Meson Nonet Research Articles

Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants

The quark-antiquark components of the U(3) lightest scalar meson nonet are investigated by considering the Nambu-Jona-Lasinio model with flavor-dependent coupling constants that were derived by considering (non-perturbative) gluon exchange. The strange quark effective mass () is varied such that the strangeness content of these scalar mesons can be analyzed further. The neutral states S 0, S 8, and S 3 are adopted as the most relevant quark-antiquark components, respectively, of the σ(500), f 0(980) and mesons. As a result, the mass hierarchy between states S 0 and S 8, and mesons, can be, respectively, inverted and corrected for quite low values of the strange quark constituent mass. In addition, for some particular values of , the masses of σ(500) and f 0(980) can also be obtained by considering the mixing coupling constant G 08. However, the masses of all the nine mesons are not described simultaneously in a self-consistent procedure and this goes along with the need of non-quark-antiquark states to completely describe their masses. A neutral-meson mixing matrix is defined and the leading mixing angle is found by fitting a correct value of the σ(500) − f 0(980) mass difference. Two different estimates for the strengths of the mixings and are proposed, leading to somewhat different behaviors. First by assuming leading transitions to intermediary flavor eigenstates and second by considering a dynamical evolution. The results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass.

Mass spectrum and decays of the first radial excitation axial vector meson nonet

In this work, the mass spectrum of the first radial excitation axial vector meson nonet is considered in the framework of the nonrelativistic constituent quark model and Regge phenomenology. After that, we investigate the strong decay characteristics of these states within the [Formula: see text] model. The results are compared to values from other phenomenological models, and they may be beneficial in the prospective search for [Formula: see text] meson nonets.

Chiral Lagrangians for strong decays K1→Kρ(ω)

A triangular quark diagram describes the vertex K1Kω with axial-vector, vector, and pseudoscalar mesons is considered in the leading order of 1NC. The application of the obtained vertex to the hadronic decays of the τ-lepton with the production of Kω, Kφ  meson pairs in the final state is discussed. Calculation of quark diagrams are considered within the  SU(3) symmetric chiral Lagrangians, which describe the interactions of four meson nonets: scalar, pseudoscalar, vector, and axial-vector in the ground and in the first radially excited states. The calculated integral decay widths of K1(1270)→K[ω,ρ] are in the agreement with the experimental data of the BES-III and Belle collaborations obtained at the BEPC II and KEK colliders. It is shown that the axial-vector channel with the intermediate meson K1A with quantum numbers  JPC=1++ plays a dominant role in describing the decay widths of τ→K[ω,ρ]ντ. In  lepton decays, the contact channel and the channel with the axial vector meson K1A are taken into account. The first of them is related with the intermediate W  boson, which products a meson pair. The second channel is related with the intermediate W boson, which transits into the axial vector state K1A and also products meson pairs. Consideration of these two channels independently of each other allows us to study the processes in more detail. The splitting of the strange axial vector state K1A into two physical mesons K1(1270) and K1(1400) due to the mixing of axial vector mesons from nonets 3P1 and  1P1 is also taken into account. The negative interference of the contact channel with the axial vector channel is established. The dependences of the integral decay widths of τ→K[ω,ρ]ντ on the value of the mixing angle of axial-vector mesons K1A and K1B are studied. A comparative analysis of the results with experimental data and theoretical estimates of other authors is carried out. The obtained theoretical predictions are in satisfactory agreement with the experimental data.

Mass and Decay of the \(s\bar {s}\) Member of the 1\(^{3}F_{4}\) Meson Nonet

Mass and Decay of the \(s\bar {s}\) Member of the 1\(^{3}F_{4}\) Meson Nonet

Revisiting the assignment of $$1^{3}D_{1}$$ meson nonet

Based on the mass relations from the Regge phenomenology, we revisit the mass spectrum of \(1^{3}D_{1}\) meson nonet. The masses of kaon and \(s{\bar{s}}\) member of \(1^{3}D_{1}\) (\(1^{3}D_{1}(s{\bar{s}})\)) meson nonet are obtained and the results are compared with the values from different theoretical models. Moreover, the strong decay properties of the kaon and \(1^{3}D_{1}(s{\bar{s}})\) are presented in the \(^{3}P_{0}\) model. On the basis of results, we suggest the assignment of \(1^{3}D_{1}\) meson nonet need further tested in the new experiment in the future. Our results also provide mass constraints for the study of these states.

Re-evaluation of the Isoscalar Mixing Angle within Selected Mesonic Nonets

Based on the relations from the meson-meson mass mixing matrix, the mixing angles of isoscalar state have been re-evaluated via mass relations and latest experimental results. The results in the present work are compared with the values from different theoretical models, meanwhile, the quarkonia content of isoscalar state are presented. In order to check the validity of analysis, some predictions on the decays of the isoscalar state are presented. These predictions may be useful for the phenomenological analysis for meson nonet in future experiments.

Towards the Assignments for \(1^{1}D_{2}\) and \(1^{3}D_{2}\) Meson Nonets

Towards the Assignments for \(1^{1}D_{2}\) and \(1^{3}D_{2}\) Meson Nonets

Conventional mesons below 2 GeV

We briefly review the status of various conventional quark-antiquark mesons below 2 GeV and outline some open questions: the status of the strangeantistrange orbitally excited vector meson, the status of the nonet of axial-tensor mesons (chiral partners of the well known tensor mesons), and the isoscalar mixing angle in the pseudotensor sector, which can eventually represent a novel manifestation of the chiral anomaly.

State mixing and masses of the π0 , η and η′ mesons from nf=1+1+1 lattice QCD+QED

We present a lattice analysis of the light pseudoscalar mesons with consideration for the mixing between the flavour-neutral states $\pi^0$, $\eta$ and $\eta^\prime$. We extract the masses and flavour compositions of the pseudoscalar meson nonet in $n_f=1+1+1$ lattice QCD+QED around an SU(3)-flavour symmetric point, and observe flavour-symmetry features of the extracted data, along with preliminary extrapolation results for the flavour compositions at the physical point. A key result of this work is the observed mass splitting between the $\pi^0$ and $\eta$ on our ensembles, which is found to exhibit behaviour that is simply related to the corresponding flavour compositions.

Trace and Axial Anomalies on Equal Footing

We discussed that for some particular nonsupersymmetric theories, a generalized symmetry that includes both the scale and axial transformations and leads to a single current may contain also a pseudoscalar term. The method, inspired by the superconformal anomalies, has important application for low-energy effective models where it allows the introduction of a single complex glueball field with a scalar and a pseudoscalar component on the same footing with the complex meson nonet fields made of quarks. Both axial and trace anomalies are satisfied in accordance to the meson structure and the QCD requirements.

Asymmetries of anti-triplet charmed baryon decays

We analyze the decay processes of Bc→BnM with the SU(3)F flavor symmetry and spin-dependent amplitudes, where Bc(Bn) and M are the anti-triplet charmed (octet) baryon and nonet meson states, respectively. In the SU(3)F approach, it is the first time that the decay rates and up-down asymmetries are fully and systematically studied without neglecting the O(15‾) contributions of the color anti-symmetric parts in the effective Hamiltonian. Our results of the up-down asymmetries based on SU(3)F are quite different from the previous theoretical values in the literature. In particular, we find that the up-down symmetry of α(Λc+→Ξ0K+)SU(3)=0.94−0.11+0.06, which is consistent with the recent experimental data of 0.77±0.78 by the BESIII Collaboration, but predicted to be zero in the literature. We also examine the KS0−KL0 asymmetries between the decays of Bc→BnKS0 and Bc→BnKL0 with both Cabibbo-allowed and doubly Cabibbo-suppressed transitions.

Extended-soft-core baryon-baryon model ESC16. I. Nucleon-nucleon scattering

Background: The Nijmegen extended-soft-core (ESC) model ESC16, as well as its predecessors ESC04--ESC08, describe the nucleon-nucleon ($NN$), hyperon-nucleon ($YN$), and hyperon-hyperon/nucleon ($YY/\mathrm{\ensuremath{\Xi}}\phantom{\rule{4pt}{0ex}}N$) interactions in a unified way using broken SU(3) symmetry. SU(3) symmetry serves to connect the $NN$ with the $YN$ and the $YY$ channels. In the spirit of the Yukawa approach to the nuclear force problem, the interactions are studied from the meson-exchange picture viewpoint, using generalized soft-core Yukawa functions. The meson exchanges are supplemented with diffractive contributions due to multiple-gluon exchanges. The extended-soft-core (ESC) meson-exchange interactions consist of local and nonlocal potentials due to (i) one-boson exchanges (OBE), which are the members of nonets of pseudoscalar, vector, scalar, and axial-vector mesons, (ii) diffractive exchanges, (iii) two-pseudoscalar exchange (PS-PS), and (iv) meson-pair exchange (MPE). The OBE and MPE vertices are regulated by Gaussian form factors producing potentials with a soft behavior near the origin. The assignment of the cutoff masses for the BBM vertices is dependent on the SU(3) classification of the exchanged mesons for OBE and a similar scheme for MPE.Purpose: The evolution of the ESC approach to the ESC16 model for the baryon-baryon (BB) interactions of the SU(3) flavor octet of baryons (N, $\mathrm{\ensuremath{\Lambda}}$, $\mathrm{\ensuremath{\Sigma}}$, and $\mathrm{\ensuremath{\Xi}}$) is described and presented. In this first of a series of papers, the $NN$ model and results are reported in detail.Methods: Important nonstandard ingredients in the OBE sector in the ESC models are (i) the axial-vector meson potentials, and (ii) a zero in the scalar- and axial-vector meson form factors. Furthermore, the strange scalar $\ensuremath{\kappa}$ meson is treated within the scheme of the Gell-Mann-Okubo mass relations, and like the $\ensuremath{\rho}$ and $\ensuremath{\epsilon}$ treated as a broad meson. The multiple-gluon exchanges are elaborated further by adding contributions due to odd number of gluon exchanges. A novel contribution is the incorporation of structural effects due to the quark core of the baryons. In establishing the parameters of the model a simultaneous fit to $NN$ and $YN$ channels has been performed. The meson-baryon coupling constants are calculated via SU(3) using the coupling constants of the $NN\ensuremath{\bigoplus}YN$ analysis as input. In ESC16 the couplings are kept completely SU(3) symmetric. About 25 physical coupling parameters and 8 cutoff and diffractive masses were searched.Results: In the fit to $NN$ and $YN$ many parameters are essentially fixed by the $NN$ data. A few, but severely constrained parameters, e.g., $F/(F+D)$ ratios, are left for determination of the $YN$ interactions and the $YY$ experimental indications. The simultaneous fit of the ESC models to the $NN$- and $YN$-scattering data with a single set of parameters has achieved excellent results for the $NN$ and $YN$ data, and for the $YY$ data in accordance with the experimental indications for $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ and $\mathrm{\ensuremath{\Xi}}N$. In the case of ESC16, the version discussed here, the achievements are: (i) For the selected 4313 $pp$ and $np$ scattering data with energies $0\ensuremath{\le}{T}_{\text{lab}}\ensuremath{\le}350\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, the model reaches a fit having ${\ensuremath{\chi}}^{2}/{N}_{\text{data}}=1.10$. (ii) The deuteron binding energy and all the $NN$ scattering lengths are fitted very nicely. (iii) The $YN$ data are described very well with ${\ensuremath{\chi}}^{2}/{N}_{\text{data}}=1.04$, giving at the same time a description of the $\mathrm{\ensuremath{\Xi}}N$ cross sections in agreement with the experimental indications.Conclusions: The ESC approach leads to an excellent description of the $NN$ and $YN$ data, and for the scarce $YY$ data. The added innovations as well as the treatment of mass broken SU(3) make it possible to keep the meson coupling parameters and the $F/(F+D)$ ratios of the model qualitatively in accordance with the predictions of the $^{3}P_{0}$-dominated quark-antiquark pair creation (QPC) model. The information about estimates of (i) the $\mathrm{\ensuremath{\Lambda}}$- and $\mathrm{\ensuremath{\Sigma}}$-nuclear well-depth, and (ii) the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ hypernuclei played an important role in the form of using constraints. In particular, the experimental indications for the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$-attraction and the $\mathrm{\ensuremath{\Sigma}}$-nuclear well-depth were directive.

Chiral phase structure of the sixteen meson states in the SU(3) Polyakov linear-sigma model for finite temperature and chemical potential in a strong magnetic field

In characterizing the chiral phase-structure of pseudoscalar ( ), scalar ( ), vector ( ) and axial-vector ( t) meson states and their dependence on temperature, chemical potential, and magnetic field, we utilize the SU(3) Polyakov linear-sigma model (PLSM) in the mean-field approximation. We first determine the chiral (non)strange quark condensates, and , and the corresponding deconfinement order parameters, and , in thermal and dense (finite chemical potential) medium and finite magnetic field. The temperature and the chemical potential characteristics of nonet meson states normalized to the lowest bosonic Matsubara frequency are analyzed. We note that all normalized meson masses become temperature independent at different critical temperatures. We observe that the chiral and deconfinement phase transitions are shifted to lower quasicritical temperatures with increasing chemical potential and magnetic field. Thus, we conclude that the magnetic field seems to have almost the same effect as the chemical potential, especially on accelerating the phase transition, i.e. inverse magnetic catalysis. We also find that increasing the chemical potential enhances the mass degeneracy of the various meson masses, while increasing the magnetic field seems to reduce the critical chemical potential, at which the chiral phase transition takes place. Our mass spectrum calculations agree well with the recent PDG compilations and PNJL, lattice QCD calculations, and QMD/UrQMD simulations.

Mixing among lowest-lying scalar mesons and scalar glueball

Scalar glueball is implemented in single nonet linear sigma model (SNLSM) which basically includes lowest lying scalar and pseudoscalar mesons. Our new version of SNLSM involves mixing among scalar matter fields and glueball field which is enforced by scale symmetry considerations and the associated anomaly. Performing iterative Monte Carlo simulations, it is found that among the three candidates of scalar glueball, i.e., f0(1370), f0(1500) and f0(1710), only f0(1500) is predominately a glueball state with the mass prediction of 1.566±0.046 GeV and the other two are predominately quarkonium. The ππ, πK and πη scatterings are reinvestigated in the presence of scalar glueball and it is found that the overall behavior of the real part of the K-matrix unitarized ππ scattering amplitude is more compatible with observed data compared with the case of SNLSM without glueball. We have also presented the predictions of the model for the masses and decay widths of the scalars obtained from the poles of the K-matrix unitarized ππ, πK and πη scattering amplitudes. Moreover the ππ scattering phase shift predicted by our model is compared with the prediction of generalized linear sigma model (GLSM) which contains two nonets of scalar mesons and two nonets of pseudoscalar mesons (a quark–antiquark nonet and a four-quark nonet). Despite the fact that at this stage our model lacks the second meson nonet above 1 GeV, its prediction for the ππ scattering phase shift is close to the prediction of GLSM for s<1.1 GeV and in better agreement with experimental data for s>1.1 GeV in comparison with GLSM.

Chiral and U(1)A restoration for the scalar and pseudoscalar meson nonets

We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1)_A$ symmetries. For that purpose, we exploit QCD Ward Identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests $U(1)_A$ partner restoration if chiral symmetry partners are also degenerated. This is also confirmed by the ChPT analysis when the light chiral limit is reached. Partner degeneration for the $I=1/2$ sector, the behavior of $I=0$ mixing and the temperature scaling of meson masses predicted by WI are also studied. Special attention is paid to the connection of our results with recent lattice analyses.

The possible members of the 5^1S_0 meson nonet

The strong decays of the 5^1S_0q{bar{q}} states are evaluated in the ^3P_0 model with two types of space wave functions. Comparing the model expectations with the experimental data for the pi (2360), eta (2320), X(2370), and X(2500), we suggest that the pi (2360), eta (2320), and X(2500) can be assigned as the members of the 5^1S_0 meson nonet, while the 5^1S_0 assignment for the X(2370) is not favored by its width. The 5^1S_0 kaon is predicted to have a mass of about 2418 MeV and a width of about 163 or 225 MeV.

Quark Matter May Not Be Strange.

If quark matter is energetically favored over nuclear matter at zero temperature and pressure, then it has long been expected to take the form of strange quark matter (SQM), with comparable amounts of u, d, and s quarks. The possibility of quark matter with only u and d quarks (udQM) is usually dismissed because of the observed stability of ordinary nuclei. However, we find that udQM generally has lower bulk energy per baryon than normal nuclei and SQM. This emerges in a phenomenological model that describes the spectra of the lightest pseudoscalar and scalar meson nonets. Taking into account the finite size effects, udQM can be the ground state of baryonic matter only for baryon number A>A_{min} with A_{min}≳300. This ensures the stability of ordinary nuclei and points to a new form of stable matter just beyond the periodic table.

Patterns and partners for chiral symmetry restoration

We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis predicts that $U(1)_A$ partners are also degenerated. Our analysis also leads to $I=1/2$ scalar-pseudoscalar partner degeneration at exact chiral restoration, and supports ideal mixing between the $\eta$-$\eta^\prime$ and the $f_0(500)$-$f_0(980)$ mesons at $O(4)\times U(1)_A$ restoration, with a possible range where the pseudoscalar mixing vanishes if the two transitions are well separated. We test our results with lattice data and provide further relevant observables regarding chiral and $U(1)_A$ restoration for future lattice and model analyses.

Excited vector mesons: phenomenology and predictions for a yet unknown vector ss state with a mass of about 1.93 GeV

The firm understanding of standard quark-antiquark states (including excited states) is necessary to search for non-conventional mesons with the same quantum numbers. In this work, we study the phenomenology of two nonets of excited vector mesons, which predominantly correspond to radially excited vector mesons with quantum numbers n2S+1LJ = 23S1 and to orbitally excited vector mesons with quantum numbers n2S+1LJ = 13D1. We evaluate the decays of these mesons into two pseudoscalar mesons and into a pseudoscalar and a ground-state vector meson by making use of a relativistic quantum field theoretical model based on flavor symmetry. Moreover, we also study the radiative decays into a photon and a pseudoscalar meson by using vector meson dominance. We compare our results to the PDG and comment on open issues concerning the corresponding measured resonances. Within our approach, we are also able to make predictions for a not-yet discovered ss state in the n2S+1LJ = 13D1 nonet, which has a mass of about 1.93 GeV. This resonance can be searched in the upcoming GlueX and CLAS12 experiments which take place at the Jefferson Lab.

Fragmentation of ω and ϕ mesons in e+e− and pp collisions at NLO

A combined analysis of both [Formula: see text] (LEP, SLD) and [Formula: see text] (RHIC-PHENIX and LHC-ALICE) hadroproduction processes are done for the first time for the vector meson nonet at the next-to-leading order (NLO) using a model with broken SU(3) symmetry. The transverse momentum ([Formula: see text]) and rapidity ([Formula: see text]) dependence of the differential cross-section for [Formula: see text] and [Formula: see text] mesons of the [Formula: see text] data are also discussed. The input universal quark (valence and singlet) fragmentation functions at a starting scale of [Formula: see text], after evolution, have values that are consistent with the earlier analysis for [Formula: see text] at NLO. However, the universal gluon fragmentation function is now well determined from this study with significantly smaller error bars, as the [Formula: see text] hadroproduction cross-section is particularly sensitive to the gluon fragmentation since it occurs at the same order as the quark fragmentation, in contrast to the [Formula: see text] hadroproduction process. Additional parameters involved in describing the strangeness and sea suppression and octet–singlet mixing are found to be close to the earlier analysis; in addition, a new relation between the gluon and sea suppression in [Formula: see text] and [Formula: see text] hadroproduction has been observed.