Abstract
We present the complete leading-order results for the azimuthal dependences and polarization observables in e+e−→ h1h2 + 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.
Highlights
Parton and/or hadron spins are involved the information we can gather is definitely much richer, allowing to reveal important spin-momentum correlations and parton orbital angular momentum effects
The last years have witnessed significant progress in the formulation of factorization theorems in terms of transverse momentum dependent (TMD) for a well defined class of processes [8,9,10,11], all characterized by the presence of two strongly ordered energy scales: namely, semi-inclusive deep inelastic scattering (SIDIS), Drell-Yan (DY) and e+e− annihilation processes, where the two scales are the virtuality of the exchanged boson and the transverse momentum of the final hadron (SIDIS), of the lepton-pair (DY) or of the hadron-pair in e+e− collisions
We present here our results starting from the former approach, which is somewhat more direct and allows us to give a complete classification of the TMD fragmentation functions at leading twist
Summary
The way the parton spin is transferred to the hadrons can be formally described, in general, by bilinear combinations of the helicity fragmentation amplitudes for the process c → h+X. The hadron helicity density matrix for a spin-1/2 hadron can be expressed in terms of the components of its polarization vector P h = (PXh , PYh, PZh) = (PTh cos φSh, PTh sin φSh, PLh) as [21]. From the above equations, giving the hadron polarization in terms of the fragmentation amplitudes and the quark polarization, we can define the eight TMD-FFs as follows. The corresponding helicity amplitudes for the hadron frame configuration are more complicate, since, even if still in the c.m. frame, the partonic scattering process occurs out of the xz plane (containing the lepton and the hadron h2 momenta) One could relate these to the canonical ones following the procedure described in ref.
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