Longitudinal and transverse polarizations of $\Lambda$ hyperon in unpolarized SIDIS and $e^{+}{e}^{-}$ annihilation

Abstract

We make a systematic study of $\Lambda$ hyperon polarizations in unpolarized lepton induced semi-inclusive reactions such as $e^{-}N\to e^{-}\Lambda X$ and $e^{+}{e}^{-}\to \Lambda hX$. We present the general form of cross sections in terms of structure functions obtained from a general kinematic analysis. This already shows that the produced hyperons can be polarized in three orthogonal directions, i.e., the longitudinal direction along the hyperon momentum, the normal direction of the production plane, and the transverse direction in the production plane. We present the parton model results at the leading twist and leading order in perturbative QCD and provide the expressions for these structure functions and polarizations in terms of parton distribution functions and fragmentation functions. We emphasize in particular that by studying the longitudinal polarization and the transverse polarization in the production plane, we can extract the corresponding chiral-odd fragmentation functions $H_{1Lq}^{\perp \Lambda }$, $H_{1Tq}^{\Lambda }$ and $H_{1Tq}^{\perp \Lambda }$. We also present numerical results of rough estimates utilizing available parameterizations of fragmentation functions and approximations. We discuss how to measure these polarizations and point out in particular that they can be carried out in future EIC and/or $e^{+}{e}^{-}$ annihilation experiments such as Belle.

13 pages, 7 figures; to be published on PRD

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Cited by in corpus (9)

• Transverse Lambda production at the future Electron-Ion Collider
• Several Topics on Transverse Momentum-Dependent Fragmentation Functions
• Transverse $\Lambda$ polarization in $e^{+}{e}^{-}$ processes within a TMD factorization approach and the polarizing fragmentation function
• Inclusive and semi-inclusive production of spin-3/2 hadrons in $e^{+}{e}^{-}$ annihilation
• Dihadron helicity correlation in photon-nucleus collisions
• Global analysis of fragmentation functions to light neutral hadrons
• Transverse spin polarization as a novel probe of medium-induced transverse-momentum-broadening effect
• Measurement of transverse polarization of $\Lambda$ and $\bar{\Lambda }$ hyperons inside jets in $pp$ collisions at $\sqrt{s}=200$ GeV
• Twist-3 Gluon Fragmentation Contribution to Hyperon Polarization in Semi-Inclusive Deep Inelastic Scattering