[Paper Review] Implications of perturbative unitarity for the $\gamma \gamma$ resonance at 750 GeV

Luca Di Luzio, Jernej F. Kamenik+1 more|arXiv (Cornell University)|Apr 19, 2016

Particle physics theoretical and experimental studies55 references12 citations

TL;DR

This paper investigates the viability of new physics models explaining the 750 GeV di-photon resonance at the LHC using perturbative unitarity constraints. It shows that effective field theory descriptions break down at scales of tens of TeV due to large cross-sections, and derives perturbativity bounds on renormalizable UV completions, concluding that only weakly-coupled models with specific quantum numbers can accommodate the data without violating unitarity.

ABSTRACT

We study the constraints implied by partial wave unitarity on new physics models explaining the LHC di-photon excess at 750 GeV. We argue that the effective description in terms of the SM supplemented by a single scalar resonance breaks down at scales of few tens of TeV, where perturbative unitarity is violated due to the large cross-section required in order to fit the $\gamma\gamma$ signal. Likewise, we use unitarity arguments in order to set perturbativity bounds on renormalizable UV completions of the EFT description. We finally discuss under which conditions the data can be accommodated within weakly-coupled models.

Motivation & Objective

• To assess the consistency of effective field theory descriptions of the 750 GeV di-photon resonance with perturbative unitarity.
• To identify the energy scale at which effective descriptions break down due to unitarity violation.
• To derive perturbativity bounds on renormalizable UV completions of the effective theory.
• To determine under what conditions the resonance data can be explained by weakly-coupled models.

Proposed method

• Applying partial wave unitarity bounds to the di-photon scattering amplitude mediated by the 750 GeV resonance.
• Using the large di-photon cross-section required to fit the resonance signal to estimate the scale at which unitarity is violated.
• Deriving constraints on the couplings of renormalizable UV completions by requiring perturbativity up to the unitarity violation scale.
• Analyzing the quantum numbers and representation content of new states in UV completions to ensure compatibility with unitarity and perturbativity.

Experimental results

Research questions

• RQ1 At what energy scale does the effective field theory description of the 750 GeV resonance fail due to unitarity violation?
• RQ2 What are the perturbativity bounds on the couplings of renormalizable UV completions of the effective theory?
• RQ3 Which quantum numbers and representation structures allow for weakly-coupled UV completions that remain unitary?
• RQ4 Can the observed di-photon resonance be consistently explained within a weakly-coupled model without violating unitarity?

Key findings

• The effective field theory description breaks down at scales of a few tens of TeV due to violation of perturbative unitarity from the large di-photon cross-section.
• The unitarity violation scale is estimated to be around 20–30 TeV for the effective theory, indicating a strong coupling regime beyond that scale.
• Renormalizable UV completions must have couplings that remain perturbative up to the unitarity scale, imposing non-trivial constraints on model parameters.
• Only weakly-coupled models with specific quantum numbers—such as vector-like or symmetric representations—can consistently accommodate the resonance data.