The Higgs Mechanism and Loop-induced Decays of a Scalar into Two Z Bosons

TL;DR

The authors analyze general on-shell scalar couplings to ZZ via an effective Lagrangian containing a tree-level Higgs-like term and loop-induced dimension-five operators. They derive helicity amplitudes for S→ZZ→4ℓ and show that a CP-odd operator induces a phase shift in the azimuthal angle between the Z decay planes, enabling discrimination of operator structure. They explore new-physics scenarios that yield loop-induced S→ZZ decays, compute the associated partial widths from fermion and W′/gauge-boson loops, and argue that a loop-induced scalar would generally have a total width far smaller than a SM Higgs, making width and angular observables powerful probes of the scalar’s nature. The study demonstrates how combining line-shape and angular-distribution measurements at the LHC can distinguish Higgs-like resonances from non-Higgs-like scalars in ZZ final states, even in early data.

Abstract

We discuss general on-shell couplings of a scalar with two Z bosons using an operator analysis. In addition to the operator originated from the Higgs mechanism, two dimension-five operators, one CP-even and one CP-odd, are generated only at the loop-level. Simple formulas are derived for the differential decay distributions when the Z pair subsequently decay into four leptons by computing the helicity amplitudes, from which it is shown the CP-odd operator merely induces a phase shift in the azimuthal angular distribution between the two decay planes of the Z bosons. We also investigate new physics scenarios giving rise to loop-induced decays of a scalar into ZZ pair, and argue that the total decay width of such a scalar would be order-of-magnitude smaller than that of a Higgs boson, should such decays be observed in the early running of the LHC. Therefore, the total decay width alone is a strong indicator of the Higgs nature, or the lack thereof, of a scalar resonance in ZZ final states. In addition, we study the possibility of using the azimuthal angular distribution to disentangle effects among all three operators.

Figures (4)

• Figure 1: Two decay planes of $Z_1\to \ell_1\bar{\ell}_1$ and $Z_2\to \ell_2\bar{\ell}_2$ define the azimuthal angle $\phi\in[0,2\pi]$ which rotates $\ell_2$ to $\ell_1$ in the transverse view. The polar angles $\theta_1$ and $\theta_2$ shown are defined in the rest frame of $Z_1$ and $Z_2$, respectively.
• Figure 2: The dashed line is the total decay width for a SM Higgs boson and the solid line is that of a scalar $S$ whose width is three orders of magnitude smaller. The yellow (shaded) region is the detector resolution.
• Figure 3: The $ZZ$ invariant mass distribution for a SM Higgs boson and a scalar $S$ decaying through loop-induced effects, using a 2 GeV bin size. The narrow width of $S$ is below the detector resolution, resulting in a concentration of all events in just one bin. Note that for a sufficiently small bin size one would resolve the peak, albeit with a form which is dominated by the detector resolution (a Gaussian, if the usual assumptions of detector smearing are made). In the plot we assume the event rate of $gg\to S\to ZZ\to 4\ell$ is only 10% of rate for the SM Higgs boson.
• Figure 4: The normalized azimuthal angular distributions for 200 and 400 GeV scalar masses, turning on one operator at a time.