Resummation of Yukawa enhanced and subleading Sudakov logarithms in longitudinal gauge boson and Higgs production

TL;DR

The paper develops a complete all-orders resummation of universal Yukawa-enhanced and subleading Sudakov logarithms for longitudinal gauge boson and Higgs production in the electroweak sector. It combines an effective high-energy theory with the Goldstone boson equivalence, virtual splitting functions, and a non-Abelian Gribov factorization check to demonstrate exponentiation of these subleading terms. The framework reproduces known one-loop results and reveals that Yukawa-enhanced SL logs can be sizable at TeV scales, often comparable to or larger than DL terms, making their inclusion essential for precision predictions at future linear colliders. It also provides explicit semi-inclusive cross-section formulas integrating high- and low-scale physics and confirms the universality of these corrections across external states, while noting residual non-universal angular terms beyond this order.

Abstract

Future colliders will probe the electroweak theory at energies much larger than the gauge boson masses. Large double (DL) and single (SL) logarithmic virtual electroweak Sudakov corrections lead to significant effects for observable cross sections. Recently, leading and subleading universal corrections for external fermions and transverse gauge boson lines were resummed by employing the infrared evolution equation method. The results were confirmed at the DL level by explicit two loop calculations with the physical Standard Model (SM) fields. Also for longitudinal degrees of freedom the approach was utilized for DL-corrections via the Goldstone boson equivalence theorem. In all cases, the electroweak Sudakov logarithms exponentiate. In this paper we extend the same approach to both Yukawa enhanced as well as subleading Sudakov corrections to longitudinal gauge boson and Higgs production. We use virtual contributions to splitting functions of the appropriate Goldstone bosons in the high energy regime and find that all universal subleading terms exponentiate. The approach is verified by employing a non-Abelian version of Gribov's factorization theorem and by explicit comparison with existing one loop calculations. As a side result, we obtain also all top-Yukawa enhanced subleading logarithms for chiral fermion production at high energies to all orders. In all cases, the size of the subleading contributions at the two loop level is non-negligible in the context of precision measurements at future linear colliders.

Figures (6)

• Figure 1: A Feynman diagram determining the DL and SL contributions to scalar quarks in the on-shell scheme. In the massless theory there are scaling violations from loop corrections which can be described by anomalous dimensions.
• Figure 2: The pictorial Goldstone boson equivalence theorem for $W$-pair production in $e^+e^-$ collisions. The correct DL-asymptotics for longitudinally polarized bosons are obtained by using the quantum numbers of the charged would be Goldstone scalars at high energies.
• Figure 3: Feynman diagrams contributing to the infrared evolution equation (\ref{['eq:mrg']}) for a process with $n$ external scalar quarks. In a general covariant gauge the virtual gluon with the smallest value of ${\hbox{\boldmath $k$}}_{\perp}$ is attached to different external lines. The inner scattering amplitude is assumed to be on the mass shell.
• Figure 4: A Feynman diagram yielding Yukawa enhanced logarithmic corrections in the on-shell scheme. At higher orders, the subleading corrections are given in factorized form according to the non-Abelian generalization of Gribov's theorem as described in the text. Corrections from gauge bosons inside the top-loop give only sub-sub leading contributions. DL-corrections at two and higher loop order are given by gauge bosons coupling to (in principle all) external legs as schematically indicated.
• Figure 5: A Feynman diagram yielding Yukawa enhanced logarithmic corrections to external longitudinal Z-bosons and Higgs lines in the on-shell scheme. At higher orders, the subleading corrections are given in factorized form according to the non-Abelian generalization of Gribov's theorem as described in the text. Corrections from gauge bosons inside the top-loop give only sub-sub leading contributions.