Constituent Quark Research Articles

Chiral quark model analysis of the K¯N interaction

In this work we analyze the K¯N interaction in the framework of a constituent quark model. The near-threshold elastic and charge-exchange cross sections are evaluated, finding a good agreement with the experimental data. Furthermore, the possible existence of K¯N bound states are explored, finding two poles in the isoscalar JP=12− sector that can be interpreted as the experimental Λ(1405) state. Published by the American Physical Society 2024

Mixing effects on spectroscopy and partonic observables of heavy mesons with logarithmic confining potential in a light-front quark model

Using the variational principle, we systematically investigate the mass spectra and wave functions of both 1S and 2S state heavy pseudoscalar (P) and vector (V) mesons within the light-front quark model. This approach incorporates a Coulomb plus logarithmic confinement potential to accurately describe the constituent quark and antiquark dynamics. Additionally, spin hyperfine interactions are introduced perturbatively to compute the masses of pseudoscalar and vector mesons. The present analyses of the 1S and 2S states require the consideration of mixing between them to account for empirical constraints. These constraints include the mass gap ΔMP>ΔMV, where ΔMP(V)=MP(V)2S−MP(V)1S and the hierarchy of the decay constants f1S>f2S. We find the optimal value of the mixing angle to be θ=18°, significantly enhancing the consistency between our spectroscopic predictions and the experimental data compiled by the Particle Data Group. Furthermore, based on the predicted mass, the newly observed resonance BJ(5840) could be assigned as a 21S0 state in the B meson family. The study also reports various pertinent observables, including twist-two distribution amplitudes, electromagnetic form factors, charge radii, ξ moments, and transition form factors that are found to be consistent with both available lattice simulations and experimental data. In addition, our predicted branching ratios for the channels of B+→τ+ντ as well as rare decays of B0 and Bs0 appear in accordance with experimental data. Published by the American Physical Society 2024

Detailed derivation of the $\mathbf{^3P_0}$ strong decay model applied to baryons

Abstract We provide an in-detail derivation, through the $^3P_0$ pair creation model, of the transition matrix for a baryon decaying into a meson baryon system. The meson's analysis was successfully conducted in Ref.~\cite{Segovia:2012cd} and we extend the same formalism to the baryon sector, focusing on the $\Delta(1232)\to \pi N$ strong decay width because all hadrons involved in the reaction are very well established, the two hadrons in the final state are stable avoiding further analysis, all quarks are light and so equivalent, and the decay width of the process is relatively well measured. Taking advantage of a very common Rayleigh-Ritz variational method for solving the 2- and 3-body Sch"odinger bound-state equation in which the hadron's radial wave functions are expanded in terms of a Gaussian basis, the expression of the invariant matrix element can be related with the mean-square radii of hadrons involved in the decay. We use their experimental measures in such a way that only the strength of the quark-antiquark pair creation from the vacuum is a free parameter. This is then taken from our previous study of strong decay widths in the meson sector~\cite{Segovia:2012cd}, obtaining a quite compatible result with experiment for the calculated $\Delta(1232)\to \pi N$ decay width and indicating a possible path towards a unified and global description of the baryon and meson strong decay widths within the same constituent quark model framework. Finally, this research work has been developed in setting the stage for a novel raft of applications to exotic hadrons, \emph{i.e.} the description of baryon's coupling to meson-baryon thresholds, one of the mechanism that is thought to be responsible of providing either a large renormalization to naive states or genuine dynamically-generated meson-baryon molecules.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd

Collision energy dependence of elliptic flow of identified hadrons in heavy-ion collisions using the PHSD model

We report the first predictions of elliptic flow (v2) of identified hadrons at mid-rapidity (|y|< 1.0) in Au+Au collisions at Elab=6.7,8,11,and 25 A GeV using the Parton Hadron String Dynamics (PHSD) model. The transverse momentum (pT) dependence of identified hadron v2 in different centrality intervals (0-10%, 10-40%, and 40-80%) is shown. A clear centrality dependence of v2(pT) is observed for particles at Elab=6.7,8,11,and 25 A GeV. Within the PHSD model, the number of constituent quark (NCQ) scaling of v2 approximately follows in Au+Au collisions at all beam energies. A collision energy (sNN) dependence of π, K, and pv2 is studied in comparison with available published experimental data in the beam energy range of 6-25 A GeV. These predictions will help in interpreting the data from the forthcoming Compressed Baryonic Matter (CBM) experiment at the Facility for Antiproton and Ion Research (FAIR) and Multi-Purpose Detector (MPD) at the Nuclotron-based Ion Collider facility (NICA).

Off-shell pion properties: Electromagnetic form factors and light-front wave functions

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and antiquark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross sections for the Sullivan process, H1(e,e′,π+)n [H. P. Blok (Jefferson Lab Fπ Collaboration), Charged pion form factor between Q2=0.60, and 2.45 GeV2. I. Measurements of the cross section for the H1(e,e′π+)n reaction, .], we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results [H.-M. Choi , Pion off-shell electromagnetic form factors: Data extraction and model analysis, .] from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor F1(Q2,t) from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10% for the extracted off-shell pion form factor g(Q2,t). We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties. Published by the American Physical Society 2024

Fully strange tetraquark resonant states as the cousins of X(6900)

We conduct systematic calculations of the S-wave fully strange systems with “normal” (JPC=0++,1+−,2++) and “exotic” (JPC=0+−,1++,2+−) C-parities, which are the strange analog of the fully charmed tetraquark state X(6900). Within a constituent quark potential model, we employ the Gaussian expansion method to solve the four-body Schrödinger equation and the complex scaling method to identify resonant states. We obtain a series of resonant states and zero-width states in the mass range of 2.7 to 3.3 GeV, with their widths ranging from less than 1 to about 50 MeV. Their rms radii strongly indicate that they are compact tetraquark states. Among these states, the T4s,2++(2714) may be the most likely one to be observed experimentally. We urge the experimental exploration of the 2++ sss¯s¯ state around 2.7 GeV in the ϕϕ channel. Since the lowest S-wave sss¯s¯ state is around 2.7 GeV, the compact wave sss¯s¯ states are expected to be heavier. Hence, ϕ(2170) and X(2370) are unlikely to be compact tetraquark states. Published by the American Physical Society 2024

Magnetic polarizability of octet baryons via lattice QCD

Drawing on recent advances in lattice QCD background-field techniques, the magnetic polarizability of octet baryons is calculated from the first principles of QCD. The results are presented in the context of new constituent quark model calculations providing a framework for understanding the lattice results and a direct comparison with simulation results at unphysical quark masses. Using smeared quark sources, low-lying Laplacian eigenmode projection and final-state Landau-mode projection, considerable attention is devoted to ensuring single-state isolation in the lattice correlation functions. We also introduce new weighting methods to reduce the sensitivity to correlation-function fits, averaging over many fits based on merit drawn from the full correlated χ2 of the fits. The techniques are implemented on the 323×64, 2+1-flavor dynamical-fermion lattices provided by the PACS-CS Collaboration following the introduction of uniform magnetic fields quantized to the lowest nontrivial values available. After some scaling of the constituent quark model parameters, we find the model captures the patterns observed in the lattice QCD results very well, providing important insights into the physics underpinning the magnetic polarizabilities. Finally, comparison with the most recent results from experiment proceeds through an effective field theory formalism which incorporates estimates of finite-volume corrections and small electroquenching corrections as the results are brought to the physical point. We find excellent agreement with experiment where available, including the proton and neutron polarizabilities. Published by the American Physical Society 2024

Birds of passage: Rudolf Peierls and Dick Dalitz in Oxford

Abstract This paper traces the different routes that Rudolf Peierls and Dick Dalitz travelled on their way to being the founding members of a new Department of Theoretical Physics in Oxford. Peierls had had the good fortune to meet all of the originators of modern quantum mechanics in Europe and had been able to apply the new theory to many areas of physics. At Birmingham with Otto Frisch he wrote the famous Frisch-Peierls Memorandum which showed that it was possible to develop an atomic bomb. Dalitz had a shorter route to Oxford and worked with Peierls at Birmingham and Hans Bethe at Cornell before rejoining Peierls in Oxford after seven years in Chicago. His pioneering work on both the τ-θ puzzle and on the constituent quark model are then briefly described. The efforts of both Rudolf and Genia Peierls to create a ‘Bohr extended family’ model for his department in both Birmingham and Oxford are described, along with some observations about their style of theoretical physics research as ‘phenomenologists’.

Exploring the mass spectrum and electromagnetic property of the ΞccK(*) and ΞccK¯(*) molecules

Using the one-boson-exchange model, we investigate the interactions between the doubly charmed baryon Ξcc(3621) and the S wave (anti-)kaon accounting for the S−D wave mixing and coupled-channel effects. We find the coupled ΞccK/ΞccK* state with I(JP)=0(1/2−), the ΞccK* state with 0(1/2−), the ΞccK¯ state with 0(1/2−), and the ΞccK¯* states with 0(1/2−,3/2−) can be recommended as good doubly charmed molecular candidates with strangeness |S|=1. We further examine their M1 radiative decay behaviors and magnetic moments within the constituent quark model framework. This information can enhance our understanding of their inner structures, including the distribution of electric charge and the orientation of the constituent quarks’ spins. Published by the American Physical Society 2024

Odd-parity nucleon electromagnetic transitions in lattice QCD

The parity-expanded variational analysis (PEVA) technique enables the isolation of opposite-parity eigenstates at finite momentum. The approach has been used to perform the first lattice QCD calculations of excited-baryon form factors. In particular, these calculations show that the low-lying odd-parity nucleon excitations are described well by constituent quark models at moderate u and d quark masses approaching the strange quark mass. Herein, we extend the PEVA technique to establish a formalism for the determination of odd-parity nucleon electromagnetic transition form factors in lattice QCD. The formalism is implemented in the first calculation of the helicity amplitudes for transitions from the ground state nucleon to the first two odd-parity excitations. Through a comparison with constituent quark-model calculations of these amplitudes, these new results give important insight into the structure of these excitations. This work is a critical step towards confronting experimental electroproduction amplitudes for the N*(1535) and N*(1650) resonances with lattice QCD calculations. Published by the American Physical Society 2024

Triply charm and bottom tetraquarks in a constituent quark model

Singly, doubly, and fully charmed tetraquark candidates, e.g., Tcs¯(2900), Tcc+(3875), and X(6900) have been recently reported by the LHCb collaboration. Therefore, it is timely to implement a theoretical investigation on triply heavy tetraquark systems; herein, the S-wave triply charm and bottom tetraquarks, Q¯Qq¯Q (q=u,d,s;Q=c,b), with spin-parity JP=0+, 1+, and 2+, isospin I=0 and 12, are systematically studied in a constituent quark model. Besides, all tetraquark configurations, i.e., meson-meson, diquark-antidiquark, and K-type arrangements, along with any allowed color structure, are comprehensively considered. The Gaussian expansion method (GEM), in combination with the complex-scaling method (CSM), which is quite ingenious in dealing with either bound or resonances, is the approach adopted in solving the complex scaled Schrödinger equation. This theoretical framework has already been applied in various tetra- and pentaquark systems. In a fully coupled-channel calculation within the GEM+CSM, narrow resonances are found in each I(JP) channel of the charm and bottom sector. In particular, triply charm and bottom tetraquark resonances are obtained in 5.6–5.9 GeV and 15.3–15.7 GeV, respectively. We provide also some insights of the compositeness of these exotic states, such as the inner quark distance, magnetic moment and dominant wave function component. All this may help to distinguish them in future high energy nuclear and particle experiments. Published by the American Physical Society 2024

Analyzing leptonic decays of heavy quarkonia in the covariant confined quark model

The leptonic decay widths of heavy quarkonia are complementary observables to the semileptonic decays of heavy mesons and provide additional insight into the possible lepton flavor universality breaking. We analyze the former in the framework of the covariant confined quark model, introducing a novel approach for the description of the radially excited quarkonia states, which is based on constituent quark mass running and the orthogonality of the states. We are able to describe the experimental observations by our approach within the Standard Model, which does not support new physics explanations. Published by the American Physical Society 2024

Radiative decay and axial-vector decay behaviors of octet pentaquark states

In this work, we systematically calculate transition magnetic moments, radiative decay widths, and axial-vector coupling constants of octet hidden-charm molecular pentaquark states with different flavor representations in constituent quark model. We discuss the relations between transition magnetic moments and decay widths for pentaquark states. For octet pentaquark states with the 81f and 82f flavor representations, decay widths of the processes Pψ|32−⟩(12+⊗1−)→Pψ|12−⟩(12+⊗0−)γ and Pψ|12−⟩(12+⊗1−)→Pψ|12−⟩(12+⊗0−)γ are quite close, and decay widths of the Pψ|32−⟩(12+⊗1−)→Pψ|12−⟩(12+⊗1−)γ process are close to zero, and we notice that the axial-vector coupling constants of the pentaquark states are generally smaller than that of the nucleon. Published by the American Physical Society 2024

Gravitational form factors and mechanical properties of quarks in protons: A basis light-front quantization approach

We compute the gravitational form factors (GFFs) and study their applications for the description of the mechanical properties such as the pressure, shear force distributions, and the mechanical radius of the proton from its light-front wave functions (LFWFs) based on basis light-front quantization (BLFQ). The LFWFs of the proton are given by the lowest eigenvector of a light-front effective Hamiltonian that incorporates a three-dimensional confining potential and a one-gluon exchange interaction with fixed coupling between the constituent quarks solved in the valence Fock sector. We find acceptable agreement between our BLFQ computations and the lattice QCD for the GFFs. Our D-term form factor also agrees well with the extracted data from the deeply virtual Compton scattering experiments at Jefferson Lab, and the results of different phenomenological models. The distributions of pressures and shear forces are similar to those from different models. Published by the American Physical Society 2024

Hadronic spectrum in the chiral large Nc extension of quantum chromodynamics

We study quantum chromodynamics in the chiral large Nc limit which contains a left-handed Weyl fermion in the fundamental representation, a left-handed Weyl fermion in the two index antisymmetric representation and (Nc−3) left-handed Weyl fermions in the antifundamental representation of the SU(Nc) gauge group. We construct gauge singlet composite operators and study their masses and correlation functions at large Nc. It is shown that all hadron masses scale as ∼Nc0nq where nq is the number of constituent quarks in the hadron. In addition by simple gluon exchange considerations it is seen that scattering amplitudes between hadrons have the same Nc scaling as the mass of the lightest hadron involved. This is the case provided the hadrons in the scattering amplitude share a sufficiently large number of constituent quarks. The chiral large Nc extension also allows for other nontrivial processes. For instance we consider two different baryonium states that are unique to this extension and that decay via emissions of two- and three-quark hadrons. Also other nontrivial scattering processes are considered. Finally, we study composites made of a mix of left- and right-handed fields. We categorize multiple groups of hadrons within the full spectrum according to their flavor structure. Within these groups all n-point functions scale the same. Published by the American Physical Society 2024

Charmonium production in hot magnetized hyperonic matter: Effects of the baryonic Dirac sea and pseudoscalar-vector mixing

We investigate the medium modifications of the masses of pseudoscalar open charm (D and D¯) mesons and the charmonium state [ψ(3770)] in hot isospin asymmetric strange hadronic medium in the presence of an external magnetic field within a chiral effective model. The in-medium partial decay widths of ψ(3770) to charged and neutral DD¯ mesons are computed from the medium modifications of the masses of the initial and final state mesons. These are computed using two light quark pair creation models—(I) the P03 model and (II) a field theoretical (FT) model of composite hadrons with quark (and antiquark) constituents. The production cross sections of ψ(3770), arising from scattering of the D and D¯ mesons, are computed from the relativistic Breit-Wigner spectral function expressed in terms of the in-medium masses and the decay widths of the charmonium state. The effects of the magnetic field are considered due to the Dirac sea (DS) of the baryons, the mixing of the pseudoscalar (S=0) and vector (S=1) meson (PV mixing), the Landau level contributions for the charged hadrons. The anomalous magnetic moments (AMMs) of the baryons are also taken into account in the present study. For magnetized nuclear matter, at ρB=ρ0, the effect of Dirac sea leads to inverse magnetic catalysis (IMC), which is drop of the magnitude of the light quark condensates (proportional to the scalar fields) with increase in the magnetic field, contrary to the opposite effect of magnetic catalysis (MC) at ρB=0. The inclusion of hyperons to the nuclear medium is observed to lead to magnetic catalysis. There are observed to be significant effects from the DS and PV mixing on the properties of the charm mesons. The production cross sections of ψ(3770) arising due to scattering of D+D−(D0D¯0) mesons in the hot magnetized strange hadronic matter are observed to have distinct peak positions, when the magnetic field is large. This is because the production cross sections have contributions from the transverse as well as longitudinal components of ψ(3770), which have nondegenerate masses due to PV [ψ(3770)−ηc′] mixing. These can have observable consequences on the dilepton spectra as well as on the production of the charm mesons in ultrarelativistic peripheral heavy ion collision experiments, where the produced magnetic field is huge. Published by the American Physical Society 2024

Transverse-momentum-dependent gluon distributions of proton within basis light-front quantization

Gluon transverse-momentum dependent distributions (TMDs) are very important for revealing the internal structure of the proton. They correspond to a variety of experiments and are among the major tasks of the future electron-ion colliders. In this paper, we calculate the T-even gluon TMDs at the leading twist within the Basis Light-front Quantization framework. We employ the light-front wave functions of the proton obtained from a light-front quantized Hamiltonian with Quantum Chromodynamics input determined for its valence Fock-sector with three constituent quarks and an additional Fock-sector, encompassing three quarks and a dynamical gluon, with a three-dimensional confinement. After obtaining the numerical results we investigate the properties of gluon TMDs by checking whether they satisfy the Mulders-Rodrigues inequalities and investigate the correlations between transverse and longitudinal degrees of freedom. With their connection to unintegrated gluon distributions in mind, we further investigate the limiting behaviors of gluon TMDs in the small-x and large-x regions.

Assessment of ϒ -states above BB¯ -threshold using a constituent-quark-model based meson-meson coupled-channels framework

The ϒ(10753) state has been recently observed by the Belle and Belle II collaborations with enough global significance to motivate an assessment of the high-energy spectrum usually predicted by any reasonable quark model. In the framework of a constituent quark model which satisfactorily describes a wide range of properties of conventional hadrons containing heavy quarks, the quark-antiquark and meson-meson degrees of freedom have been incorporated with the goal of elucidating the influence of open-bottom meson-meson thresholds into the ϒ states whose masses are within the energy range of the ϒ(10753)’s mass. It is well known that such effects could be relevant enough as to dynamically generate new states and thus provide a plausible explanation of the nature of the ϒ(10753) state. In particular, we have performed a coupled-channels calculation in which the bare states ϒ(4S), ϒ(3D), ϒ(5S), and ϒ(4D) are considered together with the threshold channels BB¯, BB¯*, B*B¯*, BsB¯s, BsB¯s*, and Bs*B¯s*. Among the results we have described, the following are of particular interest: (i) a richer complex spectrum is gained when thresholds are present and bare bound states are sufficiently nonrelativistic; (ii) those poles obtained in the complex energy plane do not have to appear as simple peaks in the relevant cross sections; and (iii) the ϒ(10753) candidate is interpreted as a dressed hadronic resonance whose structure is an equally mixture of a conventional bb¯ state and B*B¯* molecule. Published by the American Physical Society 2024

Study of weak radiative decays of D0→Vγ

The weak radiative decay of D0→Vγ with V=K¯0, and ϕ, ρ0, and ω, is systematically studied in the vector meson dominance model. It allows us to distinguish the short-distance mechanisms which can be described by the tree-level transitions in the nonrelativistic constituent quark model, and the long-distance mechanisms which are related to the final-state interactions (FSIs). We find that the FSI effects play a crucial role in D0→Vγ and the SU(3) flavor symmetry can provide a natural constraint on the relative phase between the short and long-distance transition amplitudes. Our analysis suggests that the D-meson weak radiative decays can serve as a good case for investigating the nonperturbative QCD mechanisms at the charm quark mass region. Published by the American Physical Society 2024

Quarks and quantum chromodynamics

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.