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Exa couplings2

Emanuele Roberto Nocera requested to merge exa_couplings2 into master

Created by: niclaurenti

This PR implements the alphaem exact running in the Alpha class in the validphys.photon module. In this way it is consistent with the running used in EKO for QED. Such running also considers the mixed terms between the RGEs of alphas and alphaem (therefore they are evolved together). Edit: Since the solution must enter in the fiatlux integral, and the exact solution is slower than the truncated one, the strategy is to compute \alpha for some reference values in the integration range and then interpolate with scipy (the function is continuous since the matching is applied to \alpha_s only but probably not smooth in the matching points) Edit n. 2: interpolating with scipy was still too slow so I interpolated with numpy, that is faster Edit n. 3 (Theoretical issue): the Lux formula uses \alpha(Q^2) to very low values of Q^2, below the Landau pole of \alpha_s. For this reason I had to remove the mixed terms in the evolution of \alpha(Q^2), i.e. the terms that couple the evolutions of the two couplings. In this way \alpha running is decoupled from \alpha_s running. It means that the evolution will be slightly inconsistent with the one used in EKO (but in the perturbative regions the difference is sub-permil).

I've performed a fit with this branch and it seems to be good:

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