Implement alphaem exact running in photon module
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
I've performed a fit with this branch and it seems to be good:
- report: https://vp.nnpdf.science/YxTPc_wmTNursIVaGFzrzg==/
- Photon comparison with NNPDF40_ecc_qed: https://vp.nnpdf.science/mbJ3jSqKTbCsnZkih6itLw==/#PDFscalespecs0_Basespecs1_PDFnormalize1_plot_pdfs_photon https://vp.nnpdf.science/OfKqMEFORQSWcWcvCpTkDQ==/#PDFscalespecs0_Basespecs1_PDFnormalize1_plot_pdfs_photon
- Photon comparison with NNPDF31_ecc_qed: https://vp.nnpdf.science/bjp3QArIT7qu91RPDUpIyg==/#PDFscalespecs0_Basespecs1_PDFnormalize1_plot_pdfs_photon