1-jettiness with jet axis at $O({\alpha }_s)$ in jeep inelastic scattering

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 $Q$.

32 pages, 5 figures, comments are welcome. v2: major revision including NLP expressions in (3.13) and (3.14) added, figure 5 revised, more discussions added

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