1-Jettiness with Jet axis at $O(\alpha_s)$ in Deep Inelastic Scattering

We present O(αs) analytic predictions for event shape 1-jettiness τ1 distribution aiming measurements in deep inelastic scattering process at future Electron Ion Colliders. The result depends on conventional variables x and Q as well as on τ1 and is relatively compact and easy to implement for numerical calculation. Three different choices of axis, with respect to which τ1 is measured are considered in the Breit frame. The first is the one optimally adjusted to minimize τ1 and the second and third are taken from anti-kT and Centauro jet algorithms defined with a jet radius parameter R, respectively. We find that the first and second give the same result at this order and are independent of R, while the third depends on the radius. This fixed-order result provides a nonsingular contribution to be combined with a singular log-resummed contribution to give the full spectrum in τ1 space and also shows how fixed-order and resummation regions change as a function of x and Q. *These authors made main contributions equally to this work. ar X iv :2 20 2. 08 04 0v 1 [ he pph ] 1 6 Fe b 20 22