Cosmic rays (CRs) are responsible for a tight correlation between the star formation rate (SFR) and the radio/$\gamma$-ray luminosity observed in star-forming galaxies (SFGs). This correlation can be explained by a linear scaling between the SFR and the number of CR acceleration sites, such as supernova remnants, coupled to the dependence of particle escape with galaxy properties.
Observations in radio and $\gamma$-rays are important tools to probe CR activity, but they may not be sufficient to fully characterise the confinement properties of galaxies. For instance, CR calorimetry is one of the most intriguing unanswered aspects in star-forming regions that could result not only in emission through the neutrino channel but possibly also in the hard X-ray and MeV energy bands.
We perform a multi-wavelength investigation of the CR population and the effective fields affecting their transport within SFGs with different levels of activity. In particular, we focus on the possibility of testing proton confinement in the X-ray and MeV bands. With this goal, we develop a model describing the CR transport in SFGs for a broad range of SFRs. Hadronic byproducts, pair production and leptonic emission are computed self-consistently in a multi-wavelength context ranging from radio up to X-rays and $\gamma$-rays.
We conclude that a panchromatic view of the SFR--luminosity correlations in SFGs is key to place strong constraints on the physical processes that govern the non-thermal physics of these sources.