Coalescence sum rule and the electric charge- and strangeness-dependences of directed flow in heavy ion collisions

Abstract

The rapidity-odd directed flows (v1) of identified hadrons are expected to follow the coalescence sum rule when the created matter is initially in parton degrees of freedom and then hadronizes through quark coalescence. A recent study has considered the v1 of produced hadrons that do not contain u or d constituent quarks. It has constructed multiple hadron sets with a small mass difference but given difference in electric charge Δq and strangeness ΔS between the two sides, where a nonzero and increasing Δv1 with Δq has been proposed to be a consequence of electromagnetic fields. In this study, we examine the consequence of coalescence sum rule on the Δv1 of the hadron sets in the absence of electromagnetic fields. We find that in general Δv1≠0 for a hadron set with nonzero Δq and/or ΔS due to potential v1 differences between u¯ and d¯ and between s and s¯ quarks. We further propose methods to extract the coefficients for the Δq- and ΔS-dependences of the direct flow difference, where a nonzero constant term would indicate the breaking of the coalescence sum rule. The extraction methods are then demonstrated with transport model results.