Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

Abstract

We use a nonpertubative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f 0 and a 0 resonances. The ππ → ππ , ππ → KK phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π 0 η and KK mass distributions in the T = 1 channel. Furthermore, the total and partial decay widths of the f 0 and a 0 resonances are properly reproduced including also the decay into the γγ channel. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below √ s ≃ 1.2 GeV .

Dynamical generation of hyperon resonances

“…[ 4] after obtaining a pole with S = −1 in the I = 1 channel, with mass around 1430 MeV, and two poles with I = 0, of masses around that of the Λ(1405). Similar ideas have been exploited in the meson-meson interaction where a nonet of dynamically generated mesons, made of the σ(500), f 0 (980), a 0 (980) and κ(900), has been obtained [ 14,15,16,17].…”

Resonance Extraction from the Finite Volume

“…Using the Chiral Unitary Approach of Ref. [25], one can generate realistic lattice eigenvalues for different box sizes L as shown in Fig. 1 to the left.…”

“…As the data had been originally generated from the approach of Ref. [25], the exact pole position is known (triangle in the figure). The figure thus shows that it is indeed possible to reliably reconstruct the resonance.…”

Multiquark states as di-hadronic molecules

“…But there exist little succuss towards understanding the tetra-quark and penta-quark states as di-hadron molecules due to nonperturbative nature of QCD at the hadronic scale. It is widely believed that the QCD sum rule and the instanton based models are capable nonperturbative methods to extract the properties of hadrons [3,4] but there exist little works on multiquark states, especially their systematic calculations [5]. Recently, several new states X(3.872), D sJ (2.317, 2.460, 2.632),Z(3.931), Y(3.943), Y(4.260) etc were observed in the experimental investigations of charmed mesons.…”