Alpha_s evolution bugged

[felixhekhorn]

in NLO alpha_s object does not recover the reference value

sc = StrongCoupling(..., alpha_ref, scale_ref, ...)
assert sc.a_s(scale_ref) == a_ref # this seems to fail

[felixhekhorn]

wait .. maybe not

[felixhekhorn]

so, yes, there is a bug:

# prepare
        alphas_ref = 0.118
        scale_ref = 91.0 ** 2
        nf = 3
        for order in [0,1]:
            # HERE: the problem occurs, when Q0 is not exctly Q_ref_alpha
            threshold_holder = thresholds.ThresholdsConfig(1, "FFNS", nf=nf)
            # create
            sc = StrongCoupling(constants, alphas_ref, scale_ref, threshold_holder, order)
            np.testing.assert_approx_equal(sc.a_s(scale_ref), alphas_ref/4.0/np.pi)

[felixhekhorn]

tests: see 28339fe

I believe, that this will not work, because the expanded solution for alpha_s is not strictly invertible, as it is (by construction) an expansion and so we are missing terms

I propose as solution to not scale down to Q0 always (as we are doing now), but instead to always start from the reference scale and its value; this ways we ensure at least the consistency at the reference scale ...

further more we're missing a matching condition at the thresholds which enter at NLO and NNLO level