Lattice QCD Data Research Articles

New Data-Driven Constraints on the Sign of Gluon Polarization in the Proton.

Recently, the possible existence of negative gluon helicity Δg has been observed to be compatible with existing empirical constraints, including from jet production in polarized proton-proton collisions at the Relativistic Heavy Ion Collider, and lattice QCD data on polarized gluon Ioffe time distributions. We perform a new global analysis of polarized parton distributions in the proton with new constraints from the high-x region of deep-inelastic scattering (DIS). A dramatic reduction in the quality of the fit for the negative Δg replicas compared to those with positive Δg suggests that the negative Δg solution cannot simultaneously account for high-x polarized DIS data along with lattice and polarized jet data.

Magnetic field effect on hadron yield ratios and fluctuations in a hadron resonance gas

This work studies the influence of an external magnetic field on hadron yields and fluctuations in a hadron resonance gas by performing calculations within an updated version of the open-source package. The presence of the magnetic field has a sizable influence on certain hadron yield ratios. Most notably, it leads to enhanced p/π and suppressed n/p ratios, which may serve as a magnetometer in heavy-ion collisions. By attributing the centrality dependence of the p/π ratio in Pb-Pb collisions at 5.02 TeV measured by the ALICE Collaboration entirely to the magnetic field, its maximal strength at freezeout is estimated to be eB≃0.12GeV2≃6.3mπ2 in peripheral collisions. The magnetic field also enhances various conserved charge susceptibilities, which is qualitatively consistent with recent lattice QCD data and is driven in the HRG model by the increase of hadron densities. However, the variances of hadrons do not show any enhancement when normalized by the means, therefore, measurements of second-order fluctuations in heavy-ion collisions appear to offer limited additional information about the magnetic field relative to mean multiplicities. Published by the American Physical Society 2024

Thermodynamic formulation of vacuum energy density in flat spacetime and potential implications for the cosmological constant

We propose a thermodynamical definition of the vacuum energy density ρvac, defined as 〈vac|Tμν|vac〉 = − ρvacgμν, in quantum field theory in flat Minkowski space in D spacetime dimensions, which can be computed in the limit of high temperature, namely in the limit β = 1/T → 0. It takes the form ρvac = const ∙ mD where m is a fundamental mass scale and “const” is a computable constant which can be positive or negative depending on interaction couplings. Due to modular invariance ρvac can also be computed in a different non-thermodynamic channel where one spatial dimension is compactifed on a circle of circumference β and we confirm this modularity for free massive theories for both bosons and fermions for D = 2, 3, 4. We list various properties of ρvac that are generally required, for instance ρvac = 0 for conformal field theories, and others, such as the constraint that ρvac has opposite signs for free bosons verses fermions of the same mass, which is related to constraints from supersymmetry. Using the Thermodynamic Bethe Ansatz we compute ρvac exactly for 2 classes of integrable QFT’s in 2D and interpreting some previously known results. We apply our definition of ρvac to Lattice QCD data with two light quarks (up and down) and one additional massive flavor (the strange quark), and find it is negative, ρvac ≈ − (200 MeV)4. Finally we make some remarks on the Cosmological Constant Problem since ρvac is central to any discussion of it.

Unraveling generalized parton distributions through Lorentz symmetry and partial DGLAP knowledge

Relying on the polynomiality property of generalized parton distributions, which roots on Lorentz covariance, we prove that it is enough to know them at vanishing and low skewness within the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi region to obtain a unique extension to their entire support up to a D term. We put this idea in practice using two methods: reconstruction using artificial neural networks and finite-elements methods. We benchmark our results against standard models for generalized parton distributions. In agreement with the formal expectation, we obtain very a accurate reconstruction for a maximal value of the skewness as low as 20% of the longitudinal momentum fraction. This result might be relevant for reconstruction of generalized parton distribution from experimental and lattice QCD data, where computations are, for now, restricted in skewness. Published by the American Physical Society 2024

A thermo-magnetic bag model for the quark-gluon plasma

In this work we study the pressure of the quark-gluon plasma (QGP) in the presence of a weak magnetic field, using a minimally enhanced model of a weakly interacting gas of quasi-particles in a thermal bath. We include the magnetic field effects through the quark mass that has been modified using a recently proposed thermo-magnetic coupling. This thermo-magnetic coupling emerges form the quark-gluon vertex in the HTL approximation [1]. We use Lattice QCD [2] data, to constrain the thermo-magnetic bag function of the quasi-particle model and provide an estimate of the thermo-magnetic vacuum energy density. We then compute the transverse pressure of the system and compare with similar results from the literature. We find that the inverse magnetic catalysis already built within this thermo-magnetic coupling allows a robust description of this Lattice QCD data for the pressure of the QGP in the presence of a weak magnetic field. The extension to the thermal quasi-particle model we have introduced here, makes it easier to pursue further phenomenological studies that require simulations with an EoS that has integrable quasi-particle thermodynamic variables which have the general features of lattice data in the weak magnetic field regime.

On Thermal Transition in QCD

Abstract We describe how the general mechanism of partial deconfinement applies to large-N QCD and a partially deconfined phase inevitably appears between completely confined and completely deconfined phases. Furthermore, we propose how partial deconfinement can be observed in real-world QCD with the SU(3) gauge group. For this purpose, we employ lattice configurations obtained by the WHOT-QCD Collaboration and examine our proposal numerically. In the discussion, the Polyakov loop plays a crucial role in characterizing the phases, without relying on center symmetry, and hence we clarify the meaning of the Polyakov loop in QCD at large N and finite N. At both large N and finite N, the complete confinement is characterized by the Haar-random distribution of the Polyakov line phases. Haar-randomness, which is stronger than unbroken center symmetry, indicates that Polyakov loops in any nontrivial representations have vanishing expectation values, and deviation from the Haar-random distribution at higher temperatures is quantified with the loops. We discuss that the transitions separating the partially deconfined phase are characterized by the behaviors of Polyakov loops in various representations. The lattice QCD data provide us with the signals exhibiting two different characteristic temperatures: deconfinement of the fundamental representation and deconfinement of higher representations. As a nontrivial test for our proposal, we also investigate the relation between partial deconfinement and instanton condensation and confirm the consistency with the lattice data. To make the presentation more easily accessible, we provide a detailed review of the previously known aspects of partial deconfinement.

Combining lattice QCD and phenomenological inputs on generalised parton distributions at moderate skewness

We present a systematic study demonstrating the impact of lattice QCD data on the extraction of generalised parton distributions (GPDs). For this purpose, we use a previously developed modelling of GPDs based on machine learning techniques fulfilling the theoretical requirements of polynomiality, a form of positivity constraint and known reduction limits. A special care is given to estimate the uncertainty stemming from the ill-posed character of the connection between GPDs and the experimental processes usually considered to constrain them, like deeply virtual Compton scattering (DVCS). Moke lattice QCD data inputs are included in a Bayesian framework to a prior model based on an Artificial Neural Network. This prior model is fitted to reproduce the most experimentally accessible information of a phenomenological extraction by Goloskokov and Kroll. We highlight the impact of the precision, correlation and kinematic coverage of lattice data on GPD extraction at moderate ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} which has only been brushed in the literature so far, paving the way for a joint extraction of GPDs.

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.

Toward a universal description of hadronic phase of QCD

Mean-field model quantum field theories of hadrons were traditionally developed to describe cold and dense nuclear matter and are by now very well constrained from the recent neutron star merger observations. We show that when augmented with additional known hadrons and resonances but not included earlier, these mean-field models can be extended beyond its regime of applicability. Calculating some specific ratios of baryon number susceptibilities for finite temperature and moderate values of baryon densities within mean-field approximation, we show that these match consistently with the lattice QCD data available at lower densities, unlike the results obtained from a noninteracting hadron resonance gas model. We also estimate the curvature of the line of constant energy density, fixed at its corresponding value at the chiral crossover transition in QCD, in the temperature-density plane. The number density at low temperatures and high density is found to be about twice the nuclear saturation density. Moreover from this line we can indirectly constrain the critical endpoint of QCD to be beyond μB=596 MeV for temperature ∼125 MeV. Published by the American Physical Society 2024

Vacuum free energy, quark condensate shifts and magnetization in three-flavor chiral perturbation theory to [formula omitted] in a uniform magnetic field

We study three-flavor QCD in a uniform magnetic field using chiral perturbation theory (χPT). We construct the vacuum free energy density, quark condensate shifts induced by the magnetic field and the renormalized magnetization to O(p6) in the chiral expansion. We find that the calculation of the free energy is greatly simplified by cancellations among two-loop diagrams involving charged mesons. In comparing our results with recent 2+1-flavor lattice QCD data, we find that the light quark condensate shift at O(p6) is in better agreement than the shift at O(p4). We also find that the renormalized magnetization, due to its small-ness, possesses large uncertainties at O(p6) due to the uncertainties in the low-energy constants.

Exploration of extreme QCD matter with deep learning

To study hot and dense nuclear matter, relativistic nuclear collisions are carried out experimentally, while lattice field theory provides a first-principles investigation. Meanwhile, astronomical observations of neutron stars also provide constraints on cold and dense nuclear matter. In this talk, I present the potential of deep learning based strategies to aid the exploration of QCD matter under extreme conditions, ranging from identifying essential physics from nuclear collision experiments, to facilitating lattice QCD data analysis, to efficiently exploiting astronomical observations in extracting the dense matter equation of state.

Transverse expansion of Bjorken flow in (1+1D) relativistic ideal-magnetohydrodynamics with magnetization

We study the evolution of magnetized quark gluon plasma (QGP) in the magneto hydrodynamic (MHD) framework. The fluid under investigation has a non-zero magnetization with infinite electrical conductivity. We solve the coupled Maxwell and conservation equations in (1+1D) transverse flow. We assume that the motion of fluid is longitudinally boost-invariant along beam line.In this study, we consider two different scenarios. First, we consider an ideal relativistic plasma with massless particles and infinite electrical conductivity with a constant magnetic susceptibility (χm). Thus, we solve the coupled Maxwell and conservation equations, and obtain the transverse fluid velocity, the energy density and the magnetic field as functions of both space and time. We investigate the effects of magnetic susceptibility (χm) on the evolution of thermodynamic quantities. Then, we solve the coupled Maxwell and conservation equations with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data [43,44]. We find the evaluation of temperature, energy density, the magnetic field, and the transverse fluid velocity. We improve our previous study [21] to include a nonzero magnetization, the transverse relativistic velocity ux2≠0, and a realistic equation of state.We realize the effects of non-zero magnetization on the fluid quantities are rather small. Besides, our work shows a fluid with a realistic equation and a temperature-dependent magnetic susceptibility behaves like a conformal fluid with a small constant magnetic susceptibility.

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.

Implementation of cluster expansion for hot QCD matter

We present a cluster expansion EoS model for strongly-interacting matter based on the generalized Beth-Uhlenbeck formalism to describe hadrons as bound clusters of quarks. This formalism can describe both confined and deconfined phases. Our emphasis is on the region of vanishing baryon densities, where numerical solutions available from Lattice QCD predict a smooth crossover transition from hadron to quark matter. Medium effects are taken into account as self energies, which are motivated from both perturbative QCD calculations and phenomenological models. Parameters are tuned to Lattice QCD data and result in a good agreement of the thermodynamics.

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.

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.

Low-energy constants in the chiral Lagrangian with baryon octet and decuplet fields from Lattice QCD data on CLS ensembles

We perform an analysis of Lattice QCD data on baryon octet and decuplet masses based on the chiral SU(3) Lagrangian. Low-energy constants (LEC) are adjusted to describe baryon masses from a large set of CLS ensembles, where finite-box and discretization effects are considered. The set is successfully compared against previous Lattice QCD data from ensembles generated with distinct QCD actions by the ETMC, QCDSF-UKQCD and HSC groups. Discretization effects are modelled by the use of action and lattice-scale dependent leading orders LEC, where uniform values are imposed in the limit of vanishing lattice scales. From the CLS data set we extract a pion-nucleon sigma term, sigma _{pi N}= 58.7(1.2) MeV, compatible with its empirical value.

The isospin-3 three-particle K-matrix at NLO in ChPT

The three-particle K-matrix, {mathcal{K}}_{textrm{df},3} , is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of {mathcal{K}}_{textrm{df},3} is significantly improved with respect to leading order once NLO effects are incorporated.

Pion observables calculated in Minkowski and Euclidean spaces with Ansätze for quark propagators

We study two quark--propagator meromorphic Ans\"atze that admit clear connection between calculations in Euclidean space and Minkowski spacetime. The connection is established through a modified Wick rotation in momentum space, where the integration contour along the imaginary axis is adequately deformed. The Ans\"atze were previously proposed in the literature and fitted to Euclidean lattice QCD data. The generalized impulse approximation is used to calculate the pion transition form factor and electromagnetic form factor, correcting an earlier result. The pion decay constant and distribution amplitude are also calculated. The latter is used to deduce the asymptotic behavior of the form factors. Such an asymptotic behavior is compared with those obtained directly from the generalized impulse approximation and the causes of differences are pointed out.

Revisiting Brightarrow K^{(*)} nu {bar{nu }} decays in the Standard Model and beyond

In this letter we revisit the Standard Model predictions for {mathcal {B}}(Brightarrow K^{(*)}nu {bar{nu }}) and discuss the opportunities that open up when combining its partial decay rate with that of Brightarrow K^{(*)}ell ell . In the Standard Model a suitable ratio of these two modes can be used to extract C_9^textrm{eff}, which is essential for a reliable phenomenological analysis of the Brightarrow K^{(*)}ell ell angular observables. The same ratio also proves to be more sensitive to the presence of New Physics in many plausible extensions of the Standard Model. We also suggest that the separate measurement of {mathcal {B}}(Brightarrow Knu {bar{nu }}) for high and for low q^2’s can be helpful for testing the assumed shape of the vector form factor, because the lattice QCD data are obtained at high q^2’s, whereas the low q^2 region is obtained through an extrapolation.