  Identifying quantum numbers to label elementary excitations is essential for
the correct description of light-matter interaction in solids. In monolayer
semiconducting transition metal dichalcogenides (TMDs) such as MoSe$_2$ or
WSe$_2$, most optoelectronic phenomena are described well by labelling electron
and hole states with the spin projection along the normal to the layer (S$_z$).
In contrast, for WSe$_2$/MoSe$_2$ interfaces recent experiments show that
taking S$_z$ as quantum number is not a good approximation, and spin mixing
needs to be always considered. Here we argue that the correct quantum number
for these systems is not S$_z$, but the $z$-component of the total angular
momentum -- J$_z$ = L$_z$ + S$_z$ -- associated to the C$_3$ rotational lattice
symmetry, which assumes half-integer values corresponding modulo 3 to distinct
states. We validate this conclusion experimentally through the observation of
strong intervalley scattering mediated by chiral optical phonons that --
despite carrying angular momentum 1 -- cause resonant intervalley transitions
of excitons, with an angular momentum difference of 2.
