  In this paper, we examine the potential of Higgs boson production associated
with a photon at the LHC to probe the new physics effects in the framework of
the standard model effective field theory. It is shown that the differential
kinematic distributions such as photon transverse momentum and invariant mass
of Higgs+$\gamma$ in Higgs associated production are powerful variables to
explore the coefficients of dimension six operators. The analysis is performed
in the decay channel of Higgs boson into a $b\bar{b}$ pair including the main
sources of background processes and a realistic simulation of the detector
effects. We provide constraints at $95\%$ confidence level on the Wilson
coefficients of dimension-six operators affecting Higgs boson plus a photon
production. We show to what extent these limits could be improved at the high
luminosity LHC. The effect of these constraints on a well-motivated beyond
standard model scenario is presented.
