Lepton-Jet Correlations in Deep Inelastic Scattering at the Electron-Ion Collider

We propose the lepton-jet correlation in deep inelastic scattering as a unique tool for the tomography of nucleons and nuclei at the electron-ion collider (EIC). The azimuthal angular correlation between the final state lepton and jet depends on the transverse momentum dependent quark distributions. We take the example of single transverse spin asymmetries to show the sensitivity to the quark Sivers function. When the correlation is studied in lepton-nucleus collisions, transverse momentum broadening effects can be used to explore cold nuclear matter effects. These features make lepton-jet correlations an important new hard probe at the EIC.

Figure 1

Lepton-jet correlation for the tomography of the nucleon or nucleus at the EIC.

Figure 2

The azimuthal angular correlation between the final state lepton and jet at equal rapidities $y_{\ell }=y_J=1$ in the c.m. frame of the $ep$ collisions at $\sqrt{S_{ep}}=80\mathrm{GeV}$. We show $\mathrm{\Delta }\varphi ={\varphi }_J-{\varphi }_{\ell }-\pi$, where ${\varphi }_J$ and ${\varphi }_{\ell }$ are the azimuthal angles of the jet and lepton, respectively. We choose $k_{\ell \perp }=15\mathrm{GeV}$ and integrate the jet transverse momentum over 10–20 GeV, with radius $R=0.5$. The red and blue curves show the correlations when the spin of the transversely polarized nucleon is parallel or antiparallel to ${\overrightarrow{k}}_{\ell \perp }$, respectively.

Figure 3

The single transverse spin asymmetry as a function of $\mathrm{\Delta }\varphi ={\varphi }_J-{\varphi }_{\ell }-\pi$ for different lepton transverse momenta $k_{\ell \perp }=7$, 10, and 15 GeV, respectively, which illustrates the transverse momentum dependence of the quark Sivers function.

Figure 4

$P_T$-broadening effects for the lepton jet azimuthal correlation due to the interaction with cold nuclear matter as a function of $\mathrm{\Delta }\varphi =|{\varphi }_J-{\varphi }_{\ell }-\pi |$ for two typical values of $\widehat{q}L$.