Two-Loop Threshold Singularities, Unstable Particles and Complex Masses

TL;DR

The paper tackles threshold singularities in two-loop electroweak corrections arising from unstable particles. It develops and applies the complex-mass scheme, comparing a minimal implementation with a full complex-mass approach. The authors show that full complex masses remove unphysical cusps at vector-boson thresholds and yield controlled electroweak corrections for Higgs production via gluon fusion and decay to two photons. The results highlight the importance of corresponding gauge-invariant treatments for accurate LHC Higgs phenomenology near WW/ZZ thresholds.

Abstract

The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact on radiative corrections around thresholds is thoroughly analyzed and shown to be relevant for two selected LHC and ILC applications: Higgs production via gluon fusion and decay into two photons at two loops in the Standard Model. Concerning Higgs production, it is essential to understand possible sources of large corrections in addition to the well-known QCD effects. It is shown that NLO electroweak corrections can incongruently reach a 10 % level around the WW vector-boson threshold without a complete implementation of the complex-mass scheme in the two-loop calculation.

Figures (7)

• Figure 1: Sample cut diagrams for $H \to \gamma \gamma$ showing normal thresholds for $M_{_H}=2M_{_W},2M_{_Z},2M_t$.
• Figure 2: Sample diagrams for the Higgs wave-function renormalization factor at one loop.
• Figure 3: Two-loop and mass-renormalization diagrams relevant for the analysis of square-root singularities. Gray circles represent the sum of all one-loop two-point diagrams; black dots denote a derivative.
• Figure 4: Irreducible two-loop vertex diagrams which can generate a logarithmic divergency.
• Figure 5: Percentage NLO electroweak corrections to the partial width for $H\to \gamma \gamma$; here $\Gamma^{\rm NLO}= \Gamma^{\rm LO}(1+\delta_{\rm EW})$. MCM (CM) scheme is described in Section \ref{['sec:MCMscheme']} ($4.2$). Setup is described in Section \ref{['numa']}.