Abstract
In this paper we study transverse polarization of Λ hyperons in single-inclusive leptonic annihilation. We show that when the transverse momentum of the Λ baryon is measured with respect to the thrust axis, a transverse momentum dependent (TMD) factorization formalism is required and the polarization is generated by the TMD polarizing fragmentation function (TMD PFF), D1T⊥. However, when the transverse momentum of the Λ baryon is measured with respect to the momentum of the initial leptons, a collinear twist-3 formalism is required and the polarization is generated by the intrinsic collinear twist-3 fragmentation function DT. Thus while these measurements differ from one another only by a change in the measurement axis, they probe different distribution functions. Recently, Belle measured a significant polarization in single-inclusive Λ baryon production as a function of the transverse momentum with respect to the thrust axis. However, this data can in principle be re-analyzed to measure the polarization as a function of the transverse momentum of the Λ baryon with respect to the lepton pair. This observable could be the first significant probe of the function, DT. In this paper, we first develop a TMD formalism for Λ polarization; we then present a recent twist-3 formalism that was established to describe Λ polarization. Using the TMD formalism, we demonstrate that the Λ polarization at OPAL and Belle can be described using the twist-2 TMD factorization formalism. Finally, we make a theoretical prediction for this polarization in the collinear twist-3 formalism at Belle.
Highlights
It has been a long standing challenge to describe the transverse polarization of Λ baryons in deep inelastic high energy reactions from a factorized framework in perturbative QCD
In this paper we have studied transverse polarization in single-inclusive Λ production in a thrust transverse momentum dependent (TMD) framework as well as a collinear twist-3 framework
We have shown that when the polarization is differential in the transverse momentum with respect to the thrust axis, the polarization can be used to probe the TMD Polarizing Fragmentation Function (PFF), D1⊥T
Summary
The Belle collaboration measured the production of transverse polarization of Λ-hyperons [21] in e+e−-annihilation for single-inclusive Λ production, where the hadron cross section is studied as a function of the fractional energy zΛ, and the transverse momentum j⊥ with respect to the thrust axis. They find a significant non-zero effect for this process as well as for back-to-back production of Λ and a light hadron h = π±, K±. With regard to the latter measurement, it is important to note that an observation of a non-zero ef-
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