Collision parameters needed to measure polarization-dependent nonlinear pair creation

Pair creation by a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>γ</a:mi></a:math> ray in a high-intensity electromagnetic field (the nonlinear Breit-Wheeler process) is sensitive to the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>γ</b:mi></b:math>-ray polarization. Here we study the stability required in order to measure this polarization dependence in a head-on collision between a high-power linearly polarized laser and a relativistic electron beam, where the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>γ</c:mi></c:math> rays produced via nonlinear Compton scattering are highly polarized. We find that the laser strength parameter <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>a</d:mi><d:mn>0</d:mn></d:msub></d:math> has to be known to within a few percent and that the alignment of the laser and electron beam cannot fluctuate by more than half the spot size in order to attribute the reduction in positron yield to polarization effects. These collision parameters are difficult to achieve, but may be realized in future precision experiments that focus on beam stability.