Abstract
We calculate analytically the two-loop triangle integrals entering the $\mathcal{O}(\alpha\alpha_s)$ corrections to the $HZV$ vertex with $V=Z^*,\gamma^*$ using the method of differential equations. Our result provides a prototype to study the analytic properties of multi-loop multi-scale Feynman integrals, and also allows fast numeric evaluation for phenomenological studies. We apply our results to the leptonic decay of the Higgs boson and to $ZH$ production at electron-positron colliders. Besides the top quark loop, we include also the bottom quark loop contributions, whose evaluation takes a lot of time using purely numeric methods, but is very efficient with our analytic results.
Highlights
The HZV vertex, where V 1⁄4 ZÃ; γÃ, is relevant for several important processes in Higgs physics, such as the leptonic decay H → ZÃZà → 4l which is crucial in the discovery of the Higgs boson and is important for measuring its mass and width
Given the disadvantage of the purely numeric method and the limited applicability of various approximations, the goal of this paper is to provide an exact analytic solution to the master integrals appearing in the OðααsÞ corrections to the HZV vertex
Thanks to our analytic results, it is much faster to perform the numeric computation compared to purely numeric methods such as sectoprffiffidecomposition
Summary
The HZV vertex, where V 1⁄4 ZÃ; γÃ, is relevant for several important processes in Higgs physics, such as the leptonic decay H → ZÃZà → 4l which is crucial in the discovery of the Higgs boson and is important for measuring its mass and width. The vertex enters the production of the Higgs boson through vector boson fusion (ZZ → H) at the Large Hadron Collider (LHC), as well as the associate production of the Higgs boson with a Z boson (pp → ZH) at the LHC and at future Higgs factories (eþe− → ZH). The HZV vertex probes the electroweak symmetry breaking mechanism of the standard model, and is sensitive to alternative models of the Higgs sector. If the Higgs is a composite Goldstone boson, the tree-level HZZ coupling is modified by Oðv2=f2Þ which can be as large as a few percent if the symmetry breaking scale f is in the TeV range. Precise knowledge of the HZV vertex is essential for the quest to better understand the properties of the Higgs boson and the mechanism of electroweak phase transition.
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