Electroweak Bloch-Nordsieck violation at the TeV scale: "strong" weak interactions ?

TL;DR

This paper shows that at TeV energies, electroweak double-logarithmic corrections do not cancel in inclusive observables due to the non-Abelian nature of initial-state weak charges, a Bloch-Nordsieck violation. It develops two complementary frameworks—a diagrammatic all-orders approach and a coherent-state formalism—to derive a universal, energy-dependent Sudakov suppression governed by the adjoint representation. The results yield a universal function L_W(s) that suppresses isospin-vector (LL) components while leaving singlet parts unchanged, and they quantify sizable, polarization-dependent corrections for lepton- and hadron-initiated processes. The findings have significant implications for collider phenomenology and suggest that EW effects must be integrated alongside QCD effects and potential new physics in high-energy factorization analyses.

Abstract

Hard processes at the TeV scale exhibit enhanced (double log) EW corrections even for inclusive observables, leading to violation of the Bloch-Nordsieck theorem. This effect, previously related to the non abelian nature of free EW charges in the initial state (e- e+, e- p, p p ...), is here investigated for fermion initiated hard processes and to all orders in EW couplings. We find that the effect is important, especially for lepton initiated processes, producing weak effects that in some cases compete in magnitude with the strong ones. We show that this (double log) BN violating effect has a universal energy dependence, related to the Sudakov form factor in the adjoint representation. The role of this form factor is to suppress cross section differences within a weak isospin doublet, so that at very large energy the cross sections for left-handed electron-positron and neutrino-positron scattering become equal. Finally, we briefly discuss the phenomenological relevance of our results for future colliders.

Figures (6)

• Figure 1: Unitarity diagrams for (a) virtual and (b) real emission contributions to lowest order initial state interactions in the Feynman gauge. Sum over gauge bosons a= $\gamma,Z,W$ and over permutations is understood.
• Figure 2: Resummed double log EW corrections to $e^+e^-\to$ hadrons and strong corrections (dashed line) up to 3 loops. The dash-dotted line is for a LL polarized beam, while the continuos line is for an unpolarized beam.
• Figure 3: Relative effects for $O=\frac{d\sigma}{d\cos\theta} (\nu_\mu \bar{e})$ and $O=\frac{d\sigma}{d\cos\theta} (u\bar{e})$ at $\sqrt{s}=$ 1 TeV and $\sqrt{s}=$ 5 TeV
• Figure 4: $\sigma_{12}$ and $\sigma_{11}$ as a function of energy. The vertical scale is arbitrary
• Figure 5: Soft dressing of the hard S-matrix $S_H$ is described by the coherent state operator ${\cal U}^I$ (a). At leading order, the latter is factorized into leg operators $U^{(i)}$ (b).