Luminosity constraint and entangled solar neutrino signals

The current frontier of solar neutrino physics is the observation of CNO neutrinos. The signals of CNO and PP neutrinos are however entangled: In fact, the pp-flux can be known precisely only if CNO-flux is quantified; the interpretation of the gallium experiments depends upon both fluxes; a precise knowledge of pep-flux is a precondition to extract the CNO-neutrino signal with Borexino. The luminosity constraint plays an increasingly important r\^ole: we present it in a new form, improving the expression obtained by J. Bahcall in Phys. Rev. C 65 (2002) 025801.