Constituent Quark Research Articles

Stable double-heavy tetraquarks: Spectrum and structure

Bound states of double-heavy tetraquarks are studied in a constituent quark model. Two bound states are found for isospin and spin-parity I(JP)=0(1+) in the bbu¯d¯ channel. One is deeply bound and compact made of colored diquarks, while the other is shallow and extended as a BB⁎ molecule. The former agrees well with lattice QCD results. A systematic decrease in the binding energy is seen by replacing one of the heavy quarks to a lighter one. Altogether we find ten bound states. It is shown for the first time that hadrons with totally different natures emerge from a single Hamiltonian.

Quark sea flavor asymmetries in the spin−32+ decuplet baryons

The implications of the quark sea generation through the chiral fluctuations have been studied in the context of quark flavor distribution functions for the $\text{spin}\ensuremath{-}{(3/2)}^{+}$ decuplet baryons. The chiral constituent quark model allows a simple and intuitive method to investigate the principle features of the hadron structure and is able to qualitatively generate the requisite amount of quark sea. It is also known to provide a satisfactory justification for the chiral symmetry breaking and SU(3) symmetry breaking. In light of the recent developments to test the mechanism for the quark sea generation, the quark sea asymmetries $\overline{d}\ensuremath{-}\overline{u}$, $\overline{d}/\overline{u}$ and the fraction of a particular quark ${F}_{q}^{{B}^{*}}=({q}^{{B}^{*}}+{\overline{q}}^{{B}^{*}}/{\ensuremath{\sum}}_{q}({q}^{{B}^{*}}+{\overline{q}}^{{B}^{*}}))$ have been studied for the $\text{spin}\ensuremath{-}{(3/2)}^{+}$ decuplet baryons. The suppression factors estimating the strange quark content with respect to the nonstrange quarks in the $\mathrm{\ensuremath{\Delta}}$ baryons and the suppression factors estimating the $u$ and $d$ quark contents with respect to the strange quarks in ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ baryons have also been discussed.

Towards the understanding of fully-heavy tetraquark states from various models

We use a color-magnetic interaction model (CMIM), a traditional constituent quark model (CQM) and a multiquark color flux-tube model (MCFTM) to systematically investigate the properties of the states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ ($Q=c,b$). The dynamical investigation indicates that the CMIM can not completely absorb QCD dynamical effects through the effective constituent quark mass and overestimates the color-magnetic interaction in the states under the assumption of the same spatial configurations. The Coulomb interaction plays a critical role in the dynamical model calculations on the heavy hadrons, which induces the fact that none of bound states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ can be found in the dynamical models. The color configuration $\left[[Q_1Q_2]_{\mathbf{6}_c}[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}\right]_{\mathbf{1}}$ should be taken seriously in the ground states due to the strong Coulomb attraction between the $[Q_1Q_2]_{\mathbf{6}_c}$ and $[\bar{Q}_3\bar{Q}_4]_{\bar{\mathbf{6}}_c}$. The color configuration $\left[[Q_1Q_2]_{\bar{\mathbf{3}}_c}[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}\right]_{\mathbf{1}}$ is absolutely dominant in the excited states because of the strong Coulomb attraction within the $[Q_1Q_2]_{\bar{\mathbf{3}}_c}$ and $[\bar{Q}_2\bar{Q}_4]_{\mathbf{3}_c}$. The $J/\Psi$-pair resonances recently observed by LHCb are difficult to be accommodated in the CMIM. The broad structure ranging from 6.2 to 6.8 GeV can be described as the ground tetraquark state $[cc][\bar{c}\bar{c}]$ in the various dynamical models. The narrow structure $X(6900)$ can be identified as the excited state $[cc][\bar{c}\bar{c}]$ with $L=1$ ($L=2$) in the CQM (MCFTM).

Observing the Minkowskian dynamics of the pion on the null-plane

A dynamical model is applied to the study of the pion valence light-front wave function, obtained from the actual solution of the Bethe-Salpeter equation in Minkowski space, resorting to the Nakanishi integral representation. The kernel is simplified to a ladder approximation containing constituent quarks, an effective massive gluon exchange, and the scale of the extended quark-gluon interaction vertex. These three input parameters carry the infrared scale {\Lambda}QCD and are fine-tuned to reproduce the pion weak decay constant, within a range suggested by lattice calculations. Besides f{\pi}, we present and discuss other interesting quantities on the null-plane, like: (i) the valence probability, (ii) the dynamical functions depending upon the longitudinal or the transverse components of the light-front (LF) momentum, represented by LF-momentum distributions and distribution amplitudes, and (iii) the probability densities both in the LF-momentum space and the 3D space given by the Cartesian product of the covariant Ioffe-time and transverse coordinates, in order to perform an analysis of the dynamical features in a complementary way. The proposed analysis of the Minkowskian dynamics inside the pion, though carried out at the initial stage, qualifies the Nakanishi integral representation as an appealing effective tool, with still unexplored potentialities to be exploited for addressing correlations between dynamics and observable properties.

<i>H</i>, <i>W</i>, <i>Z</i> Bosons, Dark Matter: Composite Particles?

The present article develops a model initially published in ref. [1]. It is a quasi-classical quantum model of composite particles with ultra-relativistic (UR) constituents (leptons and quarks). The model is used to calculate the mass energy of three composite particles: a UR tauonium, a UR bottomonium and a UR leptoquarkonium. The result is that these three hypothetic particles have masses close to 125 GeV: the Higgs boson mass energy. These results are recalled in the present article. Then the model is extended to calculate the mass energy of pi-mesons, W and Z bosons. Finally, the model provides a hypothesis on dark matter.

Quark matter within Polyakov chiral SU(3) quark mean field model at finite temperature

Thermodynamical properties and phase diagram of asymmetric strange quark matter using the Polyakov chiral $$\text {SU(3)}$$ quark mean field (PCQMF) model at finite temperature and chemical potential have been investigated. Within the PCQMF model, the properties of quark matter are calculated through the scalar fields $$\sigma $$ , $$\zeta $$ , $$\delta $$ and $$\chi $$ , the vector fields $$\omega $$ , $$\rho $$ and $$\phi $$ and the Polyakov loop fields $$\Phi $$ and $$\bar{\Phi }$$ . The isospin splitting of constituent quark masses is observed at large isospin asymmetry. The effect of temperature and strangeness fraction on energy per baryon and equation of state is found to be appreciable in quark matter. The effect of the Polyakov loop dynamics on several thermodynamical bulk quantities such as energy density, entropy density and trace anomaly is presented. Furthermore, within the model under mean field approximation, we explore the phase structure in $$T-\mu $$ plane and analyzed the impact of varying the strength of vector coupling and isospin chemical potential on nature of phase transition.

Mass spectrum and strong decays of strangeonium in a constituent quark model * *Supported by the National Natural Science Foundation of China (U1832173, 11775078, 11705056, 11405053)

In this work we calculate the mass spectrum of strangeonium up to the multiplet within a nonrelativistic linear potential quark model. Furthermore, using the obtained wave functions, we also evaluate the strong decays of the strangeonium states with the model. Based on our successful explanations of the well established states , , , , and , we further discuss the possible assignments of strangeonium-like states from experiments by combining our theoretical results with observations. It is found that some resonances, such as and , listed by the Particle Data Group, and and , newly observed by BESIII, may be interpreted as strangeonium states. The possibility of as a candidate for or cannot be excluded. We expect our results to provide useful references for looking for the missing states in future experiments.

Singlet, triplet, and octet axial-vector form factors of the spin−32+ decuplet baryons in the chiral quark constituent model

The axial-vector form factors of the $\mathrm{spin}\ensuremath{-}{\frac{3}{2}}^{+}$ decuplet baryons are investigated in the chiral constituent quark model using their explicit quark spin polarizations. The quark sea arises from the chiral symmetry breaking, which results in the Goldstone bosons mediating the interaction between constituent quarks. The axial-vector form factors, which have some physical significance corresponding to the flavor singlet current, flavor isovector (triplet) current, and the flavor hypercharge axial (octet) current at zero momentum transfer, are, respectively ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{0}(0)$, ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{3}(0)$, and ${G}_{\mathrm{AV},{B}^{*\frac{3}{2}}}^{8}(0)$. In order to further understand the ${Q}^{2}$ dependence of these form factors, we have used the dipole form of parametrization. The qualitative and quantitative contribution of the quark sea has also been investigated by varying the transition probability of the chiral fluctuation.

Number of constituent quark scaling of elliptic flows in high multiplicity p-Pb collisions at [formula omitted

We briefly summarize our recent study on the number of constituent quark (NCQ) scaling of hadron elliptic flows in high multiplicity p-Pb collisions at sNN=5.02TeV. With the inclusion of hadron production via the quark coalescence model at intermediate pT, the viscous hydrodynamics at low pT, and jet fragmentation at high pT, our Hydro – Coal – Frag model provides a nice description of the pT-spectra and differential elliptic flow ν2(pT) of pions, kaons and protons over the pT range from 0 to 6 GeV. Our results demonstrate that including the quark coalescence is essential for reproducing the observed approximate NCQ scaling of hadron ν2 at intermediate pT in experiments, indicating strongly the existence of partonic degrees of freedom and the formation of quark-gluon plasma in high multiplicityp-Pb collisions at the LHC.

Anisotropic electrical conductivity of magnetized hot quark matter

We studied the effect of a strong magnetic field ($B$) on the electrical conductivity of hot quark matter. The electrical conductivity is a key transport coefficient determining the time dependence and strength of magnetic fields generated in a relativistic heavy-ion collision. A~magnetic field induces Hall anisotropic conduction, phase-space Landau-level quantization and, if sufficiently strong, interferes with prominent QCD phenomena such as dynamical quark mass generation, likely affecting the quark matter electrical conductivity, which depends strongly on the quark masses. To address these issues, we used a quasi-particle description of quark matter in which the electric charge carriers are constituent quarks with temperature- and magnetic-field-dependent masses predicted by a Nambu--Jona-Lasinio model. The model accurately describes recent lattice QCD results showing magnetic catalysis at low temperatures and inverse magnetic catalysis at temperatures close to the pseudo-critical temperature ($T_{\rm pc}$) of the QCD phase transition. We found that the magnetic field increases the conductivity component parallel to it and decreases the transverse component, in qualitative agreement with recent lattice QCD results. In addition, we found that: (1)~the space anisotropy of the conductivity increases with~$B$, (2)~the longitudinal conductivity increases due to phase-space Landau-level quantization, (3)~a lowest Landau level approximation behaves poorly for temperatures close to $T_{\rm pc}$, and (5)~inverse magnetic catalysis leaves a distinctive signal in all components of the conductivity, a prominent peak at $T_{\rm pc}$. Our study adds to the existing body of work on the hot quark matter electrical conductivity by incorporating nontrivial temperature and magnetic field effects on dynamical mass generation.

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.

Evidence of coalescence sum rule in elliptic flow of identified particles in high-energy heavy-ion collisions

The major goal of high-energy heavy-ion collisions is to study the properties of the deconfined quark gluon plasma (QGP), such as partonic collectivity. The collective motion of constituent quarks can be derived from the anisotropic flow measurements of identified hadrons within the coalescence framework. Based on published results of elliptic flow (v2), we shall test the coalescence sum rule using K±, p, p¯, Λ and Λ¯, and further extract v2 values for produced u(d, u¯, d¯), s and s¯ quarks, as well as transported u(d) quarks in 10-40% Au+Au collisions at sNN=7.7, 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV. We also attempt to link the v2 difference between π− and π+ to the different numbers of u and d quarks in the initial gold ions, and to relate the v2 measurements of multi-strange hadrons to the formation times of ϕ, Ω± and Ξ+.

Tribaryons in a constituent quark model

We calculate the matrix elements of the color-spin interaction for all possible multi-quark states of tribaryons in flavor SU(3) broken case. For that purpose, we construct the flavor$\otimes$color$\otimes$spin wave functions of the tribaryons, which are taken to be antisymmetric to satisfy the Pauli exclusion principle. Furthermore, we analyze the diquark structure of the tribaryon configurations using the symmetric and antisymmetric basis set of flavor, color and spin states.

Spectroscopic properties of Δ baryons

The resonance state of the baryon, which exists in four isospin ( ) states, has been studied using the hypercentral constituent quark model (hCQM) with a simple linear potential with added first order correction. The calculated data ranges for 1S-5S, 1P-5P, 1D-4D and 1F-2F are given, with possible spin-parity assignments for all the states. The magnetic moments have also been obtained for all four configurations. The decay channel width has been calculated for a few states. The linear nature of the data has been verified through Regge trajectories.

Tetra- and Penta-Quark Structures in the Constituent Quark Model

With the development of high energy physics experiments, a large amount of exotic states in the hadronic sector have been observed. In order to shed some light on the nature of the tetraquark and pentaquark candidates, a constituent quark model, along with the Gaussian expansion method, has been employed systematically in real- and complex-range investigations. We review herein the double- and fully-heavy tetraquarks, but also the hidden-charm, hidden-bottom and doubly charmed pentaquarks. Several exotic hadrons observed experimentally were well reproduced within our approach; moreover, their possible compositeness and other properties, such as their decay widths and general patterns in the spectrum, are analyzed. Besides, we report also some theoretical predictions of tetra- and penta-quark states which have not seen by experiment yet.

Full-heavy tetraquarks in constituent quark models

The full-heavy tetraquarks bb{bar{b}}{bar{b}} and cc{bar{c}}{bar{c}} are systematically investigated within the chiral quark model and the quark delocalization color screening model. Two structures, meson–meson and diquark–antidiquark, are considered. For the full-beauty bb{bar{b}}{bar{b}} systems, there is no any bound state or resonance state in two structures in the chiral quark model, while the wide resonances with masses around 19.1-19.4 GeV and the quantum numbers J^{P}=0^{+}, 1^{+}, and 2^{+} are possible in the quark delocalization color screening model. For the full-charm cc{bar{c}}{bar{c}} systems, the results are qualitative consistent in two quark models. No bound state can be found in the meson–meson configuration, while in the diquark–antidiquark configuration there may exist the resonance states, with masses range between 6.2 to 7.4 GeV, and the quantum numbers J^{P}=0^{+}, 1^{+}, and 2^{+}. And the separation between the diquark and the antidiquark indicates that these states may be the compact resonance states. The reported state X(6900) is possible to be explained as a compact resonance state with IJ^{P}=00^{+} in present calculation. All these full-charm resonance states are worth searching in the experiments further.

Study of bottom and charmed baryons in quark-diquark model

In this work, we study the properties of charm- and bottom-flavored baryons in the approximative quark-diquark modelin which the structure of baryons is considered as the bound states of quark-diquark pairs instead of the usual three equivalent quarks. To this aim, we use the Bethe-Salpeter equation including the Yukawa potential between the constituent quarks of baryons. Performing a fit procedure on the baryon masses in their ground state, we first determine the free parameters in the Yukawa potential and then compute the heavy baryons masses and energies in their excited states. We will also compute the magnetic moments of single heavy baryons as well as their semileptonic decay widths by evaluating the Isgur-Wise functions (IWF) for heavy baryons. Our results will be compared with available experimental data and other models so that the consistencies between them ensure the validity of IWF parameters extracted for the transitions of bottom baryons into charmed ones. Relying on the diquark model, we shall also predict the properties of some levels which have not yet observed.

A New Description of Transverse Momentum Spectra of Identified Particles Produced in Proton-Proton Collisions at High Energies

The transverse momentum spectra of identified particles produced in high energy proton-proton p + p collisions are empirically described by a new method with the framework of the participant quark model or the multisource model at the quark level, in which the source itself is exactly the participant quark. Each participant (constituent) quark contributes to the transverse momentum spectrum, which is described by the TP-like function, a revised Tsallis–Pareto-type function. The transverse momentum spectrum of the hadron is the convolution of two or more TP-like functions. For a lepton, the transverse momentum spectrum is the convolution of two TP-like functions due to two participant quarks, e.g., projectile and target quarks, taking part in the collisions. A discussed theoretical approach seems to describe the p + p collisions data at center-of-mass energy s = 200 GeV , 2.76 TeV, and 13 TeV very well.

Hadronic weak decays of Λc in the quark model

The hadronic weak decays of $\Lambda_c$ are studied in the framework of a constituent quark model. With the combined analysis of the Cabbibo-favored processes, $\Lambda_c\to \Lambda\pi^+$, $\Sigma^0\pi^+$ and $\Sigma^+\pi^0$, we confirm that the non-factorizable transition mechanisms play a crucial role in the understanding of their compatible branching ratios. We emphasize that the SU(3) flavor symmetry breaking effects, which is generally at the order of $1\sim 2\%$, can be amplified by the destructive interferences among the pole terms in the diagrams with internal conversion. Some contributions are sensitive to the spatial distribution of the scalar-isoscalar light-quark sector in the $\Lambda_c$, and its overlap with the light quarks in the final state hyperon. Namely, a compact diquark configuration is disfavored.

Hyperon weak radiative decay * *Supported by the National Natural Science Foundation of China (11425525, 11521505), DFG and NSFC funds to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” (NSFC) (11261130311), Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302), National Key Basic Research Program of China (2015CB856700); Q.W. is also supported by the research

We revisit the hyperon weak radiative decays in the framework of the non-relativistic constituent quark model. This study confirms the nonlocal feature of the hyperon weak radiative transition operators, which are dominated by the pole terms, and an overall self-consistent description of the available experimental data for the Cabibbo-favored hyperon weak radiative decays is presented. It provides a natural mechanism for evading the Hara theorem, where sizeable parity-violating contributions can come from the intermediate orbital excitations. Cancellations between pole terms also explain the significant SU(3) flavor symmetry breaking manifested by the experimental data. We also discuss several interesting selection rules arising from either the electromagnetic or the weak interaction vertices. These features suggest nontrivial relations among various hyperon decays.