Study of SIDIS Unpolarized Cross Sections from a $^3$He Target with the Solenoidal Large Intensity Device at JLab

TL;DR

This work develops a comprehensive projection of unpolarized SIDIS cross sections measured with SoLID on a $^3$He target at Jefferson Lab to illuminate neutron TMD structure and test TMD factorization in the valence region. It combines a state-of-the-art MAPTMD24 framework with $N^3LL$ TMD evolution for azimuthally integrated observables and a simpler LO TMD model with Gaussian transverse-momentum dependence for azimuthal modulations, producing detailed pseudo-data for pions and kaons across multi-dimensional kinematic bins. The study shows that SoLID can substantially shrink uncertainties on unpolarized TMDs and FFs, especially for the $d$-quark, and can extract Gaussian width parameters like $igra k_ot^2igra$ and $igra P_ot^2igra$ with high precision, while also accounting for nuclear effects from Fermi motion. Nuclear effects are quantified as modest shifts in $x_{bj}$, $P_{hT}$, and $z_h$, with negligible impact on the statistical precision, supporting the feasibility of neutron structure studies and EMC-related investigations. Overall, the paper maps a clear path for leveraging absolute SIDIS cross sections to test TMD factorization, constrain TMD PDFs/FFs, and enhance our understanding of nuclear effects in light nuclei.

Abstract

In this paper we present a detailed impact study of semi-inclusive deep inelastic scattering unpolarized cross sections' measurements using the proposed SoLID apparatus at Jefferson Lab. This type of data, collected at large Bjorken $x_{bj}$, moderate values of $Q^2$ and small values of the transverse momentum of produced hadrons, $P_{hT}$, allows to study transverse momentum dependent (TMD) parton distribution and fragmentation functions in a still poorly explored region. We present the projected results for charged light mesons based on simulated data. For the azimuthal-angle integrated cross sections we adopt the TMD framework up to the next-to-next-to-next-to-leading-logarithmic (N3LL) accuracy, while a simpler TMD parton model is employed for the study of azimuthal angular dependencies.

Figures (24)

• Figure 1: Kinematics of the SIDIS process in Eq. (\ref{['eq:eqn_SIDIS']}), represented in the one-photon exchange approximation. The sketch follows the Trento conventions Bacchetta:2004jz. The $x$-$z$ plane is defined by the initial $\ell$ and scattered $\ell'$ lepton momenta. The azimuthal angle $\phi_{h}$ is given in the target rest frame. The figure is taken from Ref. Byer:2022bqf.
• Figure 2: Relevant SIDIS momenta in the $\gamma^{\ast}$-$N$ center-of-mass frame: $q$ is the virtual photon momentum, $k$ is the momentum of the initial quark with transverse momentum $k_\perp$ inside a nucleon with momentum $P$. The figure is taken from Bacchetta:2024qre, where the photon line stands for a virtual photon.
• Figure 3: Upper panel: $x_{bj}$ distributions of generated events' rate for $\pi^{+}$ as leading hadron, with (black histogram) and without (red histogram) Fermi motion of the initial nucleon in the $^{3}$He target. Lower panel: their ratio.
• Figure 4: The first plot displays the $P_{hT}$ distributions of generated events' rate for $\pi^{+}$ as leading hadron, with (black histogram) and without (red histogram) Fermi motion of the initial nucleon in the $^{3}$He target, whereas the second plot shows their ratio.
• Figure 5: The first plot displays the $z_{h}$ distributions of generated events' rate for $\pi^{+}$ as leading hadron, with (black histogram) and without (red histogram) Fermi motion of the initial nucleon in the $^{3}$He target, whereas the second plot shows their ratio.