$$\rho $$–Meson Form-factors in Point form of Poincaré-Invariant Quantum Mechanics

Form-factors investigation of $$\rho ^{\pm }$$ ρ ± –mesons was carried out within the framework of the relativistic quark model, based on point form of Poincaré-invariant quantum mechanics taking into account the internal structure of constituent quarks. It is shown that the parameters of the model obtained from the condition of the agreement of theoretical calculations with experimental data on leptonic decays for light $$\pi ^{\pm }$$ π ± — and $$\rho ^{\pm }$$ ρ ± –mesons lead to the results correlating with calculations in models based on light-front and instant forms of dynamics. The proposed scheme for the combined description of lepton transitions of pseudoscalar and vector mesons that is based on point form of dynamics, leads to the results on the magnetic moment of $$\rho ^{\pm }$$ ρ ± –meson correlating with the experimental data and other models.

The HAL QCD potential in the I = 1 π π system with the ρ meson bound state

We investigate the HAL QCD potential in $I=1$$\pi \pi$ scattering using the hybrid method for all-to-all propagators, in which a propagator is approximated by low eigenmodes, and the remaining high-eigenmode part is stochastically estimated. To verify the applicability of the hybrid method to systems containing quark creation$/$annihilation contributions such as the $\rho$ meson, we calculate the $I=1$$\pi\pi$ potential with the $(2+1)$-flavor gauge configurations on a $16^3 \times 32$ lattice with lattice spacing $a \approx 0.12$ fm and $(m_{\pi},m_{\rho}) \approx (870, 1230)$ MeV, in which the $\rho$ meson appears as a deeply bound state. While we find that the naive stochastic evaluations for quark creation$/$annihilation contributions lead to extremely large statistical fluctuations, additional noise reduction methods enable us to obtain a sufficiently precise potential, which shows a strong attractive force. We also confirm that the binding energy and $k^3 \cot \delta$ obtained from our potential are roughly consistent with an existing $\rho$ meson bound state, within the large systematic error associated with our calculation, whose possible origin is also discussed.

Generalized parton distribution functions of $\rho$ meson

We report our recent studies of generalized parton distribution functions of a \rhoρ meson with the help of a light-front constituent quark model. The electromagnetic form factors and structure functions of the system are discussed. Moreover, we show our results for its gravitational form factors (or energy-momentum tensor form factors) and other mechanical properties, like mass distributions, pressures, shear forces, and D-D−term.

${\bf I=2} \boldsymbol{\pi\pi}$ potential in the HAL QCD method with all-to-all propagators

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$$\pi\pi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on a $16^3 \times 32$ lattice at the lattice spacing $a \approx 0.12$ fm and $m_{\pi} \approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contamination to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$$\pi\pi$ system by the hybrid method within a reasonable numerical cost; these phase shifts are consistent with the result obtained with the conventional method. The knowledge that we obtain in this study will become useful for the investigation of hadron resonances that require quark annihilation diagrams such as the $\rho$ meson by the HAL QCD potential with the hybrid method.