Transverse Λ polarization in e+e− processes within a TMD factorization approach and the polarizing fragmentation function

Abstract

We perform a re-analysis of Belle data for the transverse Λ and $$ \overline{\Lambda} $$ Λ ¯ polarization in e+e− annihilation processes within a transverse momentum dependent (TMD) factorization approach. We consider two data sets, one referring to the associated production of Λ’s with a light unpolarized hadron in an almost back-to-back configuration, and one for the inclusive Λ production, with the reconstruction of the thrust axis. We adopt the Collins-Soper-Sterman framework and employ the recent formulation on the factorization of single-inclusive hadron production. This extends a previous phenomenological study carried out in a more simplified TMD approach, leading to a new extraction of the polarizing fragmentation function (FF). While confirming several features of the previous analysis, here we include the proper QCD scale dependence of this TMD FF and carefully exploit the role of its nonperturbative component. The compatibility, within a unique TMD factorization scheme, of double and single-inclusive hadron production is discussed in detail. Moreover, we consider another data set for inclusive Λ production, at much larger energies, from the OPAL Collaboration, in order to test the consistency of the entire approach. Finally, we elaborate on some fundamental issues like the role of SU(2) isospin symmetry and the heavy quark contributions.

Several Topics on Transverse Momentum-Dependent Fragmentation Functions

“…Recently, the Belle collaboration measured the transverse polarization of Λ hyperons in e + e − annihilations [19], sparking considerable theoretical interest [15,[20][21][22][23][24][25][26][27][28][29][30][31][32]. In this experiment, one first defines the hadron production plane and then measures the transverse polarization along its normal direction.…”

“…Nonetheless, since the collisional energy at Belle is not very high, a Gaussian ansatz is already a good approximation. More sophisticated approaches incorporating the p ⊥ dependence can be found in [29,31,32].…”

“…This perspective was further investigated in Ref. [31] recently, which concluded that one can obtain good fit to the Belle data with and without implementing the isospin symmetry constraint after taking into account the charm contribution. This confirms that the current Belle dataset does not represent an isospin symmetry violation in the hadronization.…”

“…The recent measurement of the spontaneous polarization of Λ from unpolarized e + e − annihilation is such an instance [19]. This observation can be explained by a naively time-reversal odd (T-odd) TMD FF D ⊥ 1T (z, k ⊥ ) and has received interests from various groups [15,[20][21][22][23][24][25][26][27][28][29][30][31][32].…”