  The critical point of strongly interacting matter is searched for at the CERN
SPS by the NA61/SHINE experiment in central $^{40}$Ar +$^{45}$Sc collisions at
13$A$, 19$A$, 30$A$, 40$A$, and 75$A$ GeV/$c$. The dependence of the
second-order scaled factorial moments of proton multiplicity distributions on
the number of subdivisions in transverse momentum space is measured. The
intermittency analysis uses statistically independent data sets for every
subdivision in transverse and cumulative-transverse momentum variables.
  The results obtained do not indicate the searched intermittent pattern. An
upper limit on the fraction of correlated protons and the intermittency index
is obtained based on a comparison with the Power-law Model.
