Observation of Beam Spin Asymmetries in the Process $ep\to e^{\prime }{\pi }^{+}{\pi }^{-}X$ with CLAS12

The observation of beam spin asymmetries in two-pion production in semi-inclusive deep inelastic scattering off an unpolarized proton target is reported. The data presented here were taken in the fall of 2018 with the CLAS12 spectrometer using a 10.6 GeV longitudinally spin-polarized electron beam delivered by CEBAF at JLab. The measured asymmetries provide the first opportunity to extract the parton distribution function $e(x)$, which provides information about the interaction between gluons and quarks, in a collinear framework that offers cleaner access than previous measurements. The asymmetries also constitute the first ever signal sensitive to the helicity-dependent two-pion fragmentation function $G_1^{\perp }$. A clear sign change is observed around the $\rho$ mass that appears in model calculations and is indicative of the dependence of the produced pions on the helicity of the fragmenting quark.

Figure 1

The coordinate system used in this analysis. The electron scattering plane is spanned by the incoming and outgoing lepton, the dihadron plane is spanned by ${\mathit{P}}_1$ and $P_2$, containing also ${\mathit{P}}_h$, $R$, and ${\mathit{R}}_T$, and the $\mathit{q}\times {\mathit{P}}_h$ plane contains only $\mathit{q}$ and ${\mathit{P}}_h$. The azimuthal angles ${\varphi }_h$ and ${\varphi }_{R_{\perp }}$ are defined within the plane transverse to $\mathit{q}$, from the electron scattering plane to, respectively, the $\mathit{q}\times {\mathit{P}}_h$ plane and the dihadron plane.

Figure 2

The measured $A_{\mathrm{LU}}^{\sin ({\varphi }_{R_{\perp }})}$ asymmetry vs $x$. The thin, black bars indicate statistical uncertainties and the vertical extent of the wide, gray bars indicates systematic uncertainties.

Figure 3

The measured $A_{\mathrm{LU}}^{\sin ({\varphi }_h-{\varphi }_{R_{\perp }})}$ asymmetry vs $M_h$. The thin, black bars indicate statistical uncertainties and the vertical extent of the wide, gray bars indicates systematic uncertainties.

Figure 4

The measured $A_{\mathrm{LU}}^{\sin ({\varphi }_h-{\varphi }_{R_{\perp }})}$ asymmetry vs $P_h^{\perp }$. The data have been split into two bins of $M_h$ above and below 0.63 GeV. Asymmetries for lower values of $M_h$ are shown in red circles and the blue crosses show the values for higher $M_h$. The thin, solid bars indicate statistical uncertainties and the vertical extent of the wide bars indicates systematic uncertainties.

Figure 5

The measured $A_{\mathrm{LU}}^{\sin ({\varphi }_h-{\varphi }_{R_{\perp }})}$ asymmetry vs $z$. The data have been split into two bins of $M_h$ above and below 0.63 GeV. Asymmetries for lower values of $M_h$ are shown in red circles and the blue crosses show the values for higher $M_h$. The thin, solid bars indicate statistical uncertainties and the vertical extent of the wide bars indicates systematic uncertainties.