Spectra and mean multiplicities of $pi^{-}$ in $central$ ${}^{40}$Ar+${}^{45}$Sc collisions at 13$A$, 19$A$, 30$A$, 40$A$, 75$A$ and 150$A$ GeV/$c$ beam momenta measured by the NA61/SHINE spectrometer at the CERN SPS

The physics goal of the strong interaction program of the NA61/SHINE experiment at the CERN Super Proton Synchrotron (SPS) is to study the phase diagram of hadronic matter by a scan of particle production in collisions of nuclei with various sizes at a set of energies covering the SPS energy range. This paper presents differential inclusive spectra of transverse momentum, transverse mass and rapidity of $pi^{-}$ mesons produced in $central$ ${}^{40}$Ar+${}^{45}$Sc collisions at beam momenta of 13$A$, 19$A$, 30$A$, 40$A$, 75$A$ and 150$A$ GeV/$c$. Energy and system size dependence of parameters of these distributions -- mean transverse mass, the inverse slope parameter of transverse mass spectra, width of the rapidity distribution and mean multiplicity -- are presented and discussed. Furthermore, the dependence of the ratio of the mean number of produced pions to the mean number of wounded nucleons on the collision energy was derived. The results are compared to predictions of several models.