A new method to clarify contribution of chiral magnetic effect in small collision system $p^{\uparrow} + A$ involving a transversely polarized proton

In this paper, we propose a new experiment method to check contribution of chiral magnetic effect (CME). With experimental data of DIS involving transversely polarized proton, we have calculated the 3-D charge density inside the polarized proton, which is found to have a significant violation to spherical symmetry. Then we have calculated the property of electromagnetic field (E-M field) generated by a single transversely polarized proton ($p^{\uparrow}$). Based on them, the E-M field generated in small collision system $p^{\uparrow}+A$ are studied. We find that the orientation of this E-M field has a significant dependence on the polarization direction of the proton, and the correlator ($\Delta\gamma$ ) has also significant dependence on the angle between reaction plane and polarization direction. As background contribution are canceled comparing two collision geometry schemes, only contribution of CME is remained.