Constituent Quark Research Articles

Toward discovering the excited Ω baryons through nonleptonic weak decays of Ωc

The nonleptonic weak decay processes $\Omega_c \to \Omega\pi^+/\Omega(1P)\pi^+/\Omega(1D)\pi^+/\Omega(2S)\pi^+$ are studied using the constituent quark model. The branching fraction of $\Omega_c \to \Omega\pi^+$ is predicted to be $1.1\%$. Considering the newly observed $\Omega(2012)$ resonance as a conventional $1P$-wave $\Omega$ excite state with spin-parity $J^P=3/2^-$, the newly measured ratio $\mathcal{B}[\Omega_c\to \Omega(2012)\pi^+ \to (\Xi\bar{K})^-\pi^+ ]/\mathcal{B}[\Omega_c\to \Omega \pi^+]$ at Belle can be well understood. Besides, the production rates for the missing $1P-$wave state $\Omega (1^2P_{1/2^-})$, two spin quartet $1D-$wave states $\Omega (1^4D_{1/2^+})$ and $\Omega (1^4D_{3/2^+})$, and two $2S$-wave states $\Omega(2^2S_{1/2^+})$ and $\Omega(2^4S_{3/2^+})$ are also investigated. It is expected that these missing excited $\Omega$ baryons should have large potentials to be discovered through the nonleptonic weak decays of $\Omega_c$ in forthcoming experiments by Belle II and/or LHCb.

Quark orbital angular momentum of ground-state octet baryons

Here we study the quark orbital angular momentum of the ground octet baryons employing an extended chiral constituent quark model, within which the baryon wave functions are taken to be superposition of the traditional $qqq$ and the $qqqq\overline{q}$ higher Fock components. Coupling between the two configurations is estimated using the $^{3}P_{0}$ quark-antiquark creation mechanism, and the corresponding coupling strength is determined by fitting the sea flavor asymmetry of the nucleon. The obtained numerical results show that the quark angular momentum of the nucleon, $\mathrm{\ensuremath{\Sigma}}, \mathrm{\ensuremath{\Lambda}}$, and $\mathrm{\ensuremath{\Xi}}$ hyperons, are in the range 0.10--0.30. In addition, the quark angular momentum of all the hyperons are a little bit smaller than that of the nucleon. And the octet baryons spin fractions taken by the intrinsic quark orbital angular momentum could be up to $60%$ in present model.

Strange hidden-charm [formula omitted] and [formula omitted] pentaquarks and additional [formula omitted], [formula omitted] and [formula omitted] candidates in a quark model approach

Hidden-charm pentaquark-like PψsΛ(4459)0 and PψsΛ(4338) resonances are studied in a constituent quark model as molecular meson-baryon structures. Such states are found in the JP(I)=12−(0) channel with masses and widths compatible with the experimental measurements in a coupled-channels calculation with all the parameters constrained from previous studies. Other candidates are explored in the JP=12−, 32− and 52− channels in the charm and bottom sectors, with isospins 0 (PψsΛ and PϒsΛ) and 1 (PψsΣ and PϒsΣ). Additionally, the formalism is extended to study the PψssN (PϒssN) pentaquarks, where eight candidates are predicted as D¯sΞc molecules in I=12, with JP=12−, 32− and 52− for the charm sector and nine candidates as BsΞb for the bottom one.

Proton quark distributions from a light-front Faddeev-Bethe-Salpeter approach

The projection onto the Light-Front of a Minkowski space Faddeev-Bethe-Salpeter equation model truncated at the valence level is applied to study the proton structure with constituent quarks. The dynamics of the model has built-in: (i) a bound diquark brought by a contact interaction, and (ii) the separation by ∼ΛQCD of the infrared and ultraviolet interaction regions. The model parameters are fine tuned to reproduce the proton Dirac electromagnetic form factor and mass. From that, the non-polarized longitudinal and transverse momentum distributions were computed. The results for the evolved non-polarized valence parton distributions suggest that: (i) the explicit consideration of the spin degree of freedom of both quark and diquark seems not relevant to it, and (ii) the comparison with the global fit from the NNPDF4.0 calls for higher Fock components of the wave function beyond the valence one.

Predicting the masses of exotic hadrons with data augmentation using multilayer perceptron

Recently, there have been significant developments in neural networks, which led to the frequent use of neural networks in the physics literature. This work focuses on predicting the masses of exotic hadrons, doubly charmed and bottomed baryons using neural networks trained on meson and baryon masses that are determined by experiments. The original dataset has been extended using the recently proposed artificial data augmentation methods. We have observed that the neural network’s predictive ability will increase with the use of augmented data. The results indicated that data augmentation techniques play an essential role in improving neural network predictions; moreover, neural networks can make reasonable predictions for exotic hadrons, doubly charmed, and doubly bottomed baryons. The results are also comparable to Gaussian Process and Constituent Quark Model.

Elliptic flow of strange and multi-strange hadrons in isobar collisions at √SNN = 200 GeV at RHIC

We report the elliptic flow (υ2) of Ks0, Λ, Ξ¯+, ϕ, Ξ−, and Ξ+ at midrapidity for Ru+Ru and Zr+Zr collisions at √SNN = 200 GeV. The transverse momentum (pT) and centrality dependence of υ2 have been studied. The number of constituent quark (NCQ) scaling for all the (multi-)strange hadrons has also been tested. The dependence in the ratio of average υ2 (〈υ2〉) on centrality shows a deviation from unity indicating a difference in nuclear structure and deformation between the isobars. The results show a systematic size dependence when compared to Cu+Cu, Au+Au, and U+U collisions at similar beam energies.

Elliptic and triangular flow of (multi-)strange hadrons and ɸ mesons in BES-II energies at STAR

In these proceedings, we present the measurements of elliptic (v2) and triangular (v3) flow of (multi-)strange hadrons and ϕ mesons in 19.6 and 14.6 GeV Au+Au collisions from the STAR. The number of constituent quark (NCQ) scaling of v2 and v3 holds well at √SNN=19.6 GeV, which indicates the collective flow is built up in the partonic stage. At these energies, the anti-particles show better NCQ scaling than the particles for both v2 and v3, which may be caused by the different contributions from the produced and transported quarks.

Particles Composition and Interactions Using the Nuon Model

The Standard Model in Particle Physics has been able to make many predictions confirmed later with a flow of experimental results. With the discovery of the Higgs boson at the LHC, one is full of admiration for the people contributing to this model fifty years ago and its predictions that have been confirmed gradually. The original particle quark constituent model has evolved with the deep inelastic experiments to a quark and gluons system, then to a more general system with virtual quarks. This work is the result of observations while working at CERN in Geneva with many different experiments at the ISR, SPS, LEP, LHC colliders. A new model based on nuons is introduced, that allows accurate evaluations of the particle masses (mesons and baryons) and magnetic moment, computes very accurately the kinematics distributions for particles and jets observed in the p-p collisions at the LHC (elastic and inelastic) and at lower energy machines. This new model looks at a first glance in contradiction with the quark model because it can build the elementary particles with nuons only, i.e. electrons and neutrinos. However, all the existing physics involved in electron, positron and neutrino interactions may be used to explain interactions between composite particles such as protons or heavy ions.

Spectroscopy of Ωccc and Ωbbb baryons

In this paper, we study the properties of triply charm and triply bottom baryon. The mass spectra of these baryons are calculated in nonrelativistic constituent quark model with Coulomb plus screened potential. Several states [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] of the [Formula: see text] and [Formula: see text] baryons with quantum number [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are determined. Regge trajectories are also plotted to determine the quantum number of baryons. Moreover, the magnetic moments are calculated for [Formula: see text].

Diffusion Monte Carlo calculations of fully heavy compact hexaquarks

We used a diffusion Monte Carlo technique to describe the properties of fully-heavy compact arrangements (no dibaryon molecules) including six quarks and no antiquarks within the framewok of a constituent quark model. Only arrangements whose wavefunctions were eigenvectors of $L^2$ with eigenvalue $\ell$ = 0 were taken into account, what means that we only considered the subset of all the possible color-spin combinations that make the total wavefunctions antisymmetric with respect to the interchange of any two quarks of the same type. This means arrangements with spin $S=0$ for $cccccc$, $bbbbbb$, $cccccb$, $bbbbbc$ and $cccbbb$ and spin $S=0,1,2$ for the $ccccbb$ and $bbbbcc$ hexaquarks. In all cases, the masses of the six-quark arrangements are larger that the ones corresponding to the sum of any of the two baryons we can split them into, but smaller that the ones for a set of six isolated quarks, i.e., all them are bound systems. The analysis of their structure indicates that all the hexaquarks considered in this work are compact objects, except the $cccbbb$, that appears to be a loose association of two baryons.

Models of $$J/\varPsi $$ photo-production reactions on the nucleon

The $J/\Psi$ photo-production reactions on the nucleon can provide information on the roles of gluons in determining the $J/\Psi$-nucleon ($J/\Psi$-N) interactions and the structure of the nucleon. The information on the $J/\Psi$-N interactions is needed to test lattice QCD (LQCD) calculations and to understand the nucleon resonances such as $N^*(P_c)$ recently reported by the LHCb Collaboration. In addition, it is also needed to investigate the production of nuclei with hidden charms and to extract the gluon distributions in nuclei. The main purpose of this article is to review six reaction models of $\gamma + p \rightarrow J/\Psi +p$ reactions which have been and can be applied to analyze the data from Thomas Jefferson National Accelerator Facility (JLab). The formulae for each model are given and used to obtain the results to show the extent to which the available data can be described. The models presented include the Pomeron-exchange model of Donnachie and Landshoff (Pom-DL) and its extensions to include $J/\Psi$-N potentials extracted from LQCD (Pom-pot) and to also use the constituent quark model (CQM) to account for the quark substructure of $J/\Psi$ (Pom-CQM). The other three models are developed from applying the perturbative QCD approach to calculate the two-gluon exchange using the generalized parton distribution (GPD) of the nucleon (GPD-based), two- and three-gluon exchanges using the parton distribution of the nucleon ($2g+3g$), and the exchanges of scalar ($0^{++}$) and tensor ($2^{++}$) glueballs within the holographic formulation (holog). The results of investigating the excitation of the nucleon resonances $N^*(P_c)$ in the $\gamma + p \rightarrow J/\Psi +p$ reactions are also given.

Counting states: A combinatorial analysis of SQM fragmentation

AbstractThe Strange Quark Matter (SQM) hypothesis states that at extreme pressure and density conditions, a new ground state of matter would arise, in which half of the down quarks become strange quarks. If true, it would mean that at least the core of neutron stars is made of SQM. In this hypothesis, SQM would be released in the interstellar medium when two of these objects merge. It is estimated that of SQM would be released this way. This matter will undergo a sequence of processes that should result in a fraction of the released SQM becoming heavy nuclei through the r‐process. In this work, we are interested in characterizing the fragmentation of SQM, with the novelty of keeping track of the quark configuration of the fragmented matter. This is accomplished by developing a methodology to estimate the energy of each fragment as the sum of its constituent quarks, the Coulomb interaction among the quarks and fragments' momenta.

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.

Production of single-charmed baryons in a quark model approach

The production of single-charmed baryons $\Lambda_c^+ \Lambda_c^-$, $\Lambda_c^+ \Sigma_c^-$+h.c. and $\Sigma_c^+ \Sigma_c^-$ in $p\bar p$ collisions is studied in the framework of a constituent quark model which has satisfactorily described the $N\bar N$ system and the strangeness production $p\bar p\to \Lambda\bar \Lambda$, $\Lambda\bar\Sigma$ and $\Sigma\bar\Sigma$ processes. Predictions on the total cross sections are analyzed for different approaches to the underlying $n\bar n\to c\bar c$ process, mediated by one gluon annihilation diagrams. The results indicate that the cross section is of the order of $1$ nb between $10-14$ GeV for $\Lambda_c^+\Lambda_c^-$ and $\Lambda_c^+ \Sigma_c^-$ channels, and around $0.01-0.1$ nb for $\Sigma_c^+\Sigma_c^-$. This estimations can be relevant for their future search in facilities like $\bar{P}$ANDA.

Electron-based Constituent Quark Model

The empirically introduced Electron-based Constituent Quark Model (ECQM) is considered from the symmetry motivated point of view, including the 3:1 ratio between the electron mass me and the QED correction MH∘(α/2π)2 to the scalar mass. Common parameters Mq=me(α/2π)−1=441MeV, 391 MeV in ECQM and NRCQM (Nonrelativistic Constituent Quark Model) and 16me=δ are used in the description existing empirical data.

Spectroscopy of light baryons: Δ resonances

The spectroscopy of light and strange baryons had been an important aspect with still unknown resonances and intrinsic baryonic properties. This paper focuses on the [Formula: see text] baryons treating [Formula: see text] and [Formula: see text] quarks with different constituent masses. The theoretical framework for calculating the resonance masses is hypercentral Constituent Quark Model (hCQM) with confining potential of the linear form. To account for the spin–orbit splitting in the correct order, first- and second-order corrections of the order [Formula: see text] and [Formula: see text] have been incorporated to the potential and spin-dependent term, respectively. The results obtained have been compared with many varied approaches as well as experimental available states. In addition to mass spectra, Regge trajectories for (n, [Formula: see text]) and ([Formula: see text], [Formula: see text]) have been plotted. The magnetic moment as well as transition magnetic moment have been calculated using effective quark mass. The radiative decay width has been studied for [Formula: see text] and [Formula: see text] channels.

Study of N(1520) and N(1535) structures via $$\gamma ^*p\rightarrow N^*$$ transitions

The helicity amplitudes of the N(1520) and N(1535) resonances in the $$\gamma ^*p\rightarrow N^*$$ electromagnetic transition are studied in the constituent quark model using the impulse approximation, with the proton and resonances assumed to be in three-quark configurations. The comparison of theoretical results and experimental data on the helicity amplitudes $$A_{1/2}$$ , $$A_{3/2}$$ , and $$S_{1/2}$$ indicates that the N(1520) and N(1535) resonances are primarily composed of three-quark $$L=1$$ states but may contain additional components. However, it is improbable that contributions from meson clouds will be dominant at low $$Q^2$$ .

Anisotropic pressure of magnetized quark matter with anomalous magnetic moment

We investigate magnetic field $(eB)$ dependence of constituent quark mass, the longitudinal and transverse pressure as well as the magnetization and magnetic susceptibility of strongly interacting quark matter. We employ the two-flavor Polyakov Nambu--Jona-Lasinio model with the inclusion of the anomalous magnetic moment (AMM) of the quarks at finite temperature ($T$) and finite quark chemical potential $({\ensuremath{\mu}}_{q})$ capturing different stages of chiral phase transition. We find that the transverse pressure, magnetization, and magnetic susceptibility become highly oscillatory for large values of $eB$ in the chiral symmetry broken phase. However, the oscillations cease to occur at higher values of $T$ and ${\ensuremath{\mu}}_{q}$ when chiral symmetry is (partially) restored and the anisotropic nature of the pressure becomes significant even at smaller values of $eB$. As the inclusion of AMM of the quarks leads to inverse magnetic catalysis of the transition temperature, we observe that the variations of transverse pressure, magnetization, and magnetic susceptibility are significantly modified in the vicinity of the chiral transition temperature. Furthermore, above the chiral transition temperature the magnetic susceptibility is found to remain positive for a wide range of $eB$, indicating a paramagnetic character of the strongly interacting quark matter. Finally, we have also examined the magnetism of strongly interacting matter in the quarkyonic phase. The obtained results could be useful for a magnetohydrodynamic evolution of hot and dense matter created in heavy-ion collisions.

Averaged transverse momentum correlations of hadrons in relativistic heavy-ion collisions

We compile experimental data for the averaged transverse momentum ($\left\langle p_{T}\right\rangle $) of proton, $\Lambda$, $\Xi^{-}$, $\Omega^{-}$ and $\phi$ at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}=$ 200, 39, 27, 19.6, 11.5, 7.7 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 2.76 TeV, and find that experimental data of these hadrons exhibit systematic correlations. We apply a quark combination model with equal-velocity combination approximation to derive analytic formulas of hadronic $\left\langle p_{T}\right\rangle $ in the case of exponential form of quark $p_{T}$ spectra at hadronization. We use them to successfully explain the systematic correlations exhibited in $\left\langle p_{T}\right\rangle $ data of $p\Lambda$, $\Lambda\Xi^{-}$, $\Xi^{-}\Omega^{-}$ and $\Xi^{-}\phi$ pairs. We also use them to successfully explain the regularity observed in $\left\langle p_{T}\right\rangle $ of these hadrons as the function of $(dN_{ch}/dy)/(N_{part}/2)$ at mid-rapidity in central heavy-ion collisions at both RHIC and LHC energies. Our results suggest that the constituent quark degrees of freedom and the equal-velocity combination of these constituent quarks at hadronization play important role in understanding the production of baryons and $\phi$ meson at these RHIC and LHC energies.

A hybrid model of constituent quarks

The paper presents a hybrid model of constituent quark which considers the preonic structure based on z0 (34 me)-preon, specific to the previously published cold genesis theory (CGT) of the author and basic concepts of the S.M. which seem experimentally sustained, explaining the constituent quarks forming from current quarks and “gammonic” gluols –in concordance with the experimentally evidenced possibility of paired quarks forming from relativist jets of negatrons and positrons, by considering that the negatrons and positrons can form ‘gammonic’ “gluols” and thereafter- current and constituent quarks, by the magnetic and electric interactions between the paired quasielectrons (degenerate electrons), which can explain the constituent u- quark’s stability until the critical temperature 2x1012 K, without the concepts of “color charge” and of “virtual” gluon/boson. The resulted hybrid model can also explain why in strong interactions the sum rule can be applied correspondent with the transferring of some quarks from an interacting particle to another with the entire or almost entire their constituent mass. Also, it suggests that the mechanism of paired current u-quarks forming from gluons, used by the S. M., can be plausible in conformity with the mass conservation law only if the quantum vacuum contains real thermalized “gammons” considered as (e+e-)*-pairs of degenerate electrons.