Light-by-light scattering in the presence of magnetic fields

Abstract

The low-energy light-by-light cross section as determined by the nonlinear Euler-Heisenberg QED Lagrangian is evaluated in the presence of constant magnetic fields in the center-of-mass system of the colliding photons. This cross section has a complicated dependence on directions and polarizations. The overall magnitude decreases as the magnetic field is increased from zero, but this trend is reversed for ultrastrong magnetic fields B B c , where the cross section eventually grows quadratically with the magnetic field strength perpendicular to the collision axis. This effect is due to interactions involving the lowest Landau level of virtual Dirac particles; it is absent in scalar QED. An even more dramatic effect is found for virtual charged vector mesons where the one-loop cross section diverges at the critical field strength due to an instability of the lowest Landau level and the possibility of the formation of a superconducting vacuum state. We also discuss (the absence of) implications for the recent observation of light-by-light scattering in heavy-ion collisions. *

Selection rules for light-by-light scattering in strong magnetic field

“…In the next Section I illustrate the influence of the anisotropic dispersion laws by considering relations among momenta and scattering angle of the photons within the same configurations of the incident photons and the magnetic fields as the ones considered in [1]. I did not find kinematical bans, analogous to those known for photon splitting, but the bans due to CP-conservation like in Adler's work [4] are expected.…”

“…The CP-selection rules derived thereof from this general consideration manifest themselves by calculations of Ref. [1] 1.1.1 Perpendicular incidence Consider first the simplest case when the incoming photon momenta are perpendicular to the magnetic field, k 1,2 ⊥ B. So are the outgoing momenta since they lie in the same (reaction) plane.…”

“…Let us take the process (1, 3) → (2, 3) to begin with. The dispersion law for mode-1 under parallel propagation is just the vacuum dispersion law ω (1)…”

“…Recently R. Baier, A. Rebhan, and M. Wödlinger [1] calculated cross sections of light-by-light scattering as functions of an external magnetic field B for low-energy long-wave photons, basing on the Heisenberg-Euler Lagrangian -considered in QED, in scalar electrodynamics and in the theory with charged vector bosons. Calculations are done for special cases of equal-wave-length photons colliding head-on, when the external field is either parallel or perpendicular to the incoming photon direction, so that the three-momenta of the two colliding photons are subject to the relation k 1 = −k 2 .This kinematical restriction cannot, generally, be avoided by a Lorentz transformation to an arbitrary frame, since -when B k 1,2 -there is no invariance under the boost in the direction of the photon propagation.…”

“…Relation between the energy and momentum of the photon is not just ω = k, but the energy of each photon may depend in two ways on the angle, which the direction of its momentum makes with the magnetic field, ω ordinary,extraordinary (k 2 , (k • B) 2 ), reflecting the anisotropy of the effective "optical medium" and birefringence. (Within the local approximation kept to in [1], and here as well, the dependence on the angle is very simple, see Eqs. ( 13), ( 25), (26) in [2]).…”