have already enabled the setting of the scale for the $N_{\rm f}=2+1$ CLS ensembles [1] and are thus an essential ingredient for the recent $α_s$ determination by the ALPHA collaboration [2]. In this paper we shortly review the strategy and present our results for both $N_{\rm f}=2$ and $N_{\rm f}=3$ lattice QCD, where we match the $β$-values of the CLS gauge configurations. In addition to the axial current renormalization, we also present precise results for the renormalized local vector current.

hep-lat↗

arXiv2018

Precision Determination of $α_s$ from Lattice QCD

We present an overview of the recent lattice determination of the QCD coupling $α_s$ by the ALPHA Collaboration. The computation is based on the non-perturbative determination of the $Λ$-parameter of $N_{\rm f}=3$ QCD, and the perturbative matching of the $N_{\rm f}=3$ and $N_{\rm f}=5$ theories. The final result: $α_s(m_Z)=0.11852(84)$, reaches sub-percent accuracy.

hep-ph↗