1-jettiness with jet axis at $O(\alpha_s)$ in jeep inelastic scattering

TL;DR

This paper provides $O(\alpha_s)$ analytic predictions for the 1-jettiness distribution in deep inelastic scattering, considering different jet axes, and discusses how fixed-order results complement resummation for future collider measurements.

Contribution

It introduces $O(\alpha_s)$ calculations of 1-jettiness with various jet axes in DIS, clarifying axis dependence and aiding combined fixed-order and resummed analyses.

Findings

First and second axis choices yield identical results at this order.

The third axis choice depends on jet radius R.

The fixed-order results inform the combination with resummation techniques.

Abstract

We present $O(\alpha_s)$ analytic predictions for event shape 1-jettiness $\tau_1$ 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 $\tau_1$ and is relatively compact and easy to implement for numerical calculation. Three different choices of axis, with respect to which $\tau_1$ is measured are considered in the Breit frame. The first is the one optimally adjusted to minimize $\tau_1$ and the second and third are taken from anti-$k_T$ 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 $\tau_1$ space and also shows how fixed-order and resummation regions change as a function of $x$ and $Q$.