The strong and electromagnetic decays of the ground-state tensor mesons are studied in an effective field approach. A fit to the well-known experimental data is performed. The decay ratios of the tensor glueball are evaluated and possible candidates are discussed.

Decays of tensor mesons and the tensor glueball in an effective field approach

In this paper we study the $$J/\Psi p$$ spectroscopy in the process of $$\Lambda _b\rightarrow J/\Psi p K^-$$. The final state interactions of coupled channel $$J/\Psi p$$–$$\bar{D} \Sigma _c$$–$$\bar{D}^{*} \Sigma _c$$ are constructed based on K-matrix with the Chew–Mandelstam function. We build the $$\Lambda _b\rightarrow J/\Psi p K^-$$ amplitude according to the Au–Morgan–Pennington method. The event shape is fitted and the decay width of $$\Lambda _b\rightarrow J/\Psi p K^-$$ is used to constrain the parameters, too. With the amplitudes we extract out the poles and their residues. Our amplitude and pole analysis suggest that the $$P_c(4312)$$ should be $$\bar{D}\Sigma _c$$ molecule, the $$P_c(4440)$$ could be an S-wave compact pentaquark state, and the structure around $$P_c(4457)$$ is caused by the cusp effect. The future experimental measurement of the decays of $$\Lambda _b\rightarrow \bar{D}\Sigma _c K^-$$ and $$\Lambda _b\rightarrow \bar{D}^*\Sigma _c K^-$$ would further help to study the nature of these resonances.

/pdf/pole-analysis-on-the-hadron-spectroscopy-of-lambda-b-3sp3yuty5r.pdf

Pole analysis on the hadron spectroscopy of $$\Lambda _b\rightarrow J/\Psi p K^-$$Λb→J/ΨpK-

In a previous paper [Commun. Theor. Phys., [arxiv:hep-ph/11081451]], we proposed a method to distinguish poles of different dynamical origin, in unitarized amplitudes of pi pi, K (K) over bar system. That is based on the observation that "A Breit-Wigner resonance should exhibit two poles on different Riemann sheets which meet each other on the real axis when N-c = infinity". In this paper, we extend our previous work [Commun. Theor. Phys., [arXiv:hep-ph/11081451]] to the pi pi-K (K) over bar-eta eta three channel system. We reconfirm most of the predictions in our previous work [Commun. Theor. Phys., [arxiv:hep-ph/11081451]]. Especially the f(0) (980) is of K (K) over bar molecule nature. Other poles, including the sigma, are of Breit-Wigner type.

Pole Analysis of Unitarized One Loop χ PT Amplitudes—A Triple Channel Study

In this paper we study the $J/\Psi p$ spectroscopy in the process of $\Lambda_b\to J/\Psi p K^-$. The final state interactions of coupled channel $J/\Psi p$ ~-~ $\bar{D} \Sigma_c$~-~$\bar{D}^{*} \Sigma_c$ are constructed based on K-matrix with the Chew-Mandelstam function. We build the $\Lambda_b\to J/\Psi p K^-$ amplitude according to the Au-Morgan-Pennington method. The event shape is fitted and the decay width of $\Lambda_b\to J/\Psi p K^-$ is used to constrain the parameters, too. With the amplitudes we extract out the poles and their residues. Our amplitude and pole analysis suggest that the $P_c(4312)$ should be $\bar{D}\Sigma_c$ molecule, the $P_c(4440)$ could be an S-wave compact pentaquark state, and the structure around $P_c(4457)$ is caused by the cusp effect. The future experimental measurement of the decays of $\Lambda_b\to \bar{D}\Sigma_c K^-$ and $\Lambda_b\to \bar{D}^*\Sigma_c K^-$ would further help to study the nature of these resonances.

/pdf/pole-analysis-on-the-hadron-spectroscopy-of-lambda-b-to-j-2ukl21c1vm.pdf

Pole analysis on the hadron spectroscopy of $\Lambda_b\to J/\Psi p K^-$

TheN-channel formalism (in more detail, 2- and 3-channel) is presented which is based on such general principles, as analyticity and unitarity, and realizes an idea of the consistent account of the nearest (to the considered physical region) singularities on all sheets of the Riemann surface of theS-matrix, thus giving a chance to obtain model-independent information on multichannel resonances from the analysis of data on the coupled processes. The resonance representations by pairs of complex-conjugate clusters of poles and zeros on the Riemann surface and the conception of standard clusters as a model-independent test of the resonance presence are discussed. The role of closed channels in forming resonances and fictitious states is investigated. The method is exemplified with the isoscalars-wave channel of coupled processes ππ→ππ, K$\overline K $, ππ and with analysing ππ scattering up to 1.9 GeV and scalar resonances.

/pdf/multichannel-approach-to-studying-scalar-resonances-4eiq7zhzwj.pdf

Multichannel approach to studying scalar resonances

In a combined analysis of the experimental data on the coupled processes ππ↦ππ, K¯K in the channel with IGJPC = 0+0+ +, the various scenarios of these reactions (with different numbers of resonances) are considered. In a model-independent approach, based only on analyticity and unitarity, a resonance is represented by a pole cluster (poles on the Riemann surface) of the definite type that is defined by the state nature. The best scenario contains the resonances f0(665) (with properties of the σ-meson), f0(980) (with a dominant s¯s component), f0(1500) (with a dominant flavour-singlet, e.g., glueball component) and the f0(1710) (with a considerable s¯s component). If the f0(1370) exists, it has a dominant s¯s component. The coupling constants of the observed states with the considered channels and the ππ and K¯K scattering lengths are obtained. The conclusion on the linear realization of chiral symmetry is drawn.

https://link.springer.com/content/pdf/10.1140/epja/i2002-10036-6

Mesons of the f0 family in processes ππ↦ππ, K¯K up to 2 GeV and the chiral-symmetry breaking

Two-and three-channel analyses of experimental data on the coupled processes ππ → ππ, k, ηη in the channel with I
 G
 J
 PC
 = 0+0++ are carried out and discussed. In a model-independent approach, confirmation of the σ-meson below 1GeV and definite indications of the QCD nature of other f0 resonances are obtained. An assignment of the scalar mesons below 1.9 GeV to lower nonets is proposed.

On lower scalar quark antiquark nonets

In approach, based on analyticity and unitarity, experimental data on the isoscalar S- and D-waves of processes ππ → ππ, , ηη, ηη′ have been analyzed for studying the status and QCD nature of the f0- and f2-mesons below 2.3 GeV. Assignment of scalar and tensor mesons to lower nonets is proposed.

Scalar and tensor states in processes with pseudoscalar mesons

The s-wave pion scattering amplitude is analysed with the aim to clarify the mass spectrum of scalar mesons and to find evidence of lightest glueball The S-matrix ππ and K¯K coupled channel formalism is used The existence of scalar mesons S* and ɛ is implied by the data The production ππ → K¯K and the elastic K¯K→K¯K coupled amplitudes are predicted from the ππ →ππ scattering data The couplings c f S* to ππ and K¯K states are determined

D. Krupa

Papers

Multichannel approach to studying scalar resonances

Mesons of the f0 family in processes ππ↦ππ, K¯K up to 2 GeV and the chiral-symmetry breaking

On lower scalar quark antiquark nonets

Scalar and tensor states in processes with pseudoscalar mesons

Scalar mesons in ππ and K¯K scattering