Photon polarization in light-by-light scattering: Finite size effects

Abstract

We derive a simple expression for the photon helicity and polarization-flip probabilities in arbitrary background fields, in the low-energy regime. Taking the background to model a focused laser beam, we study the impact of pulse shape and collision geometry on the probabilities and on ellipticity signals of vacuum birefringence. We find that models which do not account for pulse duration can overestimate all signals in near head-on collisions by up to an order of magnitude. Taking pulse duration into account, the flip probability becomes relatively insensitive to both angular incidence and the fine details of the pulse structure.PHYSICAL REVIEW D 90, 045025 (2014) 1550-7998=2014=90(4)=045025 (11) 045025-1

Prospects for studying vacuum polarisation using dipole and synchrotron radiation

“…In order to write down the flip probability, we need the 'best case' result as described above (4.2). For a focussed Gaussian beam this has been found in Dinu et al (2014a) to be…”

“…No depletion of the background field is accounted for, nor do we account for probe scattering (Lundstrom et al 2006;King & Keitel 2012;Karbstein et al 2015), for an investigation of which in vacuum birefringence, see Karbstein et al (2015). We also restrict our attention to single photon probes; beam-like probes can be accounted for using a straightforward extension of the formalism used here (Dinu et al 2014a;Torgrimsson 2015). In summary, our current approximation gives a good estimate for the on-axis birefringence signal.…”

“…where T µν is the background field energy-momentum tensor; thus we can interpret (2.5) as simply being proportional to an integrated energy density (an intensity) seen by the probe as it passes through the target (Dinu et al 2014a). That this is an integrated, rather than peak, variable will be important below.…”

“…The probability P that the probe photon flips to its opposite helicity state µ may be written P flip = |T| 2 , where the amplitude T can be approximated by a line integral over the classical (i.e. straight line) trajectory of the photon (Dinu et al 2014a), here parameterised with time t:…”

“…Given a set-up as in figure 3 we can use (2.4) to calculate the flip probability P. Let P 0 be the 'best case' flip probability for photons arriving at the focal spot at the * We consider only photons which arrive at the focal spot at the instance of peak field strength -for the impact of timing jitter, see Dinu et al (2014a) and Schlenvoigt et al (2016). instant of peak field strength and with polarisation at 45 • to that of the intense optical pulse.…”