N-Jettiness as a probe of nuclear dynamics

Abstract

We propose the use of N-jettiness (τ_N), a global event shape variable, 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 write down the factorization for the 1-jettiness ($τ_1$) distribution for the production of a single hard jet (J) in lepton-nucleus collisions: \ell+A(P) \to J(P_{J})+X. Each nuclear target gives rise to a unique pattern radiation, determined by nuclear dynamics, that can be quantified by the τ_1-distribution. Up to power corrections, the τ_1-distribution allows for a direct measurement of the nuclear PDFs. Additional nuclear-dependent effects will be dominated through power corrections of size $\sim Q_s^2(A)/(P_{JT}τ_1)$ where $Q_s(A)$ is a dynamical scale sensitive to nuclear medium effects. Such nuclear-dependent effects and the dependence of Q_s(A) on the nuclear atomic number $A$ can be probed through a dedicated program of precision measurements of τ_1-distributions for various 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.

Figures (2)

• Figure 1: $d\sigma / \sigma_0\equiv \frac{1}{\sigma_0}\frac{d^3\sigma}{dy dP_{JT} d\tau_1}$ as a function $\tau_1$ for a proton target at NLL accuracy. The bottom and top bands correspond to $\sqrt{s}=90 \>\text{GeV}, P_{JT}=20 \>\text{GeV}, y=0$ (Stage I EIC) and $\sqrt{s}=300\>\text{GeV}, P_{JT}=20 \>\text{GeV},y=0$ (HERA) respectively. The dashed curve shows the singular part of the NLO cross-section for HERA kinematics. The scale choices for $\mu_H,\mu_J,\mu_S$ are explained in the text.
• Figure 2: $d\sigma / \sigma_0\equiv \frac{1}{\sigma_0}\frac{d^3\sigma}{dy dP_{JT} d\tau_1}$ as a function $\tau_1$ for a proton target at NLL accuracy including non-perturbative $\tau_1$ values with $\sqrt{s}=300$ GeV, $P_{JT}= 20$ GeV, and $y=0$. The different curves with peak positions from left to right correspond to $(a,b,\Lambda)=(2.0, -0.2, 0.2), (1.2, -0.1, 0.3), (2.2, -0.4, 0.5),\\(1.8, -0.05, 0.4)$ in Eq. (\ref{['fmod']}) respectively.