General helicity formalism for two-hadron production in $e^+e^-$ annihilation within a TMD approach

We present the complete leading-order results for the azimuthal dependences and polarization observables in $e^+e^-\to h_1 h_2 + X$ processes, where the two hadrons are produced almost back-to-back, within a transverse momentum dependent (TMD) factorization scheme. We consider spinless (or unpolarized) and spin-1/2 hadron production and give the full set of the corresponding quark and gluon TMD fragmentation functions (TMD-FFs). By adopting the helicity formalism, which allows for a more direct probabilistic interpretation, single- and double-polarization cases are discussed in detail. Simplified expressions, useful for phenomenological analyses, are obtained by assuming a factorized Gaussian-like dependence on intrinsic transverse momenta for the TMD-FFs.