Mass gap effects and higher order electroweak Sudakov logarithms

TL;DR

The paper addresses the problem of large electroweak double-logarithmic corrections at TeV scales and the potential impact of the photon–Z mass gap on Sudakov resummation. It presents a direct two-loop calculation using physical Standard Model fields in the Feynman gauge for the process g -> f_R anti-f_L and demonstrates that the DL terms exponentiate, consistent with infrared evolution equation methods. The results corroborate exponentiation through two loops and show that the mass gap does not spoil the resummation, contradicting claims of non-exponentiating contributions. This clarifies the theoretical structure of electroweak Sudakov logs and reinforces the reliability of high-energy resummation in spontaneously broken gauge theories.

Abstract

The infrared structure of spontaneously broken gauge theories is phenomenologically very important and theoretically a challenging problem. Various attempts have been made to calculate the higher order behavior of large double-logarithmic (DL) corrections originating from the exchange of electroweak gauge bosons resulting in contradictory claims. We present results from two loop electroweak corrections for the process $g \longrightarrow f_{\rm R} {\bar f}_{\rm L}$ to DL accuracy. This process is ideally suited as a theoretical model reaction to study the effect of the mass gap of the neutral electroweak gauge bosons at the two loop level. Contrary to recent claims in the literature, we find that the calculation performed with the physical Standard Model fields is in perfect agreement with the results from the infrared evolution equation method. In particular, we can confirm the exponentiation of the electroweak Sudakov logarithms through two loops.

Figures (3)

• Figure 1: The electroweak SM Feynman rules employed in this work. For the propagators (modulo $g^{\mu \nu}$), we use the Feynman gauge. The neutral Z-boson couples to right handed fermions through a rescaled QED-like coupling. The Dirac-algebra is therefore identical to the Abelian case.
• Figure 2: The one loop electroweak SM Feynman diagrams leading to DL corrections in the Feynman gauge for $g \longrightarrow f_{\rm R} {\overline f}_{\rm L}$. Only the vertex corrections from the neutral Z-boson (zigzag-lines) and the photon propagators contribute. At higher orders only corrections to these two diagrams need to be considered in the DL approximation. The photonic corrections are regulated by a fictitious mass terms $\lambda$. In physical cross sections, the $\lambda$-dependence is canceled by the effect of the emission of soft and collinear bremsstrahlung photons.
• Figure 3: The two loop electroweak SM Feynman diagrams leading to DL corrections in the Feynman gauge for $g \longrightarrow f_{\rm R} {\overline f}_{\rm L}$. The neutral Z-boson (zigzag-lines) and the photon propagators possess different on-shell regions due to the mass gap.