Light mesons on the light front

Abstract

We study the properties of light mesons in the scalar, pseudo-scalar, and vector channels within the light-front quantization, by using the (one flavor) Nambu-Jona-Lasinio model with vector interaction. After taking into account the effects of chiral symmetry breaking, we derive the boundstate equation in each channel in the large N limit (N is the number of colors), which means that we consider the lowest qq Fock state with the constituent quark and antiquark. By solving the bound-state equation, we simultaneously obtain a mass and a light-cone (LC) wavefunction of the meson. While we reproduce the previous results for the scalar and pseudo-scalar mesons, we find that, for a vector meson, the bound-state equations for the transverse and longitudinal polarizations look different from each other. However, eventually after imposing a cutoff which is invariant under the parity and boost transformations, one finds these two are identical, giving the same mass and the same (spin-independent) LC wavefunction. When the vector interaction becomes larger than a critical value, the vector state forms a bound state, whose mass decreases as the interaction becomes stronger. While the LC wavefunction of the pseudo-scalar meson is broadly distributed in longitudinal momentum (x) space, that of the vector meson is squeezed around x = 1/2.

Vector mesons on the light front

“…For the pseudo-scalar case, this was done [19] in the NJL model with two flavor quarks. Similar analysis can be done in the vector meson case and will be reported in the future publications [15].…”

“…As we explained before, after solving the fermionic constraint (3) with the nontrivial solution M = 0 to the gap equation ( 1) and substituting its solution into the canonical Hamiltonian, one gets the "broken" Hamiltonian H LF . Its explicit form and the detailed derivation of the Hamiltonian are very complicated and will be reported elsewhere [15]. Here only the final results are shown.…”

An approach towards a constituent quark model on the light cone

“…The excitations of this condensate are massless Goldstone pions. In the light cone approach, the most developed calculation uses the NJL-model with a vector interaction [17] and obtains very interesting differences of the light cone wave function between the vector mesons and pions. In our framework, the complicated self energy correction ∆(t) of the constituent quark can give the correct chiral-symmetry behaviour of the pion mass.…”

Light cone constituent quark model

“…An interaction of the Nambu-Jona-Lasinio (NJL) type leads to a quark condensate, the excitations of which are massless Goldstone pions. In the light-cone approach, the most developed calculation uses the NJL-model with a vector interaction [15] and obtains very interesting differences of the light-cone wave function between the vector mesons and pions. In our framework, the complicated self-energy correction ∆ 2 µ 2 of the constituent quark can give the correct chiral-symmetry behavior of the pion mass.…”