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We present the leading-twist quark transverse momentum-dependent parton distribution functions (TMDs) for the spin-1 target, such as the ρ-meson, in the light-front framework. Specifically, we predict the TMDs in the light-front holographic model and compare with the light-front quark model predictions. We obtain the TMDs using the overlap of the light-front wave functions. We evaluate the k⊥ moments upto second order and compare with the available theoretical predictions. Further, we analyze the leading-twist parton distribution functions (PDFs) of the ρ-meson in the light-front holographic model which are found to be in accord with the Nambu-Jona-Lasinio (NJL) model and the light-front quark model predictions. We further study the QCD evolution of the PDFs. The positivity bounds on the TMDs and the PDFs are also discussed. We also present the quark spin densities in the transverse momentum plane for different polarization configurations of the quark and the ρ-meson target.

We predict the V → Pγ decay widths and the V → Pγ Ã transition form factors, where V ¼ ðρ; ω; K Ã ; ϕÞ and P ¼ ðπ; K; η; η 0 Þ, using spin-improved holographic light-front wave functions for the mesons. We find excellent agreement with the available data for both the decay widths and the timelike transition form factors extracted from the leptonic conversion decays V → Pl þ l − .

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We investigate the quark Wigner distributions of the pion to reveal the multidimensional picture of pion. We have used the spin improved wave functions of pion deduced from the light-front holographic model of mesons. By using the Fock-state overlap representation, the Wigner distributions of an unpolarized, longitudinally polarized and transversely polarized quark inside the pion are calculated. We have presented the results of transverse Wigner distributions in impact-parameter space as well as in momentum space. In order to understand the role of skewness which gives the longitudinal momentum transfer between the quarks, we study the six-dimensional phase-space distribution: the generalized transverse momentum dependent parton distributions of pion for the case of zero skewness as well as for nonzero value of skewness.