Quark Correlations Research Articles

Spin-orbit entanglement in the Color Glass Condensate

We compute the spin-orbit correlations of quarks and gluons at small-x and show that the helicity and the orbital angular momentum of individual partons are strongly anti-aligned even in unpolarized or spinless hadrons and nuclei. Combined with the fact that gluons in the Color Glass Condensate are linearly polarized, our finding indicates that the helicity and the orbital angular momentum of single gluons are maximally entangled in a quantum mechanical sense.

Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb gauge

Abstract Recently, it has been proposed to compute parton distributions from boosted correlators fixed in the Coulomb gauge within the framework of Large-Momentum Effective Theory. This method does not involve Wilson lines and could greatly improve the efficiency and precision of lattice QCD calculations. However, there are concerns about whether the systematic uncertainties from Gribov copies, which correspond to the ambiguity in lattice gauge-fixing, are under control. This work gives an assessment of the Gribov copies’ effect in the Coulomb-gauge-fixed quark correlators. We utilize different strategies for the Coulomb-gauge fixing, selecting two different groups of Gribov copies based on the lattice gauge configurations. We test the difference in the resulted spatial quark correlators in the vacuum and a pion state. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise. This demonstrates that the effect of the Gribov copies can be neglected in the practical lattice calculation of the quark parton distributions.

Chiral-even twist-3 GPDs for the proton in a spectator diquark model

We investigate the chiral-even twist-3 generalized parton distributions (GPDs) of valence quarks in the proton at nonzero skewness ξ, using a spectator model with scalar and axial-vector diquarks. We consider the exponential form factor for the nucleon-quark-diquark vertex and the axial-vector diquark with light-cone transverse polarization. We analyze the dependence of GPDs on the longitudinal momentum fraction x at different ξ, and on the square of the transverse momentum transfer ΔT2 at different x. Our numerical results reveal distinct discontinuities in all twist-3 GPDs except G1 and G˜1. By taking the forward limit, we obtain the twist-3 parton distribution function gT, which encodes the transverse spin distribution of quarks. We also compare the kinetic orbital angular momentum and the spin-orbit correlations of quarks defined by the twist-2 and twist-3 GPDs, respectively. Published by the American Physical Society 2024

Twist analysis of the spin-orbit correlation in QCD

We present a QCD analysis of the twist-three parton distribution functions associated with the spin-orbit correlation of quarks and gluons in spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} and spin-0 hadrons. We derive exact non-perturbative identities decomposing the spin-orbit correlations into the Wandzura-Wilczek part and the genuine twist-three part. In the spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} case, the result is partially related to the kinematical twist-three part of the gT (x) distribution familiar in the context of transverse spin physics. We use these identities to obtain a novel longitudinal momentum sum rule which may be regarded as the momentum version of the Jaffe-Manohar spin sum rule. We explore the physical interpretation of the sum rule and make a connection to the color Lorentz forces and their associated potential energies.

Spin-orbit correlations in the nucleon in the large- Nc limit

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large-Nc limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions. Published by the American Physical Society 2024

Global quark spin correlations in relativistic heavy ion collisions

The observation of the vector meson’s global spin alignment by the STAR Collaboration reveals that strong spin correlations may exist for quarks and antiquarks in relativistic heavy-ion collisions in the normal direction of the reaction plane. We propose a systematic method to describe such correlations in the quark matter. We classify them as local and long range quark spin correlations in the system. We show in particular that the effective quark spin correlations contain the genuine spin correlations originated directly from the dynamical process as well as those induced by averaging over other degrees of freedom. We also show that such correlations can be studied by measuring the vector meson’s spin density matrix and hyperon-hyperon and hyperon-anti-hyperon spin correlations. We present the relationships between these measurable quantities and spin correlations of quarks and antiquarks. Published by the American Physical Society 2024

Wigner distributions of sea quarks in the light-cone quark model

We investigate the Wigner distributions of u¯ and d¯ quarks in a proton using the overlap representation within the light cone formalism. Using the light-cone wave functions which are obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we calculate the Wigner distributions for the unpolarized/longitudinally polarized sea quarks in an unpolarized/longitudinally polarized proton. The Wigner distributions can be obtained through a Fourier transform on the generalized transverse-momentum dependent parton distributions (GTMDs). We also calculate the GTMDs of u¯ and d¯ quarks in the intermediate step. Numerical results for the Wigner distributions of u¯ and d¯ quarks in transverse momentum space, impact parameter space and the mixed plane are presented. We also study the orbital angular momentum and the spin-orbit correlations of the sea quarks. Published by the American Physical Society 2024

Two-Body Hadronic Weak Decays of Bottomed Hadrons

The structure of light diquarks plays a crucial role in formation of exotic hadrons beyond the conventional quark model, especially with regard to the line shapes of bottomed hadron decays. We study the two-body hadronic weak decays of bottomed baryons and bottomed mesons to probe the light diquark structure and to pin down the quark–quark correlations in the diquark picture. It is found that the light diquark does not favor a compact structure. For instance, the isoscalar diquark [ud] in Λb0 can be easily split and rearranged to form Σc(*)D¯(*) via the color-suppressed transition. This provides a hint that the hidden charm pentaquark states produced in Λb0 decays could be the Σc(*)D¯(*) hadronic molecular candidates. This quantitative study resolves the apparent conflicts between the production mechanism and the molecular nature of these Pc states observed in experiment.

Spin polarization and correlation of quarks from the glasma

We investigate the interaction of strong color fields in the glasma stage of high-energy nuclear collisions with the spins of quarks and antiquarks. We employ the perturbative solution of the quantum kinetic theory for the spin transport of (massive) quarks in a background color field governed by the linearized Yang-Mills equation and derive expressions for the quark-spin polarization and quark-antiquark spin correlation at small momentum in terms of field correlators. For the Golec-Biernat W\"usthoff dipole distribution the quark-spin polarization vanishes, but the out-of-plane spin correlation of quarks and antiquarks is nonzero. Our order-of-magnitude estimate of the correlation far exceeds that caused by vorticity effects, but does not fully explain the data for vector meson alignment. We identify possible mechanisms that could further increase the predicted spin correlation.

Twist-4 T-even proton TMDs in the light-front quark–diquark model

We have dealt with the twist-4 T-even transverse momentum dependent parton distributions (TMDs) for the case of proton in the light-front quark–diquark model (LFQDM). By decoding the unintegrated quark–quark correlator for the semi-inclusive deep inelastic scattering (SIDIS), we have specifically obtained the overlap form for the unpolarized [Formula: see text], longitudinally polarized [Formula: see text] and transversely polarized ([Formula: see text] and [Formula: see text]) proton TMDs. We have provided the explicit expressions for both the cases of the diquark being a scalar or a vector. Average transverse momenta and the average square transverse momenta for the TMDs have been calculated and the results have been tabulated with corresponding leading twist TMDs. In addition, the value of average transverse momentum and average square transverse momentum for TMD [Formula: see text] has been compared with the available light-front constituent quark model (LFCQM) results. From TMDs, we have also obtained and discussed the transverse momentum-dependent parton distribution functions (TMDPDFs). The model relations of the twist-4 T-even TMDs with the available leading twist T-even TMDs have also been obtained.

X(3872) ’s excitation and its connection with production at hadron colliders

The LHCb collaboration has found that the production rate of $X(3872)$ in proton-proton collisions decreases as final state particle multiplicity increases. Moreover, the ALICE experiment at CERN has observed that the number of deuterons produced increases with multiplicity, a behavior that is qualitatively different from that of the $X(3872)$. These experimental findings may point to a compact structure for the $X(3872)$ or, at least, that its hadronization could proceed through a charm-anticharm core. We have recently used a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation that describes the $X(3872)$ as a $c \bar c q \bar q$ tetraquark system with quantum numbers $I^G(J^{PC})=0^+(1^{++})$ and $1^-(1^{++})$. According to our structural analysis, the quark--(anti-)quark correlations resemble light-meson--heavy-meson molecules of type $\omega J/\psi$ and $\rho J/\psi$, rather than the most extended $D\bar D^{\ast}$ interpretation. It was argued that this fact may be the key to make compatible the molecular features of the $X(3872)$ with its production observables. The same formalism allows us to compute the first color excited $c \bar c q \bar q$ tetraquark state with either $I^G(J^{PC})=0^+(1^{++})$ or $1^-(1^{++})$. A bound-state is found in each channel, their masses are around 4.0 GeV which is an energy region where many new exotic candidates have been collected by the Particle Data Group. Concerning their structural properties, these states cluster in a compact diquark-antidiquark arrangement which matches perfectly with a so-called Born-Oppenheimer tetraquark configuration. The promptly production rates of these states in proton-proton, proton-nucleus and nucleus-nucleus collisions should fall off equal to or even faster than those of the $X(3872)$.

Windows on the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

An accurate determination of the leading-order hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon is critical to understanding the size and significance of any discrepancy between the Standard Model prediction and experimental results being obtained by the Muon g-2 experiment at Fermilab. The Standard Model prediction is currently based on a data-driven approach to the HVP using experimental results for $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons})$. Lattice QCD aims to provide a result with similar uncertainty from calculated vector-vector correlation functions, but the growth of statistical and systematic errors in the $u/d$ quark correlation functions at large Euclidean time has made this difficult to achieve. We show that restricting the lattice contributions to a one-sided window $0<t<{t}_{1}$ can greatly improve lattice results while still capturing a large fraction of the total HVP. We illustrate this by comparing windowed lattice results based on the 2019 Fermilab Lattice/HPQCD/MILC HVP analysis with corresponding results obtained from the KNT19 analysis of ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ data. For ${t}_{1}=1.5\text{ }\text{ }\mathrm{fm}$, 70% of the total HVP is contained within the window and our lattice result has an error of 0.7%, only about twice as big as the error from the ${e}^{+}{e}^{\ensuremath{-}}$ analysis. We see a tension of $2.7\ensuremath{\sigma}$ between the two results. With increased statistics in the lattice data the one-sided windows will allow stringent tests of lattice and ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ results that include a large fraction of the total HVP contribution.

Parton model description of quark and antiquark correlators and TMDs

Model studies play an important role for the understanding and elucidation of the nonperturbative properties of transverse momentum dependent parton distribution functions (TMDs). The parton model is often a helpful framework and starting point for first explorations of TMD properties and the description of deep-inelastic processes in which TMDs can be accessed. Based on a systematic exploration of the parton model concept, we reconcile the claims in literature that there are 2 independent structures in the quark correlator in the parton model vs the claim that there are 3, and explain the underlying assumptions leading to the different conclusions. We also systematically explore the antiquark correlator and, to the best of our knowledge, for the first time derive the model expressions for all T-even leading and subleading antiquark TMDs. We demonstrate the consistency of the framework which can be generalized in future studies for more sophisticated TMD modeling.

T-odd quark-gluon-quark correlation function in the light-front quark-diquark model

We have scrutinized the transverse momentum dependent quark–gluon–quark correlation function. We have utilized the light-front quark-diquark model to study the time-reversal-odd interaction-dependent twist-3 gluon distributions which we have obtained from the disintegration of the transverse momentum dependent quark–gluon–quark correlator. Specifically, we have studied the behavior of \tilde{e}_{L}ẽL and \tilde{e}_{T}ẽT while considering our diquark to be an axial-vector.

Transverse-momentum-dependent parton distribution functions for spin-1 hadrons

We show transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions by taking the decomposition of a quark correlation function in the Lorentz-invariant way with the conditions of Hermiticity and parity invariance. We found 30 new TMDs in the tensor-polarized spin-1 hadron at twists 3 and 4 in addition to 10 TMDs at twist 2. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtained new sum rules for the time-reversal-odd structure functions, {\int d^2 k_T g_{LT} = \int d^2 k_T h_{LL} = \int d^2 k_T h_{3LL} =0}∫d2kTgLT=∫d2kThLL=∫d2kTh3LL=0, at twists 3 and 4. We also indicated that transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs can probe color degrees of freedom, so that they are valuable in providing unique opportunities for creating interdisciplinary physics fields such as gluon condensate, color Aharonov-Bohm effect, and color entanglement. We also found three new collinear PDFs at twists 3 and 4, and a twist-2 relation and a sum rule were derived in analogy to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule on the structure function {g_2}g2.

Energy correlation of bottom quarks from decays of top quarks in electron–positron annihilation

Joint energy distribution of the bottom quark and antiquark from decays of the top quark and antiquark produced in the reaction is studied. Main emphasis is put on CP-violation effects in the interaction of the photon and Z boson with the top quarks. Energy asymmetries of b and quarks, which give access to the CP-violating terms, are considered. To estimate the magnitude of these asymmetries, the CP-violating γtt and Ztt couplings are calculated in one-loop model with exchange of the Higgs boson with the mass of 125 GeV. Interaction of this boson with the top quarks is assumed to include scalar and pseudoscalar couplings. Values of these couplings are constrained from the recent CMS analysis. Energy dependence of the asymmetries of b and quarks is calculated up to TeV and some interesting features of their behavior are observed. These observables can be of interest for future studies at electron–positron colliders CLIC and ILC.

Confining density functional approach for color superconducting quark matter and mesonic correlations

We present a novel relativistic density-functional approach to modeling quark matter with a mechanism to mimic confinement. The quasiparticle treatment of quarks provides their suppression due to large quark selfenergy already at the mean-field level. We demonstrate that our approach is equivalent to a chiral quark model with medium-dependent couplings. The dynamical restoration of the chiral symmetry is ensured by construction of the density functional. Beyond the mean field, quark correlations in the pseudoscalar channel are described within the Gaussian approximation. This explicitly introduces pionic states into the model. Their contribution to the thermodynamic potential is analyzed within the Beth–Uhlenbeck framework. The modification of the meson mass spectrum in the vicinity of thee (de)confinement transition is interpreted as the Mott transition. Supplemented with the vector repulsion and diquark pairing the model is applied to construct a hybrid quark-hadron EoS of cold compact-star matter. We study the connection of such a hybrid EoS with the stellar mass-radius relation and tidal deformability. The model results are compared to various observational constraints including the NICER radius measurement of PSR J0740+6620 and the tidal deformability constraint from GW170817. The model is shown to be consistent with the constraints, still allowing for further improvement by adjusting the vector repulsion and diquark pairing couplings.

Higher-order QCD corrections to H \u2192 b overline{b} from rational approximants

We use rational approximants to study missing higher orders in the massless scalar-current quark correlator. We predict the yet unknown six-loop coefficient of its imaginary part, related to Γ(H → b overline{b} ), to be c5 = −6900 ± 1400. With this result, the perturbative series becomes almost insensitive to renormalization scale variations and the intrinsic QCD truncation uncertainty is tiny. This confirms the expectation that higher-order loop computations for this quantity will not be required in the foreseeable future, as the uncertainty in Γ(H → b overline{b} ) will remain largely dominated by the Standard Model parameters.

Gluons, light and heavy quarks in the instanton vacuum

In this paper, we put our focus towards describing the nonperturbative effects in the properties of hadrons made from the light-heavy and the heavy–heavy quarks in the framework of Instanton Liquid Model (ILM) of QCD vacuum. The main features of ILM and its applicability in the heavy quark sector are briefly discussed. The properties of gluonic systems, the light and heavy quark correlators in the instanton background are also analyzed. We demonstrate that the consideration of both, perturbative and nonperturbative, gluon effects in the instanton background for a single heavy quark leads to the mass shift due to the direct-instanton nonperturbative and ILM modified perturbative contributions, respectively. For the interacting heavy quark and heavy anti-quark, the potential consists of the direct instanton-induced part and the one-gluon exchange (OGE) perturbative part. OGE interactions are screened at large distances due to the nonperturbative dynamics. The estimation of instanton contributions in the phenomenological Cornell-type potential model is presented. In relation to the experimental data, the charmonium properties, the role of instanton effects in their spectra and transitions are discussed. The main features of heavy-light quark systems in the instanton generated background are also discussed. As an example, we consider the process of pion emissions by the exited heavy quarkonium. We show that there is a sizable correction ([Formula: see text]) to the dipole approximation for the process [Formula: see text].

Distribution amplitudes of light diquarks

Accumulating evidence indicates that soft quark+quark (diquark) correlations play an important role in the structure and interactions of hadrons constituted from three or more valence-quarks; so, it is worth developing insights into diquark structure. Using a leading-order truncation of those equations needed to solve continuum two-valence-body bound-state problems, the leading-twist two-parton distribution amplitudes (DAs) of light-quark scalar and pseudovector diquarks are calculated. The diquark DAs are narrower and taller than the asymptotic profile that characterises mesons. Consequently, the valence quasiparticles in a diquark are less likely to carry a large light-front fraction of the system’s total momentum than those in a meson. These features may both influence the form of baryon DAs and be transmitted to diquark distribution functions (DFs), in which case their impact will be felt, e.g. in the proton’s u and d valence-quark DFs.