Photon decay in a strong magnetic field in heavy-ion collisions

We calculate the photon pair production rate in a strong magnetic field created in off-central heavy-ion collisions. Photon decay leads to depletion of the photon yield by a few percent at RHIC and by as much as 20% at the LHC. It also generates a substantial azimuthal asymmetry (“elliptic flow”) of the final photon distribution. We estimate v2 ≈ 2% at RHIC and v2 ≈ 14% at LHC. Photon decay measurements is an important tool for studying the magnetic fields in early stages of heavy-ion collisions. Disciplines Astrophysics and Astronomy | Physics Comments This article is from Physical Review C 83 (2011): 017901, doi: 10.1103/PhysRevC.83.017901. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/144 PHYSICAL REVIEW C 83, 017901 (2011) Photon decay in a strong magnetic field in heavy-ion collisions Kirill Tuchin Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA and RIKEN BNL Research Center, Upton, New York 11973-5000, USA (Received 30 August 2010; published 31 January 2011) We calculate the photon pair production rate in a strong magnetic field created in off-central heavy-ion collisions. Photon decay leads to depletion of the photon yield by a few percent at RHIC and by as much as 20% at the LHC. It also generates a substantial azimuthal asymmetry (“elliptic flow”) of the final photon distribution. We estimate v2 ≈ 2% at RHIC and v2 ≈ 14% at LHC. Photon decay measurements is an important tool for studying the magnetic fields in early stages of heavy-ion collisions. DOI: 10.1103/PhysRevC.83.017901 PACS number(s): 25.75.Cj Ultrarelativistic heavy ions colliding at a finite impact parameter possibly create a supercritical magnetic field B. According to the estimates in Refs. [1] and [2], the strength of this field at √ s = 200 GeV is approximately eB ≈ mπ/h̄, while the critical field is eBc = me/h̄. Thus, the magnetic field created in heavy-ion collisions is by many orders of magnitude stronger than any field that has been created using the state-of-the-art lasers (see, e.g., Ref. [3]). The possible existence of such fields opens a new avenue for studying the high-intensity regime of quantum electrodynamics (QED). Various QED processes in external magnetic fields strongly depend on the time dependence of that field. Recently we argued [4] that the magnetic field is approximately stationary during the lifetime of the quark-gluon plasma (QGP) that is formed shortly after the collision. Indeed, phenomenological models describing the evolution of a QGP indicate that the thermalized medium is formed almost immediately after the collision (after ∼0.5 fm [5,6]) when the magnetic field is near the maximum of its strength. As the heavy-ion remnants recede from the collision point, the magnetic field tends to rapidly decrease with time. This induces circular currents in the QGP that, by the Faraday law, produce an induced magnetic field in the direction of the external field. Thus, the relaxation process of the external field slows down. The characteristic relaxation time is [4] τ = R 2σ 4 , (1) whereR is the QGP size andσ is its electric conductivity. In the perturbative regime one expects a high electric conductivity σ ∼ T/e2 [8]. Lattice calculations show that the electric conductivity is high even at temperatures close to Tc [7]. In Ref. [4] we used the lattice data of Ref. [7] to estimate the relaxation time as τ ≈ 160 fm. This number is even larger if the effect of the magnetic field on the electric conductivity is taken into account [9]. It implies that the external magnetic field is a slowly varying function of time during the entire QGP lifetime. Of course, once the plasma cools down to the critical temperature and undergoes the phase transition to the hadronic gas, the conductivity becomes very small and the magnetic field cannot be sustained anymore. In Ref. [4] we discussed the properties of the synchrotron radiation of gluons by fast quarks and argued that it has significant phenomenological implications. Indeed, the corresponding energy loss in magnetic field is comparable to that sustained by the fast quark in a hot nuclear medium. The azimuthally asymmetric form of the energy loss contributes to the “elliptic flow” phenomenon observed at RHIC. In this Brief Report we consider a cross-channel process: pair production by a photon in an external magnetic field. Specifically, we are interested to determine photon decay rate w in the process γB → f f̄ B, where f stands for a charged fermion, as a function of the photon’s transverse momentum kT , rapidity η, and azimuthal angle φ. The origin of these photons in heavy-ion collisions will not be of interest in this Brief Report. The characteristic frequency of a fermion of species a of mass ma and charge zae (e is the absolute value of the electron charge) moving in an external magnetic field B (in a plane perpendicular to the field direction) is h̄ωB = zaeB ε , (2) where ε is the fermion energy. Here, in the spirit of the adiabatic approximation, B is a slow function of time. Calculation of the photon decay probability significantly simplifies if the motion of the electron is quasiclassical, i.e., quantization of the fermion motion in the magnetic field can be neglected. This condition is fulfilled if h̄ωB ε. This implies that ε √zeB. (3) For RHIC it is equivalent to ε mπ , and for LHC it is equivalent to ε 4mπ . The photon decay rate was calculated in Ref. [10] and, using the quasiclassical method, in Ref. [11], it reads