Light-cone Momentum Distribution Research Articles

Analysis of the neutron spin structure function g1n by using the Laplace transform technique

In this paper, the polarized neutron structure function [Formula: see text] in the [Formula: see text] nucleus is investigated and an analytical solution based on the Laplace transform method for [Formula: see text] is presented. It is shown that the neutron spin structure function can be extracted directly from the polarized nuclear structure function of [Formula: see text]. The nuclear corrections due to the Fermi motion of the nucleons as well as the binding energy considerations are taken into account within the framework of the convolution approach and the polarized structure function of [Formula: see text] nucleus is expressed in terms of the spin structure functions of nucleons and the light-cone momentum distribution of the constituent nucleons. Then, the numerical results for [Formula: see text] are compared with experimental data of the SMC and HERMES collaborations. We found that there is an overall good agreement between the theory and experiments.

Modern studies of the Deuteron: From the lab frame to the light front

We review the recent progress made in studies of deuteron structure at small internucleon distances. This progress is largely facilitated by the new generation of experiments in deuteron electrodisintegration carried out at unprecedentedly high momentum transfer. The theoretical analysis of these data confirms the onset of the high energy eikonal regime in the scattering process which allows one to separate long-range nuclear effects from the effects genuinely related to the short distance structure of the deuteron. Our conclusion is that for the first time the deuteron is probed at relative momenta beyond 300 MeV/c without dominating long-range effects. As a result, at these large nucleon momenta the cross-section is sensitive to the nuclear dynamics at subfermi distances. Due to large internal momenta involved we are dealing with the relativistic bound state that is best described by the light-cone momentum distribution of nucleons in the deuteron. We present the first attempt of extracting the deuteron light-cone momentum distribution function from data and discuss the importance of this quantity for studies of quantum chromodynamics (QCD) structure of the bound nucleon in deep inelastic scattering (DIS) off the deuteron. We conclude the review giving an outlook of the next generation of high energy experiments which will extend our reach to much smaller distances in the deuteron.

Pion momentum distributions in the nucleon in chiral effective theory

We compute the light-cone momentum distributions of pions in the nucleon in chiral effective theory using both pseudovector and pseudoscalar pion-nucleon couplings. For the pseudovector coupling we identify $\ensuremath{\delta}$-function contributions associated with end-point singularities arising from the pion-nucleon rainbow diagrams, as well as from pion bubble and tadpole diagrams which are not present in the pseudoscalar model. Gauge invariance is demonstrated, to all orders in the pion mass, with the inclusion of Kroll-Ruderman couplings involving operator insertions at the $\ensuremath{\pi}NN$ vertex. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.

Target mass correction on the 3He polarized structure function

Target mass correction (TMC) is employed to amend the polarized helium structure functions, 3He . The structure function can be obtained via the convolution of the light cone momentum distribution with the polarized structure of the proton and neutron. The calculation of the polarized structure function of the nucleon is based on the constituent quark model. The analytical result for 3He polarized structure function at low values of Q2 is not in good agreement with the available experimental data. The reliability of calculations is increased using TMC effect. New comparison confirms a better agreement with the experimental data.

3He and 3H polarized structure functions, using the constituent quark model

We calculate polarized structure functions for 3He and 3H, using the convolution of the light cone momentum distribution with the polarized structure of the proton and neutron. The polarized structure function of the nucleon is computed using the constituent quark model. Hypergeometric orthogonal polynomials are employed to extract the unknown parameters in this phenomenological approach. These hypergeometric polynomials are placed at the third level of Askey scheme with two free parameters. The results obtained for the polarized nuclear structure functions and the ratio of the Bjorken sum rule for proton–neutron system to 3He– 3H system are in good agreement with the available experimental data and some theoretical models. To improve the validity of the model at low x-values, the nuclear shadowing, antishadowing and Δ-resonance effects are also considered.

Transversity quark distributions in a covariant quark–diquark model

Transversity quark light-cone momentum distributions are calculated for the nucleon. We utilize a modified Nambu–Jona-Lasinio model in which confinement is simulated by eliminating unphysical thresholds for nucleon decay into quarks. The nucleon bound state is obtained by solving the relativistic Faddeev equation in the quark–diquark approximation, where both scalar and axial-vector diquark channels are included. Particular attention is paid to comparing our results with the recent experimental extraction of the transversity distributions by Anselmino et al. We also compare our transversity results with earlier spin-independent and helicity quark distributions calculated in the same approach.

Nucleon quark distributions in a covariant quark–diquark model

Spin-dependent and spin-independent quark light-cone momentum distributions and structure functions are calculated for the nucleon. We utilize a modified Nambu–Jona-Lasinio model in which confinement is simulated by eliminating unphysical thresholds for nucleon decay into quarks. The nucleon bound state is obtained by solving the Faddeev equation in the quark–diquark approximation, where both scalar and axial-vector diquark channels are included. We find excellent agreement between our model results and empirical data.

Spin-dependent parton distributions in the nucleon

Spin-dependent quark light-cone momentum distributions are calculated for a nucleon in the nuclear medium. We utilize a modified NJL model where the nucleon is described as a composite quark-diquark state. Scalar and vector mean fields are incorporated in the nuclear medium and these fields couple to the confined quarks in the nucleon. The effect of these fields on the spin-dependent distributions and consequently the axial charges is investigated. Our results for the “spin-dependent EMC effect” are also discussed.

Quark distributions in nuclear matter and the EMC effect

Quark light cone momentum distributions in nuclear matter and the structure function of a bound nucleon are investigated in the framework of the Nambu–Jona-Lasinio model. This framework describes the nucleon as a relativistic quark–diquark state, and the nuclear matter equation of state by using the mean field approximation. The scalar and vector mean fields in the nuclear medium couple to the quarks in the nucleon and their effect on the spin independent nuclear structure function is investigated in detail. Special emphasis is placed on the important effect of the vector mean field and on a formulation which guarantees the validity of the number and momentum sum rules from the outset.

Hard photodisintegration of a proton pair in 3He

Hard photodisintegration of the deuteron has been extensively studied in order to understand the dynamics of the transition from hadronic to quark–gluon descriptions of the strong interaction. In this Letter, we discuss the extension of this program to hard photodisintegration of a pp pair in the 3He nucleus. Experimental confirmation of new features predicted here for the suggested reaction would advance our understanding of hard nuclear reactions. A main prediction, in contrast with low-energy observations, is that the pp breakup cross section is not much smaller than the one for pn break up. In some models, the energy-dependent oscillations observed for pp scattering are predicted to appear in the γ3He→pp+n reaction. Such an observation would open up a completely new field in studies of color coherence phenomena in hard nuclear reactions. We also demonstrate that, in addition to the energy dependence, the measurement of the light-cone momentum distribution of the recoil neutron provides an independent test of the underlying dynamics of hard disintegration.

STRUCTURE FUNCTIONS OF THE NUCLEON IN THE QUARK–DIQUARK MODEL AND EXTENSION TO FINITE DENSITY

In this work we use a simple approximation to the relativistic Faddeev description of the nucleon in the framework of the Nambu-Jona-Lasinio (NJL) model. We discuss the flavor dependence of valence quark light-cone momentum distributions, and by comparing with the empirical informations we extract information on the strength of the axial vector diquark correlations. As an extension to finite density, we also discuss the EMC effect in nuclear matter, keeping only the scalar diquark channel in the wave function.

Initial-state interactions in the unpolarized Drell-Yan process

We show that initial-state interactions contribute to the $\cos 2 \phi$ distribution in unpolarized Drell-Yan lepton pair production $p p$ and $ p \bar p \to \ell^+ \ell^- X$, without suppression. The asymmetry is expressed as a product of chiral-odd distributions $h_1^\perp(x_1,\bm{p}_\perp^2)\times \bar h_1^\perp(x_2,\bm{k}_\perp^2) $, where the quark-transversity function $h_1^\perp(x,\bm{p}_\perp^2)$ is the transverse momentum dependent, light-cone momentum distribution of transversely polarized quarks in an {\it unpolarized} proton. We compute this (naive) $T$-odd and chiral-odd distribution function and the resulting $\cos 2 \phi$ asymmetry explicitly in a quark-scalar diquark model for the proton with initial-state gluon interaction. In this model the function $h_1^\perp(x,\bm{p}_\perp^2)$ equals the $T$-odd (chiral-even) Sivers effect function $f^\perp_{1T}(x,\bm{p}_\perp^2)$. This suggests that the single-spin asymmetries in the SIDIS and the Drell-Yan process are closely related to the $\cos 2 \phi$ asymmetry of the unpolarized Drell-Yan process, since all can arise from the same underlying mechanism. This provides new insight regarding the role of quark and gluon orbital angular momentum as well as that of initial- and final-state gluon exchange interactions in hard QCD processes.

Axial vector diquark correlations in the nucleon: structure functions and static properties

In order to extract information on the strength of quark–quark correlations in the axial vector (a.v.) diquark channel ( J P =1 +, T=1), we analyze the quark light cone momentum distributions in the nucleon, in particular their flavor dependencies, and the static properties of the nucleon. To construct the nucleon as a relativistic 3-quark bound state, we use a simple “static” approximation to the full Faddeev equation in the Nambu–Jona-Lasinio model, including correlations in the scalar ( J P =0 +, T=0) and a.v. diquark channels. It is shown that the a.v. diquark correlations should be rather weak compared to the scalar ones. From our analysis we extract information on the strength of the correlations as well as on the probability of the a.v. diquark channel.

Structure functions of unstable lithium isotopes

We study the spin-average and spin-dependent structure functions of the lithium isotopes. It is found that the light-cone momentum distribution of the valence neutron in the halo of 11Li is very sharp and symmetric around y=1, because of the weak binding. This implies that such neutrons are in an environment very close to that of a free neutron. The EMC ratios for Li isotopes are then calculated. Furthermore, we investigate a new ratio, given by the difference between the Li structure functions of mass number A ( F 2 A ) and A−1 ( F 2 A−1 ) divided by the difference between the structure functions of the deuteron and free proton. We study the possibility of extracting the neutron structure function from data for the nuclear structure functions of the Li isotopes. In particular, the ratios for A=9 and 11 present an attractive possibility for extracting the free neutron structure function. Next, as an example, we calculate the spin-dependent structure function of 9Li isotope, which has spin 3/2. The spin structure function is given in terms of the multipole spin structure functions; 3/2 1g 1 , which is analogous to the usual spin structure function, g 1, for a target with spin 1/2, and a new one, 3/2 3g 1 , which first arises for a target with spin 3/2. The effect of the nuclear binding and Fermi motion on 3/2 1g 1 is about 10% in the region x<0.7, but it becomes quite important at large x. The spin structure function, 3/2 3g 1 , is negative at small x but it becomes positive in the region 0.2< x<0.5. However, the magnitude is very small. At large x it is again negative and its absolute value becomes large because of the Fermi motion. Finally, we discuss the modification of the Gottfried and Bjorken integrals in a nuclear medium and point out several candidates for a pair of mirror nuclei to study the flavor-nonsinglet quark distributions in nuclei.

Structure functions for the three-nucleon system

The spectral functions and light-cone momentum distributions of protons and neutrons in 3He and 3H are given in terms of the three-nucleon wave function for realistic nucleon-nucleon interactions. To reduce computational complexity, separable expansions are employed for the nucleon-nucleon potentials. The results for the light-cone momentum distributions suggest that they are not very sensitive to the details of the two-body interaction, as long as it has reasonable short-range repulsion. The unpolarised and polarised structure functions are examined for both 3He and 3H in order to test the usefulness of 3He as a neutron target. It is found that the measurement of the spin structure function of polarised 3H would provide a very clear test of the predicted change in the polarised parton distributions of a bound proton.

Reaction operator approach to non-abelian energy loss

A systematic expansion of the induced inclusive gluon radiation associated with jet production in a dense QCD plasma is derived using a reaction operator formalism. Analytic expressions for the transverse momentum and light-cone momentum distributions are derived to all orders in powers of the gluon opacity of the medium, $N\sigma_g/A=L/\lambda_g$. The reaction operator approach also leads to a simple algebraic proof of the ``color triviality'' of single inclusive distributions and to a solvable set of recursion relations. The analytic solution generalizes previous continuum solutions (BDMPS) for applications to mesoscopic QCD plasmas. The solution is furthermore not restricted to uncorrelated geometries and allows for evolving screening scales as well as the inclusion of finite kinematic constraints. The later is particularly important because below LHC energies the kinematic constraints significantly decrease the non-abelian energy loss. Our solution for the inclusive distribution also generalizes the finite order exclusive (tagged) distribution case studied previously (GLV1). The form of the analytic solution is well suited for numerical implementation in Monte Carlo event generators to enable more accurate calculations of jet quenching in ultra-relativistic nuclear collisions. Numerical results illustrating the constributions of the first three orders in opacity are compared to the ``self-quenching'' hard radiation intensity. A surprising result is that the induced gluon radiation intensity is dominated by the (quadratic in $L$) first order opacity contribution for realistic geometries and jet energies in nuclear collisions.

Relativistic Faddeev description of baryons and nucleon structure function in the NJL model

In this work we use the Nambu-Jona-Lasinio (NJL) model as an effective quark theory based on QCD to describe the structure of baryons. Based on the solutions of the relativistic 3-quark Faddeev equation in the ladder approximation, we discuss the masses of the nucleon and the delta, the static properties of the nucleon, and the quark light cone momentum distributions in the nucleon.

Quark distributions in the nucleon based on a relativistic three-body approach to the Nambu–Jona-Lasinio model

Quark light cone momentum distributions in the nucleon are calculated in a relativistic 3-body approach to the NJL model by using a simple 'static approximation' for the Faddeev kernel. A method is presented which automatically satisfies the number and momentum sum rules, even in the regularized theory. In order to assess the sensitivity to the regularization scheme, two schemes which can be formulated in terms of light cone variables are discussed. The effects of the (composite) pion cloud are taken into account in a convolution approach, and the violation of the Gottfried sum rule is discussed. After performing the Q^2 evolution, the resulting distributions are compared to the empirical ones.

Pions in the nuclear medium and Drell-Yan scattering

We investigate the modification of the pion cloud in the nuclear medium and its effect on the nuclear Drell-Yan process. The pion's in-medium self-energy is calculated in a self-consistent delta-hole model, with particle-hole contributions also included. Both the imaginary and real parts of the pion's and delta's self-energy are taken into account and related through a dispersion relation assuring causality. The resulting in-medium pion light-cone momentum distribution shows only a slight enhancement compared to the one of the free nucleon. As a consequence the ratio of the cross section for Drell-Yan scattering on nuclear matter and nucleonic targets is close to unity, in agreement with experiment.

Spectral function for finite nuclei in the local-density approximation.

The spectral function for finite nuclei is computed within the framework of the local-density approximation, starting from nuclear matter spectral functions obtained with a realistic nucleon-nucleon interaction. The spectral function is decomposed into a single-particle part and a ``correlated'' part; the latter is treated in the local-density approximation. As an application momentum distributions, quasiparticle strengths and overlap functions for valence hole states, and the light-cone momentum distribution in finite nuclei are computed.