[Paper Review] The "forgotten" decay S -> Z+h as a CP analyzer

Martin Bauer, Matthias Neubert+1 more|arXiv (Cornell University)|Jul 4, 2016

Particle physics theoretical and experimental studies7 citations

TL;DR

This paper proposes the decay $S \to Zh$ as a CP-odd scalar probe, showing it is forbidden for CP-even scalars but allowed only if $S$ has CP-odd couplings. Using an effective field theory approach, the authors compute one-loop contributions from heavy fermions and find that the $S \to Zh$ rate can be comparable to or larger than the $S \to \gamma\gamma$ rate for a 750 GeV resonance, making it a powerful, model-independent CP analyzer.

ABSTRACT

Scalar particles $S$ which are gauge singlets under the Standard Model are generic features of many models of fundamental physics, in particular as possible mediators to a hidden or dark sector. We show that the decay $S o Zh$ provides a powerful probe of the CP nature of the scalar, because it is allowed only if $S$ has CP-odd interactions. We perform a model-independent analysis of this decay in the context of an effective Lagrangian and compute the relevant Wilson coefficients arising from integrating out heavy fermions to one-loop order. We illustrate our findings with the example of the 750 GeV diphoton resonance seen by ATLAS and CMS and show that the $S o Zh$ decay rate could naturally be of similar magnitude or larger than the diphoton rate.

Motivation & Objective

• To identify a model-independent, clean CP-odd signature for a heavy gauge-singlet scalar $S$ beyond the Standard Model.
• To demonstrate that the decay $S \to Zh$ is forbidden for CP-even scalars but allowed only if $S$ has CP-odd couplings.
• To compute the one-loop contributions to $S \to Zh$ via heavy fermion integration in an effective Lagrangian framework.
• To assess the phenomenological viability of $S \to Zh$ for the 750 GeV diphoton resonance observed by ATLAS and CMS.
• To show that $S \to Zh$ can have a rate comparable to or larger than the $S \to \gamma\gamma$ rate, making it a promising discovery channel.

Proposed method

• Construct a model-independent effective Lagrangian at dimension-5 and dimension-7 operators to describe $S$ couplings to $Zh$.
• Compute one-loop amplitudes involving heavy vector-like fermions, integrating them out to determine Wilson coefficients.
• Use dimensional regularization and analytic continuation to handle logarithmic and imaginary parts in loop integrals.
• Derive the Wilson coefficient $C_7$ for the dimension-7 operator $O_7$, which governs the $S \to Zh$ amplitude at leading order.
• Perform numerical estimates of the decay rate using $C_7$ and compare with the $S \to \gamma\gamma$ rate for benchmark scenarios.
• Analyze two explicit models: a sequential fourth-generation lepton model and a vector-like quark doublet model to illustrate phenomenological reach.

Experimental results

Research questions

• RQ1 Can the decay $S \to Zh$ serve as a model-independent CP analyzer for a heavy gauge-singlet scalar $S$?
• RQ2 What is the size of the $S \to Zh$ decay amplitude in the absence of tree-level $S$ couplings to SM particles?
• RQ3 How does the $S \to Zh$ rate compare to the $S \to \gamma\gamma$ rate for a 750 GeV resonance?
• RQ4 Can the $S \to Zh$ decay be enhanced in weakly coupled models with heavy vector-like fermions?
• RQ5 What are the implications of observing $S \to Zh$ for ruling out spin-2 or CP-even scalar explanations of the 750 GeV diphoton excess?

Key findings

• The decay $S \to Zh$ is strictly forbidden for a CP-even scalar but is allowed only if $S$ has CP-odd couplings, making it a clean CP analyzer.
• The $S \to Zh$ amplitude arises at dimension-5 via top-quark loops or from a dimension-7 operator $O_7$ induced by integrating out heavy fermions.
• The Wilson coefficient $C_7$ for the dimension-7 operator is estimated to be $C_7 \approx 0.036\,c_1 + 0.011\,\tilde{c}_{tt}$ for $g_t = g_b = 1$, and $C_7 \approx 0.29\,c_1 - 0.15\,\tilde{c}_{tt}$ for $g_t = 2$, $g_b = 0.5$.
• For $M \lesssim 1$ TeV, the $pp \to S \to Zh$ rate can naturally reach 1–10 fb, comparable to or exceeding the $S \to \gamma\gamma$ rate.
• In a model with a sequential fourth-generation lepton doublet, the $S \to Zh$ rate can reach up to 73 fb, near the current experimental bound.
• In a weakly coupled model with a vector-like quark doublet, the $S \to Zh$ rate is in the 1–10 fb range and can simultaneously explain the $b$-quark forward-backward asymmetry at the $Z$ pole.