Flavor, transverse momentum, and azimuthal dependence of charged pion multiplicities in SIDIS with 10.6 GeV electrons

TL;DR

This work presents high-precision SIDIS measurements of $\pi^{\pm}$ multiplicities on hydrogen and deuterium targets using a 10.6 GeV electron beam, mapped on a three-dimensional grid in $z$, $P_t$, and $\phi^{*}$ within $0.3<x<0.6$ and $3<Q^2<5\,\mathrm{GeV}^2$. The analysis extracts an azimuthally independent $M_0$ and modulations $\langle\cos(\phi^{*})\rangle$ and $\langle\cos(2\phi^{*})\rangle$ by fitting the measured yields to $M_0[1 + A\cos(\phi^{*}) + B\cos(2\phi^{*})]$, and finds a remarkably consistent $P_t$-dependence across flavor channels with Gaussian Pt-slope parameters that rise with $z$. The $\cos(\phi^{*})$ modulations are negligible for $\pi^{+}$ but often positive for $\pi^{-}$, while $\cos(2\phi^{*})$ is generally consistent with zero; the $P_t$-dependent widths imply $\langle\vec{p}_{\perp}^{2}\rangle \approx 0.185\,\mathrm{GeV}^2$ and $\langle\vec{k}_{T}^{2}\rangle \approx 0.28\,\mathrm{GeV}^2$, suggesting small differences between up/down quark ${k}_{T}$ widths and between favored/unfavored fragmentation. This high-statistics dataset provides a stringent benchmark for TMD-factorization-based descriptions and enables improved determinations of transverse-momentum distributions and higher-twist contributions in SIDIS.

Abstract

Measurements of SIDIS multiplicities for $π^+$ and $π^-$ from proton and deuteron targets are reported on a grid of hadron kinematic variables $z$, $P_{T}$, and $φ^{*}$ for leptonic kinematic variables in the range $0.3<x<0.6$ and $3<Q^2<5$ GeV$^2$. Data were acquired in 2018-2019 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 HMS and SHMS spectrometers, respectively. The multiplicities were fitted for each bin in $(x,~Q^2,~z,~P_{t})$ to extract the $φ^{*}$ independent $M_0$ and the azimuthal modulations $\langle \cos(φ^{*}) \rangle$ and $\langle \cos(2φ^{*}) \rangle$. The $P_t$-dependence of the $M_0$ results was found to be remarkably consistent for the four cases studied: $ep\rightarrow e π^+ X$, $ep\rightarrow e π^- X$, $ed\rightarrow e π^+ X$, $ed\rightarrow e π^- X$ over the range $0<P_t<0.4$ GeV, as were the multiplicities evaluated near $φ^* = 180^\circ$ over the extended range $0<P_t<0.7$ GeV. The Gaussian widths of the $P_t$-dependence exhibit a quadratic increase with $z$. The $\cos(φ^{*})$ modulations were found to be consistent with zero for $π^+$, in agreement with previous world data, while the $π^-$ moments were, in many cases, significantly greater than zero. The $\cos(2φ^{*})$ modulations were found to be consistent with zero. The higher statistical precision of this dataset compared to previously published data should allow improved determinations of quark transverse momentum distributions and higher twist contributions.

Figures (18)

• Figure 1: (left) Kinematics of the SIDIS process in the $\gamma^{*}P$ center of mass frame. (right) Simplified schematic of the pion SIDIS process, showing that the final transverse momentum of the leading pion, $P_{t}$, arises from the convolution of the struck quark's transverse momentum, $k_{T}$, with the transverse momentum generated during the fragmentation, $p_{\perp}$.
• Figure 2: Overview of the experimental setup in Hall C at JLab.
• Figure 3: Accidental-subtracted distributions of normalized HMS calorimeter energy ($E_{cal}/p_e$) for kinematic setting I (black), II (blue), and III (magenta), for electron-pion coincidence events passing all cuts except the $E_{cal}/p_e$$>$ 0.75 cut, which is indicated by the vertical dashed line.
• Figure 4: SHMS aerogel signals (in p.e.) from setting III, as a function of the arrival time of pions, kaons, and protons relative to the beam micro-pulse time (RF time), modulo the 4 ns bunch spacing, for particles with momenta $3.4<P_\pi<4.3$ GeV. The pion arrival time was shifted such that its peak is at 1 ns. The red vertical lines show the location of the pion, kaon, and proton peaks.
• Figure 5: Distributions of $E_{cal}/P_{\pi}$ in the SHMS calorimeter for positive (top panel) and negative (bottom panel) pion candidates. The sign of $P_{\pi}$ refers to the polarity of the spectrometer. The blue curves represent subsets of the black distributions with accidental coincidences subtracted. The vertical line at 0.8 indicates the cut used to reject positrons (top panel) and electrons (bottom panel).