Abstract
We consider the azimuthal distribution of the final observed hadron in semi-inclusive deep-inelastic scattering and the lepton pair in the Drell-Yan process. In particular, we focus on the cosϕ modulation of the unpolarized cross section and on its dependence upon transverse momentum. At low transverse momentum, for these observables we propose a factorized expression based on tree-level approach and conjecture that the same formula is valid in transverse-momentum dependent (TMD) factorization when written in terms of subtracted TMD parton distributions. Our formula correctly matches with the collinear factorization results at high transverse momentum, solves a long-standing problem and is a necessary step towards the extension of the TMD factorization theorems up to the subleading twist.
Highlights
The inclusive production of a system of one or more particles with a specific transverse momentum in lepton-hadron or hadronhadron collisions is in general characterized by three different scales: the nonperturbative QCD scale QCD, the hard scale of the process Q, and the magnitude of the system’s transverse momentum qT
We provide arguments in favor of this formulation and show that it leads to an agreement between the transverse-momentum dependent (TMD) and collinear results in semi-inclusive deep inelastic scattering (SIDIS) and in Drell–Yan lepton pairs (DY), in different reference frames
We analyzed the cos φ modulation of the unpolarized cross section in semi-inclusive DIS (SIDIS) and in the Drell-Yan process (DY)
Summary
The inclusive production of a system of one or more particles with a specific transverse momentum in lepton-hadron or hadronhadron collisions is in general characterized by three different scales: the nonperturbative QCD scale QCD, the hard scale of the process Q , and the magnitude of the system’s transverse momentum qT. Apart from the azimuthally independent cross sections, where unpolarized TMDs are important, various TMDs are involved in generating azimuthal modulations of unpolarized cross sections Both in SIDIS and DY, neglecting parity-violating interactions, four structure functions are needed to parametrize the cross section that depends on the azimuthal angle and transverse momentum. We study cos φ modulations: they involve twist TMD PDFs and FFs and are suppressed by a factor 1/Q with respect to the leading (twist-2) terms. These modulations have been already studied, with somewhat contradictory results, in Refs. Our results can be generalized to other observables involving twist-3 TMDs and they represent a necessary step in the direction of establishing TMD factorization at twist-3 level
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