Is helium the key parameter in the extended color spread of the first generation stars in M3?

The study of the "chromosome maps" of Galactic Globular Clusters has shown that the stars identified as `first generation' often define an extended sequence in the $m_{F275W}-m_{F814W}$ colour, whose straightforward interpretation, by comparison with synthetic spectra, is that they are inhomogeneous in helium content. The cluster M 3 (NGC 5272) is one of the most prominent example of this phenomenon, since its first generation is distributed on an extended colour range, formally corresponding to a large helium enhancement ($ \sim 0.1$). It is necessary to ask whether the bulk of photometric observations available for this cluster supports or falsifies this interpretation. For this purpose, we examine the horizontal branch morphology, the period and magnitude distributions of the RR Lyrae variables, and the main sequence colour distribution. Simulating the first generation stars with such internal variation of helium content we can not meet all the observational constraints at the same time, concluding that the origin of the first generation colour spread is still without a straightforward explanation.