Chiral symmetry breaking and the spin content of the ρ and [formula omitted] mesons

Abstract

Using interpolators with different SU(2)L×SU(2)R transformation properties we study the chiral symmetry and spin contents of the ρ and ρ′ mesons in lattice simulations with dynamical quarks. A ratio of couplings of the q¯γiτq and q¯σ0iτq interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution of ∼1 fm. In the ground state ρ meson the chiral symmetry is strongly broken with comparable contributions of both the (0,1)+(1,0) and (1/2,1/2)b chiral representations with the former being the leading contribution. In contrast, in the ρ′ meson the degree of chiral symmetry breaking is manifestly smaller and the leading representation is (1/2,1/2)b. Using a unitary transformation from the chiral basis to the LJ2S+1 basis, we are able to define and measure the angular momentum content of mesons in the rest frame. This definition is different from the traditional one which uses parton distributions in the infinite momentum frame. The ρ meson is practically a S13 state with no obvious trace of a “spin crisis”. The ρ′ meson has a sizeable contribution of the D13 wave, which implies that the ρ′ meson cannot be considered as a pure radial excitation of the ρ meson.