Predictions for double spin asymmetry $A_{LT}$ in semiinclusive DIS

In the leading order of QCD parton model of semiinclusive deep inelastic scattering (SIDIS) the double spin asymmetry $A_{LT}$ arises due to the longitudinal polarization of quarks in the transversely polarized nucleon. The corresponding $k_T^2$ weighted distribution function $g_{1T}^{(1)}$ can be related to ordinary helicity distribution $g_1(x)$ measured in DIS. Using recent parametrizations for (un)polarized distribution and fragmentation functions we calculated $A_{LT}$ asymmetry on transversely polarized proton and deuteron targets for different types of hadron production. The predictions are given for COMPASS, HERMES, and JLab energies. The role of Lorentz invariance relations and positivity constraints are discussed.

Figure 1

The ratio $g_{1T}^{q(1)}(x)/f_1^q(x)$ for different types of quarks at $Q^2=5(\mathrm{GeV}/\mathrm{c}{)}^2$.

Figure 2

Predicted dependence of $A_{LT}^{(|{\mathbf{P}}_{hT}|/M)\cos ({\varphi }_h-{\varphi }_S)}$ on $x$, $y$, and $z$ for production of positive ($h^{+}$), all charged ($h$), and negative ($h^{-}$) hadrons at COMPASS for SIDIS on transversely polarized proton (solid line) and deuteron (dashed line) targets.

Figure 3

Predicted dependence of $A_{LT}^{(|{\mathbf{P}}_{hT}|/M)\cos ({\varphi }_h-{\varphi }_S)}$ on $x$, $y$, and $z$ for ${\pi }^{+}$, ${\pi }^0$, and ${\pi }^{-}$ production at HERMES for SIDIS on transversely polarized proton (solid line) and deuteron (dashed line) targets.

Figure 4

Predicted dependence of $A_{LT}^{(|{\mathbf{P}}_{hT}|/M)\cos ({\varphi }_h-{\varphi }_S)}$ on $x$, $y$, and $z$ for ${\pi }^{+}$, ${\pi }^0$, and ${\pi }^{-}$ production at JLab for SIDIS on transversely polarized proton (solid line), deuteron (dashed line), and neutron (dot-dashed line) targets.

Figure 5

Predicted dependence of $A_{LT}^{\cos ({\varphi }_h-{\varphi }_S)}(|{\mathbf{P}}_{hT,\min }|)$ on $|{\mathbf{P}}_{hT,\min }|$ for proton target.

Figure 6

Predicted dependence of $A_{LT}^{\cos ({\varphi }_h-{\varphi }_S)}(|{\mathbf{P}}_{hT,\min }|)$ on $|{\mathbf{P}}_{hT,\min }|$ for deuteron (and neutron for JLab) target.

Figure 7

Predicted dependence of $A_{LT}^{\cos ({\varphi }_h-{\varphi }_S)}$ on $x$, $y$, and $z$ with $|{\mathbf{P}}_{hT,\min }|=0.5\mathrm{GeV}/\mathrm{c}$ for COMPASS.

Figure 8

Predicted dependence of $A_{LT}^{\cos ({\varphi }_h-{\varphi }_S)}$ on $x$, $y$, and $z$ with $|{\mathbf{P}}_{hT,\min }|=0.5\mathrm{GeV}/\mathrm{c}$ for HERMES.

Figure 9

Predicted dependence of $A_{LT}^{\cos ({\varphi }_h-{\varphi }_S)}$ on $x$, $y$, and $z$ with $|{\mathbf{P}}_{hT,\min }|=0.5\mathrm{GeV}/\mathrm{c}$ for JLab.