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Measurements of semi-inclusive deep-inelastic scattering multiplicities for ${\pi }^{+}$and ${\pi }^{-}$from proton and deuteron targets are reported on a grid of hadron kinematic variables $z, P_T$, and ${\varphi }^{*}$for leptonic kinematic variables in the range $0.3<x<0.6$and $3<Q^2<5{\mathrm{GeV}}^2$. Data were acquired in 2018 and 2019 at Jefferson Lab Hall C with a 10.6 GeV electron beam impinging on 10-cm-long liquid hydrogen and deuterium targets. Scattered electrons and charged pions were detected in the High Momentum Spectrometer and Super High Momentum Spectrometer, respectively. The multiplicities were fitted for each bin in $(x,Q^2,z,P_t)$to extract the ${\varphi }^{*}$—independent $M_0$and the azimuthal modulations $\langle cos\left({\varphi }^{*}\right)\rangle$and $\langle cos\left(2{\varphi }^{*}\right)\rangle$. The $P_t$dependence of the $M_0$results was found to be remarkably consistent for the four cases studied: $ep\to e{\pi }^{+}X, ep\to e{\pi }^{-}X, ed\to e{\pi }^{+}X, ed\to e{\pi }^{-}X$over the range $0\text{GeV}<P_t<0.4\text{GeV}$, as were the multiplicities evaluated near ${\varphi }^{*}={180}^{\circ }$over the extended range $0\text{GeV}<P_t<0.7\text{GeV}$. The Gaussian widths of the $P_t$dependence exhibit a quadratic increase with $z$. The $cos\left({\varphi }^{*}\right)$modulations were found to be consistent with zero for ${\pi }^{+}$, in agreement with previous world data, while the ${\pi }^{-}$moments were, in many cases, significantly greater than zero. The $cos\left(2{\varphi }^{*}\right)$modulations were found to be consistent with zero. The higher statistical precision of this dataset of about 20 000 individual multiplicity values, compared with previously published data, should allow improved determinations of quark transverse momentum distributions and higher twist contributions. 

Nucleon structure functions, as measured in lepton-nucleon scattering, have historically provided a critical observable in the study of partonic dynamics within the nucleon. However, at very large parton momenta, it is both experimentally and theoretically challenging to extract parton distributions due to the probable onset of nonperturbative contributions and the unavailability of high-precision data at critical kinematics. Extraction of the neutron structure and the d quark distribution have been further challenging because of the necessity of applying nuclear corrections when utilizing scattering data from a deuteron target to extract the free neutron structure. However, a program of experiments has been carried out recently at the energy-upgraded Jefferson Lab electron accelerator aimed at significantly reducing the nuclear correction uncertainties on the d quark distribution function at large partonic momentum. This allows leveraging the vast body of deuterium data covering a large kinematic range to be utilized for d quark parton distribution function extraction. In this Letter, we present new data from experiment E12-10-002, carried out in Jefferson Lab Experimental Hall C, on the deuteron to proton cross section ratio at large Bjorken $x$. These results significantly improve the precision of existing data and provide a first look at the expected impact on quark distributions extracted from parton distribution function fits.