Scalar Mesons Research Articles

Scalar isoscalar mesons and the scalar glueball from radiative J/ψ decays

A coupled-channel analysis of BESIII data on radiative J/ψ decays into ππ, KK¯, ηη and ωϕ has been performed. The partial-wave amplitude is constrained by a large number of further data. The analysis finds ten isoscalar scalar mesons. Their masses, widths and decay modes are determined. The scalar mesons are interpreted as mainly SU(3)-singlet and mainly octet states. Octet isoscalar scalar states are observed with significant yields only in the 1500-2100MeV mass region. Singlet scalar mesons are produced over a wide mass range but their yield peaks in the same mass region. The peak is interpreted as scalar glueball. Its mass and width are determined to M=1865±25−30+10MeV and Γ=370±50−20+30MeV, its yield in radiative J/ψ decays to (5.8±1.0)10−3.

Interplay between chiral dynamics and repulsive interactions in hot hadronic matter

We investigate fluctuations of the net-baryon number density in hot hadronic matter. We discuss the interplay between chiral dynamics and repulsive interactions and their influence on the properties of these fluctuations near the chiral crossover. The chiral dynamics is modeled by the parity doublet Lagrangian that incorporates the attractive and repulsive interactions mediated via the exchange of scalar and vector mesons, respectively. The mean-field approximation is employed to account for chiral criticality. We focus on the properties and systematics of the cumulants of the net-baryon number density up to the sixth order. It is shown that the higher-order cumulants exhibit a substantial suppression in the vicinity of the chiral phase transition due to the presence of repulsive interactions. We find, however, that the characteristic properties of cumulants near the chiral crossover observed in lattice QCD results are entirely linked to the critical chiral dynamics and, in general, cannot be reproduced in phenomenological models, which account only for effective repulsive interactions via excluded-volume corrections or van-der-Waals type interactions. Consequently, a description of the higher-order cumulants of the net-baryon density in the chiral crossover requires a self-consistent treatment of the chiral in-medium effects and repulsive interactions.

Nonperturbative quark-antiquark interactions in mesonic form factors

The existing theory of hard exclusive QCD processes is based on two assumptions: (i) factorization into a hard block convoluted with the light front distribution amplitudes; (ii) use of perturbative gluon exchanges within the hard block. However, unlike deep inelastic scattering and jet physics, the characteristic momentum transfer $Q$ involved in the factorized block is not large enough for this theory to be phenomenologically successful. In this work, we revisit the latter assumption (ii), by explicitly calculating the instanton-induced contributions to the hard block, and show that they contribute substantially to the vector, scalar, and gravitational form factors of the pseudoscalar, scalar, and vector mesons, over a wide range of momentum transfer.

Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD.

We introduce novel relations between the derivatives [∂^{n}ρ(λ,m_{l})/∂m_{l}^{n}] of the Dirac eigenvalue spectrum [ρ(λ,m_{l})] with respect to the light sea quark mass (m_{l}) and the (n+1)-point correlations among the eigenvalues (λ) of the massless Dirac operator. Using these relations we present lattice QCD results for ∂^{n}ρ(λ,m_{l})/∂m_{l}^{n} (n=1, 2, 3) for m_{l} corresponding to pion masses m_{π}=160-55 MeV and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings a=0.12, 0.08, 0.06fm, and lattices having aspect ratios 4-9. We find that ρ(λ→0,m_{l}) develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as a→0, and its amplitude is proportional to m_{l}^{2}. We demonstrate that this ρ(λ→0,m_{l}) is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.

One-Hadron-Exchange K−p interaction model in nonrelativistic energy region

A nonrelativistic K−p interaction model is derived as one-hadron-exchanges. The exchanged particles are the scalar meson, the vector mesons, the hyperons, and the resonances Λ*(1600),Σ*(1385). The models parameters are determined by fitting to experimental data of spin-averaged differential cross section for kaon laboratory energy range of 51.27 MeV up to 376.87 MeV. We use a 3D technique without partial wave expansion to calculate K−p scattering.

One hadron exchange non-relativistic model for potential

One of the KN Interaction is K+p interaction which one we’re interested in. K+p potential is described as one hadron exchanges. The hadrons being exchanged include scalar meson (σ), vector mesons (ω, ρ ), hyperons (Λ, Σ), and their resonances ( Λ* (1600), Σ*(1385)). This interaction model is derived for non-relativistic calculations within Blankenbecler-Sugar reduction. The values of the potential parameters are fixed by fitting to experimental data of K+p spin-averaged differential cross section for kaon laboratory energies from 88.13 MeV to 3683.22 MeV. Scattering calculations are performed by using a 3D technique without partial wave expansion.

Effect of momentum anisotropy on quark matter in the quark-meson model * *Supported by the National Natural Science Foundation of China (11935007) and the Fundamental Research Funds for the Central Universities (2020CXZZ107)

We investigate the chiral phase structure of quark matter with spheroidal momentum-space anisotropy specified by one anisotropy parameter in the 2+1 flavor quark-meson model. We find that the chiral phase diagram and the location of the critical endpoint (CEP) are significantly affected by the value of . With an increase in , the CEP is shifted to lower temperatures and higher quark chemical potentials. In addition, the temperature of the CEP is more sensitive to the anisotropy parameter than the corresponding quark chemical potential, which is the opposite to that from the finite system volume effect. The effects of the momentum anisotropy on the thermodynamic properties and scalar (pseudoscalar) meson masses are also studied at the vanishing quark chemical potential. The numerical results reveal that an increase in can hinder the restoration of chiral symmetry. We also find that shear viscosity and electrical conductivity decrease as increases. However, the bulk viscosity exhibits a significant non-trivial behavior with in the entire temperature domain of interest.

Waves that Appear From Nowhere: Complex Rogue Wave Structures and Their Elementary Particles

The nonlinear Schrödinger equation has wide range of applications in physics with spatial scales that vary from microns to kilometres. Consequently, its solutions are also universal and can be applied to water waves, optics, plasma and Bose-Einstein condensate. The most remarkable solution presently known as the Peregrine solution describes waves that appear from nowhere. This solution describes unique events localized both in time and in space. Following the language of mariners they are called “rogue waves”. As thorough mathematical analysis shows, these waves have properties that differ them from any other nonlinear waves known before. Peregrine waves can serve as ‘elementary particles’ in more complex structures that are also exact solutions of the nonlinear Schrödinger equation. These structures lead to specific patterns with various degrees of symmetry. Some of them resemble “atomic like structures”. The number of particles in these structures is not arbitrary but satisfies strict rules. Similar structures may be observed in systems described by other equations of mathematical physics: Hirota equation, Davey-Stewartson equations, Sasa-Satsuma equation, generalized Landau-Lifshitz equation, complex KdV equation and even the coupled Higgs field equations describing nucleons interacting with neutral scalar mesons. This means that the ideas of rogue waves enter nearly all areas of physics including the field of elementary particles.

Evidence of the four-quark nature of f0(980) and f0(500)

There exists a great deal of concrete evidence in favor of the exotic four-quark nature of light scalars. At the same time, the further expansion of the area of the $q^2\bar q^2$ model validity for light scalars on ever new processes seems extremely interesting and important. We analyze the BESIII data on the decay $J/\psi\to \gamma\pi^0\pi^0$ and show that the results of this high-statistics experiment can be interpreted in favor of the four-quark nature of light scalar mesons $f_0(980)$ and $f_0(500)$.

Gauge field theories and propagators in curved space-time

In this paper, DeWitt’s formalism for field theories is presented; it provides a framework in which the quantization of fields possessing infinite-dimensional invariance groups may be carried out in a manifestly covariant (non-Hamiltonian) fashion, even in curved space-time. Another important virtue of DeWitt’s approach is that it emphasizes the common features of apparently very different theories such as Yang–Mills theories and General Relativity; moreover, it makes it possible to classify all gauge theories in three categories characterized in a purely geometrical way, i.e. by the algebra which the generators of the gauge group obey; the geometry of such theories is the fundamental reason underlying the emergence of ghost fields in the corresponding quantum theories, too. These “tricky extra particles”, as Feynman called them in 1964, contribute to a physical observable such as the stress-energy tensor, which can be expressed in terms of Feynman’s Green function itself. Therefore, an entire section is devoted to the study of the Green functions of the neutron scalar meson: in flat space-time, the choice of a particular Green’s function is the choice of an integration contour in the “momentum” space; in curved space-time the momentum space is no longer available, and the definition of the different Green functions requires a careful discussion itself. After the necessary introduction of bitensors, world function and parallel displacement tensor, an expansion for the Feynman propagator in curved space-time is obtained. Most calculations are explicitly shown.

Nonrelativistic one-hadron-exchange k−p interaction model

We have derived a nonrelativistic K−p interaction model as one-hadron-exchanges. The exchanged particles are the scalar meson σ, the vector mesons ω, ρ, the hyperons Λ, Σ, and the resonances Λ* (1600), Σ*(1385). Parameters in this model are determined by fitting to experimental data of spin-averaged differential cross section for kaon laboratory energy range of 51.27 MeV up to 900.64 MeV. The K-p scattering is calculated using a 3D technique without partial wave expansion.

A unified quark-nuclear matter equation of state from the cluster virial expansion within the generalized Beth\u2013Uhlenbeck approach

We consider a cluster expansion for strongly correlated quark matter where the clusters are baryons with spectral properties that are described within the generalized Beth–Uhlenbeck approach by a medium dependent phase shift. We employ a simple ansatz for the phase shift which describes an on-shell bound state with an effective mass and models the continuum by an anti-bound state located at the mass of the three-quark continuum threshold, so that the Levinson theorem is fulfilled by construction. The quark and baryon interactions are accounted for by the coupling to scalar and vector meson mean fields modelled by density functionals. At increasing density and temperature, due to the different medium-dependence of quark and baryon masses, the Mott dissociation of baryons occurs and its contributions to the thermodynamics vanish. It is demonstrated on this simple example that this unified approach to quark-hadron matter is capable of describing crossover as well as first order phase transition behaviour in the phase diagram with a critical endpoint. Changing the meson mean field, the case of a “crossover all over” in the phase diagram is also obtained.

One hadron exchange non-relativistic model for K+p potential

K+p potential is modeled as one hadron exchange. The hadrons being exchanged include scalar meson (σ), vector mesons ( ω, p ), hyperons (Λ, Σ), and their resonances (Λ*(1600), Σ*(1385)). This interaction model is derived for non-relativistic calculations and for that purpose the potential model is formulated within Blankenbecler-Sugar reduction. The values of the potential parameters are fixed by fitting to experimental data of K+p spin-averaged differential cross section for kaon laboratory energies from 88.13 MeV to 380.58 MeV. Scattering calculations are performed by using a 3D technique without partial wave expansion.

Multilayer neutron stars with scalar mesons crossing term

It is shown that recently proposed RMF model with $\sigma$ and $\delta$ meson interaction agrees with the observational data and presents an interesting structure with phase transition in the outer part of neutron star core.

Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography

Spectra of pions, which are known as the pseudo-Goldstone bosons of spontaneous chiral symmetry breaking, as well as their relationship with chiral phase transition and pion superfluidity phase transition, have been investigated in the framework of soft-wall AdS/QCD. In chiral limit, it is proved both numerically and analytically that pions are massless Goldstone bosons even at finite temperature, which was usually considered as an assumption in soft-wall models. Above $T_c$, at which chiral condensate $\langle \bar{q}q\rangle$ vanishes, the spectra of pions and scalar mesons merge together, showing the evidence of the restored chiral symmetry in hadronic spectrum level. Extending to finite quark mass, pion masses increase with quark mass. Further, it is more interesting to observe that the pole masses of pions decrease with temperature below $T_c$, which agrees with the analysis in Phys.Rev.Lett.88(2002)202302. Meanwhile, symmetry restoration above $T_c$ could be seen in the spectra of scalar and pseudo-scalar mesons. With finite temperature and isospin chemical potential $\mu_I$, it is shown that the masses of charged pions would split. The mass of positive charged pion $\pi^+$ decreases almost linearly to zero when $\mu_I$ grows to $\mu_{I}^c$, where pion condensation starts to form. This reveals the Goldstone nature of $\pi^+$ after pion superfluidity transition, which are closely related to the experimental observation.

Perturbative QCD predictions for the decay Bs0→SS(a0(980),f0(980),f0(500))

In this work, we calculate the branching ratios and CP violations of the B^{0}_{s}\rightarrow a_{0}(980)a_{0}(980) decay modes with both charged and neutral a_{0}(980) mesons and B^{0}_{s}\rightarrow f_{0}(980)(f_{0}(500))f_{0}(980)(f_{0}(500)) for the first time in the pQCD approach. Considering the recent observation of the BESIII collaboration that provide a direct information about the constituent two-quark components in the corresponding a_{0}(980) wave functions, we regard the scalar mesons a_{0}(980), f_{0}(980) and f_{0}(500) as the q\bar{q} quark component in our present work, and then make predictions of these decay modes. The branching ratios of our calculations are at the order of the 10^{-4}\sim10^{-6} when we consider the mixing scheme. We also calculate the CP violation parameters of these decay modes. The relatively large branching ratios make it easily to be tested by the running LHC-b experiments, and it can help us to understand both the inner properties and the QCD behavior of the scalar meson.

Nonperturbative quark matter equations of state with vector interactions

Nonperturbative equations of state (EoSs) for two and three quark flavors are constructed with the functional renormalization group (FRG) within a quark-meson model truncation augmented by vector mesons for low temperature and high density. Based on previous FRG studies without repulsive vector meson interactions the influence of isoscalar vector ω- and ϕ-mesons on the dynamical fluctuations of quarks and (pseudo)scalar mesons is investigated. The grand potential as well as vector meson condensates are evaluated as a function of quark chemical potential and the quark matter EoS in β-equilibrium is applied to neutron star (NS) physics. The tidal deformability and mass-radius relations for hybrid stars from combined hadronic and quark matter EoSs are compared for different vector couplings. We observe a significant impact of the vector mesons on the quark matter EoS such that the resulting EoS is sufficiently stiff to support two-solar-mass neutron stars.

Beam Asymmetries from Light Scalar Meson Production on the Proton at GlueX

The GlueX facility, featuring a linearly polarised 9 GeV real photon beam delivered to a large-acceptance detector system, has recently completed its first phase of running, and analysis efforts of this dataset are well underway. It has been suggested that at GlueX energies, quark systems beyond the three quark and quark-antiquark systems of baryons and mesons, such as hybrid mesons, tetraquarks and glueballs, should exist, and studies of these systems could shed new light on how quarks combine under the strong force, particularly the role played by gluons.Meticulous study of the spectrum of hadronic states is required to understand the strong force in the non-perturbative energy regime, and the light scalar meson sector is an area that remains poorly understood. GlueX data encompasses final states at energies where photoproduction of the a0 (980) and f 0 (980) mesons can provide discriminatory evidence between various models, manifested in experimental observables such as the cross section and beam asymmetry, and performing detailed measurements of these quantities is considered a priority of the ongoing research program.The work presented showcases efforts to measure the beam asymmetry of the reaction γp→pηπ whose mass spectrum encompasses several mesons, including the a 0(980) light scalar, and the a 2(1320) tensor. Future prospects for related analyses in the light scalar meson sector, informed by this measurement, will also be discussed.

Relativistic Cornell-type mechanism of exotic scalar resonances

The physical masses of the lowest scalar mesons strongly disagree with the calculated $q\overline{q}$ pole values. It is the purpose of this paper to explain theoretically the unusual spectrum of scalar mesons for both the ground and excited states, using the known spectra of the corresponding $q\overline{q}$ states and their connection to the meson resonances. The well-known Cornell coupled-channel mechanism is exploited for this connection together with the quark-chiral Lagrangian without fitting parameters. In addition to the scalars previously obtained using this method, ${f}_{0}(500)$, ${f}_{0}(980)$, ${a}_{0}(980)$, we predict all ground and first excited scalar states, ${f}_{0}(500)$, ${f}_{0}(980)$, ${a}_{0}(980)$, ${a}_{0}(1450)$, ${K}_{0}^{*}(700)$, ${K}_{0}^{*}(1430)$, ${f}_{0}(1370)$, ${f}_{0}(1710)$, which are in reasonably good agreement with experimental data.

Light clusters in warm stellar matter: calibrating the cluster couplings

The abundances of light clusters within a formalism that considers in-medium effects are calculated using several relativistic mean-field models, with both density-dependent and density-independent couplings. Clusters are introduced as new quasiparticles, with a modified coupling to the scalar meson field. A comparison with experimental data from heavy ion collisions allows settling the model dependence of the results and the determination of the couplings of the light clusters to the meson fields. We find that extra experimental constraints at higher density are needed to convincingly pin down the density associated to the melting of clusters in the dense nuclear medium. The role of neutron rich clusters, such as $^6$He, in asymmetric matter is discussed.