Abstract
We calculate the amplitude of elastic photon-photon scattering via a single quark loop in the Double-Logarithmic Approximation, presuming all external photons to be off-shell and unpolarized.. At the same time we account for the running coupling effects. We consider this process in the forward kinematics at arbitrary relations between t and the external photon virtualities. We obtain explicit expressions for the photon-photon scattering amplitudes in all double-logarithmic kinematic regions. Then we calculate the small-x asymptotics of the obtained amplitudes and compare them with the parent amplitudes, thereby fixing the applicability regions of the asymptorics, i.e. fixing the applicability region for the non-vacuum Reggeons. We find that these Reggeons should be used at x < 10^{-8} only.
Highlights
For a long time, the light-by-light scattering has been an object of both experimental and theoretical interest
In order to specify a general solution of the infrared evolution equations (IREE) for Aγγðρ; y1Þ, we will use matching with the onshell amplitude Aoγγn, which has been found on the previous step
In order to avoid confusing new amplitudes with AðγMγ Þ and AðγDγ Þ obtained under assumption that t ∼ 0, we introduce a generic notation Mγγ for new amplitudes in double-logarithmic approximation (DLA) and will provide this notation with superscripts to specify the kinematics
Summary
The light-by-light scattering has been an object of both experimental and theoretical interest. [4] the resummation of double logs appearing starting from the first NLO QCD corrections to the quark box was studied Such contributions are important at high energy where arguments of the logs are large. Until recently, the inclusion of BFKL resummation effects in the NLA calculation of the γÃγà total cross section was carried out only in approximate way, by taking the BFKL Green’s function in the NLA while using the LO expression for impact factors This is the case of the pioneer paper in Ref. It was shown that the account of the Balitsky and Chirilli expression for NLO photon impact factor reduces the BFKL contribution to the cross section to very small values making it impossible to describe LEP2 data as a sum of BFKL and LO QED quark box contributions.
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