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Recently, seven produced hadron species have been used to construct multiple hadron sets with given differences in the net electric charge (∆q) and strangeness (∆S) between the two sides. A nonzero directed flow difference △v₁has been proposed as a consequence of the electromagnetic field produced in relativistic heavy ion collisions. Previously, we have shown with quark coalescence that Av1 and the slope difference △v′₁depend linearly on both △qand ∆Swith zero intercept. Here we emphasize that a two-dimensional function or fit is necessary for extracting the △q- and △S-dependences of △v₁. On the other hand, a one-dimensional fit gives a different value for the slope parameter of the ∆q- or ∆S-dependence. Furthermore, a one-dimensional fit is incorrect because its slope parameter depends on the arbitrary scaling factor of a hadron set and is thus ill-defined. We use test data of △v₁to explicitly demonstrate these points. 

Recently, the rapidity-odd directed flow (v1) of produced hadrons (K−, ϕ, p¯, Λ¯, Ξ¯+, Ω−, and Ω¯+) has been studied. Several combinations of these produced hadrons, with very small mass differences but differences in the net electric charge (Δq) and net strangeness (ΔS) on the two sides, have been considered. A difference in v1 between the two sides of these combinations (Δv1) has been proposed as a consequence of the electromagnetic field produced in relativistic heavy-ion collisions, especially if Δv1 increases with Δq. Our study is performed to understand the effect of the coalescence sum rule (CSR) on Δv1. We point out that the CSR leads to Δv1=cqΔq+cSΔS, where the coefficients cq and cS reflect the Δv1 of produced quarks. Equivalently, one can write Δv1=cqΔq+cBΔB, involving the difference in the net baryon number ΔB, where the CSR gives cB=−3cS. We then propose two methods to extract the coefficients for the Δq and ΔS dependences of Δv1.