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The Glashow-Iliopoulos-Maiani mechanism is extremely efficient to suppressthe flavour-changing neutral current decays of charmed hadrons induced by the$c \to u$ transitions, making such processes particularly sensitive tophenomena beyond the Standard Model. In particular, $c \to u$ decays with aneutrino pair in the final state are theoretically appealing due to the smalllong-distance contributions. Moreover, in the framework of the Standard ModelEffective Field Theory (SMEFT), the $SU(2)_L$ invariance allows to relate theWilson coefficients in the effective Hamiltonian governing the $c \to u \nu{\bar \nu}$ decays to the coefficients in the $c \to u \ell^+ \ell^-$Hamiltonian. We analyze the $B_c \to B^{(*)+} \nu {\bar \nu}$ decays, for whichbranching fractions of at most ${\cal O}(10^{-16})$ are predicted in theStandard Model including short- and long-distance contributions, so small thatthey can be considered as null tests. Using SMEFT and the relation to the $c\to u \ell^+ \ell^-$ processes we study the largest enhancement achievable ingeneric new physics scenarios. Then we focus on a particular extension of theStandard Model, the 331 model. SMEFT relations and the connection with $c \to u\ell^+ \ell^-$ imply that ${\cal B}(B_c \to B^{(*)+} \nu {\bar \nu})$ couldeven reach ${\cal O}(10^{-6})$, an extremely large enhancement. A lesspronounced effect is found in the 331 model, with ${\cal O}(10^{-11})$predicted branching fractions. Within the 331 model correlations exist amongthe $B_c \to B^{(*)+}\nu \bar \nu$ and $K\to \pi \nu \bar \nu$, $B\to (X_s, K,K^*) \nu \bar \nu$ channels.

$c \to u \nu {\bar \nu}$ transitions of $B_c$ mesons: 331 model facing Standard Model null tests