Meson Nonet Research Articles

Strong and radiative decays of excited vector mesons and predictions for a new ϕ(1930) resonance

We study the phenomenology of two nonets of excited vector mesons, $\{\rho(1450)$, $K^{\ast}(1410)$, $\omega(1420)$, $\phi(1680)\}$ and $\{\rho(1700),$ $K^{\ast}(1680),\omega(1650),$ $\phi(???)\},$ which (roughly) correspond to radially excited $2^{3}S_{1}$ and to orbitally excited $1^{3}D_{1}$ vector mesons. We evaluate the strong and radiative decays of these mesons into pseudoscalar and ground-state vector mesons by using an effective relativistic QFT model based on flavour symmetry. We compare decay widths and branching ratios with various experimental results listed in the PDG. An overall agreement of theory with experiment reinforces the standard quark-antiquark assignment of the resonances mentioned above. Predictions for not yet measured quantities are also made. In particular, we shall also make predictions for the not-yet discovered $s\bar{s}$ state of the $1^{3}D_{1}$ nonet, denoted as $\phi(???)$. Its mass can be estimated to be about $1930$ MeV, hence we shall call this putative state $\phi(1930).$ Its main decays are into $KK^{\ast}(892)$ (about $200$ MeV) and $KK$ (about $100$ MeV). Since this state couples also to $\gamma\eta,$ it can be searched in the near future in the photoproduction-based experiments GlueX and CLAS12 at Jefferson Lab.

Study of the B¯q*→DM decays with perturbative QCD approach

The $\bar{B}_{q}^{\ast}$ ${\to}$ $DP$, $DV$ weak decays are studied with the perturbative QCD approach, where $q$ $=$ $u$, $d$ and $s$; $P$ and $V$ denote the ground $SU(3)$ pseudoscalar and vector meson nonet. It is found that the branching ratios for the color-allowed $\bar{B}_{q}^{\ast}$ ${\to}$ $D_{q}{\rho}^{-}$ decays can reach up to $10^{-9}$ or more, and should be promisingly measurable at the running LHC and forthcoming SuperKEKB experiments in the near future.

Constructing new pseudoscalar meson nonets with the observed X(2100) , X(2500) , and η(2225)

Stimulated by the BESIII observation of $X(2100)$, $X(2500)$, and $\eta(2225)$, we try to pin down new pseudoscalar meson nonets including these states. The analysis of mass spectra and the study of strong decays indicate that $X(2120)$ and $\eta(2225)$ associated with $\pi(2070)$ and the predicted kaon $K(2150)$ may form a new pseudoscalar meson nonet. In addition, more experimental data for $X(2100)$ are necessary to determine its structure of nonets. Then, $X(2500)$, $X(2370)$, $\pi(2360)$, and the predicted kaon $K(2414)$ can be grouped into another new nonet. These assignments to the discussed pseudoscalar states can be further tested in experiment.

Masses of the lowest spin-0 and spin-1 meson nonets: Explicit symmetry breaking effects

We extend a known multi-quark three-flavor Lagrangian of the Nambu-Jona-Lasinio type, which includes a set of effective interactions proportional to the current quark masses, to include the multi-quark interactions of vector and axial-vector types. It is shown that the mass spectrum of the four low-lying meson nonets are in agreement with current phenomenological expectations. The role of the new interactions is analyzed in detail.

Spin 1 Low-lying Meson Spectra and the Subtle Link to the Spin 0 Mesons

An NJL-type three-flavor quark model with a complete set of explicit chiral symmetry breaking terms is extended to include vector and axial vector effective interaction terms. The bosonized Lagrangian is written up to quadratic order in the bosonic fields and the role of the new interactions is analysed in detail. The model's parameters are fitted to yield reasonable values to the four low-lying spin 0 and spin 1 meson nonets' masses.

Strong Decays of Excited Vector Mesons

We study two nonets of excited vector mesons, predominantly corresponding to radially excited vector mesons with quantum numbers $n\hspace{0.08cm} ^{2S+1}L_{J}$ $=2^3S_1$ and to orbitally excited vector mesons with quantum numbers $n\hspace{0.08cm} ^{2S+1}L_{J}=1^3D_1$. We evaluate two types of decays of these mesons: into two pseudoscalar mesons and into a pseudoscalar and a ground-state vector meson. We compare the results with experimental data taken from PDG. We also make predictions for the strange-antistrange state in the $1^3D_1$ nonet denoted as $\phi(1930)$, which has not yet been discovered.

Phenomenology of pseudotensor mesons and the pseudotensor glueball

We study the decays of the pseudotensor mesons $[ \pi_{2}(1670) , K_{2}(1770) , \eta_{2}(1645) , \eta_{2}(1870) ]$ interpreted as the ground-state nonet of $1^1 D_{2}$ $\bar{q}q$ states using interaction Lagrangians which couple them to pseudoscalar, vector, and tensor mesons. While the decays of $\pi_2 (1670)$ and $K_2 (1770)$ can be well described, the decays of the isoscalar states $\eta_2 (1645)$ and $\eta_2 (1870)$ can be brought in agreement with experimental data only if the mixing angle between nonstrange and strange states is surprisingly large (about $-42^\circ$, similar to the mixing in the pseudoscalar sector, in which the chiral anomaly is active). Such a large mixing angle is however at odd with all other conventional quark-antiquark nonets: if confirmed, a deeper study of its origin will be needed in the future. Moreover, the $\bar{q}q$ assignment of pseudotensor states predicts that the ratio $[ \eta_2 (1870) \rightarrow a_2 (1320) \pi]/[\eta_2 (1870) \rightarrow f_2 (1270) \eta]$ is about $23.5$. This value is in agreement with Barberis et al., ($20.4 \pm 6.6$), but disagrees with the recent reanalysis of Anisovich et al., ($1.7 \pm 0.4$). Future experimental studies are necessary to understand this puzzle. If Anisovich's value shall be confirmed, a simple nonet of pseudoscalar mesons cannot be able to describe data (different assignments and/or additional state, such as an hybrid state, will be needed). In the end, we also evaluate the decays of a pseudoscalar glueball into the aforementioned conventional $\bar{q}q$ states: a sizable decay into $K^\ast_2 (1430) K$ and $a_2 (1230) \pi$ together with a vanishing decay into pseudoscalar-vector pairs [such as $\rho(770) \pi$ and $K^\ast (892) K$] are expected. This information can be helpful in future studies of glueballs at the ongoing BESIII and at the future PANDA experiments.

Analysis of the scalar nonet mesons with QCD sum rules

In this article, we assume that the nonet scalar mesons below $1\,\rm{ GeV}$ are the two-quark-tetraquark mixed states and study their masses and pole residues using the QCD sum rules. In calculation, we take into account the vacuum condensates up to dimension 10 and the $\mathcal{O}(\alpha_s)$ corrections to the perturbative terms in the operator product expansion. We determine the mixing angles, which indicate the two-quark components are much larger than $50\%$, then obtain the masses and pole residues of the nonet scalar mesons.

Description of EM Structure of Nonet of Pseudoscalar Mesons by Unitary and Analytic Model Leads to More Accurate Muon $g-2$ Anomaly and QED $\alpha (M^2_Z)$ Evaluation

Description of EM Structure of Nonet of Pseudoscalar Mesons by Unitary and Analytic Model Leads to More Accurate Muon $g-2$ Anomaly and QED $\alpha (M^2_Z)$ Evaluation

Constraints on theηη′decay rate of a scalar glueball from gauge/gravity duality

Predictions of glueball decay rates in the holographic Witten-Sakai-Sugimoto model for low-energy QCD can be uniquely extended to include finite quark masses up to an as yet undetermined parameter in the coupling of glueballs to the nonanomalous part of the pseudoscalar mass terms. The assumption of a universal coupling of glueballs to mass terms of the full nonet of pseudoscalar mesons leads to flavor asymmetries in the decay rates of scalar glueballs that agree well with experimental data for the glueball candidate $f_0(1710)$ and implies a vanishing decay rate into $\eta\eta'$ pairs, for which only upper bounds for the $f_0(1710)$ meson are known at present from experiment. Relaxing this assumption, the holographic model gives a tight correlation between the decay rates into pairs of pseudo-Goldstone bosons of same type and $\eta\eta'$ pairs. If $\Gamma(G\to KK)/\Gamma(G\to\pi\pi)$ is kept within the range reported currently by the Particle Data Group for the $f_0(1710)$ meson, the rate $\Gamma(G\to\eta\eta')/\Gamma(G\to\pi\pi)$ is predicted to be $\lesssim 0.04$. The corresponding situation for $f_0(1500)$ is also discussed, which however is found to be much less compatible with the interpretation of a largely unmixed glueball.

The light scalar mesons as tetraquarks

We present a numerical solution of the four-quark Bethe–Salpeter equation for ground-state scalar tetraquarks with JPC=0++. We find that the four-body equation dynamically generates pseudoscalar-meson poles in the Bethe–Salpeter amplitude. The resulting tetraquarks are genuine four-quark states that are dominated by pseudoscalar meson–meson correlations. Diquark–antidiquark contributions are subleading because of their larger mass scale. In the light quark sector, the sensitivity of the tetraquark wave function to the pion poles leads to an isoscalar tetraquark mass Mσ∼350 MeV which is comparable to that of the σ/f0(500). The masses of its multiplet partners κ and a0/f0 follow a similar pattern. This provides support for a tetraquark interpretation of the light scalar meson nonet in terms of ‘meson molecules’.

Chiral nonet mixing inπKscattering

The underlying mixing of quark components of scalar mesons is probed in $\ensuremath{\pi}K$ scattering within a generalized linear sigma model that contains two scalar meson nonets and two pseudoscalar meson nonets (a quark-antiquark and a four-quark). In the leading order of this model, all free parameters have been previously fixed using the mass spectra and several low-energy parameters known from experiment and consistent predictions have been made. As in other predictions of the model, in the present work the isospins $I=1/2$, $3/2$ and $J=0$ projection of the $\ensuremath{\pi}K$ scattering amplitude (as well as phase shifts) are computed and compared with experiment. In the $I=1/2$ channel, it is shown that within the uncertainties of the model parameters a good agreement with experimental data up to an energy of about 1 GeV is obtained, whereas in the $I=3/2$ channel there is a better agreement with experiment which extends to about 1.4 GeV. The effect of final state interactions of $\ensuremath{\pi}K$ in the $I=1/2$ channel is approximated by the K-matrix method and the poles of the unitarized scattering amplitude are found. It is shown that the model predicts a light and broad kappa resonance with a mass and decay width of 670--770 MeV and 640--750 MeV consistent with other prior works. Moreover, the scattering lengths in the $I=1/2$, $3/2$ are also computed and shown to qualitatively agree with experiment. The overall predictions presented here further support previous findings that the scalar mesons below and above 1 GeV have substantial underlying mixings and that those below 1 GeV have dominant four-quark substructures while those above 1 GeV are closer to conventional $P$-wave quark-antiquark states.

Semi-leptonic [formula omitted] decays in the standard model and in the universal extra dimension model

In this article, we assume the two nonets of scalar mesons below and above 1 GeV are all q¯q states, and study the semi-leptonic decays B→Sℓ−ν¯ℓ, B→Sℓ+ℓ− and B→Sν¯ν both in the standard model and in the universal extra dimension model using the B–S form-factors calculated by the light-cone QCD sum rules in our previous work. We obtain the partial decay widths and decay widths, which can be confronted with the experimental data in the future to examine the natures of the scalar mesons and constrain the basic parameter in the universal extra dimension model, the compactification scale 1/R.

$$B-S$$ B - S transition form-factors with the light-cone QCD sum rules

In the article, we assume the two scalar nonet mesons below and above 1 GeV are all $\bar{q}q$ states, in case I, the scalar mesons below 1 GeV are the ground states, in case II, the scalar mesons above 1 GeV are the ground states. We calculate the $B-S$ form-factors by taking into account the perturbative ${\mathcal{O}}(\alpha_s)$ corrections to the twist-2 terms using the light-cone QCD sum rules and fit the numerical values of the form-factors into the single-pole forms, which have many phenomenological applications.

Polyakov SU(3) extended linear-σmodel: Sixteen mesonic states in chiral phase structure

The derivative of the grand potential in mean field approximation, non-strange and strange condensates and deconfinement phase-transition in thermal and dense hadronic medium are verified in extended SU(3) linear sigma-model (eLSM). In determining the chiral phase-transition, the chiral condensates sigma_x and sigma_y are analysed. The chiral mesonic phase-structures in temperature- and density-dependence are taken as free parameters to be fitted. These parameters are classified corresponding to scalar meson nonets; (pseudo)-scalar and (axial)-vector. For deconfinement phase-transition, effective Polyakov loop-potentials phi and phi^* are utilized. We investigated the in-medium effects on the masses of sixteen mesonic states states. The results are presented for two different forms for the effective Polyakov loop-potential and compared with other models with and without anomalous terms. The Polyakov loop potential in LSM has considerable effects on the chiral phase-transition in meson masses so that the restoration of the chiral symmetry becomes sharper and faster than LSM. We normalize all mesonic states with respect to the lowest Matsubara frequency. It has been found that the various mesonic states have different dissolving temperatures and chemical potentials, i.e. they survive the typically-averaged QCD phase boundary, defined by the QCD critical temperatures with varying chemical potentials. The thermal behavior of all meson masses has been investigated in the large-$N_c$ limit and found that the scalar meson masses are T-independent at large $N_c$ and high $T$ (except pi and sigma). For the pseudoscalar meson masses, the large N_c limit unifies the $T$-dependence of all states in a universal bundle. The same is also observed for axial and axialvector meson masses in the large-N_c limit.

Chiral nonet mixing inη′→ηππdecay

Underlying mixing of scalar mesons is studied in $\eta'\rightarrow \eta\pi\pi$ decay within a generalized linear sigma model of low-energy QCD which contains two nonets of scalar mesons and two nonets of pseudoscalar mesons (a quark-antiquark nonet and a four quark nonet). The model has been previously employed in various investigations of the underlying mixings among scalar mesons below and above 1 GeV (as well as those of their pseudoscalar chiral partners) and has provided a coherent global picture for the physical properties and quark substructure of these states. It is found that the linear sigma model with only a single lowest-lying nonet is not accurate in predicting the decay width, but inclusion of the mixing of this nonet with the next-to-lowest lying nonet, together with the effect of final state interaction of pions, significantly improves this prediction and agrees with experiment up to about 1\%. It is also shown that while the prediction of the leading order of the generalized model for the Dalitz parameters is not close to the experiment, the model is able to give a reasonable prediction of the energy dependencies of the normalized decay amplitude squared and that this is expected to improve with further refinement of the complicated underlying mixings. Overall this investigation provides further support for the global picture of scalar mesons: those below 1 GeV are predominantly four-quark states and significantly mix with those above 1 GeV which are closer to the conventional p-wave quark-antiquark states.

Phenomenological study of theBc→BP,BVdecays with perturbative QCD approach

Inspired by the recent LHCb measurements and forthcoming great potential on $B_{c}$ meson, we study the exclusive $B_{c}$ ${\to}$ $B_{q}P$, $B_{q}V$ decays with the perturbative QCD approach, where $q$ $=$ $u$, $d$, $s$; $P$ and $V$ denote the lightest pseudoscalar and vector $SU(3)$ nonet meson, respectively. By retaining the quark transverse momentum, employing the Sudakov factors, and choosing the typical scale as the maximum virtualities of the internal particles, we calculate the $B_{c}$ ${\to}$ $B$ transition from factors, and our results show that about 90\% contribution to form factors come from the ${\alpha}_{s}/{\pi}$ $<$ $0.3$ region. The contributions of penguin and annihilation to branching ratios are very small due to the serious suppression by the CKM factors. There is some hierarchy relations among the $B_{c}$ ${\to}$ $BP$, $BV$ decays. The branching ratios for $B_{c}$ ${\to}$ $B_{d,s}{\pi}$, $B_{d,s}{\rho}$, $B_{s}K$ are large and could be measured by the running LHCb.

Electromagnetic structure of vector mesons

Electromagnetic structure of the complete nonet of vector mesons (ρ 0 ,ρ + ,ρ − ,ω , φ,K ∗0 , K ∗+ , ¯ K ∗0 , K ∗− ) is investigated in the framework of the Unitary and Analytic model and insufficient experimental information on it is discussed.

Comparing symmetry restoration trends for meson masses and mixing angles in the QCD-like three quark flavor models

We are computing the modifications for the scalar and pseudoscalar meson masses and mixing angles due to the proper accounting of fermionic vacuum fluctuation in the framework of the generalized 2+1 flavor quark meson model and the Polyakov loop augmented quark meson model(PQM). The renormalized contribution of the divergent fermionic vacuum fluctuation at one loop level makes these models effective QCD-like models. It has been explicitly shown that analytical expressions for the model parameters, meson masses, and mixing angles do not depend on any arbitrary renormalization scale. We have investigated how the incorporation of fermionic vacuum fluctuation in quark meson and PQM models qualitatively and quantitatively affects the convergence in the masses of the chiral partners in pseudoscalar ($\pi$, $\eta$, $\eta'$, $K$) and scalar ($\sigma$, $a_0$, $f_0$, $\kappa$) meson nonets as the temperature is varied on the reduced temperature scale. Comparison of present results in the quark meson model with vacuum term and PQM model with vacuum term with the already existing calculations in the bare 2+1 quark meson and PQM models, shows that the restoration of chiral symmetry becomes smoother due to the influence of the fermionic vacuum term. We find that the melting of the strange condensate registers a significant increase in the presence of the fermionic vacuum term and its highest melting is found in the PQM model with vacuum term. The role of the $U_A(1)$ anomaly in determining the isoscalar masses and mixing angles for the pseudoscalar ($\eta$ and $\eta'$) and scalar ($\sigma$ and $f_0$) meson complex has also been significantly modified due to the fermionic vacuum correction. In its influence, the interplay of chiral symmetry restoration and the setting up of the $U_A(1)$ restoration trends have also been shown to be significantly modified.

Study of vector mesons and its excited states

Based on the Regge phenomenology, we first study the mass relations for six mesons involving three flavors in one spin-parity multiplet. Using the examined mass relation, mass of the unobserved vector doubly heavy charm-bottom Bc*(13S1) is calculated. Masses of the unobserved radial excited vector (23S1) mesons and the orbital excited 13G5 meson nonet are given. Our predictions are discussed. We suggest searching Bc* near 6355 MeV. D(2600) and Ds1(2700) can be considered as candidates for nc(23S1 and sc(23S1) dominated states, respectively. We suggest searching B*(2S), Bs*(2S) and Bc*(2S) near 5812, 5917 and 6896 MeV, respectively. We suggest restudying 5(2350) near 2259 MeV, searching 5(13G5) near 2438 MeV and identifying 5(2250) as isoscalar member of 13G5 nonet. The results may be profoundly useful for the JP assignment of related states and the discovery of the unobserved excited mesons.