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Directed flow of photons in Cu+Au collisions at RHIC

Event-by-event fluctuations in the positions of nucleons in two colliding identical nuclei can lead to non-uniform initial energy density distribution on the transverse plane. In addition to initial state fluctuations, the difference in the number of participating nucleons in collision of two non-identical nuclei can also result in significant anisotropy in the initial geometry and energy density distributions. Thus, Cu+Au collisions are expected to provide interesting new aspects in the understanding of anisotropic flow in heavy ion collisions. We calculate directed flow co-efficient $v_1$ of thermal photons using a hydrodynamic model with fluctuating initial conditions at 200A GeV Cu+Au collisions at RHIC and compare it with the elliptic and triangular flow parameters obtained at same initial conditions. The photon $v_1$ as a function of transverse momentum is found to be non-zero and significantly large. However, it shows a different nature compared to the elliptic and triangular flow parameters. The $v_1$ is found to be completely dominated by QGP radiation in the region $1 < p_T < 6$ GeV and contribution from the hadronic phase to photon $v_1$ is only marginal. At $p_T < 2$ GeV, it is negative and it decreases further with smaller values of $p_T$. However, at $p_T > 2 $ GeV, $v_1$ is positive and rises slowly with $p_T$. In addition, the photon $v_1$ is found to be more sensitive to the initial formation time of the plasma compared to the elliptic and triangular flow parameters. We suggest that a simultaneous measurements of photon $v_n$ co-efficients, (n=1, 2, 3) can provide valuable information about the initial state produced in heavy ion collisions as well as help us understanding the direct photon puzzle.