Hadronic Degrees Of Freedom Research Articles

Entanglement between valence and sea quarks in hadrons of 1+1 dimensional QCD

The conceptual interpretation of valence- and sea-quark separation, which is a key aspect of the parton model and of an intuitive picture of hadron structure, becomes obscured by quantum effects in QCD. This suggests that there may be measures of entanglement between quark degrees of freedom that are present in QCD, but absent in the intuitive picture with a clear valence-sea (VS) separation. In this paper, we define the first rigorous measure of VS entanglement in QCD in an attempt to bring conceptual clarity to this issue, and, potentially, to find a measure of the applicability of the parton model to QCD bound states. This VS entanglement vanishes in the large-Nc limit, and it remains low when finite-Nc states resemble their large-Nc counterparts. We perform a numerical study of VS entanglement in 1 + 1 dimensional discrete light-cone quantized QCD, and in the process develop a method for building the color-singlet basis of 1 + 1d QCD that is manifestly complete and orthogonal by construction. We calculate this VS entanglement entropy for the first time and find that it is relatively low for the first few excited states of both mesons and baryons compared to all other states in the spectrum, with the VS entropy of ground state hadrons providing a minimum. We also see that for ground state mesons the entropy is well described in the 1/Nc approximation. These results suggest that low energy hadrons may be the only QCD bound states for which the large-Nc expansion, and perhaps the parton model, provide an accurate description. This work also provides the first evidence that the VS entanglement entropy of QCD in 3 + 1d, which would likely serve as an order parameter for the transition between quark and hadron degrees of freedom, may be perturbatively accessible through a large-Nc expansion.

Inverse scattering problem with a bare state

In hadron physics, molecular-like multihadron states can interact with compact multiquark states. The latter are modeled as bare states in the Hilbert space of a potential model. In this work, we study several potential models relevant to the bare state, and solve their inverse scattering problems. The first model, called ``cc,'' is a separable potential model. We show that it can approximate (single-channel short-range) $S$-wave near-threshold physics with an error of $\mathcal{O}({\ensuremath{\beta}}^{3}/{M}_{V}^{3})$, where $\ensuremath{\beta}$ sets the maximum momentum of the near-threshold region and ${M}_{V}$ is the typical scale of the potential. The second model, called ``bc,'' serves as the bare-state-dominance approximation, where interaction between continuum states is ignored. Under this model, even though the bare state is always crucial for a bound state's generation, a shallow bound state naturally tends to have a small bare-state proportion. Therefore, we need other quantities to quantify the importance of the bare state. The last model, called ``bcc,'' is a combination of the first two models. This model not only serves as a correction to the bare-state-dominance approximation, but can also be used to understand the interplay between quark and hadron degrees of freedom. This model naturally leads to the presence of a Castillejo-Dalitz-Dyson (CDD) zero. We consider the energy decomposition of a bound state. The potential ratio of the bare-continuum interaction to the continuum self-interaction is proposed to understand how the bound state is generated. Model independently, an inequality for the potential ratio is derived. Based on the model ``bcc,'' the CDD zero can be used to estimate the potential ratio. Finally, we apply these studies to the deuteron, $\ensuremath{\rho}$ meson, and ${D}_{s0}^{*}(2317)$, and analyze their properties.

J-PARC Hadron Physics and Future Possibilities on Color Transparency

The Japan Proton Accelerator Research Complex (J-PARC) is a hadron-accelerator facility that aims to provide secondary beams of kaons, pions, neutrinos, muons, and others together with the primary proton beam for investigating a wide range of science projects. High-energy hadron physics can be studied by using high-momentum beams of unseparated hadrons, which are essentially pions, and also primary protons. In this report, possible experiments are explained on color transparency and generalized parton distributions (GPDs). These projects are complementary to lepton-scattering experiments at Jefferson Laboratory (JLab), COMPASS/AMBER, and future electron-ion colliders. Thank to hadron-beam energies up to 30 GeV, J-PARC is a unique facility to investigate the transition region from the hadron degrees of freedom to the quark-gluon degrees of freedom. It is suitable for finding mechanisms of the olor transparency. Such color-transparency studies are also valuable for clarifying the factorization of hadron production processes in extracting the GPDs from actual measurements. These studies will lead to the understanding of basic high-energy hadron interactions in nuclear medium and to clarifications on the origins of hadron spins, masses, and internal pressure mechanisms.

Analysis of coupled-channel potentials with quark and hadron degrees of freedom

The quark-antiquark potentials are known to be confining in the absence of the q̅q pair creation. On the other hand, the inter-hadron potentials vanish at large distance, because the interaction range is limited by the inverse pion mass. When the q̅q pair creation and annihilation are switched on, the channel coupling occurs between the quark and hadron degrees of freedom, modifying the behavior of potentials. In this work, we investigate the properties of the effective potentials obtained by eliminating one of the channels. We show that the coupling to the eliminated channel induces a non-local and energy dependent effective potential, irrespective of the properties of the transition potential. In addition, when the hadron channel having continuous scattering eigenstates is eliminated, the resulting inter-quark potential contains an imaginary part above the threshold to describe the decay effect into the meson pair.

Mystery of Bloom-Gilman duality: A light-front holographic QCD perspective

Light-front wave functions motivated by holographic constructions are used to study Bloom-Gilman duality, a feature of deep inelastic scattering. Separate expressions for structure functions in terms of quark and hadronic degrees of freedom (involving transition form factors) are presented, with an ultimate goal of obtaining a relationship between the two expressions. A specific two-parton model is defined and resonance transition form factors are computed using previously derived light-front wave functions. A new form of global duality (integral over all values of $x$ between 0 and 1) is derived from the valence quark-number sum rule. Using a complete set of hadronic states is necessary for this new global duality to be achieved, and the previous original work does not provide such a set. This feature is remedied by amending the model to include a longitudinal confining potential, and the resulting complete set is sufficient to carry out the study of Bloom-Gilman duality. Specific expressions for transition form factors are obtained and all are shown to fall as $1/{Q}^{2}$, at asymptotically large values. This is because the Feynman mechanism dominates the asymptotic behavior of the model. These transition form factors are used to assess the validity of the global and local duality sum rules, with the result that both are not satisfied within the given model. Evaluations of the hadronic expression for $q(x,{Q}^{2})$ provide more details about this lack. This result is not a failure of the current model because it shows that the observed validity of both global and local forms of duality for deep inelastic scattering must be related to a feature of QCD that is deeper than completeness. Our simple present model suggests a prediction that Bloom-Gilman duality would not be observed if deep inelastic scattering experiments were to be made on the pion. The underlying origin of the duality phenomenon in deep inelastic scattering is deeply buried within the confinement aspects of QCD, and its origin remains a mystery.

Hybrid Quark–Hadron Equation of State for Multi-messenger Astronomy

We present the recent progress of the hybrid quark-meson-nucleon model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. The obtained equation of state is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. The mass-radius relations and tidal deformabilities for compact stars are calculated and compared with the latest astrophysical observations. The phase diagram of the isospin-symmetirc matter is studied as well in terms of the higher-order cumulants of the net-baryon number.

Toward a unified equation of state for multi-messenger astronomy

Aims. We aim to present a first step in developing a benchmark equation-of-state (EoS) model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. Methods. A Lagrangian approach to the thermodynamic potential of quark-meson-nucleon matter was used. In this approach, dynamical chiral-symmetry breaking is described by the scalar mean-field dynamics coupled to quarks and nucleons and their chiral partners, whereby its restoration occurs in the hadronic phase by parity doubling, as well as in the quark phase. Quark confinement was achieved by an auxiliary scalar field that parametrizes a dynamical infrared cut-off in the quark sector, serving as an ultraviolet cut-off for the nucleonic phase space. The gap equations were solved for the isospin-symmetric case, as well as for neutron star (NS) conditions. We also calculated the mass-radius (MR) relation of NSs and their tidal deformability (TD) parameter. Results. The obtained EoS is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. For isospin-asymmetric matter, a sequential occurrence of light quark flavors is obtained, allowing for a mixed phase of chirally-symmetric nucleonic matter with deconfined down quarks. The MR relations and TDs for compact stars fulfill the constraints from the latest astrophysical observations for PSR J0740+6620, PSR J0030+0451, and the NS merger GW170817, whereby the tension between the maximum mass and compactness constraints rather uniquely fixes the model parameters. The model predicts the existence of stars with a core of chirally restored but purely hadronic (confined) matter for masses beyond 1.8 M⊙. Stars with pure-quark matter cores are found to be unstable against the gravitational collapse. This instability is shifted to even higher densities if repulsive interactions between quarks are included.

Hidden and Open Heavy-Flavor Hadronic States

We discuss the stability of hidden and open heavy-flavor hadronic states made of either two or three mesons. References are made in passing to studies regarding two and three-body systems containing baryons. We perform a comparative study analyzing the results in terms of quark and hadron degrees of freedom. Compact and molecular states are found to exist in very specific situations. We estimate the decay width for the different scenarios: weak decays for bound states by the strong interaction, and strong decays for hadronic resonances above a decay threshold. The experimental observation of narrow hadrons lying well above their lowest decay threshold is theoretically justified.

Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories

The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU(2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantumly simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of $d+1$-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss's law built in to them. LSH operators are then factored into products of "normalized" ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to $d=3$. The LSH formalism makes little use of structures specific to SU(2) and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).

Bound state properties from the functional renormalization group

We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a quantitative manner. This allows us to estimate the validity range of low energy effective models. We also present first results for pole masses and decay widths. Next steps involving real-time formulations of the functional renormalisation group are discussed.

Constituent counting rule and the production of at high energies * * Supported by the National Natural Sciences Foundations of China (11475192, 11475181, 11521505, 11565007, 11635009), the Sino-German CRC 110 "Symmetries and the Emergence of Structure in QCD" project by NSFC (11621131001), the Key Research Program of Frontier Sciences, CAS, (Y7292610K1) and the IHEP Innovation Fund (Y4545190Y2)

The constituent counting rule, determining the scaling behavior of the transition amplitudes in an exclusive process at high energies, is applied to probe the internal structure of the newly observed resonance. Several selected exclusive processes at high energies for the production of are discussed. Results of two structural scenarios for , a hexaquark dominant compact system in the quark degrees of freedom, and a three-body bound state in the hadronic degrees of freedom, are analyzed and compared. A rather remarkable difference between the results of these two scenarios for the mentioned processes are addressed.

Non-perturbative Approach to Equation of State and Collective Modes of the QGP

We discuss a non-perturbative T-matrix approach to investigate the microscopic structure of the quark-gluon plasma (QGP). Utilizing an effective Hamiltonian which includes both light- and heavy-parton degrees of freedoms. The basic two-body interaction includes color-Coulomb and confining contributions in all available color channels, and is constrained by lattice-QCD data for the heavy-quark free energy. The in-medium T-matrices and parton spectral functions are computed selfconsistently with full account of off-shell properties encoded in large scattering widths. We apply the T-matrices to calculate the equation of state (EoS) for the QGP, including a ladder resummation of the Luttinger-Ward functional using a matrix-log technique to account for the dynamical formation of bound states. It turns out that the latter become the dominant degrees of freedom in the EoS at low QGP temperatures indicating a transition from parton to hadron degrees of freedom. The calculated spectral properties of one- and two-body states confirm this picture, where large parton scattering rates dissolve the parton quasiparticle structures while broad resonances start to form as the pseudocritical temperature is approached from above. Further calculations of transport coefficients reveal a small viscosity and heavy-quark diffusion coefficient.

Tests of Lorentz andCPTsymmetry with hadrons and nuclei

We explore the breaking of Lorentz and CPT invariance in strong interactions at low energy in the framework of chiral perturbation theory. Starting from the set of Lorentz-violating operators of mass-dimension five with quark and gluon fields, we construct the effective chiral Lagrangian with hadronic and electromagnetic interactions induced by these operators. We develop the power-counting scheme and discuss loop diagrams and the one-pion-exchange nucleon-nucleon potential. The effective chiral Lagrangian is the basis for calculations of low-energy observables with hadronic degrees of freedom. As examples, we consider clock-comparison experiments with nuclei and spin-precession experiments with nucleons in storage rings. We derive strict limits on the dimension-five tensors that quantify Lorentz and CPT violation.

Conserved charge fluctuations in a chiral hadronic model including hadrons and quarks

In this work the baryon number and strange susceptibility of second and fourth order are presented. The results at zero baryon-chemical potential are obtained using a well tested chiral effective model including all known hadron degrees of freedom and additionally implementing quarks and gluons in a PNJL-like approach. Quark and baryon number susceptibilities are sensitive to the fundamental degrees of freedom in the model and signal the shift from massive hadrons to light quarks at the deconfinement transition by a sharp rise at the critical temperature. Furthermore, all susceptibilities are found to be largely suppressed by repulsive vector field interactions of the particles. In the hadronic sector vector repulsion of baryon resonances restrains fluctuations to a large amount and in the quark sector above Tc even small vector field interactions of quarks quench all fluctuations unreasonably strong. For this reason, vector field interactions for quarks have to vanish in the deconfinement limit.

PHOTOPRODUCTION OF PHI MESON NEAR THE THRESHOLD

Photoproduction of ϕ, γp → ϕ + p, is revisited in a model with Pomeron and hadron degrees of freedom. The scattering equation is written such that the final state interaction is included at the one-loop level of hadrons. We find a parameter set to reproduce the bump-like structure near the threshold in a way consistent with other meson production data.

Solid quantization for nonpoint particles

In quantum field theory, elemental particles are assumed to be point particles. As a result, the loop integrals are divergent in many cases. Regularization and renormalization are necessary to get the physical finite results from the infinite, divergent loop integrations. We propose new quantization conditions for nonpoint particles. With this solid quantization, divergence could be treated systematically. This method is useful for effective field theory, which is on hadron degrees of freedom. The elemental particles could also be nonpoint ones. They can be studied in this approach as well.

Nuclear and partonic dynamics in the EMC effect

It has been recently confirmed that the magnitude of the EMC effect measured in electron deep inelastic scattering is linearly related to the Short Range Correlation scaling factor obtained from electron inclusive scattering. By using a $x$-rescaling approach we are able to understand the interplay between the quark-gluon and hadronic degrees of freedom in the discussion of the EMC effect.

Chiral hadronic mean field model including quark degrees of freedom

In an approach inspired by Polyakov loop extended Nambu–Jona-Lasinio models, we present a nonlinear hadronic SU(3) σ–ω mean field model augmented by quark degrees of freedom. By introducing the effective Polyakov loop related scalar field Φ and an associated effective potential, the model includes all known hadronic degrees of freedom at low temperatures and densities as well as a quark phase at high temperatures and densities. Hadrons in the model exhibit a finite volume in order to suppress baryons at high T and μ. This ensures that the right asymptotic degrees of freedom are attained for the description of strongly interacting matter and allows one to study the QCD phase diagram in a wide range of temperatures and chemical potentials. Therefore, with this model it is possible to study the phase transition of chiral restoration and deconfinement. In this paper, the impact of quarks on the resulting phase diagram is shown. The results from the chiral model are compared with recent data from lattice QCD.

Dynamics of hot and dense nuclear and partonic matter

The dynamics of hot and dense nuclear matter is discussed from the microscopic transport point of view. The basic concepts of the Hadron-String-Dynamical transport model (HSD)—derived from Kadanoff-Baym equations in phase phase—are presented as well as “highlights” of HSD results for different observables in heavy-ion collisions from 100 A MeV (SIS) to 21 A TeV(RHIC) energies. Furthermore, a novel extension of the HSD model for the description of the partonic phase—the Parton—Hadron-String-Dynamics (PHSD) approach—is introduced. PHSD includes a nontrivial partonic equation of state—in line with lattice QCD—as well as covariant transition rates from partonic to hadronic degrees of freedom. The sensitivity of hadronic observables to the partonic phase is demonstrated for relativistic heavy-ion collisions from the FAIR/NICA up to the RHIC energy regime.

Equation of state in the PNJL model with the entanglement interaction

The equation of state and the phase diagram in two-flavor quantum chromodynamics (QCD) are investigated by the Polyakov-loop extended Nambu–Jona-Lasinio (PNJL) model with an entanglement vertex between the chiral condensate and the Polyakov loop. The entanglement-PNJL (EPNJL) model reproduces lattice QCD (LQCD) data at μ ⩾ 0 better than the PNJL model. Hadronic degrees of freedom are taken into account by the free-hadron-gas approximation with the volume-exclusion effect due to the hadron generation. The hadron degrees of freedom improve agreement of the EPNJL model with LQCD data particularly at low temperature. The quarkyonic phase survives, even if the correlation between the chiral condensate and the Polyakov loop is strong and hadron degrees of freedom are taken into account. However, the location of the quarkyonic phase is sensitive to the strength of the volume exclusion.