Meson spectrum in a non-relativistic model with instanton-induced interaction

Abstract

On the basis of the phenomenological non-relativistic quark model, we have obtained the ground-state masses of the light pseudo-scalar and vector mesons. The full Hamiltonian used in the investigation includes the kinetic energy, the confinement potential, the one-gluon-exchange potential and the instanton-induced quark–antiquark interaction. A good agreement is obtained with the experimental masses. The η–η′ splitting is explained. The limitation of the perturbative treatment for estimating the π–ρ splitting using OGEP is also pointed out.

The effect of instanton-induced interaction on P-wave meson spectra in constituent quark model

“…In computing the meson masses we have diagonalized the matrix ( Ψ ip |H|Ψ jp ) i,j=0,1,2,3,4 in the relative space, where we have restricted the angular momentum of center-of-mass wave function to zero. There are nine parameters associated with the central parts of the potentials as mentioned in the previous paper [22]. These are the masses of the u, d and s quarks, the confinement strength a c , the harmonic oscillator size parameter b, the strong coupling constant α s and the strength parameters of III, namely, g, g and Λ respectively (eqs (2.2)-(2.7)).…”

“…These are the masses of the u, d and s quarks, the confinement strength a c , the harmonic oscillator size parameter b, the strong coupling constant α s and the strength parameters of III, namely, g, g and Λ respectively (eqs (2.2)-(2.7)). To reproduce the S-wave spectra of light mesons we needed these nine parameters [22]. In the current work, these parameter values are fixed at the values chosen in [22] and are given in table 1.…”

“…Previously, we had employed the NRQM [22] and the relativistic harmonic model (RHM) [23] along with III to investigate the ground state masses of pseudoscalar and vector mesons. In the RHM Hamiltonian of [23], we had used, in addition to III, a Lorentz scalar plus vector confinement potential along with the OGEP.…”

“…In the RHM Hamiltonian of [23], we had used, in addition to III, a Lorentz scalar plus vector confinement potential along with the OGEP. The NRQM [22] had, besides the III, the usual kinetic energy term along with confinement potential and OGEP. In both the cases the results showed that the inclusion of III diminished the relative importance of OGEP for the hyperfine splitting.…”

“…Having met with reasonable success, in this work we have extended the NRQM to study P -wave spectra. The full Hamiltonian used in the investigation has, in addition to the central part of NRQM [22], spinorbit and tensor terms of OGEP and III. In addition, III also has antisymmetric spin-orbit term proportional to L · Δ where Δ is defined in terms of the Pauli matrices as 1 2 ( σ 1 − σ 2 ).…”