$$ρ $$ ρ meson transverse momentum-dependent parton distributions - Jin-Li Zhang; Jun Wu (European Physical Journal C: Particles and Fields)
Abstract In this paper, the light-front wave functions (LFWFs) of the $$ρ $$ ρ meson are evaluated in the framework of the Nambu–Jona-Lasinio model using the proper time regularization scheme. The transverse momentum-dependent parton distributions (TMDs) of the $$ρ $$ ρ meson are derived from the overlap representations of the LFWFs. We investigate the $$\varvec{k}_{\perp }$$ k ⊥ -weighted moments and the x-dependent average transverse momentum $$\langle k_{\perp }^n(x)\rangle _{α }$$ ⟨ k ⊥ n ( x ) ⟩ α of $$ρ $$ ρ meson TMDs. The $$\langle k_{\perp }^n(x)\rangle _{α }$$ ⟨ k ⊥ n ( x ) ⟩ α shows the typical transverse momenta of quark TMDs in our model. Our findings indicate that the average transverse momenta of $$\langle k_{\perp }(x)\rangle _{α }$$ ⟨ k ⊥ ( x ) ⟩ α fall within the range of [0.3, 0.45] GeV, while $$\langle k_{\perp }^2(x)\rangle _{α }$$ ⟨ k ⊥ 2 ( x ) ⟩ α are in the region of [0.15, 0.30] $$GeV^2$$ G e V 2 . Our TMDs and parton distribution functions (PDFs) exhibit excellent adherence to positive constraints. The investigation of spin densities within the $$ρ $$ ρ meson in transverse momentum space reveals axially symmetric distributions for quarks and targets polarized in either the longitudinal or transverse direction. 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 $$ρ $$ ρ meson PDFs indicate that $$\langle x\rangle _{g_L}$$ ⟨ x ⟩ g L is larger using LFWFs than with the covariant approach. Additionally, analysis of quark spin densities within the $$ρ $$ ρ meson reveals that $$ρ _{\uparrow \downarrow }\left( k_x,k_y\right) =f-g_L-\frac{1}{3}f_{LL}$$ ρ ↑ ↓ k x , k y = f - g L - 1 3 f LL yields a negative result using the covariant approach, whereas $$ρ _{\uparrow \downarrow }\left( k_x,k_y\right) $$ ρ ↑ ↓ k x , k y derived from LFWFs produces a positive outcome.