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We show that there exists only a quite limited number of higher dimensionaloperators which can naturally lead to a slow decay of dark matter particlesinto monochromatic photons. As each of these operators inevitably inducesdecays into particles other than photons, we show that the gamma-lines itinduces are always accompanied by a continuum flux of cosmic rays. Henceconstraints on cosmic-ray fluxes imply constraints on the intensity ofgamma-lines and vice-versa. A comparison with up to date observational boundsshows the possibilities to observe or exclude cosmic rays associated togamma-line emission, so that one could better determine the properties of theDM particle, possibly discriminating between some of the operators.

Effective Theory of Dark Matter Decay into Monochromatic Photons and its Implications: Constraints from Associated Cosmic-Ray Emission