Abstract
We study the polar and azimuthal decay angular distributions of J/ψ mesons produced in semi-inclusive, deep-inelastic electron-proton scattering. For the description of the quarkonium formation mechanism, we adopt the framework of nonrelativistic QCD, with the inclusion of the intermediate color-octet channels that are suppressed at most by a factor v4 in the velocity parameter v relative to the leading color-singlet channel. We put forward factorized expressions for the helicity structure functions in terms of transverse momentum dependent gluon distributions and shape functions, which are valid when the J/ψ transverse momentum is small with respect to the hard scale of the process. By requiring that such expressions correctly match with the collinear factorization results at high transverse momentum, we determine the perturbative tails of the shape functions and find them to be independent of the J/ψ polarization. In particular, we focus on the cos 2ϕ azimuthal decay asymmetry, which originates from the distribution of linearly polarized gluons inside an unpolarized proton. We therefore suggest a novel experiment for the extraction of this so-far unknown parton density that could be performed, in principle, at the future Electron-Ion Collider.
Highlights
By requiring that such expressions correctly match with the collinear factorization results at high transverse momentum, we determine the perturbative tails of the shape functions and find them to be independent of the J/ψ polarization
In the high-qT region, namely qT ΛQCD, in a frame where the J/ψ meson is at rest, the photon transverse momentum is generated by perturbative radiation
This suggests that smearing effects need to be taken into account in those helicity structure functions which depend on the unpolarized gluon transverse momentum dependent (TMD) distribution, through the inclusion of a suitable shape function [21, 22]
Summary
With X being an undetected hadronic system, and the subsequent leptonic decay J/ψ(Pψ) → +(l) + −(l ) ,. The hadronic tensor Wμν is a function of the four-vectors qμ, P μ, Pψμ and contains the information on the proton structure as well as on the J/ψ formation process and polarization. It has to fulfill certain constraints due to electromagnetic gauge invariance, parity, and hermiticity. As a first step of our derivation, it might be useful to write separately the contributions coming from transversely and longitudinally polarized virtual photons This can be achieved by expressing the leptonic tensor in eq (2.6) in the form μν 2 Q2. In eq (2.18), we have introduced the projector to the space orthogonal to both q and P μν νμ
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