Galactic or extragalactic chemical tagging for NGC3201? Discovery of an anomalous CN-CH relation

(ABRIDGED) The origin of the globular cluster (GC) NGC3201 is under debate. Its retrograde orbit points to an extragalactic origin, but no further chemical evidence supports this idea. Light-element chemical abundances are useful to tag GCs and can be used to shed light on this discussion. We aim to derive CN and CH band strengths for red giant stars in NGC3201 and compare these with photometric indices and high-resolution spectroscopy and discuss in the context of GC chemical tagging. We found three groups in the CN-CH distribution. A main sequence (S1), a secondary less-populated sequence (S2), and a group of peculiar (pec) CN-weak and CH-weak stars, one of which was previously known. The three groups seem to have different C+N+O and/or s-process element abundances, to be confirmed by high-resolution spectroscopy. These are typical characteristics of anomalous GCs. The CN distribution of NGC 3201 is quadrimodal, which is more common in anomalous clusters. However, NGC3201 does not belong to the trend of anomalous GCs in the mass-size relation. Three scenarios are postulated here: (i) if the sequence pec-S1-S2 has increasing C+N+O and s-process element abundances, NGC3201 would be the first anomalous GC outside of the mass-size relation; (ii) if the abundances are almost constant, NGC3201 would be the first non-anomalous GC with multiple CN-CH anti-correlation groups; or (iii) it would be the first anomalous GC without variations in C+N+O and s-process element abundances. In all cases, the definition of anomalous clusters and the scenario in which they have an extragalactic origin must be revised.