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[Background] Proton-induced knockout reactions of the form $(p,pN)$ haveexperienced a renewed interest in recent years due to the possibility ofperforming these measurements with rare isotopes, using inverse kinematics.Several theoretical models are being used for the interpretation of these newdata, such as the distorted-wave impulse approximation (DWIA), the transitionamplitude formulation of the Faddeev equations due to Alt, Grassberger andSandhas (FAGS) and, more recently, a coupled-channels method here referred toas transfer-to-the-continuum (TC).  [Purpose] Our goal is to compare the momentum distributions calculated withthe DWIA and TC models for the same reactions, using whenever possible the sameinputs (e.g. distorting potential). A comparison with already published resultsfor the FAGS formalism is performed as well.  [Method] We choose the $^{15}$C($p$,$pn$)$^{14}$C reaction at an incidentenergy of 420 MeV/u, which has been previously studied with the FAGS formalism.The knocked-out neutron is assumed to be in a $2s$ single-particle orbital.Longitudinal and transverse momentum distributions are calculated for differentassumed separation energies.  [Results] For all cases considered, we find a very good agreement betweenDWIA and TC results. The energy dependence of the distorting optical potentialsis found to affect in a modest way the shape and magnitude of the momentumdistributions. Moreover, when relativistic kinematics corrections are omitted,our calculations reproduce remarkably well the FAGS result.  [Conclusions] The results found in this work provide confidence on theconsistency and accuracy of the DWIA and TC models for analyzing momentumdistributions for $(p,pn)$ reactions at intermediate energies.

Benchmarking theoretical formalisms for $(p,pn)$ reactions: the $^{15}$C($p,pn$)$^{14}$C case