Procedure for measuring photon and vector meson circular polarization variation with respect to the reaction plane in relativistic heavy-ion collisions

The electromagnetic (EM) field pattern created by spectators in relativistic heavy-ion collisions plants a seed of positive (negative) magnetic helicity in the hemisphere above (below) the reaction plane. Owing to the chiral anomaly, the magnetic helicity interacts with the fermionic helicity of the collision system and causes photons emitted in upper and lower hemispheres to have different preferences in the circular polarization. Similar helicity separation for massive particles, owing to the global vorticity, is also possible. In this paper, we lay out a procedure to measure the variation of the circular polarization with respect to the reaction plane in relativistic heavy-ion collisions for massless photons, as well as similar polarization patterns for vector mesons decaying into two daughters. We propose to study the yield differentially and compare the yield between upper and lower hemispheres to identify and quantify such effects.

Figure 1

A left (a) or right (b) circularly polarized photon is converted into an electron-positron pair with the help of the recoil of an atomic nucleus.

Figure 2

Illustration of the helicity frame (left), in which $b_1$ and $b_2$ are beam directions in the quarkonium rest frame and the orientation of the polar axis ($Z_{HX}$) is set to be the opposite of the direction of motion of the interaction point. The polar angle ($\beta$) is defined as the angle between the polar axis and the positive lepton (right).

Figure 3

Probability distribution $y(\varphi ,\beta )$ for $A=0$ (top), $A=0.5$ (middle), and $A=1$ (bottom). For all three cases, ${\lambda }_{\beta }$ and $v_2$ are $-0.1$ and 0.1, respectively.