Double-spin asymmetry $A_{LT}^{\cos {\varphi }_S}$ in semi-inclusive DIS at CLAS12 and EIC within the collinear framework

We study the longitudinal-transverse double-spin asymmetry with a $\cos {\varphi }_S$ modulation in semi-inclusive deep inelastic scattering for charged and neutral pion production. We consider the particular case in which the transverse momentum of the final-state hadron is integrated out. The corresponding asymmetry may be contributed by two parts: one is the convolution of the twist-3 distribution function $g_T(x)$ and the unpolarized fragmentation function $D_1(z)$; the other is related to the coupling of the transversity distribution function $h_1(x)$ and the collinear twist-3 fragmentation function $\tilde{E}(z)$. We take into account both contributions to predict the $\cos {\varphi }_S$ asymmetry at the kinematics of CLAS12 and a future Electron Ion Collider. We find that the asymmetry of pion production at CLAS12 is sizable, and $\tilde{E}(z)$ can play an important role in the asymmetry in the large-$z$ region.

Figure 1

The definition of azimuthal angles in SIDIS [14]. The lepton plane is defined by $l$ and $l^{\prime }$. $S$ stands for the spin of the proton target, while $P_h$ is for the momentum of the produced pion. $S_{\perp }$ is the transverse component of $S$ with respect to the virtual photon momentum.

Figure 2

The twist-3 distribution function $x{g}_T^q(x)$ for up and down quarks vs $x$ at $Q^2=1{\mathrm{GeV}}^2$.

Figure 3

Longitudinal-transverse double-spin asymmetry $A_{LT}^{\cos {\varphi }_S}$ of ${\pi }^{+}$, ${\pi }^0$ and ${\pi }^{-}$ production in SIDIS at CLAS12. The left panels show the $x$-dependent asymmetry, while the right ones show the $z$-dependent asymmetry.

Figure 4

Similar to Fig. 3, but at EIC for $\sqrt{s}=45\mathrm{GeV}$.

Figure 5

Longitudinal-transverse double-spin asymmetry $A_{LT}^{\cos {\varphi }_S}$ of ${\pi }^{+}$, ${\pi }^0$ and ${\pi }^{-}$ production in SIDIS at CLAS12, but using Eq. (34) for $\tilde{E}$ instead of Eq. (25).