  We predict cross sections in deep inelastic scattering (DIS) for the
production of two jets---one along the proton beam direction created by initial
state radiation (ISR) and another created by final state radiation after the
hard collision. Our results include fixed order corrections and a summation of
large logarithms up to next-to-next-to-leading logarithmic (NNLL) accuracy in
resummed perturbation theory. We make predictions for three versions of a DIS
event shape 1-jettiness, each of which constrains hadronic final states to be
well collimated into two jets along the beam and final-state jet directions,
but which differ in their sensitivity to the transverse momentum of the ISR
from the proton beam. We use the tools of soft collinear effective theory
(SCET) to derive factorization theorems for these three versions of
1-jettiness. The sensitivity to the ISR gives rise to significantly different
structures in the corresponding factorization theorems---for example,
dependence on either the ordinary or the generalized kperp-dependent beam
function. Despite the differences among 1-jettiness definitions, we show that
the leading nonperturbative correction that shifts the tail region of their
distributions is given by a single universal nonperturbative parameter Omega1,
even accounting for hadron mass effects. Finally, we give numerical results for
Q^2 and x values explored at the HERA collider, emphasizing that the target of
our factorization-based analyses is to open the door for higher-precision jet
phenomenology in DIS.
