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Register a new userChiral symmetry breaking and the spin content of the rho and rho mesons
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Using interpolators with different SU(2)_L times SU(2)_R transformation properties we study the chiral symmetry and spin contents of the rho- and rho-mesons in lattice simulations with dynamical quarks. A ratio of couplings of the $qbargamma^i{tau}q$ and $qbarsigma^{0i}{tau}q$ 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 rho 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 rho 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 {2S +1}L_J 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 rho meson is practically a 3S_1 state with no obvious trace of a spin crisis. The rho meson has a sizeable contribution of the 3D_1 wave, which implies that the rho meson cannot be considered as a pure radial excitation of the rho meson.
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From the parton distributions in the infinite momentum frame one finds that only about 30% of the nucleon spin is carried by spins of the valence quarks, which gave rise to the term spin crisis. Similar results hold for the lowest mesons, as it follows from the lattice simulations. We define the spin content of a meson in the rest frame and use a complete and orthogonal $bar q q$ chiral basis and a unitary transformation from the chiral basis to the (2S+1)LJ basis. Then, given a mixture of different allowed chiral representations in the meson wave function at a given resolution scale, one can obtain its spin content at this scale. To obtain the mixture of the chiral representations in the meson we measure in dynamical lattice simulations a ratio of couplings of interpolarors with different chiral structure. For the rho meson we obtain practically the 3S1 state with no trace of the spin crisis. Then a natural question arises: which definition does reflect the spin content of a hadron?
The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the nonperturbatively determined physical state. It is then possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark component of a meson in the infrared, where mass is generated. Using a unitary transformation from the chiral basis to the $^{2S+1}L_J$ basis one may extract the partial wave content of a meson. We present results for the $rho$- and $rho$-mesons using a simulation with $N_f=2$ dynamical quarks, all for lattice spacings close to 0.15 fm. Our results indicate a strong chiral symmetry breaking in the $rho$ state and its simple $^3S_1$-wave composition in the infrared. For the $rho$-meson we find a small chiral symmetry breaking in the infrared as well as a leading contribution of the $^3D_1$ partial wave, which is contradictory to the quark model.
We compute couplings between the $rho$-meson and $D$- and $D^ast$-mesons - $D^{(ast)}rho D^{(ast)}$ - that are relevant to phenomenological meson-exchange models used to analyse nucleon-$D$-meson scattering and explore the possibility of exotic charmed nuclei. Our framework is built from elements constrained by Dyson-Schwinger equation studies in QCD, and therefore expresses a consistent, simultaneous description of light- and heavy-quarks and the states they constitute, We find that all interactions, including the three independent $D^{ast} rho ,D^{ast}$ couplings, differ markedly amongst themselves in strength and also in range, as measured by their evolution with $rho$-meson virtuality. As a consequence, it appears that no single coupling strength or parametrization can realistically be employed in the study of interactions between $D^{(ast)}$-mesons and matter.
It is possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark Fock component of a meson in the infrared, where mass is generated. Using the variational method and a set of interpolators that span a complete chiral basis we extract in a lattice QCD Monte Carlo simulation with two dynamical light quarks the orbital angular momentum and spin content of the rho-meson. We obtain in the infrared a simple 3S1 component as a leading component of the rho-meson with a small admixture of the 3D1 partial wave, in agreement with the SU(6) flavor-spin symmetry.
In the framework of non-perturbative QCD we calculate high-energy diffractive production of vector mesons $rh, rh$ and $rh$ by real and virtual photons on a nucleon. The initial photon dissociates into a $qbar{q}$-dipole and transforms into a vector meson by scattering off the nucleon which, for simplicity, is represented as quark-diquark. The relevant dipole-dipole scattering amplitude is provided by the non-perturbative model of the stochastic QCD vacuum. The wave functions result from considerations in the frame of light-front dynamics; the physical $rh$- and $rh$-mesons are assumed to be mixed states of an active 2S-excitation and some residual rest (2D- and/or hybrid state). We obtain good agreement with the experimental data and get an understanding of the markedly different $pi^+pi^-$-mass spectra for photoproduction and $e^+e^-$-annihilation.
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