Abstract
The difference between the flow ellipticities of oppositely charged pions, \Delta v_2=v_2[\pi-]-v_2[\pi+], measured recently by STAR collaboration at RHIC shows a linear dependence on the event charge asymmetry A_+-={(N_+-N_-)/ (N_++N_-)}: \Delta v_2(A_+-)= \Delta v_2(0)+ r A_+- with a slope r>0 and a non-zero intercept \Delta v_2(0)>0 of order 10^{-4}. We point out two novel mechanisms which could explain the non-zero value of the charged elliptic flow \Delta v_2 at zero charge asymmetry A_+-=0, i.e., the non-zero positive intercept \Delta v_2(0). Both effects are due to the electric fields created by the colliding ions. These fields have quadrupole asymmetry of the magnitude and the sign needed to account for the nonzero intercept \Delta v_2(0) in the RHIC data. One of the mechanisms also involves chiral magnetic effect. This mechanism, although negligible at RHIC energies, may become important at LHC energies.
Highlights
The recent analysis [1, 2] of STAR event-by-event measurements of the difference between the elliptic flows of positive and negative pions, ∆v2 ≡ v2[π−] − v2[π+], finds an interesting behavior of this quantity as a function of the event charge asymmetry A± ≡ (N+ − N−)/(N+ + N−)
We discuss two sources of such a net positive electric quadrupole moment. Both involve electric fields created by the heavy ions which are similar in strength to the magnetic fields responsible for the Chiral Magnetic Wave (CMW)
We identified two possible sources of the charged elliptic flow ∆v2(A±) at zero charge asymmetry, i.e., ∆v2(0)
Summary
The recent analysis [1, 2] of STAR event-by-event measurements of the difference between the elliptic flows of positive and negative pions, ∆v2 ≡ v2[π−] − v2[π+], finds an interesting behavior of this quantity as a function of the event charge asymmetry A± ≡ (N+ − N−)/(N+ + N−). 2: The Chiral Magnetic Wave (CMW) evolution of the initial charge asymmetry (taken to be positive in this example) produces a net electric quadrupole moment responsible for a non-zero ∆v2 ≡ v2[π−] − v2[π+] (positive in this this case). We discuss two sources of such a net positive (out of reaction plane) electric quadrupole moment Both involve electric fields created by the heavy ions which are similar in strength to the magnetic fields responsible for the CMW. One of the sources is the quadrupole component of the electric field, which has been pointed out in Ref.[9], and we shall show that it has the right magnitude and sign to account for the intercept ∆v2(0) observed at RHIC. We describe the two mechanisms in the subsequent sections and make an order of magnitude estimate of their effect on the charged elliptic flow ∆v2(0)
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