The thermodynamic quantities of the ideal gas of hadrons and the $(2+1)$--flavor lattice QCD scaled by the effective degeneracy factors of the corresponding models are compared. We have found that in terms of the scaled variables the quark-hadron duality of the lattice QCD and the hadron resonance gas (HRG) model disappears. However, we have unexpectedly revealed that the scaled variables lead to the quark-hadron duality of the lattice QCD and the quantum ideal gas of kaons and antikaons, namely, the ideal gas of those hadrons that contain all the three quarks $u,d,s$ and their antiquarks. Satisfactory agreement between the scaled results of the kaon ideal gas and the lattice QCD data is achieved at large values of the volume in the entire temperature range. In the ideal gas of kaons there is no any phase transition. Nevertheless, in our calculations the scaled thermodynamic quantities of the ideal gas and the lattice QCD follow the same qualitative behavior and are consistent with each other especially at high temperatures in the perturbative region.
The shear ($η$) and bulk ($ζ$) viscosities are calculated in a quasiparticle relaxation time approximation for a hadron matter described within the relativistic mean-field based model with scaled hadron masses and couplings. Comparison with results of other models is presented. We demonstrate that a small value of the shear viscosity to entropy density ratio required for explaining a large elliptic flow observed at RHIC may be reached in the hadron phase. Large values of the bulk viscosity are noted in case of the baryon enriched matter.
While quark-hadron duality is well-established experimentally, the current theoretical understanding of this important phenomenon is quite limited. To expose the essential features of the dynamics behind duality, we use a simple model in which the hadronic spectrum is dominated by narrow resonances made of valence quarks. We qualitatively reproduce the features of duality as seen in electron scattering data within our model. We show that in order to observe duality, it is essential to use the appropriate scaling variable and scaling function. In addition to its great intrinsic interest in conn…
We apply a model for the study of quark-hadron duality in inclusive electron scattering to the calculation of spin observables. The model is based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively reproduce the features of quark-hadron duality for all potentials considered, and discuss the onset of scaling and duality for the responses, spin structure functions, and polarization asymmetries. Duality may be applied to gain access to kinematic regions which are hard to access in deep inelastic scattering, name…
Quark-hadron duality is an interesting and potentially very useful phenomenon, as it relates the properly averaged hadronic data to a perturbative QCD result in some kinematic regions. While duality is well established experimentally, our current theoretical understanding is still incomplete. We employ a simple model to qualitatively reproduce all the features of Bloom-Gilman duality as seen in electron scattering. In particular, we address the role of relativity, give an explicit analytic proof of the equality of the hadronic and partonic scaling curves, and show how the transition from coher…
We show how quark-hadron duality can emerge for valence spin averaged structure functions, and for the non-forward distributions of Deeply Virtual Compton Scattering. Novel factorisations of the non-forward amplitudes are proposed. Some implications for large angle scattering and deviations from the quark counting rules are illustrated.
We present a phenomenological model of the quark-hadron transition in neutrino-nucleon scattering. Using recently extracted weak nucleon transition form factors, we investigate the extent to which local and global quark-hadron duality is applicable in the neutrino F_1, F_2 and F_3 structure functions, and contrast this with duality in electron scattering. Our findings suggest that duality works relatively well for neutrino-nucleon scattering for the F_2 and F_3 structure functions, but not as well for F_1. We also calculate the quasielastic, resonance and deep inelastic contributions to the Ad…
The duality between partonic and hadronic descriptions of physical phenomena is one of the most remarkable features of strong interaction physics. A classic example of this is in electron-nucleon scattering, in which low-energy cross sections, when averaged over appropriate energy intervals, are found to exhibit the scaling behavior expected from perturbative QCD. We present a comprehensive review of data on structure functions in the resonance region, from which the global and local aspects of duality are quantified, including its flavor, spin and nuclear medium dependence. To interpret the e…
The changes of hadron properties in dense and/or hot matter are discussed in terms of effective chiral Lagrangians with the parameters of the theory scaled in a simple way. The phenomenologically successful Walecka model is identified as a mean field chiral Lagrangian with the scaled parameters. Kaon condensation and chiral restoration transitions can be described within the same mean field framework.
The quark-hadron duality in CC and NC neutrino interactions is discussed under assumptions that single pion production is described accurately by the Rein-Sehgal model and that it allows reconstruction of the inclusive cross section in the resonance region. The duality is measured by means of integrals of structure functions in the Nachtmann variable for $Q^2<3$ GeV$^2$. The results depend on the precision with which contributions from single pion production channels in the overall cross sections are known. Several approaches to evaluate them are compared. The duality is predicted to be seen f…
We examine the origin of Bloom-Gilman duality and the relationship between resonances and scaling in deep-inelastic scattering. A simple quantum mechanical model is used to illustrate the essential features of Bloom-Gilman duality at low momentum transfer. As an application of local duality, we discuss model-independent relations between structure functions at x ~ 1 and elastic electromagnetic form factors.
The proposed earlier relativistic mean-field model with hadron masses and coupling constants depending on the $σ$-meson field is generalized to finite temperatures. Within this approach we simulate the in-medium behavior of the hadron masses motivated by the Brown-Rho scaling. The high-lying baryon resonances and boson excitations as well as excitations of the $σ$, $ω$ and $ρ$ fields interacting via mean fields are incorporated into this scheme. Thermodynamic properties of hot and dense hadronic matter are elaborated with the constructed equation of state. Even at zero baryon density, effectiv…
We review how Quark-Hadron Duality (QHD) for (u,d) flavors at high energies and in the scaling regime suggests a radial and angular behaviour of mesonic and baryonic resonance masses of the Regge form $M^2_{nJ} = μ^2 n + β^2 J + M_0^2 $. The radial mass dependence is asymptotically consistent with a common two-body dynamics for mesons and baryons in terms of the quark-antiquark ($q \bar q)$ and quark-diquark ($qD$) degrees of freedom, respectively. This formula is validated phenomenologically within an uncertainty determined by half the width of the resonances, $ΔM_{nJ}^2 \sim Γ_{nJ} M_{nJ}$. …
A novel procedure for extracting hadron characteristics from QCD sum rules, based on effective continuum thresholds (necessary for the implementation of quark-hadron duality) which may depend on the involved momenta and on the Borel parameter(s), enables us to quantify the uncertainties induced by the quark-hadron duality approximation and to achieve a significantly higher accuracy of our predictions for the properties of hadronic bound states.
Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and $Δ$ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the $Δ$…
Here we continue to elaborate properties of the relativistic mean-field based model (SHMC) proposed in ref. [6] where hadron masses and coupling constants depend on the $σ$-meson field. The validity of approximations used in [6] is discussed. We additionally incorporate contribution of meson excitations to the equations of motion. We also estimate the effects of the particle width. It is demonstrated that the inclusion of the baryon-baryon hole and baryon-antibaryon loop terms, if performed perturbatively, destroys the consistency of the model.
We employ a novel new approach to study local quark-hadron duality using "truncated" moments, or integrals of structure functions over restricted regions of x, to determine the degree to which individual resonance regions are dominated by leading twist. Because truncated moments obey the same Q^2 evolution equations as the leading twist parton distributions, this approach makes possible for the first time a description of resonance region data and the phenomenon of quark-hadron duality directly from QCD.
At low temperatures we expect that all QCD observables are defined in terms of hadrons. This includes the partition function as well as the Polyakov loop in all representations. We analyze the physics underlying a microscopic derivation of the hadron resonance gas.
Quark-meson duality for two-point functions of vector and axial-vector QCD currents is investigated in the large-Nc approximation. We find that the joint constraints of duality and chiral symmetry imply degeneracy of excited vector and axial-vector mesons in the large-Nc limit. We compare model-independent constraints with expectations based on the Veneziano-Lovelace-Shapiro string model. Several models of duality are constructed, and phenomenological implications are discussed.
We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex $q^2$ plane. Starting from the dispersive representation for the associated polarization, the analytic continuation of the operator product expansion from the Euclidean to the Minkowski region is performed by means of a generalized Borel-Laplace transform, borrowing techniques from hyperasymptotics. We establish a connection between singularities in the Borel plane and quark-hadron duality violating contributions. Starting with…
In this paper, we have discussed the transverse momentum dependence of elliptic flow measured in relativistic heavy-ion collisions. The transverse momentum dependence of the number of constituent quarks ($n_{q}$) scaled $v_{2}$ is obtained for all the measured identified hadrons. The $n_{q}$ scaled $ϕ$ $v_{2}$ is found to be similar to $n_{q}$ scaled $Ω$ $v_{2}$. This indicates that both $ϕ$ and $Ω$ are produced through quark recombination at RHIC energies. We also find $n_{q}$ scaled proton $v_{2}$ ($v_{2}$ of light quarks) is higher than $n_{q}$ scaled $ϕ$ and $Ω$ $v_{2}$ ($v_{2}$ of strange…
We apply a recently developed technique to extract for the first time the neutron F_2^n structure function from inclusive proton and deuteron data in the nucleon resonance region, and test the validity of quark-hadron duality in the neutron. We establish the accuracy of duality in the low-lying neutron resonance regions over a range of Q^2, and compare with the corresponding results on the proton and with theoretical expectations. The confirmation of duality in both the neutron and proton opens the possibility of using resonance region data to constrain parton distributions at large x.
We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $σ$ field, studied previously to incorporate $Δ(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $Δ$s with meson fields. Conditions for the appearance of $Δ$s are studied. We demonstrate that with inclusion of the $Δ$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars…
Recent data on polarized proton knockout reactions off He-4 nuclei suggest a small but nonzero modification of proton electromagnetic form factors in medium. Using model independent relations derived on the basis of quark-hadron duality, we relate the medium modification of the form factors to the modification at large x of the deep-inelastic structure function of a bound proton. This places strong constraints on models of the nuclear EMC effect which assume a large deformation of the intrinsic structure of the nucleon in medium.
Combining data on unpolarized and polarized inclusive proton structure functions, we perform the first detailed study of quark-hadron duality in individual helicity-1/2 and 3/2 virtual photoproduction cross sections. We find that duality is realized more clearly in the helicity-1/2 channel, with duality violating corrections < 10% over the entire nucleon resonance region, while larger, < 20% corrections are found in the helicity-3/2 sector. The results are in general agreement with quark model expectations, and suggest that data above the Delta resonance region may be used to constrain both sp…
We examine the interference γZ box corrections to parity-violating elastic electron--proton scattering in the light of the recent observation of quark-hadron duality in parity-violating deep-inelastic scattering from the deuteron, and the approximate isospin independence of duality in the electromagnetic nucleon structure functions down to Q^2 \approx 1 GeV^2. Assuming that a similar behavior also holds for the γZ proton structure functions, we find that duality constrains the γZ box correction to the proton's weak charge to be \Re e\, \square_{γZ}^V = (5.4 \pm 0.4) \times 10^{-3} at the kinem…
Using data from the recent BONuS experiment at Jefferson Lab, which utilized a novel spectator tagging technique to extract the inclusive electron-free neutron scattering cross section, we obtain the first direct observation of quark-hadron duality in the neutron F_2 structure function. The data are used to reconstruct the lowest few (N=2, 4 and 6) moments of F_2 in the three prominent nucleon resonance regions, as well as the moments integrated over the entire resonance region. Comparison with moments computed from global parametrizations of parton distribution functions suggest that quark--h…
We identify conditions under which a summation over nucleon resonances can yield, via quark-hadron duality, parton model results for electromagnetic and neutrino structure functions at large x. While a summation over the lowest even and odd parity multiplets is sufficient to achieve duality in the symmetric quark model, a suppression of transitions to specific final states is required for more realistic cases incorporating SU(6) breaking. We outline several scenarios consistent with duality, discuss their implications for the high Q^2 behavior of transition form factors, and illustrate how the…
Within the relativistic mean-field framework with hadron masses and coupling constants dependent on the mean scalar field we study properties of nuclear matter at finite temperatures, baryon densities and isospin asymmetries relevant for heavy-ion collisions at laboratory energies below 2$A$ GeV. Previously constructed (KVORcut-based and MKVOR-based) models for the description of the cold hadron matter, which differ mainly by the density dependence of the nucleon effective mass and symmetry energy, are extended for finite temperatures. The baryon equation of state, which includes nucleons and …
In this work we discuss a modified version of Excluded Volume Hadron Resonance Gas model and also study the effect of Lorentz contraction of the excluded volume on scaled pressure and susceptibilities of conserved charges. We find that the Lorentz contraction, coupled with the variety of excluded volume parameters reproduce the lattice QCD data quite satisfactorily.
Analyzing the single inclusive annihilation spectrum of charged hadrons in $e^+e^-$ collisions, I confront the hadronization hypothesis of local parton-hadron duality with a systematic resummation of the dependence on the small energy fraction. This resummation is based on the reciprocity between time-like and space-like splitting processes in $4-2ε$-dimensions, which I extend to resum all the soft terms of the cross-section for inclusive jet production. Under the local-parton-hadron duality hypothesis, the resulting distribution of jets essentially determines the spectrum of hadrons as the je…
Modifying the standard approaches to nonperturbative QCD based on Borel-transformed dispersive sum rules by allowing the effective continuum thresholds required for the implementation of quark-hadron duality to depend on the Borel parameters and on any relevant momentum promises to provide higher accuracy and reliable error estimates for the extracted predictions of hadron characteristics. A careful analysis reveals that the exact effective continuum thresholds do indeed exhibit dependence on the Borel parameter (and on external momenta) and that they are not universal but vary with the correl…
We investigate implications of quark-hadron duality for hybrid mesons in the large-Nc limit. A simple formalism is developed which implements duality for QCD two-point functions of currents of quark bilinears, with any number of gluons. We argue that the large-Nc meson masses share a common parameter, which is related to the QCD string tension. This parameter is fixed from correlators of conserved vector and axial-vector currents, and using lattice QCD determinations of the string tension. Our results predict towers of hybrid mesons which, within expected 1/Nc corrections, naturally accommodat…
A phenomenological study of quark--hadron duality in electron and neutrino scattering on nuclei is performed. We compute the structure functions $F_2$ and $xF_3$ in the resonance region within a framework that includes the Dortmund-group model for the production of the {f}{i}rst four lowest-lying baryonic resonances and a relativistic mean-field model for nuclei. We consider four-momentum transfers between 0.2 and 2.5 GeV$^2$. The results indicate that nuclear effects play a different role in the resonance and DIS region. We find that global but not local duality works well. In the studied ran…
The origin of quark-hadron Duality Violations (DVs) can be related to the sigularities of the Laplace transform of the spectral function. With the help of rather generic properties of the large-$N_c$ approximation and a generalized form for the radial trajectories found in Regge Theory, we may locate these singularities in the complex plane and obtain an expression for the DVs which turns out to agree with general expectations. Using the two-point vector correlator as a test laboratory, we show how the usual dispersion relation may give rise to perturbation theory, the power corrections from t…
A dynamical model of electroweak pion production reactions in the Delta(1232) region has been extended to include the neutral current contributions for examining the local Quark-Hadron Duality in neutrino-induced reactions and for investigating how the axial N-Delta form factor can be determined by the parity violating asymmetry of N(\vec{e},e') reactions. We first show that the recent data of (e,e') structure functions F_1 and F_2, which exhibit the Quark-Hadron Duality, are in good agreement with our predictions. For possible future experimental tests, we then predict that the structure func…
Particle seismology: mechanical and gravitational properties from parton-hadron duality
Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional（原子、分子和核物理系及卡洛斯一世理论与计算物理研究所）；The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院H.涅沃德尼察斯基核物理研究所）
We show how deviations from the dimensional scaling laws for exclusive processes may be related to a breakdown in the locality of quark-hadron duality. The essential principles are illustrated in a pedagogic model of a composite system with two spinless charged constituents, for which a dual picture for the low-energy resonance phenomena and high-energy scaling behavior can be established. We introduce the concept of "restricted locality" of quark-hadron duality and show how this results in deviations from the pQCD quark counting rules above the resonance region. In particular it can be a poss…
We explore the relationship between exclusive and inclusive electromagnetic scattering from the pion, focusing on the transition region at intermediate Q^2. Combining Drell-Yan data on the leading twist quark distribution in the pion with a model for the resonance region at large x, we calculate QCD moments of the pion structure function over a range of Q^2, and quantify the role of higher twist corrections. Using a parameterization of the pion elastic form factor and phenomenological models for the pi -> rho transition form factor, we further test the extent to which local duality may be vali…
The equation of state of cold baryonic matter is studied within a relativistic mean-field model with hadron masses and coupling constants depending on a scalar field. We demonstrate that if the effective nucleon mass stops to decrease with a density increase at densities $n>n_*>n_0$, where $n_0$ is the nuclear saturation density, the equation of state stiffens for these densities and the limiting neutron star mass increases. The stabilization of the nucleon mass can be realised if in the equation of motion for the scalar mean-field there appear a term sharply varying in a narrow vicinity of th…
When baryon-quark continuity is formulated in terms of a topology change without invoking "explicit " QCD degrees of freedom at a density higher than twice the nuclear matter density $n_0$ the core of massive compact stars can be described in terms of fractionally charged particles, behaving neither like pure baryons nor deconfined quarks. Hidden symmetries, both local gauge and pseudo-conformal (or broken scale), lead to the pseudo-conformal (PC) sound velocity $v_{pcs}^2/c^2\approx 1/3$ at $\gsim 3n_0$ in compact stars. We argue these symmetries are "emergent" from strong nuclear correlation…
We discuss the electromagnetic form factors, axial form factors, and structure functions of a bound nucleon in the quark-meson coupling (QMC) model. Free space nucleon form factors are calculated using the improved cloudy bag model (ICBM). After describing finite nuclei and nuclear matter in the quark-based QMC model, we compute the in-medium modification of the bound nucleon form factors in the same framework. Finally, limits on the medium modification of the bound nucleon $F_2$ structure function are obtained using the calculated in-medium electromagnetic form factors and local quark-hadron …
In this paper, we investigate deep inelastic and elastic scattering on a polarized spin-1/2 hadron using gauge/string duality. This spin-1/2 hadron corresponds to a supergravity mode of the dilatino. The polarized deep inelastic structure functions are computed in supergravity approximation at large t' Hooft coupling $λ$ and finite $x$ with $λ^{-1/2}\ll x<1$. Furthermore, we discuss the moments of all structure functions, and propose an interesting sum rule $\int_{0}^{1} \textrm{d}x g_2(x, q^2) =0$ for $g_2$ structure function which is known as the Burkhardt-Cottingham sum rule in QCD. In the …
An equation of state of cold nuclear matter with an arbitrary isotopic composition is studied within a relativistic mean-field approach with hadron masses and coupling constants depending self-consistently on the scalar mean-field. All hadron masses decrease universally with the scalar field growth, whereas meson-nucleon coupling constants can vary differently. More specifically we focus on two modifications of the KVOR model studied previously. One extension of the model (KVORcut) demonstrates that the equation of state stiffens if the increase of the scalar-field magnitude with the density i…
We introduce a generalization of 1+1 dimensional large Nc QCD, which we refer to as ``reduced'' QCD, or rQCD. In this model gluons and quark momenta live in 1+1 dimensions only, but the quark spin and all other particles (leptons, and the photon) live in the full 1+3 dimensions. The bound states of quarks and antiquarks are identical to those originally described by 't Hooft (except that there are new transversely polarized states previously excluded), so the model is exactly soluable. However, significant differences arise when the model is applied to electromagnetic interactions. After revie…
Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the b…
Light front wave functions motivated by holographic constructions are used to study Bloom-Gilman duality of deep inelastic scattering. Separate expressions for structure functions in terms of quark and hadronic degrees of freedom are presented, with a goal of relating the two expressions. A 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 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.…
We study exclusive scattering of `hadrons' at high energy and fixed angle in (nonconformal) noncommutative gauge theories. Via gauge-string duality, we show that the noncommutativity renders the scattering soft, leading to exponential suppression. The result fits with the picture that, in noncommutative gauge theory, fundamental partons consist of extremely soft constituents and `hadrons' are made out of open Wilson lines.
Charged particle multiplicity fluctuations in pp collisions at $\sqrt s$ = 13 TeV have been studied by the method of scaled factorial moment for the minimum bias events generated by Ultra Relativistic Quantum Molecular Dynamics (UrQMD) model in the pseudo-rapidity (η), azimuthal angle ($ϕ$) and two dimensional anisotropic ($η$-$ϕ$) phase space. Strong intermittent type of fluctuations have been observed for the UrQMD simulated data. Systematic studies of intermittent fluctuations in terms of scaled factorial moments was utilized to extract the anomalous fractal dimension in the pseudo-rapidity…
The charged hadron multiplicity fluctuations are considered in the canonical ensemble. The microscopic correlator method is extended to include three conserved charges: baryon number, electric charge and strangeness. The analytical formulae are presented that allow to include resonance decay contributions to correlations and fluctuations. We make the predictions for the scaled variances of negative, positive and all charged hadrons in the most central Pb+Pb (Au+Au) collisions for different collision energies from SIS and AGS to SPS and RHIC.
