$\rho$ meson transverse momentum dependent parton distributions

TL;DR

This paper models the transverse momentum dependent parton distributions of the $ ho$ meson using light-front wave functions within the Nambu--Jona-Lasinio framework, revealing detailed transverse momentum and spin structure insights.

Contribution

It introduces a novel calculation of $ ho$ meson TMDs using LFWFs in the NJL model, comparing with covariant approaches and analyzing spin densities.

Findings

Average transverse momenta range between 0.3 and 0.45 GeV.

TMDs satisfy positive constraints and show specific spin density symmetries.

LFWF-based PDFs yield larger $ ho$ meson gluon momentum fractions.

Abstract

In this paper, the light-front wave functions (LFWFs) of $\rho$ meson are evaluated in the framework of Nambu--Jona-Lasinio model using the proper time regularization scheme. The transverse momentum dependent parton distributions (TMDs) of the $\rho$ meson are derived from the overlap representations of the LFWFs. We investigate the $\bm{k}_{\perp}$-weighted moments and the $x$-dependent average transverse momentum $\langle k_{\perp}^n(x)\rangle_{\alpha}$ of $\rho$ meson TMDs, $\langle k_{\perp}^n(x)\rangle_{\alpha}$ shows the typical transverse momenta of quark TMDs in our model. Our findings indicate that the average transverse momenta of $\langle k_{\perp}(x)\rangle_{\alpha}$ fall within the range of $[0.3, 0.45]$ GeV, while $\langle k_{\perp}^2(x)\rangle_{\alpha}$ are in the region of $[0.15, 0.30]$ GeV$^2$. Our TMDs and parton distribution function (PDFs) exhibit excellent adherence to positive constraints. The investigation of spin densities within the $\rho$ meson in transverse momentum space reveals axially symmetric distributions for quarks and targets polarized in either longitudinal or transverse directions. Conversely, unpolarized symmetric distributions occur when the quark is longitudinally polarized and the target is transversely polarized, while exhibiting dipolar distortions in the opposite scenario. A comparison between TMDs from LFWFs and those from a covariant approach demonstrates that TMDs from LFWFs more effectively satisfy positive constraints than their counterparts from the covariant approach. Furthermore, the $x$-moments of $\rho$ meson PDFs indicate that $\langle x\rangle_{g_L}$ is larger using LFWFs compared to the covariant approach.