  Simulations of extensive air showers using current hadronic interaction
models predict too small numbers of muons compared to events observed in the
air-shower experiments, which is known as the muon-deficit problem. In this
work, we present a new method to calculate the factor by which the muon signal
obtained via Monte-Carlo simulations must be rescaled to match the data, as
well as the beta exponent from the Heitler-Matthews model which governs the
number of muons found in an extensive air shower as a function of the mass and
the energy of the primary cosmic ray. This method uses the so-called z variable
(difference between the total reconstructed and the simulated signals), which
is connected to the muon signal and is roughly independent of the zenith angle,
but depends on the mass of the primary cosmic ray. Using a mock dataset built
from QGSJetII-04, we show that such a method allows us to reproduce the average
muon signal from this dataset using Monte-Carlo events generated with the
EPOS-LHC hadronic model, with accuracy better than 6%. As a consequence of the
good recovery of the muon signal for each primary included in the analysis,
also the beta exponent can be obtained with accuracy of less than 1% for the
studied system. Detailed simulations show a dependence of the beta exponent on
hadronic interaction properties, thus the determination of this parameter is
important for understanding the muon deficit problem.
