The one-jettiness distribution contains super-super-leading logarithms
Andrea Banfi, Jeffrey R. Forshaw, Jack Holguin
TL;DR
The paper shows that one-jettiness $\tau_1$ in colour-singlet plus jet production hosts super-leading coherence-violating logarithms beginning at $\alpha_s^4 L^6$ with $L = \ln(1/\tau_1)$, contradicting previous claims of no such logs. Using a coherence-violation framework with Coulomb gluon exchanges and a Sudakov operator, the authors derive an explicit CVL contribution, revealing a color-structure-dependent, $N_c$-suppressed but nonzero effect: $\frac{d\sigma_1^{\rm CVL}}{dx_a dx_b d\mathcal{B}} \approx \sum_a A_a \left(\frac{\alpha_s}{\pi}\right)^4 (-i\pi)^2 \frac{1}{480} (\ln\frac{1}{\tau_1})^6$, with higher orders scaling as $\alpha_s^n L^{2n-2}$ for $n\ge4$. This leads to a revised understanding of log counting for global observables and highlights significant challenges for resumming such logs in $\tau_1$, potentially requiring many soft-gluon insertions or numerical approaches. The findings imply important implications for LHC analyses using $\tau_1$, motivate further theoretical development in EFT and resummation, and reinforce the role of PDFs and factorization at the scale $\tau_1 Q$ in preserving well-defined soft contributions.
Abstract
We show that one-jettiness ($τ_1$) in colour-singlet plus jet production suffers from super-leading logarithms starting at order $α_{\mathrm s}^4 \ln(1/τ_1)^6$ relative to the Born level. This is one logarithm more dominant than any previously identified super-leading logarithms. The extra logarithm is not associated with additional poles, and is therefore consistent with the factorization of universal parton distribution functions at scale $τ_1 Q$, where $Q$ is the hard scale.