Quark-gluon Fock States Research Articles

Importance of Strange Sea to the Charge Radii and Quadrupole Moment of $J^P=\frac{1}{2}^+,\frac{3}{2}^+$ Baryons

Abstract A statistical framework in conjugation with the principle of detailed balance is employed to examine the low-energy properties, i.e. charge radii and quadrupole moment, of JP = $\frac{1}{2}^+$ octet and JP = $\frac{3}{2}^+$ decuplet baryons. The statistical model relies on the assumption that the baryons can be expanded in terms of quark–gluon Fock states. We systematically apply operator formalism along with the statistical approach to study the charge radii and quadrupole moment of baryons. Based on the probabilities of all possible Fock states in spin, flavor, and color space, the importance of sea with quarks and gluons is studied. The individual contribution of the constituent quarks and sea (scalar, vector, and tensor sea) is explored. Due to the large mass difference between strange and nonstrange content, the SU(3) breaking effect is also investigated. The extent to which strange $q\bar{q}$ pairs are considered in sea is constrained by the mass of hadrons and the free energy of gluons, in accordance with experimental evidence. We focus on the individual contribution of strange and nonstrange sea ($g, \langle u\bar{u}\rangle$, $\langle d\bar{d}\rangle$, and $\langle s\bar{s}\rangle$) accommodability in the respective hadrons for their charge radii and quadrupole moment. The present work has been compared with various theoretical approaches and some known experimental observations. The obtained results may give valuable information for upcoming experimental findings.

Properties of $J^{P}=1/2^{+}$ baryon octets at low energy

The statistical model in combination with detailed balance principle is able to phenomenological calculate and analyze spin and flavor dependent properties like magnetic moments (with effective masses, effective charge, with both effective mass and effective charge), quark spin polarization and distribution, strangeness suppression factor. The magnetic moments of the octet baryons are analyzed within the statistical model, by putting emphasis on the SU(3) symmetry breaking effects generated by the mass difference between the strange and non strange quarks. The work presented here assume hadrons with a sea having admixture of quark-gluon Fock states. The results obtained have been compared with theoretical models and experimental data.

Magnetic moments of JP = $ {\frac{{3}}{{2}}}$ + decuplet baryons using the statistical model

A suitable wave function for baryon decuplet is framed with inclusion of sea containing quark- gluon Fock states. Relevant operator formalism is applied to calculate magnetic moments of JP = 3 2 + baryon decuplet. Statistical model assumes decomposition of baryonic state in various quark-gluon Fock states such as jqqqijgi; jqqqijggi; jqqqijgggi with possibility gluon emitting qq pairs condensates due to the subprocesses like g , qq; g , gg and g , qg where qq = uu; dd; ss. Statistical approach and detailed balance principle in combination is used to find the relative probabilities of these Fock states in avor, spin and color space. The total number of partons (sea) in this formalism are restricted to three gluons due to limited free energy of gluon and suppressed number of strange quark-antiquark pairs. The combined approach is used to calculate the magnetic moments, importance of strangeness in the sea (scalar, vector and tensor). Our approach has confirmed the scalar-tensor sea dominancy over vector sea. Various modifications in the model are used to check the validity of statistical approach. The results are matched with theoretical data available. Good consistency with the experimental data have been achieved for Delta++, Delta+ and Omega-.

Sea-quark and gluonic contributions to strange baryons and its properties

We treat the hadrons as an ensemble of quark-gluon Fock states where contributions from sea-quarks and gluons can be studied in detail for the properties of low lying baryons. Statistical model is applied to calculate individual probabilities from various scalar, vector and tensor sea components in flavour, spin and colour subspaces for each quark-gluon Fock state. The mass of strange quark is imposed in terms of constraints to the availability of strange quarks in the sea and free energy of gluons in conformity with experimental indications. We calculate multiplicities for different sets of Fock states to compute the role of strange sea for cascade doublet Ξ+ and Ξ0. The low energy properties like magnetic moment, weak decay matrix elements and axial coupling constant ratios have been studied. The incorporation of strange quark gluon sea is discussed and they are found to affect the results by almost 46%.The results provide deeper understanding for baryon structure thereby motivating experiments for further inspection, especially the spin distribution among the quarks and gluons.

Strange mass corrections to hyperonic semi-leptonic decays in statistical model

The spin distributions, weak decay matrix elements for strange baryon octets with SU(3) breaking effects is studied. We systematically apply operator formalism along with statistical method to study JP= strange baryon octets for their low energy properties. Baryon is taken as an ensemble of quark-gluon Fock states in sea with three valence quarks to have spin-1/2, color-1 and flavor-8 quantum numbers. Detailed balance principle is applied to calculate the probabilities of each Fock states, with the inclusion of mass correction of strange quark in order to check the SU(3) breaking in weak decays constants and spin distributions. A dominant contribution from the vector sea is verified as compared to scalar and tensor sea, also the symmetry breaking correction leads to the deviations in the value of axial vector matrix elements ratio from experimental values by 17%. Present framework suggests a stronger base to choose statistical model with detailed balance principle to verify the experimental and theoretical values available and hence provide a deeper understanding to the strange baryon structure. Symmetry breaking effects lead to reduction in the values of axial matrix elements. Its contribution has a significant role in determining the validity of present approach.

DETAILED BALANCE AND SPIN CONTENT OF Λ USING STATISTICAL MODEL

The spin structure of lambda has its special importance in analyzing the spin content of other hadrons. Assuming hadrons as a cluster of quarks and gluons (generally referred as valence and sea), statistical approach has been applied to study spin distribution of lambda among quarks. We apply the principle of detailed balance to calculate the probability of various quark–gluon Fock states and check the impact of SU(3) breaking on these probabilities particularly in sea for the Fock states containing strange quark. The flavor probability when multiplied by spin and color multiplicities of these quark–gluon Fock states results in estimating the individual contributions from valence and sea. We conclude that breaking in symmetry significantly affects the polarization of quarks inside the hyperons.

Importance of sea contribution to nucleons

We studied the statistical model of nucleons consisting of sea having various quark-gluon Fock states in addition to valence quarks. Using statistical consideration and taking 86% of the total Fock states contributing to the low energy properties of nucleon, we aim to find the contributions to these properties coming from the scalar, vector and tensor sea. We checked its validity against the assumption where the contributions from scalar and tensor sea have been suppressed and justified to be unimportant. We took the approximation that sea is getting a zero contribution from H_0 G_\bar10 and H_1 G_\bar10 in three gluon states. Under above considerations, the calculated magnetic moment, spin distribution and weak decay coupling constant ratio for proton and neutron states have been tabulated. We hereby confirm that the suppression of the scalar and tensor sea leads to modification in the parameters of the nucleons showing deviation from the experimental data.

Spin studies of nucleons in a statistical model

We decompose various quark–gluon Fock states of a nucleon in a set of states in which each of the three-quark core and the rest of the stuff, termed as sea, appears with definite spin and colour quantum number, their weights being determined, statistically, from their multiplicities. The expansion coefficients in the quark–gluon Fock state expansion have been taken from a recently proposed statistical model. We have also considered two modifications of this model with a view to reducing the contributions of the sea components with higher multiplicities. With certain approximations, we have calculated the quark contributions to the spin of the nucleon, the ratio of the magnetic moments of nucleons, their weak decay constant and the ratio of SU(3) reduced matrix elements for the axial current.

FLAVOR ASYMMETRY OF NUCLEON SEA FROM DETAILED BALANCE

In this study, the proton is taken as an ensemble of quark-gluon Fock states. Using the principle of detailed balance, we find [Formula: see text], which is in surprisingly agreement with the experimental observation.

Principle of balance and the sea content of the proton

In this study, the proton is taken as an ensemble of quark-gluon Fock states. Using the principle of balance that every Fock state should be balanced with all of the nearby Fock states (denoted as the balance model), instead of the principle of detailed balance that any two nearby Fock states should be balanced with each other (denoted as the detailed balance model), the probabilities of finding every Fock state of the proton are obtained. The balance model can be taken as a revised version of the detailed balance model, which can give an excellent description of the light flavor sea asymmetry (i.e., $\bar{u}\not= \bar{d}$) without any parameter. In case of $g\Leftrightarrow gg$ sub-processes not considered, the balance model and the detailed balance model give the same results. In case of $g\Leftrightarrow gg$ sub-processes considered, there is about 10 percent difference between the results of these models. We also calculate the strange content of the proton using the balance model under the equal probability assumption.

Parton distribution of proton in a simple statistical model

Taking proton as an ensemble of quark-gluon Fock states and using the principle of detailed balance, we construct a simple statistical model for parton distribution of proton. The recent observed Bjorken-$x$ dependent light flavor sea quark asymmetry $\bar{d}(x)-\bar{u}(x)$ can be well reproduced by Monte Carlo simulation as a pure statistical effect.

Detailed balance and sea-quark flavor asymmetry of proton

In this study, the proton is taken as an ensemble of quark-gluon Fock states. Using the principle of detailed balance, the probabilities of finding every Fock states of the proton are obtained without any parameter. A new origin of the light flavor sea quark asymmetry, i.e., $\bar{u} \not= \bar{d}$, is given as a pure statistical effect. It is found that $\bar{d}-\bar{u} \approx 0.124$, which is in surprisingly agreement with the experimental observation.

From hard to soft diffraction and return

The long standing mystery of smallness of diffractive dissociation of hadrons to large effective masses (the Pomeron-proton cross section is only 2 mb) witnesses that the gluonic clouds of valence quarks are so small ( r 0 = 0.3 fm) that soft interaction hardly resolves those gluons (diffraction is ∝ r 4 0). A color-dipole light-cone (LC) approach is developed which incorporates a strong nonperturbative interaction of the LC gluons. The energy dependent part of the total hadronic cross section is calculated in a parameter-free way employing the nonperturbative LC wave functions of the quark-gluon Fock states. It rises with energy as s Δ, and we predict Δ = 0.17 ± 0.01, as well as the normalization. However, the energy independent part of the cross section related to inelastic collisions with no gluon radiated (gluons are not resolved) cannot be calculated reliably and we treat it as an adjustable parameter which is fixed fitting just one experimental point for total cross section. Then the energy dependence of the total cross section (the Pomeron part) and the elastic slope are fully predicted, as well as the effective Pomeron trajectory in impact parameter space, in a good agreement with data. These results naturally explain the x-dependence of the diffractive DIS observed at HERA. Although diffraction is expected to be dominated by soft interactions the observed effective Δ is about twice as large as one (0.08) known for total cross sections. Diffractive excitations of large effective mass correspond to diffractive gluon radiation and should be associated with our calculated Δ.