We investigate the structure of constituent quarks and study implications for quark distribution functions of hadrons. Constituent quarks are constructed by dressing bare quarks with Goldstone bosons using the chiral quark model. We calculate resulting corrections to the twist-2 structure functions $f_1(x)$, $g_1(x)$ and $h_1(x)$. The Goldstone boson fluctuations produce a flavor asymmetry of the quark distribution in the nucleon in agreement with experimental data. They also generate significant depolarization effects which reduce the fraction of the nucleon spin carried by quarks. Corrections to the transversity spin structure function $h_1(x)$ differ from those to $g_1(x)$, and in particular we find a large reduction (40%) of the $d$-quark tensor charge, which is consistent with recent lattice calculations. We also study the pion structure function and find the momentum fraction carried by the sea quarks in the pion to be considerably larger than that in the nucleon.
A qualitative QCD analysis and a quantitative model calculation are given to show that the constituent quark model remains a good approximation even with the nucleon spin structure revealed in polarized deep inelastic scattering taking into account.
We define a constituent quark within QCD. It is shown that the spin of such a quark and hence also the spin of the nucleon reduced due to $\bar{q}q$-pairs, in agreement with experiment. A solution to the spin problem is given.
We calculate the differential cross section for semi-inclusive pion production in electron proton reactions using a model where the physical quark fluctuates with some probability to quark plus pion. The kinematic regions for a determination of this `pion cloud' are evaluated.
Pion loop fluctuations of the constituent u and d quarks are shown to give only a minute contribution to the intrinsic charge radius of the neutron, under the assumption that the pion-quark coupling constant has its conventional value, with a cut-off scale of the order of 1.0 GeV. The contribution from the pion loops to the anomalous magnetic moment of the neutron represents a small ($\sim$ 12-14%) increase over of the static quark model value.
Light constituent quark masses and the corresponding dynamical quark masses are determined by data, the quark-level linear sigma model, and infrared QCD. This allows to define effective nonstrange and strange current quark masses, which reproduce the experimental pion and kaon masses very accurately, by simple additivity. In contrast, the usual nonstrange and strange current quarks employed by the Particle Data Group and Chiral Perturbation Theory do not allow a straightforward quantitative explanation of the pion and kaon masses.
The nucleon-nucleon problem is studied as a six-quark system in a nonrelativistic chiral constituent quark model where the Hamiltonian contains a linear confinement and a pseudoscalar meson (Goldstone boson) exchange interaction between the quarks. This hyperfine interaction has a long-range Yukawa-type part, depending on the mass of the exchanged meson and a short-range part, mainly responsible for the good description of the baryon spectra.
The two-pion exchange interaction between constituent quarks is shown to enhance the effect of the the isospin dependent spin-spin component of the one-pion exchange interaction, and to cancel out its tensor component. It therefore provides a partial explanation for the phenomenological observation that the hyperfine interaction between constituent quarks is well described by a flavor dependent spin-spin interaction, which is attractive at short and repulsive at long range. The spin-orbit component of the two-pion exchange interaction is stronger than and has the opposite sign from that associ…
Results for all elastic electroweak nucleon form factors are presented for the chiral constituent quark model based on Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure.
The spin properties and the flavor asymmetric sea of the nucleon can be well explained by assuming that each constituent quark is surrounded with about 30% probability by a quark-antiquark pair coupled to the pion quantum numbers. We show that about one quarter of these quark-antiquark pairs show up as the pion in $\p\to\nπ^+$ and $\p\to\pπ^0$ fluctuation in agreement with the observed value in the ($\e+\p\to\e+$ forward neutron+X) experiment.
We summarize recent results for the spectrum and properties of light pseudoscalar and scalar hadrons in a functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. We focus in particular on the role of pions as virtual constituents in light mesons ('pion cloud effects') as well as their role as constituents of tetraquark bound states. An extension of our framework into the charm quark sector reveals an all-charm tetraquark in the mass region around 5.5 GeV.
The main statement of the nucleon constituent quark model with a fixed number of particles as basic ansatz are considered in a framework of the single-time (quasipotential) approach to the bound state problem. The scaling law breacking for the proton form factor is investigated for Q^2 = 0 -- 2 Gev^2.
In this work, a compilation of effective electromagnetic field couplings to pions and constituent quarks and their effective interactions derived previously, including corrections to the NJL model, is presented. The particular case of a weak external magnetic field along the $\hat{z}$ direction is considered shortly and effective coupling constants are redefined to incorporate the weak-$B_0$ dependence. They correspond to corrections to well known pion-constituent quark couplings and to the NJL and vector NJL effective couplings that break isospin and chiral symmetries.
The charge form factor of the pion is calculated for momentum transfer range of Jefferson Lab experiments. The approach is based on the instant form of the relativistic Hamiltonian dynamics. It is shown that the form-factor dependence on the choice of the model for quark wave function in pion is weak, while the dependence on the constituent--quark mass is rather significant. It is possible to estimate the mass of constituent quark and the sum of anomalous magnetic moments of $u$- and $\bar d$- quarks from the JLab experiments.
Instanton effects can give large contribution to strong interacting processes, especially at the energy scale where perturbative QCD is no longer valid. However instanton contribution to the gluon contribution in constituent quark and nucleon has never been calculated before. Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon for the first time. We find that the pion field plays an important role in producing both the unpolarized and the polarized gluon di…
The electromagnetic form factors of the nucleon have been calculated in a chiral constituent-quark model. The nucleon wave functions are obtained by solving a Schrödinger-type equation for a semi-relativistic Hamiltonian with an effective interaction derived from the exchange of mesons belonging to the pseudoscalar octet and singlet and a linear confinement potential. The charge-density current operator has been constructed consistently with the model Hamiltonian in order to preserve gauge invariance and to satisfy the continuity equation.
Elastic pion-pion and pion-nucleon scattering are reviewed in the context of chiral perturbation theory. Theoretical results from systematic low-energy expansions to O(p^6) for pion-pion and to O(p^3) for pion-nucleon scattering are compared with experimental data. Possible future developments are outlined.
We calculate the transition form factor of the neutral pion where one photon is virtual and another photon is real in the model where the light constituent quark mass and the quark-pion vertex are taken to be momentum independent. Radiative corrections to the lowest order triangle quark Feynman amplitude are calculated. The resummation of the lowest radiative corrections to the virtual photon vertex is done by applying the Sudakov exponential hypothesis. Using fitting parameters, the quark mass and the strong coupling constant, the results on the pion transition form factor are compared with e…
We study the interactions of an elementary pion with a nucleon made of constituent quarks and show that the enforcement of chiral symmetry requires the use of a two-body operator, whose form does not depend on the choice of the pion-quark coupling. The coordinate space NN effective potential in the pion exchange channel is given as a sum of terms involving two gradients, that operate on both the usual Yukawa function and the confining potential. We also consider an application to the case of quarks bound by a harmonic potential and show that corrections due to the symmetry are important.
The electromagnetic form factors are the most fundamental quantities to describe the internal structure of the nucleon and the shape of a spatially extended particle is determined by its intrinsic quadrupole moment which can be related to the charge radii. We have calculated the electromagnetic form factors, nucleon charge radii and the intrinsic quadrupole moment of the nucleon in the framework of chiral constituent quark model. The results obtained are comparable to the latest experimental studies and also show improvement over some theoretical interpretations.
This thesis constitute an investigation of finding out whether or not the Goldstone Boson Exchange (GBE) model can give rise to a short-range repulsion in the the nucleon-nucleon (NN) interaction. We used two different approaches based on the Born-Oppenheimer approximation and taking into account Harvey's transformations. Next, we study the NN interaction in a dynamical way using the resonating group method (RGM). We present results for the s-wave phase shifts in the NN scattering. We also introduce some necessary extensions of the GBE model like the contribution of the sigma-meson exchange in…
Single pion transitions of S wave to S wave, P wave to S wave and P wave to P wave heavy baryons are analyzed in the framework of the Heavy Quark Symmetry limit (HQS). We use a constituent quark model picture for the light diquark system with an underlying SU(2N_{f}) X O(3) symmetry to reduce the number of the HQS coupling factors required to describe these transitions. We also use the quantum theory of angular momentum to rewrite the one-pion transitions constituent quark model results in a more general form using the 6j- and 9j-symbols. We finally estimate the decay rates of some single pion…
The first moment of longitudinal and transverse spin densities of quarks in the nucleon are calculated in a light-front constituent quark model for the different cases of quark and nucleon polarization. Significant distortions are found for the transverse spin densities. In particular the Sivers function is predicted with opposite sign for up and down quarks and the Boer-Mulders function is predicted large and negative for both up and down quarks, in agreement with lattice calculations. Quite a different spin distribution is obtained for up and down quarks in the cases of quarks and proton tra…
An overview of the vector and tensor Generalized Parton Distributions for a charged pion is presented. Such observables, belonging to the set of quantities fundamental for a detailed investigation of the hadronic inner dynamics, have been evaluated within a fully covariant Constituent Quark Model, based on a proper Ansatz of the pion Bethe-Salpeter Amplitude and the Mandelstam formula for matrix elements of operators acting on relativistic composite systems. Given the very encouraging results already obtained for the vector distribution of a charged pion, the model has been extended to the ten…
A nonrelativistic decomposition for the quark energy by the ratio of the dispersion of quark momentum squared and the effective quark mass is investigated in the framework of the relativistic oscillator constituent quark model as bound systems of three valence quarks. It is shown that relativistic corrections are defined by dispersion of the squared absolute value of the quark momentum. The variations of the quark mass and oscillator parameter are studied in detail both in the spectrum and in the nucleon magnetic moments.
We extend the investigation of the Generalized Parton Distribution for a charged pion within a fully covariant constituent quark model, in two respects: (i) calculating the tensor distribution and (ii) adding the treatment of the evolution, needed for achieving a meaningful comparison with both the experimental parton distribution and the lattice evaluation of the so-called generalized form factors. Distinct features of our phenomenological covariant quark model are: (i) a 4D Ansatz for the pion Bethe-Salpeter amplitude, to be used in the Mandelstam formula for matrix elements of the relevant …
Gribov's theory of confinement offers a simple explanaton of the value of the pion nucleon sigma term. There is no need to invoke a large strange quark component in the nucleon.
We provide a precise calculation for the contribution of hard near threshold pion electro production to all nucleon structure functions. This framework will allow us to split the required nucleon to pion nucleon transition probability matrix element into an exact threshold part parametrized by nucleon to pion nucleon transition form factors plus soft pion structures. These transition form factors will be related to nucleon form factors by taking into account symmetric and antisymmetric contributions of the needed leading twist nucleon distribution amplitude. Whereas the relations generated by …
The pretzelosity distribution function $h_{1T}^\perp$ is studied in a covariant the quark-parton model which describes the structure of the nucleon in terms of 3D quark intrinsic motion. This relativistic model framework supports the relation between helicity, transversity and pretzelosity observed in other relativistic models {\sl without} assuming SU(6) spin-flavor symmetry. Numerical results and predictions for SIDIS experiments are presented.
We study the form factors of the low energy anomalous pion-2-photon and photon-3-pion processes in the nonlocal chiral quark model which incorporates the momentum dependence of the dynamical quark mass and realizes correctly the chiral symmetries. The obtained slope parameter for pion-2-photon is in reasonable agreement with the direct experimental results but smaller than the ones invoking vector meson dominance. Our result for the photon-3-pion form factor interpolates between the two extremes of theoretical approaches, with the largest one provided by the vector meson dominance and the smal…
Using a simple picture of the constituent quark as a composite system of point-like partons, we construct the polarized parton distributions by a convolution between constituent quark momentum distributions and constituent quark structure functions. We achieve good agreement with experiments in the unpolarized as well as in the polarized case, though a good description of the recent polarized neutron data requires the introduction of one more parameter. When our results are compared with similar calculations using non-composite constituent quarks, the accord with the experiments of the present…
It was shown by careful consideration of the time--dependent classic solution for the rotated skyrmion, that such solution at large distances has radiational component similar to the Lienart-Viehart retarded potential in Electrodynamics. We consider such solution as stationary phase configuration of the pion field in path integrals for the correlators of $n$ isovector axial currents $J_μ^{A,i}$ and two nucleon currents $J_N$. $n$ pion -- nucleon amplitudes are extracted from these correlators. The careful account of the asymptotics of this stationary phase configuration of the pion field (rota…
The interaction mediated by irreducible pion and gluon exchange between constituent quarks is calculated and shown to have a strong tensor component, which tends to cancel the pion exchange tensor interaction between quarks. Its spin-spin component is somewhat weaker than the pion exchange spin-spin interaction, while its central and spin-orbit components are small in comparison to the corresponding single gluon exchange interactions. The combination of the $π-$gluon exchange interaction with the single pion exchange interaction and a weak gluon exchange interaction between constituent quarks …
This is a short presentation of the results for the pion-nucleon distribution amplitudes which are expressed in terms of the nucleon distribution amplitudes with the help of current algebra. Everything is considered to be at threshold.
The number of pions in the nucleon is a theoretical concept and its value is model dependent. It is, however, a useful tool to understand the pionic contribution to several nucleon observables such as electric charge radii, magnetic moments, axial charge, pion-nucleon coupling constant, amplitudes for electroexcitation of baryon resonances and electroproduction of pions above such resonances.
A new result for the pion nucleon Sigma term from a George Washington University/TRIUMF group analysis of pion nucleon data is presented. The value Sigma=79$\pm$7 MeV was obtained, compared to the canonical value 64$\pm$8 MeV found by Koch. The difference is explained simply by the PSI pionic hydrogen value for a(pi -p), the latest results for the $πNN$ coupling onstant, and a narrower Delta resonance. Many systematic effects have been investigated, including Coulomb corrections, and database changes, and our results are found to be robust. In the standard interpretation, our value of Sigma im…
Generalized parton distributions (GPDs) are studied at the hadronic (nonperturbative) scale within different assumptions based on a relativistic constituent quark model. In particular, by means of a meson-cloud model we investigate the role of nonperturbative antiquark degrees of freedom and the valence quark contribution. A QCD evolution of the obtained GPDs is used to add perturbative effects and to investigate the GPDs' sensitivity to the nonperturbative ingredients of the calculation at larger (experimental) scale.
Using the vacuum-to-pion matrix element of the correlation function of the interpolating fields of the two nucleons, the isospin splitting in the diagonal pion-nucleon coupling constant has been studied in the framework of the conventional QCD sum rule. Some of the implications of this splitting has also been discussed.
Within an extended chiral constituent quark formalism, we investigate contributions from all possible five-quark components in the octet baryons to the pion-baryon ($σ_{πB}$) and strangeness-baryon ($σ_{s B}$) sigma terms; $B \equiv N,~Λ,~Σ,~Ξ$. The probabilities of the quark-antiquark components in the ground-state baryon octet wave functions are calculated by taking the baryons to be admixtures of three- and five-quark components, with the relevant transitions handled {\it via} the $^{3}$P$_{0}$ mechanism. Predictions for $σ_{πB}$ and $σ_{s B}$ obtained by using input parameters taken from t…
In the present work we study the effect of the scalar spin coupling of constituent quarks on the nucleon electroweak properties by introducing a valence light-front wave function with two momentum scales. By comparing the results obtained with the one scale and two scale wave function models, we have found that the last one has shown a reasonable description of the static observables and $μ_pG_{Ep}/G_{Mp}$ ratio in which the position of the zero appears around 10~[GeV/c]$^2$ or for higher squared momentum transfers. We have also shown results for the axial-vector coupling $g_{A}$ and the nucle…
We calculate the partonic structure of constituent quark in the Next-to-Leading Order for the first time. The structure of any hadron can be obtained thereafter using a convolution method. Such a procedure is used to generate the structure function of proton and pion in NLO. It is shown that while the constituent quark structure is generated purely perturbatively and accounts to most part of the hadronic structure, there is a few percent contributions coming from the nonperturbative sector in the hadronic structure. This contribution plays the key role in explaining the SU(2) symmetry breaking…
A dispersion framework, appropriate for discussing the low-energy pion-nucleon interaction, is reviewed. Sensitivity of the isoscalar D-amplitude at the unphysical Cheng-Dashen point to input from different phase shift analyses and low-energy experiments is discussed.
The recent unbiased measurements of the electric form factor of the neutron suggest that its shape may be interpreted as a smooth broad distribution with a bump at Q^2 \approx 0.3(GeV/c)^2 superimposed. As a consequence the corresponding charge distribution in the Breit frame shows a negative charge extending as far out as 2fm. It is natural to identify this charge with the pion cloud. This realisation is then used to reanalyse all old and new data of the electric and magnetic from factors of the proton and the neutron by a phenomenological fit and by a fit based on the constituent quark model…
The pion-deuteron scattering length is computed to next-to-next-to-leading order in baryon chiral perturbation theory. A modified power-counting is then formulated which properly accounts for infrared enhancements engendered by the large size of the deuteron, as compared to the pion Compton wavelength. We use the precise experimental value of the real part of the pion-deuteron scattering length determined from the decay of pionic deuterium, together with constraints on pion-nucleon scattering lengths from the decay of pionic hydrogen, to extract the isovector and isoscalar S-wave pion-nucleon …
We present a study of inclusive direct-photon and neutral pion production in hadronic interactions that focuses on a comparison of the ratio of photon and pion yields with expectations from next-to-leading order perturbative QCD (NLO pQCD).
We present results for the nucleon magnetic moments in the context of an extended chiral constituent quark model based on the mechanism of the Goldstone boson exchange, as suggested by the spontaneous breaking of chiral symmetry in QCD. The electromagnetic charge-current operator is consistently deduced from the model Hamiltonian, which includes all force components for the pseudoscalar, vector and scalar meson exchanges. Thus, the continuity equation is satisfied for each piece of the interaction, avoiding the introduction of any further parameter. A good agreement with experimental values is…
We develop a generalized version of heavy-baryon chiral perturbation theory to describe pion-nucleon scattering in a kinematic domain that extends continuously from threshold to the delta-isobar peak. The $P$-wave phase shifts are used to illustrate this framework.
The electromagnetic form factors have attracted lot of theoretical and experimental attention recently as they encode extensive information on the internal structure of the hadron. An understanding of the form factors is necessary to describe the strong interactions as they are sensitive to the pion cloud and provide a test for the QCD inspired effective field theories based on the chiral symmetry. In view of the very exciting recent developments in the field, we propose to apply the techniques of chiral constituent quark model to measure the electromagnetic form factors of the nucleon.The res…
The pion nucleon sigma-term is extracted on the basis of the soliton picture of the nucleon from the mass spectrum of usual and the recently observed exotic baryons, assuming that they have positive parity. The value found is consistent with that inferred by means of conventional methods from pion nucleon scattering data. The study can also be considered as a phenomenological consistency check of the soliton picture of baryons.
We consider the two-flavor version of the extended linear sigma model (eLSM), which contains (pseudo)scalar and (axial-)vector quark-antiquark mesons, a scalar glueball (predominantly corresponding to $f_{0}(1710)$), as well as the nucleon and its chiral partner. We extend this model by the additional light scalar meson $f_{0}(500)$, predominantly a putative four-quark state. We investigate various interaction terms of the four-quark and glueball states with the other particles, some of which preserve and some of which explicitly break the $U(1)_{\textrm{A}}$ symmetry. We test our model by per…
We study the very recently discovered $Θ^+$ (1540) at SPring-8, at ITEP and at CLAS-Thomas Jefferson Lab. We apply the same RGM techniques that already explained with success the repulsive hard core of nucleon-nucleon, kaon-nucleon exotic scattering, and the attractive hard core present in pion-nucleon and pion-pion non-exotic scattering. We find that the K-N repulsion excludes the Theta+ as a K-N s-wave pentaquark. We explore the Theta+ as heptaquark, equivalent to a N+pi+K borromean boundstate, with positive parity and total isospin I=0. We find that the kaon-nucleon repulsion is cancelled b…
We study the very recently discovered Theta+ (1540) at SPring-8, at ITEP and at CLAS-Thomas Jefferson Lab. We apply the same RGM techniques that already explained with success the repulsive hard core of nucleon-nucleon, kaon-nucleon exotic scattering, and the attractive hard core present in pion-nucleon and pion-pion non-exotic scattering. We find that the K-N repulsion excludes the Theta+ as a K-N s-wave pentaquark. We explore the Theta+ as a heptaquark, equivalent to a N+pi+K borromean bound-state, with positive parity and total isospin I=0. We find that the kaon-nucleon repulsion is cancell…
We propose an intensity-dependent pion-nucleon coupling Hamiltonian within a unitary multiparticle-production model of the AABS type in which the pion field is represented by the thermal-density matrix. Using this Hamiltonian, we explain the appearance of the negative- binomial (NB) distribution for pions and the well-known empirical relation, the so-called Wroblewski relation. The Hamiltonian of our model is expressed linearly in terms of the generators of the SU(1,1) group.
A dependence of the value of the pion-nucleon sigma term on higher partial waves is discussed. Two recent predictions of a high value of sigma term are scrutinezed. It has been concluded that the main reason for obtaining high values of the sigma term are input D waves that are not consistent with analyticity.
We calculate the phase shifts in the pion-nucleon scattering using the heavy baryon formalism. We consider phase shifts for the pion energy range of 140 to $200 $ MeV. We employ two different methods for calculating the phase shifts - the first using the full third order calculation of the pion-nucleon scattering amplitude and the second by including the resonances $Δ$ and $N^*$ as explicit degrees of freedom in the Lagrangian. We compare the results of the two methods with phase shifts extracted from fits to the pion-nucleon scattering data. We find good to fair agreement between the calculat…
We study off-shell effects of the pion cloud on the sea quark distribution in the nucleon. The structure function of the off-mass-shell pion is obtained within the Nambu and Jona-Lasinio model, where the shape of the distribution function depends on the pion momentum. By using the momentum dependent pion structure function, the SU(2) flavor asymmetry in the nucleon see is reexamined within the pionic model, in which the sea quark distribution of the nucleon is given as a convolution of the off-shell pion structure function. We calculate experimentally observed quantities related to the SU(2) a…
The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon's electromagnetic form-factor at high $Q^2$ is proportional to the bare nucleon probability $Z$ and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to $Z^2$. Our present knowledge of the pion-nucleon system is consistent with $Z = 0.7 \pm 0.2$. If we…
A model independent expression for the electromagnetic corrections to a phenomenological hadronic pion-nucleon scattering length, extracted from pionic hydrogen, is obtained. In a non-relativistic approach and using an extended charge distribution, these corrections are derived up to terms of order (alpha)**2 log(alpha) in the limit of a short-range hadronic interaction. We infer a charged pion-proton scattering length of 0.0870(5) in units of inverse pion mass, which gives for the charged pion-proton-neutron coupling, through the GMO relation, a value of 14.04(17).
We investigate hard exclusive reactions on the nucleon with soft pion emission. A parametrization of corresponding hadronic matrix elements in terms of parton distributions for final pion-nucleon state is provided. These distributions are calculated in terms of nucleon and pion GPDs and the pion distribution amplitude via soft-pion theorems. Some observables for the process of hard charged pion production on the proton with soft pion emission are computed.
We evaluate the form factors describing the exclusive decay B-> pi l nu by using a Constituent Quark-Meson model based on an effective quark-meson Lagrangian (CQM). The model allows for an expansion in the pion momenta and we consider terms up to the first order in the pion field derivatives. We compute the leading terms in the soft pion limit and consider corrections to this limit.
