Aspects of CP violation in the HZZ coupling at the LHC

TL;DR

This paper develops a model‑independent framework to probe CP violation in the Higgs coupling to ZZ using the decay channel $H\to ZZ^{(*)}\to 4\ell$ at the LHC. It introduces a general $HZZ$ vertex with CP‑even and CP‑odd form factors and derives the complete angular distribution, enabling both total rate tests and CP/CP̃T‑odd observables. A set of asymmetries (from $O_i$ and $A_i$) is constructed to directly access the real and imaginary parts of the non‑SM form factors, with several asymmetries showing potentially observable signals at the LHC given sizable couplings. The study also analyzes kinematic distributions (phases, angles, and threshold behavior) as complementary CP probes, particularly valuable for lighter Higgs masses where event rates are limited. Together, these methods provide a path to extract all CP‑related HZZ couplings and to test CP violation in the Higgs sector using $H\to ZZ^{(*)}\to 4\ell$ data.

Abstract

We examine the CP-conserving (CPC) and CP-violating (CPV) effects of a general HZZ coupling through a study of the process H -> ZZ* -> 4 leptons at the LHC. We construct asymmetries that directly probe these couplings. Further, we present complete analytical formulae for the angular distributions of the decay leptons and for some of the asymmetries. Using these we have been able to identify new observables which can provide enhanced sensitivity to the CPV $H ZZ$ coupling. We also explore probing CP violation through shapes of distributions in different kinematic variables, which can be used for Higgs bosons with mH < 2 mZ.

Figures (17)

• Figure 1: The definition of the polar angles ${\theta_i}$ ($i=1,2$) and the azimuthal angle $\phi$ for the sequential decay $H \rightarrow ZZ^{(*)} \rightarrow (f_1\bar{f}_1) \, (f_2\bar{f}_2)$.
• Figure 2: The number of standard deviations from the SM which can be obtained in the process $gg\to H\to Z^* Z^* \to 4$leptons, as a scan over the $(a,|c|)$ plane. The Higgs mass has been chosen to be $150\,$GeV (left) and $200\,$GeV (right). The white region is where the deviation from the SM is less than $3 \, \sigma$; in the light blue/light grey region the deviation is between $3\,\sigma$ and $5\,\sigma$; while for the dark blue/dark grey region the deviation is greater than $5\,\sigma$.
• Figure 3: The normalized differential width for $H \rightarrow Z Z \rightarrow (f_1\bar{f}_1)\,(f_2\bar{f}_2)$ and $m_H=200\,$ GeV with respect to the cosine of the fermion $f_1$'s polar angle $\theta_1$. The solid (black) curve shows the SM case ($a=1$, $b=c=0$) while the dashed (blue) curve is for a pure CP-odd state ($a=b=0$, $c=i$). The dot-dashed (red) curve is for a state with a CP violating coupling ($a=1$, $b=0$, $c=i$). One can clearly see an asymmetry about $\cos \theta_1=0$ for the CP violating case.
• Figure 4: The asymmetry ${\cal A}_1$ given by Eq. (\ref{['gmm_asym1_eq']}) as a function of the ratio $\Im m(c)/a$, for a Higgs boson of mass $150\,$GeV ( left) and 200 GeV ( right). We chose $b=0$. The inserts show the same quantities for a larger range of $\Im m(c)/a$.
• Figure 5: The significances corresponding to the asymmetry ${\cal A}_1$ as a function of $\Im m(c)$, for a Higgs boson of mass $150\,$GeV ( left) and 200 GeV ( right). We chose the CP-even coupling coefficient $a=1$ and $b=0$. The inserts show the same quantities for a larger range of $\Im m(c)$.