Factorization Beyond Coherence

Abstract

We derive a novel factorization theorem for $N$-jettiness at hadron colliders, which incorporates coherence-violating effects induced by Glauber gluons and several new momentum modes. Their interplay generates coherence-violating logarithms (CVLs) starting at four-loop ($N\ge1$) or five-loop order ($N=0$). We calculate the anomalous dimensions required for the resummation of CVLs and establish a general framework for the systematic treatment of coherence violation. Our findings imply that most existing factorization formulas for global LHC observables must be revised.

Figures (3)

• Figure 1: Examples of factorization-breaking diagrams at the collinear (top) and ultra-soft (bottom) scales. A space-like collinear splitting (blue) connects to soft modes (orange) through Glauber-gluon exchange (red dashed). A colored blob indicates a measurement on the respective line, and $\mathcal{M}_N$ denotes the hard scattering amplitude.
• Figure 2: Scale hierarchy and mode structure for $N$-jettiness, color coded for their appearance in diagrams. The soft modes at the collinear scale $(\mathcal{T}_N{\space} Q)^{1/2}$ may only appear as virtual particles, while the ultra-collinear modes at the ultra-soft scale $\mathcal{T}_N$ do not contribute to the measurement.
• Figure 3: Mapping of the one-loop space-like splitting function onto a box diagram. The external momentum of the double line is off-shell, $(p_c-q_c+p_{\bar{c}})^2\neq 0$.