First measurement of unpolarized semi-inclusive deep-inelastic scattering cross sections from a ${}^3\mathrm{He}$ target

The unpolarized semi-inclusive deep-inelastic scattering (SIDIS) differential cross sections in ${}^3\mathrm{He}(e,e^{\prime }{\pi }^{\pm })X$ have been measured for the first time in Jefferson Lab experiment E06-010 with a $5.9\mathrm{GeV}{e}^{-}$ beam on a ${}^3\mathrm{He}$ gas target. The experiment focuses on the valence quark region, covering a kinematic range $0.12<x_{bj}<0.45,1<Q^2<4{\left(\mathrm{GeV}/c\right)}^2,0.45<z_h<0.65$, and $0.05<P_t<0.55\mathrm{GeV}/c$. The extracted SIDIS differential cross sections of ${\pi }^{\pm }$ production are compared with existing phenomenological models while the ${}^3\mathrm{He}$ nucleus approximated as two protons and one neutron in a plane-wave picture, in multidimensional bins. Within the experimental uncertainties, the azimuthal modulations of the cross sections are found to be consistent with zero.

Figure 1

The invariant mass $W$ comparisons between data and simulation (MC) for $1.23\mathrm{GeV}$ (top panel) and $2.4\mathrm{GeV}$ (bottom panel) beam elastic $ep$ calibration run using BigBite. The error bars represent the statistical uncertainties. The red solid circles are from the data. The black open circles are from the simulation.

Figure 2

The scattered electron momentum $\left(P_e^{\prime }\right)$ comparison of the ${}^3\mathrm{He}$ inclusive DIS channel in BigBite between the data and the simulation (MC). The error bars represent statistical uncertainties. The red solid circles are from the data. The black open circles are from the simulation.

Figure 3

The scattered electron momentum $\left(P_e^{\prime }\right)$ comparison of the ${\mathrm{H}}_2$ inclusive DIS channel in the HRS between the data and the simulation (MC). The error bars represent statistical uncertainties. The red solid circles are from the data. The black open circles are from the simulation.

Figure 4

The scattered electron momentum $\left(P_e^{\prime }\right)$ comparison of the ${}^3\mathrm{He}$ inclusive DIS channel in the HRS between the data and the simulation (MC). The error bars represent statistical uncertainties. The red solid circles are from the data. The black open circles are from the simulation.

Figure 5

The correlations between $x_{bj}$ and other kinematic variables in experiment E06-010.

Figure 6

The differential cross sections in 3D bins: the ${\pi }^{+}$ SIDIS production channel. The red circles are from the data, the black solid lines are from the model [17], the blue dashed lines are from the model [15], and the green dotted lines are from the model [16]. The error bars represent the statistical uncertainties of the data. The error band on the bottom of each panel represents the experimental systematic uncertainty. The $P_t$ (in unit of GeV) and $x_{bj}$ ranges of each plot are presented at the top and the bottom of the panel, respectively.

Figure 7

The differential cross sections in 3D bins: the ${\pi }^{-}$ SIDIS production channel. The definitions of the markers, the lines, and the bands are the same as Fig. 6 for the ${\pi }^{+}$ channel.

Figure 8

The differential cross sections in 2D bins: the ${\pi }^{+}$ SIDIS production channel. The red circles are from the data, the black solid lines are from the model [17], the blue dashed lines are from the model [15] and the green dotted lines are from the model [16]. The error bars represent the statistical uncertainties of the data. The error band on the bottom of each panel represents the experimental systematic uncertainty. The $x_{bj}$ range of each plot is presented at the bottom of the panel.

Figure 9

The differential cross sections in 2D bins: the ${\pi }^{-}$ SIDIS production channel. The definitions of the markers, the lines, and the bands are the same as in Fig. 8 for the ${\pi }^{+}$ channel.

Figure 10

The SIDIS differential cross sections (defined in text) comparison between the data and the simulation in pseudo-1D $x_{bj}$ bins. The red solid circles are from the data and the black open circles are from the quark-parton model. The error bar of each point represents the statistical uncertainty, mostly smaller than the markers. The error band on the bottom of each panel represents the experimental systematic uncertainty. The top and bottom panels are for ${\pi }^{+}$ and ${\pi }^{-}$ production channels, respectively.

Figure 11

The differential cross sections in 3D bins: the ${\pi }^{+}$ SIDIS production channel. The red circles are from the data, the black solid lines are from the model [17], and the blue dashed lines are from the model [17] with $F_{UU}^{cos{\varphi }_h}$ and $F_{UU}^{cos2{\varphi }_h}$ set to zero. The error bars represent the statistical uncertainties of the data. The error band on the bottom of each panel represents the experimental systematic uncertainty. The $P_t$ (in unit of GeV) and $x_{bj}$ ranges of each plot are presented at the top and the bottom of the panel, respectively.

Figure 12

The differential cross sections in 3D bins: the ${\pi }^{-}$ SIDIS production channel. The definitions of the markers, the lines, and the bands are the same as the figure above for the ${\pi }^{+}$ channel.

Figure 13

The SIDIS differential cross section ratio ${\sigma }^{{\pi }^{+}}/{\sigma }^{{\pi }^{-}}$ comparison between data and model in pseudo-1D $x_{bj}$ bins. The red solid circles are from the data and the black open circles are from the quark-parton model. The error bar of each point of data represents the statistical uncertainty. The error bars for the model parametrization uncertainty are smaller than the marker size. The error band on the bottom represents the systematic uncertainty of the data.

Figure 14

Results of $B$ in 3D bins from the $A(1-Bcos{\varphi }_h)$ fit. The red solid circles and black open circles represent the results in the ${\pi }^{+}$ and ${\pi }^{-}$ production channels, respectively.

Figure 15

Fitting contours with the functional form of the total unpolarized SIDIS cross section (refer to the text). The top panel is for the fitting results using the 2D bins $\left(10\times 10\right)$ data, the bottom panel for the 3D bins $\left(2\times 5\times 10\right)$. The central values of the fitting are the black crosses. The three contours from the smallest to the largest in each panel correspond to $\delta {\chi }^2=1$, 2.3, and 6.2, respectively.

Figure 16

Fitting contours with the functional form of the nonmodulated unpolarized SIDIS cross section $(F_{UU}^{cos{\varphi }_h}$ and $F_{UU}^{cos2{\varphi }_h}$ set to zero; refer to the text). The top panel is for the fitting results using the 2D bins $\left(10\times 10\right)$ data, the bottom panel for the 3D bins $\left(2\times 5\times 10\right)$. The central values of the fitting are the black crosses. The three contours from the smallest to the largest in each panel correspond to $\delta {\chi }^2=1$, 2.3, and 6.2, respectively.

Figure 17

The differential cross sections in 2D bins: the ${\pi }^{+}$ SIDIS production channel. The red circles are from the data. The black solid lines are from the model including the structure functions $F_{UU},F_{UU}^{cos{\varphi }_h}$, and $F_{UU}^{cos2{\varphi }_h}$ with parameters $\langle k_{\perp }^2\rangle$ and $\langle p_{\perp }^2\rangle$ from stand-alone data fitting. The blue dashed lines are from the model including only the structure functions $F_{UU}$ with parameters $\langle k_{\perp }^2\rangle$ and $\langle p_{\perp }^2\rangle$ from fitting the data of this work only. The error bars represent the statistical uncertainties of the data. The error band on the bottom of each panel represents the experimental systematic uncertainty. The $x_{bj}$ range of each plot is presented at the bottom of the panel.

Figure 18

The differential cross sections in 2D bins: the ${\pi }^{-}$ SIDIS production channel. The definitions of the markers, the lines, and the bands are the same as the figure above for ${\pi }^{+}$ channel.