Analytic Calculation of 1-Jettiness in DIS at $\mathcal O(\alpha_s)$

Abstract

We present an analytic $\mathcal O(\alpha_s)$ calculation of cross sections in deep inelastic scattering (DIS) dependent on an event shape, 1-jettiness, that probes final states with one jet plus initial state radiation. This is the first entirely analytic calculation for a DIS event shape cross section at this order. We present results for the differential and cumulative 1-jettiness cross sections, and express both in terms of structure functions dependent not only on the usual DIS variables $x$, $Q^2$ but also on the 1-jettiness $\tau$. Combined with previous results for log resummation, predictions are obtained over the entire range of the 1-jettiness distribution.