Transverse Lambda production at the future Electron-Ion Collider

TL;DR

This paper explores how the future Electron-Ion Collider can measure transverse Lambda polarization and spin transfer, significantly improving constraints on related TMD fragmentation functions through projections and impact studies.

Contribution

It provides the first impact study of EIC projections on TMD polarization functions and performs the first extraction of transversity TMD FF from recent data.

Findings

EIC projections will significantly reduce uncertainties in TMD PFFs.

EIC can constrain transversity TMD FF more effectively than current data.

Impact studies show potential for precise measurements of Lambda polarization at the EIC.

Abstract

We provide a comprehensive overview of transversely polarized $\Lambda$ production at the future Electron-Ion Collider (EIC). In particular, we study both spontaneous transverse $\Lambda$ polarization as well as the transverse spin transfer within the Transverse Momentum Dependent (TMD) factorization region. To describe spontaneous $\Lambda$ polarization, we consider the contribution from the TMD Polarizing Fragmentation Function (TMD PFF). Similarly, we study the contribution of the transverse spin transfer originating from the transversity TMD Fragmentation Function (TMD FF). We provide projections for the statistical uncertainties in the corresponding spin observables at the future EIC. Using these statistical uncertainties, we characterize the role that the future EIC will play in constraining these distributions. We perform an impact study in the semi-inclusive deep inelastic scattering process for spontaneous $\Lambda$ polarization with a proton beam. We find that the projected experimental data leads to a significant decrease in the uncertainties for the $u$ and sea TMD PFFs. Furthermore, to access the impact of the EIC on the transversity TMD FF, we perform the first extraction of the transversity TMD FF from the recent COMPASS data. We compare the statistical uncertainties of the future EIC with the theoretical uncertainties from our extraction and find that the EIC could have a significant role in constraining this distribution. Finally, we also provide projections for both spontaneous $\Lambda$ polarization as well as the transverse spin transfer inside the jets in back-to-back electron-jet production at the EIC.