Exploration of a physical picture for the QCD scalar channel

Amir H Fariborz,Renata Jora,Joseph Schechter

doi:10.1016/j.nuclphysbps.2008.12.067

Amir H Fariborz, Renata Jora + Show 1 more

Open Access

https://doi.org/10.1016/j.nuclphysbps.2008.12.067

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Abstract

A generalized linear sigma model is employed to study the quark structure of low lying scalar as well as pseudoscalar states. The model allows the possible mixing of quark anti-quark states with others made of two quarks and two antiquarks but no a priori assumption is made about the quark contents of the predicted physical states. Effects of SU(3) symmetry breaking are included. The lighter conventional pseudoscalars turn out to be primarily of two quark type whereas the lighter scalars have very large four quark admixtures.

Highlights

The Belle collaboration [1] provided strong evidence for the Z(4430) resonance in the Ψ′- π channel
Note that the level inversion of four quark states would hold either for “molecular” or diquark- antidiquark pictures. There is another side to this story
Note that QCD with massless light quarks obeys SU(3)L x SU(3)R symmetry spontaneously broken to SU(3)V

Summary

TOY MODEL TO CHECK MIXING PICTURE

Note that QCD with massless light quarks obeys SU(3)L x SU(3)R symmetry spontaneously broken to SU(3)V. There are twelve parameters describing the Lagrangian and the vacuum These include the six coupling constants given in Eq(6), the two quark mass parameters, (A1 = A2, A3) and the four vacuum parameters (α1 = α2, α3, β1 = β2, β3).The four minimum equations reduce the number of needed input parameters to eight. Note that the presence of the last two terms in Eq(6)- which exactly mock up the QCD U(1)A anomaly - decouples the initial treatment of the other particles from that of the complicated pseudoscalar singlet sector. Given these inputs there are a very large number of predictions. At the level of the quadratic terms in the Lagrangian, we predict all the remaining masses and decay constants as well as the angles describing the mixing between each of (π, π′), (K, K′), (a0, a′0), (κ, κ′) multiplets and each of the 4×4 isosinglet mixing matrices (each formally described by six angles)

BRIEF SUMMARY OF RESULTS

PHYSICAL INTERPRETATION OF SCALAR MASSES