Abstract
We study the transverse-momentum spectrum of quarkonium production from single light-parton fragmentation mechanism. In the case of semi-inclusive deep inelastic scattering, we observe that there are two possible initiating processes, namely photon-gluon fusion and light-quark fragmentation. For the second case we derive the factorization theorem, which involves a new hadronic quantity: the quarkonium transverse-momentum-dependent fragmentation functions in NRQCD. We calculate their matching onto the non-perturbative long distance matrix elements at the lowest order in the strong-coupling constant, mathcal{O}left({alpha}_s^2right) . Focusing on the case of the electron-ion collider, we make a comparative phenomenological study of the two production mechanisms and find the regions of the phase space where one is dominant over the other.
Highlights
On the other hand, in semi-inclusive deep inelastic scattering (SIDIS) the hard scale Λ is usuallyAset by the invariant mB1as+s mofirtrohredviairgtruamal ton, Λ = Q = −Cq2, with q the photon momentum
In this paper we have studied the quarkonium transverse-momentum-dependent fragmentation functions (TMDFFs) within the framework of non-relativistic QCD (NRQCD)
We decompose the TMDFFs in a similar way as done in the corresponding collinear fragmentation functions [65]
Summary
The momenta of quarkonium production in SIDIS are specified by (l) + h(p) → (l ) + H(P ) + X,. Where is a lepton, h and H are respectively the initial and the final hadrons, and X is the undetected final state. The masses of the hadrons are p2 = m2, P 2 = M 2,. For the moment we continue to consider hadron masses in order to control their effects. The cross section in eq (2.3) is proportional to the phase-space differentials for the detected lepton and heavy hadron, with E and EH being their energies. The leptonic and hadronic tensors (Lμν and W μν) are. P, X|Jν(0)|p , where e is the lepton charge, and Jμ is the electro-magnetic current
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