Pion valence quark distributions from maximum entropy method

We present an attempt of maximum entropy principle to determine valence quark distributions in the proton at very low resolution scale $Q_0^2$. The initial three valence quark distributions are obtained with limited dynamical information from quark model and QCD theory. Valence quark distributions from this method are compared to the lepton deep inelastic scattering data, and the widely used CT10 and MSTW08 data sets. The obtained valence quark distributions are consistent with experimental observations and the latest global fits of PDFs. Maximum entropy method is expected to be particularly useful in the case where relatively little information from QCD calculation is given.

In this study we demonstrate the application of the maximum entropy method (MEM) to determine the valence quark distribution of exotic hadrons. Our investigation yields three key findings. Firstly, we observe a significant shift towards smaller Bjorken scale x in the peak position of the valence quark distribution for hadrons with an increasing number of valence quarks, consistent with previous results by Kawamura and Kumano. Secondly, assuming that the Zc(3900) initially consists of four valence quarks, we employ MEM to determine its initial valence quark distribution, estimating a radius of rc=1.276 fm at an extremely low resolution scale Q2. Furthermore, we identify a notable discrepancy between our computed charge form factor Gc(q) at leading order and the outcomes of hadron molecular state calculations. We propose that this form factor can be extracted from the QCD counting rule cross-section, which is grounded in generalized distribution amplitudes (GDA) linked to the multi-quark states.

The effects of in determining the flavor structure of the octet baryons have been investigated in the chiral constituent quark model. The chiral constituent quark model is able to qualitatively generate the requisite amount of quark sea and is also known to provide a satisfactory explanation of the spin and related issues in the nonperturbative regime. The phenomenological implications of the quark sea asymmetries in the nucleon have been investigated to understand the importance of quark sea at lower values of the Bjorken scaling variable. After the first direct evidence for the point-like constituents in the nucleon, identified as the valence quarks with spin-1/2 in the naive constituent quark model (NQM) (1-3), a lot of experiments have been conducted to probe the structure of the in the deep inelastic scattering (DIS) experiments. Surprisingly, the DIS results in the early 80's (4) indicated that the valence quarks of the carry only about 30% of its spin and is referred to as the proton spin crisis in the NQM. These results provided the first evidence for the being composed of three valence quarks surrounded by an indistinct sea of quark-antiquark pairs (henceforth referred to as the sea). In the present day, the study of the composition of hadrons can be said to be primarily the study of the quark sea and gluons and is considered as one of the active areas in hadronic physics. The conventional expectation that the quark sea perhaps can be obtained through the perturbative production of the quark-antiquark pairs by gluons produces nearly equal numbers of ¯ u and ¯ d. Until early 90's a symmetric sea w.r.t. ¯ u and ¯ d was assumed, however, the famous New Muon Collaboration in 1991 (5) established the quark sea asymmetry of the unpolarized quarks in the case of nucleon by measuring ¯ d − ¯ u giving first clear evidence for the nonperturbative origin of the quark sea. This was later confirmed by the Drell-Yan experiments (6) which measured a large quark sea asymmetry ratio ¯ d/¯ u reminding us that the study of the quark sea is intrinsically a nonperturbative phenomena and it is still a big challenge to perform these calculations from the first principles of QCD. The chiral constituent quark model (CQM) (7) can yield an adequate description of the quark sea generation through the chiral fluctuations. The basic idea is based on the possibility that chiral symmetry breaking takes place at a distance scale much smaller than the confinement scale. In this region, the effective degrees of freedom are the valence quarks and the internal Goldstone bosons (GBs) which are coupled to the valence quarks (8-10) allowing a simple and intuitive method to investigate

Valence quark distributions in transversally and longitudinally polarizied ρ mesons in the region of intermediate x are obtained by generalizied QCD sum rules. Power corrections up to d=6 are taken into account. Comparison of the results for π and ρ mesons shows, that polarization effects are very significant and SU(6) symmetry of distribution functions is absent. The strong suppression of quark and gluon sea distributions in longitudinally polarizied ρ mesons is found.

We have used the Meson Cloud Model (MCM) to calculate the charm and strange antiquark distribution in the nucleon. The resulting curve, in the case of charm, is very similar to the intrinsic charm momentum distribution. This allows us to identify the intrinsic quark distribution with the valence quark distribution in the cloud and, at the same time, explains why other MCM calculations fail in reproducing the low x region data. From the intrinsic strange quark distribution in the nucleon, we have extracted information about the relative importance of various intermediate states that should be considered in a loop calculation.

Symmetry violation and quark distributions in mesons

We present a model for the γ*N → N* helicity amplitudes, where N is the nucleon and N* is a negative parity nucleon excitation, member of the SU(6)-multiplet [70, 1-]. The model combines the results from the single quark transition model for the helicity amplitudes with the results of the covariant spectator quark model for the γ*N → N* (1535) and γ*N → N* (1520) transitions. With the knowledge of the amplitudes A1/2 and A3/2 for those transitions we calculate three independent coefficients defined by the single quark transition model and make predictions for the helicity amplitudes associated with the γ*N → N* (1650), γ*N → N* (1700), γ*N → Δ (1620), and γ*N → Δ (1700) transitions. In order to facilitate the comparison with future experimental data at high Q2, we provide also simple parametrizations for the amplitudes, compatible with the expected falloff at high Q2.

The chiral quark-soliton model of the nucleon contains a mechanism for an attractive interaction between nucleons. This, along with the exchange of vector mesons between nucleons, is used to compute the saturation properties of infinite nuclear matter. This provides a new way to assess the effects of the nuclear medium on a nucleon that includes valence and sea quarks. We show that the model simultaneously describes the nuclear EMC effect and the related Drell-Yan experiments.

A higher-twist modified parton evolution equation is used to evolve the initial valence quark distributions in pions, which are derived based on light-front quantization via BLFQ collaboration. The results are consistent with the valence quark distributions of the E615 experiment, and the pion structure function of the H1 experiment. The structure function data highlight the necessity for a higher-twist modification in the small x region. Comparisons with some other models are also given.

We show how the double parton distributions may be obtained consistently from the many-body light-cone wave functions. We illustrate the method on the example of the pion with two Fock components. The procedure, by construction, satisfies the Gaunt-Stirling sum rules. The resulting single parton distributions of valence quarks and gluons are consistent with a phenomenological parametrization at a low scale.

The modification of the Paschos-Wolfenstein relation is investigated when the charge symmetry violations of valence and sea quark distributions in the nucleon are taken into account. We also study qualitatively the impact of charge symmetry violation (CSV) effect on the extraction of ${sin}^{2}{\ensuremath{\theta}}_{w}$ from deep-inelastic neutrino- and antineutrino-nuclei scattering within the light-cone meson-baryon fluctuation model. We find that the effect of CSV is too small to give a sizable contribution to the NuTeV result with various choices of mass difference inputs, which is consistence with the prediction that the strange-antistrange asymmetry can account for largely the NuTeV deviation in this model. It is noticeable that the effect of CSV might contribute to the NuTeV deviation when the larger difference between the internal momentum scales, ${\ensuremath{\alpha}}_{p}$ of the proton and ${\ensuremath{\alpha}}_{n}$ of the neutron, is considered.

In this article, we calculate the axial and the induced pseudoscalar form-factors $G_A(t=-Q^2)$ and $G_P(t=-Q^2)$ of the nucleons in the framework of the light-cone QCD sum-rules approach up to twist-6 three valence quark light-cone distribution amplitudes, and observe that the form-factors $G_A(t=-Q^2)$ and $G_P(t=-Q^2)$ at intermediate and large momentum transfers with $Q^2> 2 GeV^2$ have significant contributions from the end-point (soft) terms. The numerical values for the axial form-factor $G_A(t=-Q^2)$ are compatible with the experimental data and theoretical calculations, for example, the chiral quark models and lattice QCD. The numerical values for the induced pseudoscalar form-factor $G_P(t=-Q^2)$ are compatible with the calculation from the Bethe-Salpeter equation.

We investigate the unpolarized transverse momentum dependent (TMD) structure of light nuclei in the modified chiral quark exchange model (QEM), for the first time. To this end, we calculate the TMD quark and gluon distributions inside the bound state nucleons of the light nuclei based on the modified chiral quark model in which the TMD bare quark distributions of the bounded nucleons are needed. In order to compute these bare distributions, we first obtain the bare quark momentum densities using the QEM and then calculate the TMD bare distributions applying a theoretical method in which the light-cone variables are used. Finally, considering the nucleon structure of helium, tritium and deuteron nuclei, we obtain their TMD quark and gluon densities at low Q2 scale. It is shown that our results have appropriate properties that are expected for the TMD distribution functions.

Based on a QCD analysis of the parton momentum distributions in the proton, the ratior v =d v /u v of thed andu valence quark distributions is determined as function ofx in the range 0.01<x<0.7. The analysis uses data from neutrino and antineutrino charged current interactions on hydrogen and deuterium, obtained with BEBC in the (anti)neutrino wideband beam of the CERN SPS. Since v mainly depends on the deuterium/hydrogen ratios of the normalisedx-y-Q2-distributions many systematic effects cancel. It is found thatr v decreases with increasingx, and drops below the naiveSU(6) expectation of 0.5 forx≳0.3. An extrapolation ofr v tox=1 is consistent with the hypothesisr v (1)=0.

Nucleon structure functions from relativistic constituent quarks