Light-front Constituent Quark Model Research Articles

Sub-leading twist transverse momentum dependent parton distributions in the light-front quark-diquark model

In this study, the T-even sub-leading twist transverse momentum dependent distributions (TMDs) of proton in the light-front quark-diquark model (LFQDM) have been investigated. We have derived the overlap form of the light-front wave functions (LFWFs) for the sub-leading twist proton TMDs by detangling the un-integrated quark-quark correlator for the semi-inclusive deep inelastic scattering (SIDIS). We have obtained the explicit expressions of TMDs for both the cases of the diquark being a scalar or a vector and analyzed their relationships with leading twist TMDs within the same model. Average transverse momenta and average square transverse momenta for the TMDs have been tabulated and compared with the results from the light-front bag model and the light-front constituent quark model (LFCQM). In addition to this, we have also compared our results for the PDF e(x) with the recent CLAS collaboration results.Transverse momentum dependent parton distributions of proton; T-even sub-leading twist TMDs; light-front quark-diquark model.

Twist-4 T-even proton TMDs in the light-front quark–diquark model

We have dealt with the twist-4 T-even transverse momentum dependent parton distributions (TMDs) for the case of proton in the light-front quark–diquark model (LFQDM). By decoding the unintegrated quark–quark correlator for the semi-inclusive deep inelastic scattering (SIDIS), we have specifically obtained the overlap form for the unpolarized [Formula: see text], longitudinally polarized [Formula: see text] and transversely polarized ([Formula: see text] and [Formula: see text]) proton TMDs. We have provided the explicit expressions for both the cases of the diquark being a scalar or a vector. Average transverse momenta and the average square transverse momenta for the TMDs have been calculated and the results have been tabulated with corresponding leading twist TMDs. In addition, the value of average transverse momentum and average square transverse momentum for TMD [Formula: see text] has been compared with the available light-front constituent quark model (LFCQM) results. From TMDs, we have also obtained and discussed the transverse momentum-dependent parton distribution functions (TMDPDFs). The model relations of the twist-4 T-even TMDs with the available leading twist T-even TMDs have also been obtained.

Semileptonic weak decays of antitriplet charmed baryons in the light-front formalism

We systematically study the semileptonic decays of ${\bf B_c} \to {\bf B_n}\ell^+ \nu_{\ell}$ in the light-front constituent quark model, where ${\bf B_c}$ represent the anti-triplet charmed baryons of $(\Xi_c^0,\Xi_c^+,\Lambda_c^+)$ and ${\bf B_n}$ correspond to the octet ones. We determine the spin-flavor structures of the constituents in the baryons with the Fermi statistics and calculate the decay branching ratios (${\cal B}$s) and averaged asymmetry parameters ($\alpha$s) with the helicity formalism. In particular, we find that ${\cal B}( \Lambda_c^+ \to \Lambda e^+ \nu_{e}, ne^+ \nu_{e})=(3.55\pm1.04, 0.36\pm0.15)\%$, ${\cal B}( \Xi_c^+ \to \Xi^0 e^+ \nu_{e},\Sigma^0 e^+ \nu_{e},\Lambda e^+ \nu_{e})=(11.3\pm3.35), 0.33\pm0.09,0.12\pm0.04\%$ and ${\cal B}( \Xi_c^0 \to \Xi^- e^+ \nu_{e},\Sigma^- e^+ \nu_{e})=(3.49\pm0.95,0.22\pm0.06)\%$. Our results agree with the current experimental data. Our prediction for ${\cal B}( \Lambda_c^+ \to n e^+ \nu_{e})$ is consistent with those in the literature, which can be measured by the charm-facilities, such as BESIII and BELLE. Some of our results for the $\Xi_c^{+(0)}$ semileptonic channels can be tested by the experiments at BELLE as well as the ongoing ones at LHCb and BELLEII.

The Drell-Yan process with pions and polarized nucleons

The Drell-Yan process provides important information on the internal struc- ture of hadrons including transverse momentum dependent parton distribution functions (TMDs). In this work we present calculations for all leading twist structure functions de- scribing the pion induced Drell-Yan process. The non-perturbative input for the TMDs is taken from the light-front constituent quark model, the spectator model, and available parametrizations of TMDs extracted from the experimental data. TMD evolution is im- plemented at Next-to-Leading Logarithmic precision for the first time for all asymmetries. Our results are compatible with the first experimental information, help to interpret the data from ongoing experiments, and will allow one to quantitatively assess the models in future when more precise data will become available.

Pion and kaon distribution amplitudes in the continuum limit

We present a lattice-QCD calculation of the pion, kaon and $\eta_s$ distribution amplitudes using large-momentum effective theory (LaMET). Our calculation is carried out using three ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC collaboration, at 310 MeV pion mass with 0.06, 0.09 and 0.12 fm lattice spacings. We use clover fermion action for the valence quarks and tune the quark mass to match the lightest light and strange masses in the sea. The resulting lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction (RI/MOM) scheme and extrapolated to the continuum. We use two approaches to extract the $x$-dependence of the meson distribution amplitudes: 1) we fit the renormalized matrix elements in coordinate space to an assumed distribution form through a one-loop matching kernel; 2) we use a machine-learning algorithm trained on pseudo lattice-QCD data to make predictions on the lattice data. We found the results are consistent between these methods with the latter method giving a less smooth shape. Both approaches suggest that as the quark mass increases, the distribution amplitude becomes narrower. Our pion distribution amplitude has broader distribution than predicted by light-front constituent-quark model, and the moments of our pion distributions agree with previous lattice-QCD results using the operator production expansion.

Semileptonic decays of Λc+ in dynamical approaches

We study the semileptonic decays of $\Lambda_c^+ \to \Lambda(n)\ell^+ \nu_{\ell}$ in two relativistic dynamical approaches of the light-front constituent quark model (LFCQM) and MIT bag model (MBM). By considering the Fermi statistic between quarks and determining spin-flavor structures in baryons along with the helicity formalism in the two different dynamical models, we calculate the branching ratios (${\cal B}$s) and averaged asymmetry parameters ($\alpha$s) in the decays. Explicitly, we find that ${\cal B}( \Lambda_c^+ \to \Lambda e^+ \nu_{e})=(3.36\pm0.87,3.48)\%$ and ${\alpha}( \Lambda_c^+ \to \Lambda e^+ \nu_{e})=(-0.97\pm0.03,-0.83)$ in (LFCQM, MBM), in comparison with the data of ${\cal B}( \Lambda_c^+ \to \Lambda e^+ \nu_{e})=(3.6\pm0.4)\%$ and ${\alpha}( \Lambda_c^+ \to \Lambda e^+ \nu_{e})=-0.86\pm 0.04$ given by the Particle Data Group, respectively. We also predict that ${\cal B}( \Lambda_c^+ \to n e^+ \nu_{e})=(0.57\pm0.15, 3.6\pm1.5)\times 10^{-3}$ and ${\alpha}( \Lambda_c^+ \to n e^+ \nu_{e})=(-0.98\pm0.02,-0.96\pm0.04)$ in LFCQM with two different scenarios for the momentum distributions of quarks in the neutron, and ${\cal B}( \Lambda_c^+ \to n e^+ \nu_{e})= 0.279\times 10^{-2}$ and ${\alpha}( \Lambda_c^+ \to n e^+ \nu_{e})=-0.87$ in MBM, which could be tested by the ongoing experiments at BESIII, LHCb and BELLEII.

Gravitational form factors of ρ meson with a light-cone constituent quark model

The $\rho$ meson gravitational form factors are studied based on a light-front constituent quark model which has been successfully employed to calculate its generalized parton distributions and some low-energy observables. The distributions of energy, spin, pressures, and shear forces inside the $\rho$ meson are explicitly given.

Generalized parton distribution functions of $\rho$ meson

We report our recent studies of generalized parton distribution functions of a \rhoρ meson with the help of a light-front constituent quark model. The electromagnetic form factors and structure functions of the system are discussed. Moreover, we show our results for its gravitational form factors (or energy-momentum tensor form factors) and other mechanical properties, like mass distributions, pressures, shear forces, and D-D−term.

ρ meson GPDs and IPDs with a light-front constituent quark model

We investigate the ρ meson unpolarized Generalized Parton Distributions based on a Light-Front Constituent Quark Model. Moreover, by employing a Gaussian form wave packet, we apply the obtained generalized parton distributions to get the Impact Parameter dependent parton Distributions.

ρ-Meson properties in medium

Properties of ρ-meson in symmetric nuclear matter are investigated in a light-front constituent quark model (LFCQM), using the in-medium inputs calculated by the quark–meson coupling (QMC) model. The LFCQM used in this study was already applied for the studies of the electromagnetic properties of ρ-meson in vacuum, namely, the charge G0, magnetic G1, and quadrupole G2 form factors, electromagnetic charge radius, and electromagnetic decay constant. Using the two different density dependence of the regulator mass in medium, we predict that the charge radius, and quadrupole moment are enhanced as increasing the nuclear matter density, while the magnetic moment is slightly quenched. Furthermore, we predict the value Qzero2, which crosses zero of the charge form factor, G0(Qzero2)=0 (Q2=−q2>0 with q being the four-momentum transfer), decreases as increasing the nuclear matter density by the two different density dependence of the regulator mass. On the other hand, for the electromagnetic decay constant of the ρ-meson, the two different density dependence of the regulator mass predict the opposite density dependence. Namely, as increasing the nuclear matter density, the naive treatment with the density independent regulator mass as in the vacuum, predicts the increase of the decay constant, while the other that assumes the same density dependence of the regulator mass as that of the in-medium constituent quark mass, predicts the decrease of the decay constant. Thus, although the other physical quantities are predicted to have similar density dependence by the two different density dependence of the regulator mass applied, the density dependence of the ρ-meson electromagnetic decay constant is predicted to have opposite density dependence, and the facts suggest that the in-medium ρ-meson decay constant needs to be investigated further in the future.

ρ meson unpolarized generalized parton distributions with a light-front constituent quark model

We study $\rho$ meson unpolarized generalized parton distributions based on a light-front constituent quark model where the quark-antiquark-meson vertex is constructed under the symmetric loop momentum convention. The form factors and some other low-energy observables of the $\rho$ meson are calculated. Moreover, the contributions to the form factors and generalized parton distributions from the valence and nonvalence regimes are discussed and analyzed in detail. In the forward limit, the usual structure functions are estimated as well. In addition, by evolving the moments of the obtained structure functions to the scale of the lattice calculation, we give the factorization scale of our quark model. It is found that the present phenomenological model is reasonable to describe the general properties of $\rho$ meson.

Euclidean bridge to the relativistic constituent quark model

${\bf Background}$ Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years. At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger Equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models). ${\bf Purpose}$ Seeking to bridge these complementary worldviews, we explore the potential of a Euclidean constituent quark model (ECQM). This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework. ${\bf Method}$ To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark $+$ scalar diquark picture of the nucleon. We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter Equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data. ${\bf Results}$ From this formalism, we define and compute a new quantity --- the Euclidean density function (EDF) --- an object that characterizes the nucleon's various charge distributions as functions of the quark's Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the dressing effect on the proton's axial-singlet charge to be small in magnitude and consistent with zero. ${\bf Conclusions}$ The scalar quark $+$ diquark ECQM is a step toward a realistic quark model in Euclidean space, and urges additional refinements. The small size we obtain for the impact of the dressed vertex on the axial-singlet charge suggests that models without this effect are on firm ground to neglect it.

In-Medium $$\varvec{\rho }$$ ρ -Meson Properties in a Light-Front Approach

Properties of \r{ho}-meson in symmetric nuclear matter are investigated within a light-front constituent quark model (LFCQM), using the in-medium input calculated by the quark-meson coupling (QMC) model. The LFCQM used here was previously applied in vacuum to calculate the \r{ho}-meson electromagnetic properties, namely, charge G 0 , magnetic G 1 , and quadrupole G 2 form factors, as well as the electromagnetic radius and decay constant. We predict the in-medium modifications of the \r{ho}-meson electromagnetic form factors in symmetric nuclear matter.

In-medium pion valence distributions in a light-front model

Pion valence distributions in nuclear medium and vacuum are studied in a light-front constituent quark model. The in-medium input for studying the pion properties is calculated by the quark-meson coupling model. We find that the in-medium pion valence distribution, as well as the in-medium pion valence wave function, are substantially modified at normal nuclear matter density, due to the reduction in the pion decay constant.

Correlations in double parton distributions: perturbative and non-perturbative effects

The correct description of Double Parton Scattering (DPS), which represents a background in several channels for the search of new Physics at the LHC, requires the knowledge of double parton distribution functions (dPDFs). These quantities represent also a novel tool for the study of the three-dimensional nucleon structure, complementary to the possibilities offered by electromagnetic probes. In this paper we analyze dPDFs using Poincar\'e covariant predictions obtained by using a Light-Front constituent quark model proposed in a recent paper, and QCD evolution. We study to what extent factorized expressions for dPDFs, which neglect, at least in part, two-parton correlations, can be used. We show that they fail in reproducing the calculated dPDFs, in particular in the valence region. Actually measurable processes at existing facilities occur at low longitudinal momenta of the interacting partons; to have contact with these processes we have analyzed correlations between pairs of partons of different kind, finding that, in some cases, they are strongly suppressed at low longitudinal momenta, while for other distributions they can be sizeable. For example, the effect of gluon-gluon correlations can be as large as 20 $\%$. We have shown that these behaviors can be understood in terms of a delicate interference of non-perturbative correlations, generated by the dynamics of the model, and perturbative ones, generated by the model independent evolution procedure. Our analysis shows that at LHC kinematics two-parton correlations can be relevant in DPS, and therefore we address the possibility to study them experimentally.

Spin/Orbital Structure of the Nucleon from Wigner Distributions

We present results for the Wigner distributions of the nucleon, which provide multidimensional images of the quark distributions in the phase space and can be seen as the mother distributions of the standard generalized and transverse-momentum dependent parton distributions. We discuss the general features of these distributions within a light-front constituent quark model, emphasizing the new information that can be deduced about the spin-orbit correlations of the quarks in the nucleon.

Electromagnetic Spin-1 Form-Factor Free of Zero-Modes

The electromagnetic current~$J^+$ for spin-1, is used here to extract the electromagnetic form-factors of a light-front constituent quark model. The charge ($G_0$), magnetic ($G_1$) and quadrupole $G_2$ form factors are calculated using different prescriptions known in the literature, for the combinations of the four independent matrix elements of the current between the polarisations states in the Drell-Yan frame. However, the results for some prescriptions relying only on the valence contribution breaks the rotational symmetry as they violate the angular condition. In the present work, we use some relations between the matrix elements of the electromagnetic current in order to eliminate the breaking of the rotational symmetry, by computing the zero-mode contributions to matrix elements resorting only to the valence ones.

Unpolarized transverse momentum dependent parton distribution functions beyond leading twist in quark models

Higher-twist transverse momentum dependent parton distribution functions (TMDs) are a valuable probe of the quark-gluon dynamics in the nucleon, and play a vital role for the explanation of sizable azimuthal asymmetries in hadron production from unpolarized and polarized deep-inelastic lepton-nucleon scattering observed in experiments at CERN, DESY and Jefferson Lab. The associated observables are challenging to interpret, and still await a complete theoretical explanation, which makes guidance from models valuable. In this work we establish the formalism to describe unpolarized higher-twist TMDs in the light-front framework based on a Fock-space expansion of the nucleon state in terms of free on-shell parton states. We derive general expressions and present numerical results in a practical realization of this picture provided by the light-front constituent quark model. We review several other popular quark model approaches including free quark ensemble, bag, spectator and chiral quark-soliton model. We discuss how higher-twist TMDs are described in these models, and obtain results for several TMDs not discussed previously in literature. This study contributes to the understanding of non-perturbative properties of subleading twist TMDs. The results from the light-front constituent quark model are also compared to available phenomenological information, showing a satisfactory agreement.

Double parton correlations in Light-Front constituent quark models

Double parton distribution functions (dPDF) represent a tool to explore the 3D proton structure. They can be measured in high energy proton-proton and proton nucleus collisions and encode information on how partons inside a proton are correlated among each other. dPFDs are studied here in the valence quark region, by means of a constituent quark model, where two particle correlations are present without any additional prescription. This framework allows to understand the dynamical origin of the correlations and to clarify which, among the features of the results, are model independent. Use will be made of a relativistic light-front scheme, able to overcome some drawbacks of the previous calculation. Transverse momentum correlations, due to the exact treatment of the boosts, are predicted and analyzed. The role of spin correlations is also shown. Due to the covariance of the approach, some symmetries of the dPDFs are seen unambigously. For the valence sector, the study of the QCD evolution of the model results, which can be performed safely thanks to the property of good support, has been also completed.

WIGNER DISTRIBUTIONS AND QUARK ORBITAL ANGULAR MOMENTUM

We discuss the quark phase-space or Wigner distributions of the nucleon which combine in a single picture all the information contained in the generalized parton distributions and the transverse-momentum dependent parton distributions. In particular, we present results for the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-front constituent quark model. We show how the quark orbital angular momentum can be extracted from the Wigner distributions and compare it with alternative definitions.