Lattice Data Research Articles

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.

Nucleon isovector axial form factors

We present results for the isovector axial vector form factors obtained using thirteen 2+1+1-flavor highly improved staggered quark (HISQ) ensembles generated by the MILC collaboration. The calculation of nucleon two- and three-point correlation functions has been done using Wilson-clover fermions. In the analysis of these data, we quantify the sensitivity of the results to strategies used for removing excited state contamination and invoke the partially conserved axial current relation between the form factors to choose between them. Our data driven analysis includes removing contributions from multihadron Nπ states that make significant contributions. Our final results are gA=1.292(53)stat(24)sys for the axial charge; gS=1.085(50)stat(103)sys and gT=0.991(21)stat(10)sys for the scalar and tensor charges; ⟨rA2⟩=0.439(56)stat(34)sys fm2 for the mean squared axial charge radius, gP*=9.03(47)stat(42)sys for the induced pseudoscalar charge; and gπNN=14.14(81)stat(85)sys for the pion-nucleon coupling. We also provide a parametrization of the axial form factor GA(Q2) over the range 0≤Q2≤1 GeV2 for use in phenomenology and a comparison with other lattice determinations. We find that the various lattice data agree within 10% but are significantly different from the extraction of GA(Q2) from the ν-deuterium scattering data. Published by the American Physical Society 2024

Quark mass dependence of D*s0 (2317) and Ds1(2460) states

Abstract. We investigate the dependence of both light and heavy quark masses on the properties of low-lying charmed mesons within the framework of one-loop HHX PT. Determination of the low energy constants is accomplished through an analysis of lattice data obtained from various Lattice Quantum Chro-modynamics (LQCD) simulations. Model selection tools are employed to identify the pertinent parameters needed to achieve higher precision alignment with the data. Our study extends to the analysis of HSC energy levels for DK scattering in I = 0, considering different boosts and two pion masses. A comprehensive global fit is performed, incorporating HSC energy levels along with those from DK and D* K scattering obtained from RQCD and Prelovsek et al. Finally, we extract the dependence of D*s0(2317) and Ds1(2460) resonances on the pion mass.

Lattice-based equation of state with 3D ising critical point

The BEST Collaboration equation of state combining lattice data with the 3D Ising critical point encounters limitations due to the truncated Taylor expansion up to μB/T ~ 2.5. This truncation consequently restricts its applicability at high densities. Through a resummation scheme, the lattice results have been extended to μB/T = 3.5. In this article, we amalgamate these ideas with the 3D-Ising model, yielding a family of equations of state valid up to μB = 700MeV with the correct critical behavior. Our equations of state feature tunable parameters, providing a stable and causal framework-a crucial tool for hydrodynamics simulations.

Mapping the critical equation of state by resummations

Determining the existence and the location of the QCD critical point remains a major goal in the heavy-ion collision experiments. A crucial theoretical input for achieving this goal is mapping the QCD equation of state in the presence of baryon chemical potential (μ) which at the moment is limited to small values of μ, away from the critical point. We present a new framework for reconstructing the equation of state from a truncated Taylor series expansion for small μ by using novel resummation techniques. We show how this resummation method can be used to (i) determine the location of the critical point and (ii) constrain the form of the critical contribution to the QCD equation of state which has a direct impact on the shape of the experimental signatures of the critical point. Using the recent lattice data from the HotQCD collaboration we estimate that Tc ≈ 100 MeV, μc ≈ 580 MeV, the crossover slope at the critical point α1 ≈ 9°, and further constrain the non-universal mapping parameters between the Ising model and QCD (scaling) equations of state.

Dealing with location uncertainty for modeling network-constrained lattice data

The spatial analysis of traffic accidents has long been a useful tool for authorities to implement effective preventive measures. Initial studies were conducted at the areal level considering administrative or traffic-related units, but a more precise analysis at the street level is necessary for developing targeted interventions. In recent years, there has been a significant increase in studies conducted at the road network level, which require using new statistical techniques that are suitable for linear networks. However, modeling accident counts at the street level presents several challenges, primarily due to the need for accurate georeferenced data to correctly assign events to specific streets or road segments. Despite advancements in geocoding methods, discrepancies can still arise between the true event locations and the locations mapped by a geocoding method. In this paper, we propose a model to deal with the presence of location uncertainty and enable an analysis of accident intensity constrained to the road network. The model does not assume any specific mechanism for location uncertainty, as this reflects the most common practical scenario. By tackling this inherent problem, the proposed model aims to enhance the accuracy of accident analysis and contribute to the development of effective preventive measures for traffic safety. The model is evaluated with both a simulation study and a case study on the city of Valencia, Spain. For the latter, the proposed model reveals a greater association of road intersections with accident rates than that estimated by the standard model.

Schwinger displacement of the quark–gluon vertex

The action of the Schwinger mechanism in pure Yang–Mills theories endows gluons with an effective mass, and, at the same time, induces a measurable displacement to the Ward identity satisfied by the three-gluon vertex. In the present work we turn to Quantum Chromodynamics with two light quark flavors, and explore the appearance of this characteristic displacement at the level of the quark–gluon vertex. When the Schwinger mechanism is activated, this vertex acquires massless poles, whose momentum-dependent residues are determined by a set of coupled integral equations. The main effect of these residues is to displace the Ward identity obeyed by the pole-free part of the vertex, causing modifications to its form factors, and especially the one associated with the tree-level tensor. The comparison between the available lattice data for this form factor and the Ward identity prediction reveals a marked deviation, which is completely compatible with the theoretical expectation for the attendant residue. This analysis corroborates further the self-consistency of this mass-generating scenario in the general context of real-world strong interactions.

The spatial string tension from the field correlator method

The behaviour of spatial string tension sigma _s(T) as a function of the temperature T is found in the framework of the Field Correlator Method (FCM). Here the string tension is calculated using the gluelump Green’s function, where gluons in the gluelump are interacting via the same spatial string tension. The resulting T-dependence was obtained without extra parameters in the region T_c< T < 5 T_c using the formalism of elliptic functions theta _3, demonstrating good agreement with available lattice data.

Role of Left-Hand Cut Contributions on Pole Extractions from Lattice Data: Case Study for T_{cc}(3875)^{+}.

We discuss recent lattice data for the T_{cc}(3875)^{+} state to stress, for the first time, a potentially strong impact of left-hand cuts from the one-pion exchange on the pole extraction for near-threshold exotic states. In particular, if the left-hand cut is located close to the two-particle threshold, which happens naturally in the DD^{*} system for the pion mass exceeding its physical value, the effective-range expansion is valid only in a very limited energy range up to the cut and as such is of little use to reliably extract the poles. Then, an accurate extraction of the pole locations requires the one-pion exchange to be implemented explicitly into the scattering amplitudes. Our findings are general and potentially relevant for a wide class of hadronic near-threshold states.

Can the two-pole structure of the D_{0}^{*}(2300) be understood from recent lattice data?

It was demonstrated in a series of papers employing unitarized chiral perturbation theory that the phenomenology of the scalar open-charm state, the D_0^*(2300), can be understood as the interplay of two poles, corresponding to two scalar-isospin doublet states with different SU(3) flavor content. Within this formalism the lightest open charm positive parity states emerge as being dynamically generated from the scattering of the Goldstone-boson octet off D mesons, a picture that at the same time solves various problems that the experimental observations posed. However, in recent lattice studies of Dpi scattering at different pion masses only one pole was reported in the D_0^* channel, while it was not possible to extract reliable parameters of a second pole from the lattice data. In this paper we demonstrate how this seeming contradiction can be understood and that imposing SU(3) constraints on the fitting amplitudes allows one to extract information on the second pole from the lattice data with minimal bias. The results may also be regarded as a showcase how approximate symmetries can be imposed in the K-matrix formalism to reduce the number of parameters.

Representative volume elements of strain/stress fields measured by diffraction techniques.

Finite-element modelling has been used to simulate local strains and stresses within free-standing polycrystalline slabs of W, Cu and W-Cu, heated with free or constrained boundaries. The elastic strain values in crystallites that satisfied the diffraction condition were used to simulate the lattice strain data that would be obtained from diffraction analysis, from which the average stresses within diffracting domains were computed. Comparison of direct-space stresses in the model with the average stresses determined from diffraction analysis shows that the representative volume elements (RVEs) required to obtain equivalent stress/strain values depend on the deformation mode suffered by the material. Further, the direct-space and diffraction stress values agree only under strict sampling and strain/stress uniformity conditions. Consequently, in samples where measurements are conducted in volumes smaller than the RVE, or where the uniformity conditions are not satisfied, further experimental and numerical techniques might be needed for the accurate determination of applied or residual stress distributions.

Approaches to inclusive semileptonic B(s)-meson decays from Lattice QCD

We address the nonperturbative calculation of the inclusive decay rate of semileptonic B(s)-meson decays from lattice QCD. Precise Standard-Model predictions are key ingredients in searches for new physics, and this type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements |Vcb| and |Vub|. We present results from a pilot lattice computation for Bs → Xclνl, where the initial b quark described by the relativistic-heavy-quark (RHQ) formalism on the lattice and the other valence quarks discretised with domain-wall fermions are simulated approximately at their physical quark masses. We compare two different methods for computing the decay rate from lattice data of Euclidean n-point functions, namely Chebyshev and Backus-Gilbert approaches. We further study how much the ground-state meson dominates the inclusive decay rate and indicate our strategy towards a computation with a more comprehensive systematic error budget.

One-loop analysis of the interactions between doubly charmed baryons and Nambu-Goldstone bosons

The interactions between the spin-1/2 doubly charmed baryons and Nambu-Goldstone bosons are analyzed within a manifestly relativistic baryon chiral perturbation theory up to next-to-next-to leading order, by using the so-called extended-on-mass-shell scheme. We utilize heavy diquark-antiquark symmetry to estimate the low-energy constants in the chiral effective Lagrangians. The S- and P-wave scattering lengths are predicted. We find that those diagrams, vanishing exactly in the heavy-quark limit, do contribute slightly to the S-wave scattering lengths in reality. The influence of the spin-3/2 doubly charmed baryons, as heavy-quark spin partners of the spin-1/2 ones, on the scattering lengths is discussed as well. Finally, S-wave phase shifts for elastic scattering processes are presented in the energy region near threshold. Our results in this work will not only be very useful for performing chiral extrapolations of future lattice QCD data, but also provide us chiral inputs for the investigation of the spectroscopy of doubly heavy baryons.

Leading power accuracy in lattice calculations of parton distributions

In lattice-QCD calculations of parton distribution functions (PDFs) via large-momentum effective theory, the leading power (twist-three) correction appears as O(ΛQCD/Pz) due to the linear-divergent self-energy of Wilson line in quasi-PDF operators. For lattice data with hadron momentum Pz of a few GeV, this correction is dominant in matching, as large as 30% or more. We show how to eliminate this uncertainty through choosing the mass renormalization parameter consistently with the resummation scheme of the infrared-renormalon series in perturbative matching coefficients. An example on the lattice pion PDF data at Pz=1.9 GeV shows an improvement of matching accuracy by a factor of more than 3∼5 in the expansion region x=0.2∼0.5.

From Ds → γ in lattice QCD to Bs → μμγ at high q2

We use a recent lattice determination of the vector and axial Ds → γ form factors at high squared momentum transfer q2 to infer their Bs → γ counterparts. To this end, we introduce a phenomenological approach summarized as follows. First, we describe the lattice data with different fit templates motivated by vector-meson dominance, that is expected to hold in the high-q2 region considered. We identify reference fit ansaetze with one or two physical poles, that we validate against alternative templates. Then, the pole residues can be unambiguously related to the appropriate couplings involving the pseudoscalar, the vector mesons concerned, and the photon — or tri-couplings — and the latter can be expressed as sums over quark magnetic moments, weighed by their e.m. charges. This description obeys a well-defined heavy-quark scaling, that allows to parametrically scale up the form factors to the Bs → γ case. We discuss a number of cross-checks of the whole approach, whose validation rests ultimately in a first-principle determination, e.g. in lattice QCD. Finally, we use our obtained form factors to reassess the SM prediction of ℬ(Bs → μ+μ−γ) in the range sqrt{q^2}in [4.2, 5.0] GeV, where an experimental measurement is awaited.

Study of Quarkonium in QGP from Unquenched Lattice QCD

This paper discusses the charmonium and bottomonium correlators in the pseudoscalar channel and the corresponding spectral reconstruction on the lattice. The absence of a transport peak in the pseudoscalar channel spectral function allows for an easier study of the in-medium modification of bound states. However, extracting spectral information from Euclidean correlators is still a numerically ill-posed problem. To constrain the spectral reconstruction, we use an ansatz motivated from perturbation theory. The perturbative model spectral function has two main contributions: a thermal part around the threshold obtained from pNRQCD and the vacuum part well above the threshold. These two regions are matched continuously, and the model spectral function is obtained by introducing parameters that control the overall thermal shift of the peak and the overall amplitude. The lattice correlator data is computed using clover-improved Wilson valence fermions on large and fine gauge field configurations generated using N_f=2+1 flavors Highly Improved Staggered Quark action with physical strange quark mass m_s, and slightly heavy degenerate up and down quark masses m_l=m_s/5 that correspond to m_pi simeq 320 MeV. Our results obtained at T=220 MeV and T=251 MeV suggest that no resonance peaks are needed to describe the charmonium lattice data at these temperatures, while for bottomonium thermally broadened resonance peaks persists.

Quark mass dependence of the low-lying charmed mesons at one loop in HHχPT

We study the light and heavy quark mass dependence of the low-lying charmed mesons in the framework of one-loop HHχPT. The low energy constants are determined by analyzing the available lattice data from different LQCD simulations. Model selection tools are implemented to determine the relevant parameters as required by data with a higher precision. Discretization and other effects due to the charm quark mass setting are discussed.

In-medium properties of the light and heavy-light mesons in a light-front quark model

We investigate the in-medium properties of pseudoscalar and vector mesons with the light-light and heavy-light quarks in a light-front quark model, using the in-medium quark properties computed by the quark-meson coupling model. Both models are constructed on an equal footing with the constituent quark degree of freedom. Here, we particularly focus on the weak decay constants and distribution amplitudes (DAs) of the mesons in symmetric nuclear matter. We find that the weak decay constants decrease as nuclear density increases for $\ensuremath{\pi}$, $K$, $D$, and $B$ pseudoscalar as well as $\ensuremath{\rho}$, ${K}^{*}$, ${D}^{*}$, and ${B}^{*}$ vector mesons, where their properties in free space have good agreement with the available experimental and lattice QCD data. A larger reduction is found for the light-light quark pseudoscalar mesons, while a smaller reduction is found for the heavy-light quark vector mesons, in particular, with the bottom quark. We discuss the effect of the vector potential on the weak decay constants, and present our predictions for the in-medium modifications of DAs. Also, a comparison with the free space lattice QCD data is made.

Refined Gribov-Zwanziger theory coupled to scalar fields in the Landau gauge

The Refined Gribov-Zwanziger (RGZ) action in the Landau gauge accounts for the existence of infinitesimal Gribov copies as well as the dynamical formation of condensates in the infrared of Euclidean Yang-Mills theories. We couple scalar fields to the RGZ action and compute the one-loop scalar propagator in the adjoint representation of the gauge group. We compare our findings with existing lattice data. The fate of BRST symmetry in this model is discussed, and we provide a comparison to a previous proposal for a non-minimal coupling between matter and the RGZ action. We find good agreement with the lattice data of the scalar propagator for the values of the mass parameters that fit the RGZ gluon propagator to the lattice. This suggests that the non-perturbative information carried by the gluon propagator in the RGZ framework provides a suitable mechanism to reproduce the behavior of correlation functions of colored matter fields in the infrared.

Octet and decuplet baryon σ terms and mass decompositions

We present a comprehensive analysis of the SU(3) octet and decuplet baryon masses and $\sigma$-terms using high-precision lattice QCD data and chiral SU(3) effective theory with finite range regularization. The effects of various systematic uncertainties, including from the scale setting of the lattice data and the regularization prescriptions, are quantified. We find the pion-nucleon and strange nucleon $\sigma$-terms to be $\sigma_{\pi N} = 44(3)(3)$ MeV and $\sigma_{N s} = 50(6)(1)$ MeV, respectively. The results provide constraints on the energy-momentum tensor mass decompositions of the SU(3) octet and decuplet baryons, where we find the trace anomaly and quark/gluon energies decrease for strange baryons due to their larger strange $\sigma$-terms.