The search for experimental signatures of the critical point (CP) of strongly interacting matter is one of the main objectives of the NA61/SHINE experiment at the CERN SPS. In the course of the experiment, an energy (beam momentum 13A -- 150/158A GeV/c) and system size (p+p, p+Pb, Be+Be, Ar+Sc, Xe+La) scan is performed. Proposed observables include non-monotonic fluctuations of integrated quantities, as well as local critical fluctuations connected to the critical behavior of the order parameter in the neighborhood of the CP, which scale according to universal power-laws.

We investigate proton density fluctuations as a possible order parameter of the phase transition in the
neighborhood of the CP. To this end, we perform an intermittency analysis of the proton second scaled
factorial moments (SSFMs) in transverse momentum space. A previous analysis of this sort revealed
significant power-law fluctuations in the NA49 heavy ion collision experiment for the "Si"+Si system at 158A
GeV/c. The fitted power-law exponent was consistent with the theoretically expected critical value, within
errors, a result suggesting a baryochemical potential for the critical point in the vicinity of ~250 MeV. We now
extend the analysis to NA61 systems of similar size, Be+Be and Ar+Sc, at 150A GeV/c.

We adapt statistical techniques for the calculation of scaled factorial moments, in order to subtract non-critical
background and enhance the signal in cases of low statistics. Our analysis is supplemented by both critical and
non-critical Monte Carlo simulations, through which we estimate non-critical background effects on the
quality and magnitude of uncertainties of the intermittency power-law fit, as well as explore the possibility of
non-critical effects producing an intermittency signal.