A Better Angle on Hadron Transverse Momentum Distributions at the EIC

Abstract

We propose an observable $q_{\ast }$ sensitive to transverse momentum dependence (TMD) in $eN\to ehX$, with $q_{\ast }/E_N$ defined purely by lab-frame angles. In 3D measurements of confinement and hadronization this resolves the crippling issue of accurately reconstructing small transverse momentum $P_{hT}$. We prove factorization for $\mathrm{d}{\sigma }_h/\mathrm{d}{q}_{\ast }$ for $q_{\ast }\ll Q$ with standard TMD functions, enabling $q_{\ast }$ to substitute for $P_{hT}$. A double-angle reconstruction method is given which is exact to all orders in QCD for $q_{\ast }\ll Q$. $q_{\ast }$ enables an order-of-magnitude improvement in the expected experimental resolution at the EIC.

Comments: 5 pages + 4 figures, 9 pages of supplemental material