Search

Convenient and consistent phase convention is important in the construction of the hadronic Lagrangian. However, the importance of phase convention has been overlooked for a long time, and the sources of different conventions are never explicitly addressed. This obscure situation can cause mistakes and misinterpretations in hadron physics. In this paper, we systematically analyze and compare the flavor S U 3 phase conventions from the perspective of the quark model. All sources that could lead to different conventions are pointed out and carefully studied. With the tool of the quark model, we also clarify some misconceptions and demonstrate a consistent way to incorporate different conventions. [ABSTRACT FROM AUTHOR]

A written account of my talk delivered at the Harald Fritzsch Memorial Symposium in Munich is given. The emphasis is on Harald's achievements specifically in quark physics and in quantum chromodynamics. Beyond that exemplary results for low-energy baryons are discussed, as obtained over the past years in the framework of the relativistic constituent-quark model based on Goldstone-boson-exchange dynamics. [ABSTRACT FROM AUTHOR]

Motivated by the intriguing discovery of X (6900) by the LHCb collaboration, we undertake a comprehensive study of the s s ¯ s s ¯ tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, the diquark–antidiquark ( s s - s ¯ s ¯ ) structure and meson–meson ( s s ¯ - s s ¯ ) structure, covering all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with J P = 0 + , namely, R (0 , 2150) and R (0 , 2915) , as well as a resonant state with J P = 1 + , denoted as R (1 , 2950) , and a resonant state with J P = 2 + , denoted as R (2 , 2850) , utilizing the real-scaling method. By comparing their energies and widths, we suggest that R (0 , 2915) and R (1 , 2950) may share characteristics with X (6900) , while R (0 , 2150) could be a promising candidate for the experimental state f 0 (2100) . We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states. [ABSTRACT FROM AUTHOR]

Convenient and consistent phase convention is important in the construction of the hadronic Lagrangian. However, the importance of phase convention has been overlooked for a long time, and the sources of different conventions are never explicitly addressed. This obscure situation can cause mistakes and misinterpretations in hadron physics. In this paper, we systematically analyze and compare the flavor SU3 phase conventions from the perspective of the quark model. All sources that could lead to different conventions are pointed out and carefully studied. With the tool of the quark model, we also clarify some misconceptions and demonstrate a consistent way to incorporate different conventions.

In the framework of the factorization approach we calculate the branching fractions of 100 two-body nonleptonic decay channels in total, including 44 channels of the charm meson decays and 56 channels of the bottom meson decays. For charm meson decays, we test and confirm the previous observation that taking the limit for the number of colors N → ∞ significantly improves theoretical predictions. For bottom meson decays, the penguin contributions are included in addition. As an essential input, we employ the weak decay form factors obtained in the framework of the relativistic quark model based on the quasi-potential approach. These form factors have well been tested by calculating observables in the semileptonic D and B meson decays and confronting obtained results with experimental data. In general, the predictions for the nonleptonic decay branching fractions are acceptable. However, for a quantitative calculation it is necessary to account for a more subtle effects of the final-state interaction. [ABSTRACT FROM AUTHOR]

Spectrum of the doubly heavy tetraquarks is studied in a constituent quark model including one-pion exchange (OPE) potential. Central and tensor forces induced by OPE between two light quarks are considered. Our results show that I(JP)=0(1+) compact bound states are shifted up because of the repulsive central force between q¯q¯. This effect possibly leads to the small binding energy in Tcc. In addition, a I(JP)=1(1+) resonant state is reported with E=10641MeV,Γ=15MeV and E=10640 MeV,Γ=15 MeV, without and with including OPE potential, respectively. The repulsive central force and attractive tensor force almost cancel with each other and leave a small energy difference when OPE potential is included.

The aim of this text is to present the covariant confined quark model (CCQM) and review its applications in the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we also review. The physics principles are, in detail, exposed for the CCQM; the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering, successively, three categories of decay processes: leptonic, semileptonic and non-leptonic. [ABSTRACT FROM AUTHOR]

The goal of this study is to check which, if any, of the published versions of the pion and kaon fragmentation functions (FFs) is compatible with the STAR data on semi-inclusive pion and kaon production in proton–proton collisions, and on the basis of this analysis to make reliable predictions for the p T spectra of the pions and kaons in inclusive pion and kaon production at the future NICA proton–proton collider. The calculations are carried out in next-to-leading order (NLO) of perturbative quantum chromodynamics (pQCD), using the well-tested CTEQ6 parton distributions. We consider the following pion and kaon FFs — DSEHS-14 [D. de Florian, R. Sassot, M. Epele, R. J. Hernández-Pinto and M. Stratmann, Phys. Rev. D 91, 014035 (2015), 1410.6027], DSEHS-17 [D. de Florian, M. Epele, R. J. Hernandez-Pinto, R. Sassot and M. Stratmann, Phys. Rev. D 95, 094019 (2017), 1702.06353], LSS-15 [E. Leader, A. V. Sidorov and D. B. Stamenov, Phys. Rev. D 93, 074026 (2016), 1506.06381], HKNS-07 [M. Hirai, S. Kumano, T. H. Nagai and K. Sudoh, Phys. Rev. D 75, 094009 (2007), hep-ph/0702250] and AKK-08 [S. Albino, B. A. Kniehl and G. Kramer, Nucl. Phys. B 803, 42 (2008), 0803.2768]. Our analysis shows that within the experimental errors all tested sets of FFs provide a good fit to STAR data at the c.m. energy S = 2 0 0 GeV , and the best ones are both LSS-15 and DSEHS-14 for pions and DSEHS-17 for kaons. From comparison of the LO and NLO results it is clear that the latter fit data much better, specially in the region of small p T . The NLO cross-sections are also less scale- Q 2 dependent, where p T / 2 ≤ Q ≤ 2 p T , than the LO ones. In order to make predictions for NICA energies, we compare the NLO pQCD results with the existing experimental BES STAR data on semi-inclusive hadron production in the most peripheral Au+Au collisions where the nuclear effects can be neglected. The comparison for lower energy scales, like at NICA, shows that a purely pQCD approach is inadequate and suggests the necessity to take into account also higher-order effects of initial-state soft-gluon radiation. Nevertheless, these data on the p T spectra of π + , K + and also the ratios π − / π + and K − / K + seem to favor LSS-15 and DSEHS-14 FFs for pions and DSEHS-17 for kaons, similarly as at the energy scale S = 2 0 0 GeV. [ABSTRACT FROM AUTHOR]

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review articles on exotic hadrons available so far; the present article tries to focus on the recent experimental and theoretical progress on the exotic states from the perspective of the quark model. Although lattice quantum chromodynamics may give the final answer of the problem, the phenomenological models are still powerful tools to explore the exotic states and to provide insight on the phenomenology of hadrons. The spatial and color structures of multiquark states and the channel coupling calculation are emphasized through reviewing some bound states, molecular and color structure resonances. Finally, the unquench effects of some exotic states are reviewed. With the accumulation of experimental data on multiquark states and inspiration of underlying theory developments, more reasonable phenomenological models incorporating multi-body interactions and high Fock components to unify the description of normal hadrons and exotic hadrons are expectable. [ABSTRACT FROM AUTHOR]

Inspired by the LHCb observation of hidden-charm pentaquarks, i.e., P c (4312) , P c (4440) , and P c (4457) in the J / ψ p invariant mass spectrum, a calculation of the J / ψ p scattering cross-section was performed using the quark-delocalization color screening model. The results show that P c (4312) can be identified as a hidden-charm molecular state Σ c D with J P = 1 2 − . The two-peak structure can be reproduced around 4450 MeV, which corresponds to P c (4440) and P c (4457) . They are the resonances molecular states Σ c D * of J P = 1 2 − and J P = 3 2 − . Moreover, the Σ c * D * of both J P = 1 2 − and J P = 3 2 − are possible molecular pentaquarks. Moreover, in the same theoretical frame, the calculation is extended to the P c -like molecular pentaquarks, denoted as P b . Several hidden-bottom pentaquarks with masses above 11 GeV and narrow widths were obtained. All of these heavy pentaquarks are worth exploring in future experiments. [ABSTRACT FROM AUTHOR]

We show that each irreducible tensor representation of weight 2 of the rotation group in the space of rank 3 tensors over three-dimensional space gives rise to an associative algebra with unity. We find the algebraic conditions to be satisfied by the generators of these algebras. Part of these relations is of binary, and another part is of ternary type. The structure of the latter one is based on the use of the cyclic group ℤ 3 generated by the primitive cubic root of unity given by q = exp (2 π i / 3). The subspace of each algebra spanned by triple products of generators is five-dimensional (5D) and is identical with the space of irreducible tensor representation of weight 2 of the rotation group SO (3). We define a Hermitian scalar product in this 5D subspace and construct its orthonormal basis in terms of triple products of generators. Then we find an explicit formula for the Lie algebra homomorphism so (3) → su (5). We suggest that the algebras constructed in this way, with binary and ternary constitutive relations, may find applications in the quark model and the Grand Unified Theories. [ABSTRACT FROM AUTHOR]

Nowadays, exploring dibaryon candidates has attracted much attention, both theoretically and experimentally. It is important to find a reasonable model to predict the possible dibaryon candidates. The chiral SU(3) quark model is just one of the most successful models, with which we can reasonably explain the experimental binding energies of baryon's ground state and the properties of deuteron, NN and YN scattering processes. By utilizing the same set of model parameters, we predicted the nonstrange d * dibaryon with a binding energy of 84 MeV , which is consistent with a recent experiment in which we also found that the hidden color (CC) channel plays an important role in forming this bound state. Due to the theoretical investigation of the CC channel being scarce for dibaryons, we explore other possible and interesting dibaryon candidates in the present work. According to the symmetry properties, we chose six interesting candidates, including strangeness 0 , − 1 , − 5 , − 6 systems. All the hidden color wave functions were built, and the spin-flavor-color matrix elements were systematically evaluated. Then, we applied these obtained matrix elements to further dynamically solve the corresponding resonating group method's equation in a coupled-channel calculation. The results show that the coupling to the CC channel plays an significant role in forming each spin S = 3 state, where tensor coupling is also included and has an obvious effect in forming each S = 0 state. The present work is significant in helping us to acquire deeper understanding of the effects of the hidden color channel and QCD phenomenology. [ABSTRACT FROM AUTHOR]

We propose a unital associative algebra, motivated by a generalization of the Pauli’s exclusion principle proposed for the quark model. The generators of this algebra satisfy the following relations: The sum of squares of all generators is equal to zero (binary relation) and the sum of cyclic permutations of the factors in any triple product of generators is equal to zero (ternary relations). We study the structure of this algebra and calculate the dimensions of spaces spanned by homogeneous monomials. We establish a relation between our algebra and the irreducible representations of the rotation group. In particular, we show that the 10-dimensional space spanned by triple monomials is the space of a double irreducible unitary representation of the rotation group. We use ternary q- and ¯q-commutators, where q,q¯ are primitive 3rd order roots of unity, to split the 10-dimensional space spanned by triple monomials into a direct sum of two 5-dimensional subspaces. We endow these subspaces with a Hermitian scalar product by means of an orthonormal basis of triple monomials. In each subspace, there is an irreducible unitary representation so(3) → su(5). We calculate the matrix of this representation. The structure of this matrix indicates a possible connection between our algebra and the Georgi–Glashow model. [ABSTRACT FROM AUTHOR]

Motivated by the intriguing discovery of X(6900) by the LHCb collaboration, we undertake a comprehensive study of the ss¯ss¯ tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, the diquark–antidiquark (ss-s¯s¯) structure and meson–meson (ss¯-ss¯) structure, covering all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with JP=0+, namely, R(0,2150) and R(0,2915), as well as a resonant state with JP=1+, denoted as R(1,2950), and a resonant state with JP=2+, denoted as R(2,2850), utilizing the real-scaling method. By comparing their energies and widths, we suggest that R(0,2915) and R(1,2950) may share characteristics with X(6900), while R(0,2150) could be a promising candidate for the experimental state f0(2100). We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.

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.

The aim of this text is to present the covariant confined quark model (CCQM) and review its applications in the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we also review. The physics principles are, in detail, exposed for the CCQM; the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering, successively, three categories of decay processes: leptonic, semileptonic and non-leptonic.

In this work, we calculate the mass spectrum of the bottom mesons with a modified nonrelativistic quark model by involving the screening effect, and explore their strong decay properties within the 3P0 model. Our results suggest that the B 1 (5 7 2 1) , B 2 ∗ (5 7 4 7) , B J (5 8 4 0) and B J (5 9 7 0) could be reasonably assigned as the B 1 ′ (1 P) , B (1 3 P 2) , B (2 1 S 0) and B (1 3 D 3) , respectively. The more precise measurements of the excited bottom mesons are crucial to confirm these assignments. [ABSTRACT FROM AUTHOR]

We have investigated the internal structure of the open- and hidden-charmed (DD ∗ /D¯D ∗ ) molecules in the unified framework. We first fit the experimental lineshape of the T cc + state and extract the DD ∗ interaction, from which the T cc + is assumed to arise solely. Then we obtain the DD‾ ∗ interaction by charge conjugation. Our results show that the DD‾ ∗ interaction is attractive but insufficient to form X(3872) as a bound state. Instead, its formation requires the crucial involvement of the coupled channel effect between the DD¯ ∗ and cc¯ components, although the cc¯ accounts for approximately 1% only. Besides X(3872), we have obtained a higher-energy state around 3957.9 MeV with a width of 16.7 MeV, which may be a potential candidate for the X(3940). In J PC =1 +- sector, we have found two states related to the iso-scalar X̃(3872) and h c (2P), respectively. Our combined study provides valuable insights into the nature of these DD ∗ /DD¯ ∗ exotic states., Competing Interests: Conflict of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare that they have no conflict of interest., (Copyright © 2024 Science China Press. Published by Elsevier B.V. All rights reserved.)

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review articles on exotic hadrons available so far; the present article tries to focus on the recent experimental and theoretical progress on the exotic states from the perspective of the quark model. Although lattice quantum chromodynamics may give the final answer of the problem, the phenomenological models are still powerful tools to explore the exotic states and to provide insight on the phenomenology of hadrons. The spatial and color structures of multiquark states and the channel coupling calculation are emphasized through reviewing some bound states, molecular and color structure resonances. Finally, the unquench effects of some exotic states are reviewed. With the accumulation of experimental data on multiquark states and inspiration of underlying theory developments, more reasonable phenomenological models incorporating multi-body interactions and high Fock components to unify the description of normal hadrons and exotic hadrons are expectable.

Inspired by the LHCb observation of hidden-charm pentaquarks, i.e., Pc(4312), Pc(4440), and Pc(4457) in the J/ψp invariant mass spectrum, a calculation of the J/ψp scattering cross-section was performed using the quark-delocalization color screening model. The results show that Pc(4312) can be identified as a hidden-charm molecular state ΣcD with JP=12−. The two-peak structure can be reproduced around 4450 MeV, which corresponds to Pc(4440) and Pc(4457). They are the resonances molecular states ΣcD* of JP=12− and JP=32−. Moreover, the Σc*D* of both JP=12− and JP=32− are possible molecular pentaquarks. Moreover, in the same theoretical frame, the calculation is extended to the Pc-like molecular pentaquarks, denoted as Pb. Several hidden-bottom pentaquarks with masses above 11 GeV and narrow widths were obtained. All of these heavy pentaquarks are worth exploring in future experiments.

Nowadays, exploring dibaryon candidates has attracted much attention, both theoretically and experimentally. It is important to find a reasonable model to predict the possible dibaryon candidates. The chiral SU(3) quark model is just one of the most successful models, with which we can reasonably explain the experimental binding energies of baryon’s ground state and the properties of deuteron, NN and YN scattering processes. By utilizing the same set of model parameters, we predicted the nonstrange d* dibaryon with a binding energy of 84MeV, which is consistent with a recent experiment in which we also found that the hidden color (CC) channel plays an important role in forming this bound state. Due to the theoretical investigation of the CC channel being scarce for dibaryons, we explore other possible and interesting dibaryon candidates in the present work. According to the symmetry properties, we chose six interesting candidates, including strangeness 0,−1,−5,−6 systems. All the hidden color wave functions were built, and the spin-flavor-color matrix elements were systematically evaluated. Then, we applied these obtained matrix elements to further dynamically solve the corresponding resonating group method’s equation in a coupled-channel calculation. The results show that the coupling to the CC channel plays an significant role in forming each spin S = 3 state, where tensor coupling is also included and has an obvious effect in forming each S = 0 state. The present work is significant in helping us to acquire deeper understanding of the effects of the hidden color channel and QCD phenomenology.

The typical transverse momentum of a quark in the proton is a basic property of any QCD based model of nucleon structure. However, calculations in phenomenological models typically give rather small values of transverse momenta, which are difficult to reconcile with the larger values observed in high energy experiments such as Drell-Yan reactions and Semi-inclusive deep inelastic scattering. In this letter we calculate the leading twist transverse momentum dependent distribution functions (TMDs) using a generalization of the Adelaide group's relativistic formalism that has previously given good fits to the parton distributions. This enables us to examine the kT dependence of the TMDs in detail, and determine typical widths of these distributions. These are found to be significantly larger than those of previous calculations. We then use TMD factorization in order to evolve these distributions up to experimental scales where we can compare with data on 〈kT〉 and 〈kT2〉. Our distributions agree well with this data.

Spectrum of the doubly heavy tetraquarks, bbq¯q¯, is studied in a constituent quark model. Four-body problem is solved in a variational method where the real scaling technique is used to identify resonant states above the fall-apart decay thresholds. In addition to the two bound states that were reported in the previous study we have found several narrow resonant states above the BB⁎ and B⁎B⁎ thresholds. Their structures are studied and are interpreted by the quark dynamics. A narrow resonance with spin-parity JP=1+ is found to be a mixed state of a compact tetraquark and a B⁎B⁎ scattering state. This is driven by a strong color Coulombic attraction between the bb quarks. Negative-parity excited resonances with JP=0−, 1− and 2− form a triplet under the heavy-quark spin symmetry. It turns out that they share a similar structure to the λ-mode of a singly heavy baryon as a result of the strongly attractive correlation for the doubly heavy diquark.

We study some of the main properties (masses and open-flavor strong decay widths) of 4P and 5P charmonia. While there are two candidates for the χc0(4P,5P) states, the X(4500) and X(4700), the properties of the other members of the χc(4P,5P) multiplets are still completely unknown. With this in mind, we start to explore the charmonium interpretation for these mesons. Our second goal is to investigate if the apparent mismatch between the Quark Model (QM) predictions for χc0(4P,5P) states and the properties of the X(4500) and X(4700) mesons can be overcome by introducing threshold corrections in the QM formalism. According to our coupled-channel model results for the threshold mass shifts, the χc0(5P)→X(4700) assignment is unacceptable, while the χc0(4P)→X(4500) or X(4700) assignments cannot be completely ruled out.

The phenomena of strong running coupling and hadron mass generating have been studied in the framework of a QCD-inspired relativistic model of quark-gluon interaction with infrared-confined propagators. We derived a meson mass equation and revealed a specific new behavior of the mass-dependent strong coupling α ^ s ( M ) defined in the time-like region. A new infrared freezing point α ^ s ( 0 ) = 1.03198 at origin has been found and it did not depend on the confinement scale Λ > 0 . Independent and new estimates on the scalar glueball mass, ‘radius’ and gluon condensate value have been performed. The spectrum of conventional mesons have been calculated by introducing a minimal set of parameters: the masses of constituent quarks and Λ . The obtained values are in good agreement with the latest experimental data with relative errors less than 1.8 percent. Accurate estimates of the leptonic decay constants of pseudoscalar and vector mesons have been performed.

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.