$ρ$ meson form factors and parton distribution functions in impact parameter space
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912177224417280 |
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| author | Zhang, Jin-Li |
| author_facet | Zhang, Jin-Li |
| contents | In this paper, we investigate the form factors and impact parameter space parton distribution functions of the $ρ$ meson derived from the generalized parton distributions within the framework of the Nambu--Jona-Lasinio model,employing a proper time regularization scheme. We compare the charge $G_C$, magnetic $G_M$, and quadrupole $G_Q$ form factors with lattice data. The dressed form factors, $G_C^D$ and $G_M^D$, exhibit good agreement with lattice results; however, $G_Q^D$ is found to be harder than what is observed in lattice calculations. The Rosenbluth cross section for elastic electron scattering on a spin-one particle can be expressed through the structure functions $A(Q^2)$ and $B(Q^2)$. Additionally, the tensor polarization $T_{20}(Q^2,θ)$ can also be formulated in terms of these form factors. We analyze the structure functions $A(Q^2)$, $B(Q^2)$ and tensor polarization function $T_{20}(Q^2,θ)$; our findings quantitatively align with predicted values across various limits. In impact parameter space, we examine parton distribution functions along with their dependence on longitudinal momentum fraction $x$ and impact parameter $\bm{b}_{\perp}$. The width distributions in impact parameter space reveal that the range of the charge distribution \( q_C(x,\bm{b}_{\perp}^2) \) is the most extensive. In contrast, the transverse magnetic radius falls within a moderate range, while the quadrupole distribution \( q_Q(x,\bm{b}_{\perp}^2) \) demonstrates the narrowest extent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19525 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $ρ$ meson form factors and parton distribution functions in impact parameter space Zhang, Jin-Li High Energy Physics - Phenomenology In this paper, we investigate the form factors and impact parameter space parton distribution functions of the $ρ$ meson derived from the generalized parton distributions within the framework of the Nambu--Jona-Lasinio model,employing a proper time regularization scheme. We compare the charge $G_C$, magnetic $G_M$, and quadrupole $G_Q$ form factors with lattice data. The dressed form factors, $G_C^D$ and $G_M^D$, exhibit good agreement with lattice results; however, $G_Q^D$ is found to be harder than what is observed in lattice calculations. The Rosenbluth cross section for elastic electron scattering on a spin-one particle can be expressed through the structure functions $A(Q^2)$ and $B(Q^2)$. Additionally, the tensor polarization $T_{20}(Q^2,θ)$ can also be formulated in terms of these form factors. We analyze the structure functions $A(Q^2)$, $B(Q^2)$ and tensor polarization function $T_{20}(Q^2,θ)$; our findings quantitatively align with predicted values across various limits. In impact parameter space, we examine parton distribution functions along with their dependence on longitudinal momentum fraction $x$ and impact parameter $\bm{b}_{\perp}$. The width distributions in impact parameter space reveal that the range of the charge distribution \( q_C(x,\bm{b}_{\perp}^2) \) is the most extensive. In contrast, the transverse magnetic radius falls within a moderate range, while the quadrupole distribution \( q_Q(x,\bm{b}_{\perp}^2) \) demonstrates the narrowest extent. |
| title | $ρ$ meson form factors and parton distribution functions in impact parameter space |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2409.19525 |