Constituent Quark Research Articles

Deep learning predicted elliptic flow of identified particles in heavy-ion collisions at the RHIC and LHC energies

Recent developments on a deep learning feed-forward network for estimating elliptic flow ($v_2$) coefficients in heavy-ion collisions have shown us the prediction power of this technique. The success of the model is mainly the estimation of $v_2$ from final state particle kinematic information and learning the centrality and the transverse momentum ($p_{\rm T}$) dependence of $v_2$. The deep learning model is trained with Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV minimum bias events simulated with a multiphase transport model (AMPT). We extend this work to estimate $v_2$ for light-flavor identified particles such as $\pi^{\pm}$, $\rm K^{\pm}$, and $\rm p+\bar{p}$ in heavy-ion collisions at RHIC and LHC energies. The number of constituent quark (NCQ) scaling is also shown. The evolution of $p_{\rm T}$-crossing point of $v_2(p_{\rm T})$, depicting a change in meson-baryon elliptic flow at intermediate-$p_{\rm T}$, is studied for various collision systems and energies. The model is further evaluated by training it for different $p_{\rm T}$ regions. These results are compared with the available experimental data wherever possible.

Quark condensate and magnetic moment in a strong magnetic field

This paper studies the quark condensate, magnetic moment, magnetic polarization, and magnetic susceptibility in a strong external magnetic field by employing the Dyson–Schwinger equations (DSE). The results show these physical quantities as functions of the magnetic field. We note that the quark’s spin polarizations are approximately proportional to the magnetic field magnitude. For comparison, we investigate the magnetic moments and susceptibility of the nucleon in the constituent quark model framework and demonstrate that both these quantities increase as the magnetic field rises.

Nature of the doubly-charmed tetraquark [formula omitted] in a constituent quark model

The recently discovered Tcc+ is evaluated as a DD⁎ molecular structure in the JP=1+ sector. A coupled-channels calculation in charged basis, considering the D0D⁎+, D+D⁎0 and D⁎0D⁎+ channels, is done in the framework of a constituent quark model that successfully described other molecular candidates in the charmonium spectrum such as the X(3872). The Tcc+ is found as a D0D⁎+ molecule (87%) with a binding energy of 387 keV/c2 and a width of 81 keV, in agreement with the experimental measurements. The quark content of the state forces the inclusion of exchange diagrams to treat indistinguishable quarks between the D mesons, which are found to be essential to bind the molecule. The D0D0π+ line shape, scattering lengths and effective ranges of the molecule are also analyzed, which are found to be in agreement with the LHCb analysis. We search for further partners of the Tcc+ in other charm and bottom sectors, finding different candidates. In particular, in the charm sector we find a shallow JP=1+D+D⁎0 molecule (83%), dubbed Tcc′, just 1.8 MeV above the Tcc+ state. In the bottom sector, we find an isoscalar and an isovector JP=1+ bottom partners, as BB⁎ molecules lying 21.9 MeV/c2 (I=0) and 10.5 MeV/c2 (I=1), respectively, below the B0B⁎+ threshold.

Mass spectra of neutral mesons K0,π0,η,η′ at finite magnetic field, temperature and quark chemical potential

The mass spectra of neutral mesons $K_0, \pi_0, \eta, \eta'$ on temperature-quark chemical potential $(T-\mu)$ plane in the presence of a constant magnetic field is investigated in the $SU(3)$ NJL model. As a Goldstone boson of chiral symmetry breaking, the mass of $K_0$ meson increases with temperature and/or quark chemical potential, and we observe two kinds of mass jumps of $K_0$ meson in media, which is induced by the mass jump of constituent quarks and the magnetic field, respectively. Due to the breaking of isospin symmetry between $u$ and $d$ quarks in magnetic fields, the mixing of $\pi_0-\eta- \eta'$ mesons occurs and this leads to rich structures of their mass spectra. For instance, $\pi_0$ mass is influenced by the strange quark. There appear the change of increase ratio of $\pi_0$ mass at high $\mu$ and vanishing $T$ and the $\pi_0$ mass jump crossing over the threshold of two times of strange quark mass at finite $T$ and $\mu$. The mass ordering of $\pi_0, \ \eta,\ \eta'$ mesons varies in media, due to their mass jumps, which are induced by the mass jump of constituent quarks or the magnetic field.

Doubly heavy tetraquark multiplets as heavy antiquark-diquark symmetry partners of heavy baryons

Symmetries play important roles in the understanding of hadron structures and spectroscopy. Motivated by the discovery of the doubly charmed tetraquark ${T}_{cc}^{+}(3875)$, we study the ground states of the doubly heavy tetraquarks with the QCD inspired heavy antiquark-diquark symmetry in the constituent quark model. Six ground states of ${T}_{QQ}(Q=c,b)$ are predicted and the lightest ${T}_{cc}$ state has a mass of $3875.8\ifmmode\pm\else\textpm\fi{}7.6\text{ }\text{ }\mathrm{MeV}$ and spin-parity ${1}^{+}$, which are consistent with those of the observed ${T}_{cc}^{+}(3875)$. In addition, the magnetic moments of the predicted tetraquarks ${T}_{cc}^{+}(3876)$ and ${T}_{bb}^{\ensuremath{-}}(10396)$ are also estimated in the same model, which provide further information to distinguish the structures of the ${T}_{QQ}$ states.

Mass spectra of singly, doubly, triply light-strange baryons in light of 𝒪(1m2) relativistic correction

The hypercentral Constituent Quark Model (hCQM) has been employed to obtain the resonance masses of hadrons ranging from light, strange to heavy sector. This work is dedicated towards incorporating the higher order correction in the mass so as to improve the spin-order hierarchy. The potential is Coulomb-like part and linear term as confinement part along with the spin–spin interaction terms. In this paper, the light, strange baryon masses have been revisited with correction term with [Formula: see text] and [Formula: see text] and compared with earlier results as well as various other approaches. The slope and intercepts have been recalculated for obtained masses which are expected to aid in experimental findings. The recent results are found to be in good accordance with the experimental range as well as theoretical models.

Spectroscopic Study of $$\pmb {\varOmega _{cc}}$$, $$\pmb {\varOmega _{cb}}$$ and $$\pmb {\varOmega _{bb}}$$ Baryons

In this paper, we presented the mass spectra of the doubly heavy $\Omega$ baryons containing one light (strange) quark and two heavy (charm and bottom) quarks. Our predicted masses can be consider to determine the $J^p$ value for the resonances detected by experimental facilities in future. The masses of ground excited states (1S-6S, 1P-3P, 1D-2D, 1F-2F) are calculated for all possible $J^p$ values, using the Hypercentral Constituent Quark Model (hCQM), by employing screened potential as confining potential with color-Coloumb potential. Regge trajectories are also plotted in $(J, M^2)$ plane for natural and unnatural parities. Doubly heavy Omega states are not declared yet by any experimental facility. We compared our results to the predictions gained from other theoretical approaches, and we found that our predictions are quite close to those of them. Other properties such as magnetic moment (for spin state $\frac{1}{2}$ and $\frac{3}{2}$) and radiative decay width are calculated using the enuerated masses.

Dirac sea effects on heavy quarkonia decay widths in magnetized matter: A field theoretical model of composite hadrons

We study the partial decay widths of charmonium (bottomonium) states to $D\bar D (B\bar B)$ mesons in magnetized (nuclear) matter using a field theoretic model of composite hadrons with quark (and antiquark) constituents. These are computed from the mass modifications of the decaying and produced mesons, including the nucleon Dirac sea effects within a chiral effective model. The Dirac sea contributions are observed to lead to an rise (drop) in the quark condensates as the magnetic field is increased, an effect called the (inverse) magnetic catalysis. In the presence of a magnetic field, there are mixings of spin 0 (pseudoscalar) and spin 1 (vector) states (PV mixing) The nucleon Dirac sea effects are observed to be significant and the anomalous magnetic moments (AMMs) of the nucleons are observed to play an important role. For $\rho_B$=0, there is observed to be magnetic catalysis (MC) without and with AMMs, whereas, for $\rho_B=\rho_0$, the inverse magnetic catalysis (IMC) is observed when the AMMs are taken into account, contrary to MC, when the AMMs are ignored. The magnetic field effects on the heavy quarkonium decay widths should have observable consequences on the production of the hidden and open heavy flavour mesons from ultra-relativistic peripheral heavy ion collision experiments, at RHIC and LHC, where the produced magnetic fields are extremely large.

Ground state baryons in the flux-tube three-body confinement model using diffusion Monte Carlo

We make a systematical diffusion Monte Carlo (DMC) calculation for all ground state baryons in two confinement scenarios, the pairwise confinement and the three-body flux-tube confinement. With the baryons as an example, we illustrate a feasible procedure to investigate the few-quark states with possible few-body confinement mechanisms, which can be extended to the multiquark states easily. For each baryon, we extract the mass, mean-square radius, charge radius, and the quark distributions. We use the Jackknife resampling method to estimate the statistical uncertainties of masses to be less than 1 MeV. To determine the baryon charge radii, we include the constituent quark size effect, which is fixed by the experimental and lattice QCD results. Our results show that both two-body and three-body confinement mechanisms can give a good description of the experimental data if the parameters are chosen properly. In the flux-tube confinement, introducing different tension parameters for the baryons and mesons are necessary, specifically, $\sigma_Y= 0.9204 \sigma_{Q\bar{Q}}$. The lesson from the calculation of the nucleon mass with the DMC method is that the improper pre-assignment of the channels may prevent us from obtaining the real ground state. With this experience, we obtain the real ground state (the $\eta_c \eta_c$ threshold with the di-meson configuration) of the $cc\bar{c}\bar{c}$ system with $J^{PC}=0^{++}$ starting from the diquark-antidiquark spin-color channels alone, which is hard to achieve in the variational method and was not obtained in the previous DMC calculations.

Small parameters in infrared QCD: The pion decay constant

We continue our investigation of the QCD dynamics in terms of the Curci-Ferrari effective Lagrangian, a deformation of the Faddeev-Popov one in the Landau gauge with a tree-level gluon mass term. In a previous work we have studied the dynamics of chiral symmetry breaking at the level of the quark propagator and, in particular, the dynamical generation of a constituent quark mass. In the present article, we study the associated Goldstone mode, the pion, and we compute the pion decay constant in the chiral limit. Our approach exploits the fact that the coupling (defined in the Taylor scheme) in the pure gauge sector is perturbative, as observed in lattice simulations which, together with a $1/N_c$-expansion, allows for a systematic, controllable approximation scheme in the low energy regime of QCD. At leading order, this leads to the well-known rainbow-ladder resummation. We study the region of parameter space of the model that gives physical values of the pion decay constant. This allows one to constrain the gluon mass parameter as a function of the coupling using a physically measured quantity.

Cancellation of the Sigma Mode in the Thermal Pion Gas by Quark Pauli Blocking

In this study, we calculate the pressure of the interacting pion gas using the Beth–Uhlenbeck approach to the relativistic virial expansion with Breit–Wigner phase shifts for the σ- and ϱ-meson resonances. The repulsive phase shift δ02 is taken from the quark interchange model of Barnes and Swanson, which is in very good agreement with the experimental data. In this work we show that the cancellation of the attractive (I = 0) and repulsive (I = 2) isospin channel contributions to the scalar ππ interaction in the low-energy region that is known for the vacuum phase shifts also takes place at a finite temperature. This happens despite the strong medium dependence of these phase shifts that enters our model by the temperature dependence of the σ-meson and constituent quark masses, because for these masses the relation Mσ(T)≈2mq(T) holds and the scattering length approximation is valid as long as the strong decay channel σ→ππ is open. Exploiting the Nambu–Jona-Lasinio model for describing the dynamical breaking of chiral symmetry in the vacuum and its restoration at a finite temperature, we justify with our approach that the σ-meson should be absent from the hadron resonance gas description at low temperatures because the above cancellation holds. However, since this cancellation breaks down in the vicinity of the hadronization transition, where due to chiral symmetry restoration the decay channel σ→ππ closes and the σ-meson becomes a good resonance, the latter should be included into the statistical model description of chemical freeze-out in heavy-ion collisions.

Independence of current components, polarization vectors, and reference frames in the light-front quark model analysis of meson decay constants

The issue of resulting in the same physical observables with different current components, in particular from the minus current, has been challenging in the light-front quark model (LFQM) even for the computation of the two-point functions such as meson decay constants. At the level of one-body current matrix element computation, we show the uniqueness of pseudoscalar and vector meson decay constants using all available components including the minus component of the current in the LFQM consistent with the Bakamjian-Thomas construction. Regardless of the current components, the polarization vectors, and the reference frames, the meson decay constants are uniquely determined in the noninteracting constituent quark and antiquark basis while the interactions of the constituents are added to the meson mass operator in the LFQM.

Strong decay widths and mass spectra of charmed baryons

The total decay widths of the charmed baryons are calculated by means of the $^{3}{P}_{0}$ model. Our calculations consider in the final states: the charmed baryon-(vector/pseudoscalar) meson pairs and the (octet/decuplet) baryon-(pseudoscalar/vector) charmed meson pairs, within a constituent quark model. Furthermore, we calculate the masses of the charmed baryon ground states and their excitations up to the $D$-wave in a constituent quark model both in the three-quark and in the quark-diquark schemes, utilizing a Hamiltonian model based on a harmonic oscillator potential plus a mass splitting term that encodes the spin, spin-orbit, isospin, and flavor interactions. The parameters of the Hamiltonian model are fitted to the experimental data of the charmed baryon masses and decay widths. As the experimental uncertainties of the data affect the fitted model parameters, we have thoroughly propagated these uncertainties into our predicted charmed baryon masses and decay widths via a Monte Carlo bootstrap approach, which is often absent in other theoretical studies on this subject. Our quantum number assignments and predictions of the masses and strong partial decay widths are in reasonable agreement with the available data. Thus, our results show the ability to guide future measurements in LHCb, Belle and Belle II experiments. Finally, the appendices provide some details of our calculations, in which we include the flavor coupling coefficients, which are useful for further theoretical investigations.

Inverse mass ordering of light scalar mesons in the Nambu–Jona-Lasinio model

AbstractThe masses of the low-lying scalar mesons are investigated in the three-flavor Nambu–Jona-Lasinio (NJL) model by treating the scalar mesons as composite objects of a quark and an antiquark. It is known that a simple $\bar{q}q$ picture fails to reproduce the so-called inverse mass ordering for the scalar mesons. Recently a new mechanism to reproduce the observed mass spectrum of the scalar mesons was proposed in a linear sigma model by introducing flavor symmetry breaking induced by the U(1) axial anomaly. Motivated by this proposal, we examine whether this new mechanism also works in the NJL model. By calculating the scalar meson masses, we find that the NJL model reproduces the observed mass ordering with sufficient strength of the new term. With this mechanism, it turns out that the constituent strange quark mass becomes degenerate to that of the up and down quarks if the inverse mass ordering is reproduced. We also discuss the scalar diquark masses to check the consistency of the degeneracy of the constituent quark masses with the light baryon masses.

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.