  The 1-Jettiness (tau_1) event shape for Deep Inelastic Scattering (DIS),
allows for a quantitative and global description of the pattern of QCD
radiation for single jet (J) production in electron-nucleus (N_A) collisions
e^- + N_A \to e^- + J + X. It allows for precision studies of QCD and is a
sensitive probe of nuclear structure and dynamics. The large transverse
momentum (P_{J_T}) of the final state jet $J$, characterizes the hard scale in
the problem. The region of phase space where tau_1 << P_{J_T}, corresponds to
configurations where energetic radiation (E~ P_{J_T}) is only along either the
single jet direction or the beam direction with only soft radiation (E ~ \tau_1
<<P_{J_T}) in between. Thus, the restriction tau_1 << P_{J_T} corresponds to a
veto on additional jets and leads to large Sudakov logarithms of \tau_1/P_{J_T}
that must be resummed. Based on a factorization framework, derived using the
Soft Collinear Effective Theory (SCET), we provide resummation results at the
NNLL level of accuracy and match them onto the NLO result in fixed order
perturbation theory, appropriate in the \tau_1 \sim P_{J_T} region where
additional jets and hard radiation are allowed. The \tau_1-distribution depends
on the jet algorithm used to find the leading jet in the region tau_1 ~
P_{J_T}, unlike the resummation region where this dependence is power
suppressed in tau_1/P_{J_T} << 1. We give results for the entire tau_1
spectrum, with a smooth matching between the resummation region and fixed-order
region, where we make use of the anti-kt jet algorithm. The 1-Jettiness event
shape can be a powerful probe of nuclear and QCD dynamics at future
electron-ion colliders and by analyzing existing HERA data.

High Energy Physics - Phenomenology