Quark-parton Model Research Articles

Bogolyubov–Medvedev–Polivanov S-matrix Method and Its Application to Multi-Particle Systems and in High-Energy Physics

The connection between field-theoretic equations based on the Bogolyubov–Medvedev–Polivanov and Lehman–Szymanczyk–Zimmerman $$S$$ -matrix methods is discussed [1]. These equations are used to derive three-dimensional time-ordered relativistic Lippmann–Schwinger-type equations for hadronic collision amplitudes with and without quark degrees of freedom [2, 3]. Quark degrees of freedom are considered following the Huang–Weldon approach [4], in which hadrons are considered as bound states of quarks. Numerical solutions of the obtained equations made it possible to describe well the experimental phase shifts of elastic $$\pi N$$ and $$NN$$ scattering in the low-energy region. Using a separable approximation, a quark–parton model for inclusive production of particles with a large transverse momentum was reproduced [6]. This made it possible to describe the experimental data of inclusive production of a $$\rho $$ meson with a large transverse momentum (≤1.5 GeV/c) in a proton–proton collision in the energy region 2.9 ≤ $$\sqrt s $$ ≤ 64 GeV [5].

Neutral-current weak interactions at an EIC

A simulation study of measurements of neutral current structure functions of the nucleon at the future high-energy and high-luminosity polarized electron-ion collider (EIC) is presented. A new series of $\gamma-Z$ interference structure functions, $F_1^{\gamma Z}$, $F_3^{\gamma Z}$, $g_1^{\gamma Z}$, $g_5^{\gamma Z}$ become accessible via parity-violating asymmetries in polarized electron-nucleon deep inelastic scattering (DIS). Within the context of the quark-parton model, they provide a unique and, in some cases, yet-unmeasured combination of unpolarized and polarized parton distribution functions. The uncertainty projections for these structure functions using electron-proton collisions are considered for various EIC beam energy configurations. Also presented are uncertainty projections for measurements of the weak mixing angle $\sin^2 \theta_W$ using electron-deuteron collisions which cover a much higher $Q^2$ than that is accessible in fixed target measurements. QED and QCD radiative corrections and effects of detector smearing are included with the calculations.

Spin Physics Experiments at NICA-SPD

Nuclotron based Ion Collider fAcility (NICA) is a flagship project of the Joint Institute for Nuclear Research which is expected to be operational by 2021. Main tasks of “NICA Facility” are study of hot and dense baryonic matter, investigation the polarisation phenomena and the nucleon spin structure. The material presented here based on the Letter of Intent (LoI) dedicated to nucleon spin structure studies at NICA. Measurements of asymmetries in the lepton pair (Drell-Yan) production in collisions of non-polarised, longitudinally and transversely polarised proton and deuteron beams to be performed using the specialized Spin Physics Detector (SPD). These measurements can provide an access to all leading twist collinear and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs) in nucleons. The measurements of asymmetries in production of J/ψ and direct photons, which supply complimentary information on the nucleon structure, will be performed simultaneously. The set of these measurements permits to tests the quark-parton model of nucleons at the QCD twist-2 level with minimal systematic errors.

Baryon properties from light-front holographic QCD

We investigate the properties of octet and decuplet baryons in a light-front holographic model. By taking into account the effect of nonvanishing quark mass, we obtain the modified light-front wave functions which are applicable at both low and high energy scales. We calculate the spectra, form factors, magnetic moments and electromagnetic radii of octet and decuplet baryons with the results all matching the experiments well. The axial charge, which describes the contribution of quark helicity to the proton spin in the quark-parton model at the high energy scale, is also consistent with the experimental value. Therefore, the light-front holographic method is successful in studying hadronic physics at all energy scales, and the nonzero quark mass is essential to understand the spin structures together with other low energy properties.

A new hadron spectroscopy

QCD-motivated models for hadrons predict an assortment of "exotic" hadrons that have structures that are more complex than the quark-antiquark mesons and three-quark baryons of the original quark-parton model. These include pentaquark baryons, the six-quark H-dibaryon, and tetraquark, hybrid and glueball mesons. Despite extensive experimental searches, no unambiguous candidates for any of these exotic configurations have been identified. On the other hand, a number of meson states, one that seems to be a proton-antiproton bound state, and others that contain either charmed-anticharmed quark pairs or bottom-antibottom quark pairs, have been recently discovered that neither fit into the quark-antiquark meson picture nor match the expected properties of the QCD-inspired exotics. Here I briefly review results from a recent search for the H-dibaryon, and discuss some properties of the newly discovered states --the proton-antiproton state and the so-called XYZ mesons-- and compare them with expectations for conventional quark-antiquark mesons and the predicted QCD-exotic states.

On the role of quark orbital angular momentum in the proton spin

We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark spins and orbital angular momenta, which collectively contribute to the proton spin. The spin structure functions $g_{1}$ and $g_{2}$ corresponding to the many-quark state $J=1/2$ are studied and it is shown they satisfy constraints and relations well compatible with the available experimental data including proton spin content $\Delta\Sigma\lesssim1/3$. The suggested Lorentz invariant 3D approach for calculation of the structure functions is compared with the approach based on the conventional collinear parton model.

Spin Physics Experiments at NICA-SPD with polarized proton and deuteron beams

We propose to perform measurements of asymmetries of the Drell-Yan (DY) pairs production in collisions of non-polarized, longitudinally and transversally polarized protons and deuterons which provide an access to all leading twist collinear and TMD PDFs of quarks and anti-quarks in nucleons. The measurements of asymmetries in production of J/\Psi and direct photons will be performed as well simultaneously with DY using dedicated triggers. The set of these measurements will supply complete information for tests of the quark-parton model of nucleons at the QCD twist-two level with minimal systematic errors.

QCD exotics

QCD-motivated models for hadrons predict an assortment of "exotic" hadrons that have structures that are more complex then the quark-antiquark mesons and three-quark baryons of the original quark-parton model. These include pentaquark baryons, the six-quark H-dibaryon, and tetra-quark, hybrid, and glueball mesons. Despite extensive experimental searches, no unambiguous candidates for any of these exotic configurations have yet to be identified. On the other hand, a number of meson states, one that seems to be a proton-antiproton bound state, and others that contain either charmed-anticharmed quark pairs or bottom-antibottom quark pairs, have been recently discovered that neither fit into the quark-antiquark meson picture nor match the expected properties of the QCD-inspired exotics. Here I briefly review results from a recent search for the H-dibaryon, and discuss some properties of the newly discovered states --the so-called XYZ mesons-- and compare them with expectations for conventional quark-antiquark mesons and the predicted QCD-exotic states.

Proton spin in leading order of the covariant approach

We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark spins and orbital angular momenta, which collectively contribute to the proton spin. The spin structure functions $g_{1}$ and $g_{2}$ corresponding to the many-quark state $J=1/2$ are studied and it is shown they satisfy constraints and relations well compatible with the available experimental data including proton spin content $\Delta\Sigma\lesssim1/3$. The suggested Lorentz invariant 3D approach for calculation of the structure functions is compared with the approach based on the conventional collinear parton model.

New hadron spectroscopies

QCD-motivated models for hadrons predict an assortment of "exotic" hadrons that have structures that are more complex than the quark-antiquark mesons and three-quark baryons of the original quark-parton model. These include pentaquark baryons, the six-quark H-dibaryon, and tetraquark and glueball mesons. Despite extensive experimental searches, no unambiguous candidates for any of these exotic configurations have yet to be identified. On the other hand, a number of meson states, one that seems to be a proton-antiproton bound state, and others that contain either charmed-anticharmed quark pairs or bottom-antibottom quark pairs, have been recently discovered that neither fit into the quark-antiquark meson picture nor match the expected properties of the QCD-inspired exotics. Here I briefly review results from a recent search for the H-dibaryon, and discuss some properties of the newly discovered states –the so-called XYZ mesons– and compare them with expectations for conventional quark-antiquark mesons and the predicted QCD-exotic states.

Semi-inclusive charged-pion electroproduction off protons and deuterons: Cross sections, ratios, and access to the quark-parton model at low energies

A large set of cross sections for semi-inclusive electroproduction of charged pions (π±) from both proton and deuteron targets was measured. The data are in the deep-inelastic scattering region with invariant mass squared W2>4 GeV2 (up to ≈7 GeV2) and range in four-momentum transfer squared 2<Q2<4 (GeV/c)2, and cover a range in the Bjorken scaling variable 0.2<x<0.6. The fractional energy of the pions spans a range 0.3<z<1, with small transverse momenta with respect to the virtual-photon direction, Pt2<0.2 (GeV/c)2. The invariant mass that goes undetected, Mx or W′, is in the nucleon resonance region, W′<2 GeV. The new data conclusively show the onset of quark-hadron duality in this process, and the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark→pion production mechanisms. The x, z, and Pt2 dependences of several ratios (the ratios of favored-unfavored fragmentation functions, charged pion ratios, deuteron-hydrogen and aluminum-deuteron ratios for π+ and π−) have been studied. The ratios are found to be in good agreement with expectations based upon a high-energy quark-parton model description. We find the azimuthal dependences to be small, as compared to exclusive pion electroproduction, and consistent with theoretical expectations based on tree-level factorization in terms of transverse-momentum-dependent parton distribution and fragmentation functions. In the context of a simple model, the initial transverse momenta of d quarks are found to be slightly smaller than for u quarks, while the transverse momentum width of the favored fragmentation function is about the same as for the unfavored one, and both fragmentation widths are larger than the quark widths.19 MoreReceived 7 March 2011DOI:https://doi.org/10.1103/PhysRevC.85.015202©2012 American Physical Society

Drell-Yan Experiment: Studying Anti-Quarks in the Proton

The internal structure of the proton is one of the most vital topic in the present hadron physics. At a high-energy scale the proton reveals its complicated parton structure which is beyond the scope of the Quark Parton Model (QPM), i.e. quarks (q), anti-quarks (q̄) and gluons (g). Gluons and anti-quarks are dynamically created via q → q + g and g → q + q̄, respectively. The dynamics of the proton structure is being investigated in both experiment and theory.The Drell-Yan process in proton+proton collisions is the reaction in which a quark in one proton and an anti-quark in the other proton annihilate into a virtual photon and then create a muon pair: q + q̄ → γ* → μ+ + μ−. This process is suited to study the anti-quarks in the proton, and many experiments measuring the Drell-Yan process have been carried out in the past 20 years. The E906/SeaQuest experiment at Fermi National Accelerator Lab (FNAL) in USA is a Drell-Yan experiment being prepared now to explore a new kinematic region with very high statistics. The main purpose of this experiment is to precisely measure the asymmetry of ū and d̄ distributions in the proton at the xBj range from 0.25 to 0.45.In this paper, the anti-quark flavor asymmetry in the proton and the past Drell-Yan experiments are summarized, and the status of the E906 experiment is reported.

Top quark effects on the virtual photon structure function at ILC

We investigated top quark effects on virtual photon structure functions by pQCD. We include the top quark mass effects on the virtual photon structure function with the quark parton model and with the operator product expansion up to the next-to-leading order in QCD. We also consider the threshold effect on the running coupling constant in the calculation to the effective photon structure function with a matching condition. The numerical calculations are investigated in the kinematical region expected at the future international linear collider.

Spin Structure Functions

Spin-dependent observables have been a powerful tool to probe the internal structure of the nucleon and to understand the dynamics of the strong interaction. Experiments involving spin degrees of freedom have often brought out surprises and puzzles. The so-called "spin crisis" in the 1980s revealed the limitation of naive quark-parton models and led to intensive worldwide efforts, both experimental and theoretical, to understand the nucleon spin structure. With high intensity and high polarization of both the electron beam and targets, Jefferson Lab has the world's highest polarized luminosity and the best figure-of-merit for precision spin structure measurements. It has made a strong impact in this subfield of research. This chapter will highlight Jefferson Lab's unique contributions in the measurements of valence quark spin distributions, in the moments of spin structure functions at low to intermediate Q2, and in the transverse spin structure.

Cross section and polarization of neutrino-produced τ's made simple

Practical formulae are derived for the cross section and polarization vector of the τ lepton produced in deep inelastic neutrino–nucleon scattering in the frame of the simple quark–parton model.

Parton distribution functions and quark orbital motion

Covariant version of the quark-parton model is studied. Dependence of the structure functions and parton distributions on the 3D quark intrinsic motion is discussed. The important role of the quark orbital momentum, which is a particular case of intrinsic motion, appears as a direct consequence of the covariant description. Effect of orbital motion is substantial especially for polarized structure functions. At the same time, the procedure for obtaining the quark momentum distributions of polarized quarks from the combination of polarized and unpolarized structure functions is suggested.

Study of cosmic ray interaction model based on atmospheric muons for the neutrino flux calculation

We have studied the hadronic interaction for the calculation of the atmospheric neutrino flux by summarizing the accurately measured atmospheric muon flux data and comparing with simulations. We find the atmospheric muon and neutrino fluxes respond to errors in the $\ensuremath{\pi}$-production of the hadronic interaction similarly, and compare the atmospheric muon flux calculated using the HKKM04 [M. Honda, T. Kajita, K. Kasahara, and S. Midorikawa, Phys. Rev. D 70, 043008 (2004).] code with experimental measurements. The ${\ensuremath{\mu}}^{+}+{\ensuremath{\mu}}^{\ensuremath{-}}$ data show good agreement in the $1\ensuremath{\sim}30\text{ }\text{ }\mathrm{GeV}/c$ range, but a large disagreement above $30\text{ }\text{ }\mathrm{GeV}/c$. The ${\ensuremath{\mu}}^{+}/{\ensuremath{\mu}}^{\ensuremath{-}}$ ratio shows sizable differences at lower and higher momenta for opposite directions. As the disagreements are considered to be due to assumptions in the hadronic interaction model, we try to improve it phenomenologically based on the quark parton model. The improved interaction model reproduces the observed muon flux data well. The calculation of the atmospheric neutrino flux will be reported in the following paper [M. Honda et al., Phys. Rev. D 75, 043006 (2007).].

One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up toO(ε2)

We present complete analytical ${\mathcal O}(\epsilon^2)$ results on the one-loop amplitudes relevant for the NNLO quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.

Q2Dependence of the Neutron Spin Structure Functiong2nat LowQ2

We present the first measurement of the Q2 dependence of the neutron spin structure function g2(n) at five kinematic points covering 0.57 (GeV/c)2 < or = Q2 < or = 1.34 (GeV/c)2 at x approximately = 0.2. Though the naive quark-parton model predicts g2 = 0, nonzero values occur in more realistic models of the nucleon which include quark-gluon correlations, finite quark masses, or orbital angular momentum. When scattering from a noninteracting quark, g2(n) can be predicted using next-to-leading order fits to world data for g1(n). Deviations from this prediction provide an opportunity to examine QCD dynamics in nucleon structure. Our results show a positive deviation from this prediction at lower Q2, indicating that contributions such as quark-gluon interactions may be important. Precision data obtained for g1(n) are consistent with next-to-leading order fits to world data.

Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region

We report on measurements of the neutron spin asymmetries $A_{1,2}^n$ and polarized structure functions $g_{1,2}^n$ at three kinematics in the deep inelastic region, with $x=0.33$, 0.47 and 0.60 and $Q^2=2.7$, 3.5 and 4.8 (GeV/c)$^2$, respectively. These measurements were performed using a 5.7 GeV longitudinally-polarized electron beam and a polarized $^3$He target. The results for $A_1^n$ and $g_1^n$ at $x=0.33$ are consistent with previous world data and, at the two higher $x$ points, have improved the precision of the world data by about an order of magnitude. The new $A_1^n$ data show a zero crossing around $x=0.47$ and the value at $x=0.60$ is significantly positive. These results agree with a next-to-leading order QCD analysis of previous world data. The trend of data at high $x$ agrees with constituent quark model predictions but disagrees with that from leading-order perturbative QCD (pQCD) assuming hadron helicity conservation. Results for $A_2^n$ and $g_2^n$ have a precision comparable to the best world data in this kinematic region. Combined with previous world data, the moment $d_2^n$ was evaluated and the new result has improved the precision of this quantity by about a factor of two. When combined with the world proton data, polarized quark distribution functions were extracted from the new $g_1^n/F_1^n$ values based on the quark parton model. While results for $\Delta u/u$ agree well with predictions from various models, results for $\Delta d/d$ disagree with the leading-order pQCD prediction when hadron helicity conservation is imposed.