arXiv subjects

Nazario Tantalo

Publications and source records attributed to Nazario Tantalo.

At least 19 recordsLinked to original sources

arXiv2026

Inclusive $\bar B_s\mapsto X_{\bar sc} \ell \bar ν$ decays from lattice QCD: computational strategy and a first physical result

We present a strategy to compute the inclusive decay rate for the process $\bar B_s \mapsto X_{\bar sc} \ell \barν$ from first principles in lattice QCD. The physical decay rate is obtained from the interpolation of non-perturbative lattice data, obtained at lighter than physical heavy meson masses ($M_{\bar B_s}^\mathrm{max}=4.3$GeV), with the Operator Product Expansion predictions, which become exact in the limit of infinitely heavy quarks. We also present a new method for the computation of the required lattice four-point correlators, which represents a considerable improvement over the state-of-the-art on the subject. We show the effectiveness of the strategy by performing the calculation on a subset of the available $n_f=2+1+1$ physical-point Extended Twisted Mass Collaboration (ETMC) gauge ensembles. Our current determination of the inclusive decay rate has a 7% total error, that is dominated by uncertainties due to the relatively limited configuration ensembles considered herein, and can be significantly reduced in the near future.

hep-lat↗

arXiv2026

Extraction of spectral densities from lattice correlators: decoupling signal from noise

We expand the treatment of the problem of the extraction of smeared spectral densities from Euclidean correlators introduced in [Phys. Rev. D 99, 094508], providing an alternative which does not rely on the Backus-Gilbert regularization. This is possible due to the observation that the solution can be decomposed into a sum of terms, in the spirit of the singular value decomposition, where those with the largest contribution to the statistical noise happen to contribute the least to the central value of the smeared spectral density. The analysis of the systematics of the inverse problem is then shifted to finding the optimal truncation of such summation, so that the signal is saturated before the noise explodes. We scrutinise the performance and systematics of this approach either as a standalone procedure, or to complement the stability analysis required to extrapolate the unbiased result in the Backus-Gilbert regulated version of the solution.

hep-lat↗

arXiv2026

Comparing RM123 and non-perturbative QCD+QED approaches to the HVP with C-periodic boundary conditions

Isospin-breaking corrections to the HVP are among the leading sources of uncertainty in the Standard Model prediction of the muon $g-2$. In recent work by the RC$^{\star}$ collaboration, we compute the intermediate window contribution for a flavour non-singlet current using two strategies to include isospin-breaking corrections: the RM123 approach and a fully non-perturbative dynamical QCD+QED simulation. In both computations, we use $C$-periodic spatial boundary conditions to ensure that locality, gauge invariance, and translational invariance are preserved throughout the calculation. At fixed lattice spacing and volume with $N_f =1+2+1$ dynamical fermions, and fully including sea-quark effects in both computations, we find that simulating the full QCD+QED distribution yields smaller uncertainties for a fixed statistics. We summarize the comparison of the two approaches and discuss the implications for future lattice QCD+QED computations.

hep-lat↗

arXiv2026

First-principle evaluation of inclusive hadronic $τ$ decays in QCD+QED

We present a strategy to extend lattice calculations of inclusive hadronic $τ$ decays from isosymmetric QCD to QCD+QED. The inclusive decay rate can be related to suitable Euclidean correlation functions, allowing for a first-principles evaluation of electromagnetic and isospin-breaking effects. Within the RM123 framework, radiative corrections are decomposed into leptonic, factorizable and non-factorizable contributions. We report preliminary results for the leptonic and factorizable terms in the electro-quenched approximation and discuss the remaining steps towards a complete calculation. This programme aims at a first-principles determination of inclusive $τ$ decay rates with direct implications for the extraction of the CKM matrix element $|V_{us}|$.

hep-lat↗

arXiv2026

The smeared $R$-ratio in isoQCD from first-principles lattice simulations

The $R$-ratio is a phenomenological observable of great relevance, both in itself and in applications such as the dispersive approach to the muon anomalous magnetic moment. It can be investigated from first-principles with controlled statistical and systematic errors in lattice QCD by introducing an arbitrary smearing kernel and employing spectral reconstruction techniques, such as the well-known Hansen-Lupo-Tantalo method. Improving upon a first study published in 2023, we show preliminary results using the correlation functions produced by ETMC in $N_f = 2+1+1$ lattice simulations at four lattice spacings, different volumes and with higher statistics w.r.t. our previous study. The new correlators, thanks to the implementation of the Low Mode Average technique, allow the determination of the $R$-ratio smeared with Gaussian kernels of widths down to $σ\sim 200$ with phenomenologically relevant precision.

hep-lat↗

arXiv2025

Inclusive semileptonic decays of the $D_s$ meson: A first-principles lattice QCD calculation

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the $D_s$ meson. We performed a state-of-the-art lattice QCD calculation using the gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with dynamical light, strange and charm quarks with physical masses and employed the so-called Hansen-Lupo-Tantalo (HLT) method to extract the decay rate and the first two lepton-energy moments from the relevant Euclidean correlators. We have carefully taken into account all sources of systematic errors, including the ones associated with the continuum and infinite-volume extrapolations and with the HLT spectral reconstruction method. We obtained results in very good agreement with the currently available experimental determinations and with a total accuracy at the few-percent level, of the same order of magnitude of the experimental error. Our total error is dominated by the lattice QCD simulations statistical uncertainties and is certainly improvable. From the results presented and thoroughly discussed in this paper we conclude that it is nowadays possible to study heavy mesons inclusive semileptonic decays on the lattice at a phenomenologically relevant level of accuracy. The phenomenological implications of our physical results are the subject of a companion letter [1].

hep-lat↗

arXiv2025

Inclusive semileptonic decays of the $D_{s}$ meson: Lattice QCD confronts experiments

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the $D_{s}$ meson. We performed a state-of-the-art lattice QCD calculation by taking into account all sources of systematic errors. A detailed discussion of our lattice calculation, demonstrating that inclusive semileptonic decays can nowadays be studied on the lattice at a phenomenologically relevant level of accuracy, is the subject of a companion paper [1]. Here we focus on the phenomenological implications of our results. Using the current best estimates of the relevant Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, our theoretical predictions for the decay rate and for the first two lepton-energy moments are in very good agreement with the corresponding experimental measurements. We also argue that, while the inclusive $D_{s}$ channel is not yet competitive with the exclusive channels in the $|V_{cs}|$ determination, the situation can be significantly improved in the near future.

hep-lat↗

arXiv2025

Smeared $R$-ratio in isospin symmetric QCD with Low Mode Averaging

Low Mode Average (LMA) is a technique to improve the quality of the signal-to-noise ratio in the long time separation of Euclidean correlation functions. We report on its beneficial impact in computing the vector-vector light connected two-point correlation functions and derived physical quantities in the mixed action lattice setup adopted by ETM collaboration. We focus on preliminary results of the computation within isospin symmetric QCD (isoQCD) of the $R$-ratio smeared with Gaussian kernels of widths down to $σ\sim250$ MeV, which is enough to appreciate the $ρ$ resonance around 770 MeV, using the Hansen-Lupo-Tantatlo (HLT) spectral-density reconstruction method.

hep-lat↗

arXiv2025

Valence leading isospin breaking contributions to $a_μ^{\mathrm{HVP-LO}}$

By employing the RM123 approach to QCD+QED, we computed the valence quark-connected isospin-breaking corrections to the light, strange and charm contributions at leading order in $α_{\mathrm{em}}$ and $\left(μ_d-μ_u\right) / Λ_{\mathrm{QCD}}$. Here we report the preliminary results on two different volumes ($L \sim 3.8$ fm and $L \sim 5.1$ fm) and a fixed lattice spacing (corresponding to $a_{\text {isoQCD }} \sim 0.07951(4)$ fm), obtained in the framework of the ongoing computation by ETMC of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_μ^{\mathrm{HVP}}$ in QCD+QED.

hep-lat↗

arXiv2024

Approaches to the Inverse Problem

The analytical continuation of correlation functions from imaginary to real time is a crucial step in lattice gauge theories, and it challenges our ability to derive non-perturbative predictions from lattice simulations. We review aspects of this "inverse problem", which has driven both theoretical and algorithmic advancements in recent years, opening new promising avenues for non-perturbative studies of the Standard Model and beyond. The focus of this proceeding will be on variations of Backus-Gilbert and Bayesian methods.

hep-lat↗

arXiv2024

Bayesian solution to the inverse problem and its relation to Backus-Gilbert methods

The problem of obtaining spectral densities from lattice data has been receiving great attention due to its importance in our understanding of scattering processes in Quantum Field Theory, with applications both in the Standard Model and beyond. The problem is notoriously difficult as it amounts to performing an inverse Laplace transform, starting from a finite set of noisy data. Several strategies are now available to tackle this inverse problem. In this work, we discuss how Backus-Gilbert methods, in particular the variation introduced by some of the authors, relate to the solution based on Gaussian Processes. Both methods allow computing spectral densities smearing with a kernel, whose features depend on the detail of the algorithm. We will discuss such kernel, and show how Backus-Gilbert methods can be understood in a Bayesian fashion. As a consequence of this correspondence, we are able to interpret the algorithmic parameters of Backus-Gilbert methods as hyperparameters in the Bayesian language, which can be chosen by maximising a likelihood function. By performing a comparative study on lattice data, we show that, when both frameworks are set to compute the same quantity, the results are generally in agreement. Finally, we adopt a strategy to systematically validate both methodologies against pseudo-data, using covariance matrices measured from lattice simulations. In our setup, we find that the determination of the algorithmic parameters based on a stability analysis provides results that are, on average, more conservative than those based on the maximisation of a likelihood function.

hep-lat↗

arXiv2024

Scattering Amplitudes from Euclidean Correlators: Haag-Ruelle theory and approximation formulae

In this work we provide a non-perturbative solution to the theoretical problem of extracting scattering amplitudes from Euclidean correlators in infinite volume. We work within the solid axiomatic framework of the Haag-Ruelle scattering theory and derive formulae which can be used to approximate scattering amplitudes arbitrarily well in terms of linear combinations of Euclidean correlators at discrete time separations. Our result generalizes and extends the range of applicability of a result previously obtained by Barata and Fredenhagen [Commun. Math. Phys. 138 (1991) 507-520]. We provide a concrete procedure to construct such approximations, making our formulae ready to be used in numerical calculations of non-perturbative QCD scattering amplitudes. A detailed numerical investigation is needed to assess whether the proposed strategy can lead to the calculation of scattering amplitudes with phenomenologically satisfactory precision with presently available lattice QCD data. This will be the subject of future work. Nevertheless, the numerical accuracy and precision of lattice simulations is systematically improvable, and we have little doubts that our approach will become useful in the future.

hep-lat↗

arXiv2024

Teaching to extract spectral densities from lattice correlators to a broad audience of learning-machines

We present a new supervised deep-learning approach to the problem of the extraction of smeared spectral densities from Euclidean lattice correlators. A distinctive feature of our method is a model-independent training strategy that we implement by parametrizing the training sets over a functional space spanned by Chebyshev polynomials. The other distinctive feature is a reliable estimate of the systematic uncertainties that we achieve by introducing several ensembles of machines, the broad audience of the title. By training an ensemble of machines with the same number of neurons over training sets of fixed dimensions and complexity, we manage to provide a reliable estimate of the systematic errors by studying numerically the asymptotic limits of infinitely large networks and training sets. The method has been validated on a very large set of random mock data and also in the case of lattice QCD data. We extracted the strange-strange connected contribution to the smeared $R$-ratio from a lattice QCD correlator produced by the ETM Collaboration and compared the results of the new method with the ones previously obtained with the HLT method by finding a remarkably good agreement between the two totally unrelated approaches.

hep-lat↗

arXiv2023

On the study of inclusive semileptonic decays of $B_s$-meson from lattice QCD

In this contribution we describe a recent study focused on the lattice calculation of inclusive decay rates of heavy mesons. We show how the inclusive calculation can be achieved starting from four-point lattice correlation functions normalised appropriately. The correlators used in this project come from gauge ensembles provided by the JLQCD and ETM collaborations. An essential point of this method is the extraction of spectral densities from lattice correlators which is obtained using two of the most recent approaches in the literature. Our results are in remarkable agreement with analytical predictions from the operator-product expansion. This study represents the first step towards a full lattice QCD study of heavy mesons inclusive semileptonic decays.

hep-lat↗

arXiv2023

Extraction of lattice QCD spectral densities from an ensemble of trained machines

In this talk we discuss a novel method, that we have presented in Ref. [1], to extract hadronic spectral densities from lattice correlators by using deep learning techniques. Hadronic spectral densities play a crucial role in the study of the phenomenology of strong-interacting particles and the problem of their extraction from Euclidean lattice correlators has already been approached in the literature by using machine learning techniques. A distinctive feature of our method is a model-independent training strategy that we implement by parametrizing the training sets over a functional space spanned by Chebyshev polynomials. The other distinctive feature is a reliable estimate of the systematic uncertainties that we obtain by introducing an ensemble of machines in order to study numerically the asymptotic limits of infinitely large networks and training sets. The method is validated on a very large set of random mock data and also in the case of lattice QCD data.

hep-lat↗

arXiv2023

Bayesian interpretation of Backus-Gilbert methods

The extraction of spectral densities from Euclidean correlators evaluated on the lattice is an important problem, as these quantities encode physical information on scattering amplitudes, finite-volume spectra, inclusive decay rates, and transport coefficients. In this contribution, we show that the Bayesian approach to this "inverse" problem, based on Gaussian processes, can be reformulated in a way that yields a solution equivalent, up to statistical uncertainties, to the one obtained in a Backus-Gilbert approach. After discussing this equivalence, we point out its implications for a reliable determination of spectral densities from lattice simulations.

hep-lat↗

arXiv2023

The quenched glueball spectrum from smeared spectral densities

The standard approach to compute the glueball spectrum on the lattice relies on the evaluation of effective masses from two-point correlation functions of operators with the quantum numbers of the desired state. In this work, we propose an alternative procedure, based on the numerical computation of smeared spectral densities. Even though the extraction of the latter from lattice correlators is a notoriously ill-posed inverse problem, we show that a recently developed numerical method, based on the Backus-Gilbert regularization, provides a robust way to evaluate a smeared version of the spectral densities. Fitting the latter to a combination of Gaussians, we extract the masses of the lightest glueball and of its first excitation in the spectrum of the theory. While the preliminary results presented in this contribution are restricted to simulations at finite lattice spacing and finite volume, and for the purely gluonic sector of QCD, they represent the first step in a systematic investigation of glueballs using spectral-reconstruction methods.

hep-lat↗

arXiv2023

Inclusive hadronic decay rate of the $τ$ lepton from lattice QCD

Inclusive hadronic decays of the $τ$ lepton are very interesting from the phenomenological point of view since they give access to the CKM matrix elements $V_{ud}$ and $V_{us}$. In this paper, for the first time, by employing the HLT method for hadronic smeared spectral densities we compute on the lattice the inclusive decay rate of the processes $τ\to X_{ud}\, ν_τ$, where $X_{ud}$ is a generic hadronic state with $\bar{u} d$ flavor quantum numbers. Our computation, which avoids any recourse to OPE and/or perturbative approximations, is carried out in isospin symmetric $N_{f}=2+1+1$ lattice QCD at physical quark masses, using ensembles produced by the ETMC at three lattice spacings and two volumes. All uncertainties, except for isospin breaking effects, are taken into account and a result with a subpercent error is obtained for $|V_{ud}|$, which is nicely consistent with the current world average. These findings validate our approach and also motivate the inclusion of isospin breaking corrections and its extension to the inclusive decay $τ\to X_{us}\, ν_τ$, paving the way towards a high-precision first principles determination of $|V_{us}|$ and $|V_{ud}|$ from inclusive $τ$ decay.

hep-lat↗