Better angle on hadron transverse momentum distributions at the Electron-Ion Collider

We propose an observable q* sensitive to transverse momentum dependence (TMD) in eN -> ehX, with q*=EN defined purely by lab-frame angles. In 3D measurements of confinement and hadronization this resolves the crippling issue of accurately reconstructing small transverse momentum PhT. We prove factorization for d sigma h=dq* for q* MUCH LESS-THAN Q with standard TMD functions, enabling q* to substitute for PhT. A double-angle reconstruction method is given which is exact to all orders in QCD for q* MUCH LESS-THAN Q. q* enables an order-of-magnitude improvement in the expected experimental resolution at the EIC.