N-jet event shapes as probes of nuclear dynamics

Abstract

We propose the use of $N$-jettiness (${\ensuremath{\tau}}_{N}$), a global event shape, as a probe of nuclear dynamics in lepton-nucleus collisions. It characterizes the amount of soft radiation between the jet and nuclear beam directions. We give a new factorization formula for the 1-jettiness (${\ensuremath{\tau}}_{1}$) distribution for the production of a single hard jet ($J$) in lepton-nucleus collisions: $\ensuremath{\ell}+A(P)\ensuremath{\rightarrow}J({P}_{J})+X$. Each nuclear target gives rise to a unique pattern of radiation, affected by nuclear dynamics, that can be quantified by the ${\ensuremath{\tau}}_{1}$ distribution. Up to power corrections, the ${\ensuremath{\tau}}_{1}$ distribution allows for a direct measurement of the nuclear parton distribution functions. Additional nuclear-dependent effects will be dominated through power corrections of size $\ensuremath{\sim}{Q}_{s}^{2}(A)/({\ensuremath{\tau}}_{1}{P}_{JT})$, where ${Q}_{s}(A)$ is a dynamical nuclear scale and ${P}_{JT}$ is the transverse momentum of the jet. Such nuclear-dependent effects can be studied through a dedicated program to measure ${\ensuremath{\tau}}_{1}$ distributions for a range of nuclei and kinematics. We give numerical results for the 1-jettiness distribution for the simplest case of a proton target at next-to-leading-log accuracy.