  After the Higgs boson discovery, LHC can be used as a precision machine to
explore its properties. Indeed, in case new resonances will not be found, the
only access to New Physics would be via measuring small deviations from the SM
predictions. A consistent approach is provided by a bottom-up Effective Field
Theory, with dimension six operators built of Standard Model fields (SMEFT). We
discuss how this approach works in case of the transverse momentum spectrum of
the Higgs particle. In our calculation we augmented the Standard Model with
three additional operators describing modifications of the top and bottom
Yukawa couplings, and a point-like Higgs coupling to gluons. Based on recently
presented resummed transverse-momentum spectra including these operators at
NLL+NLO accuracy,which we recently presented in Ref [1], in this note we show
the extension of the calculation to NNLL+NNLO. We find that such modifications,
while affecting the total rate within the current uncertainties, can lead to
significant distortions of the spectrum. Additionally, through significant
reduction of the scale uncertainty we improve the sensitivity to the new
operators.
