Is the New Resonance Spin 0 or 2? Taking a Step Forward in the Higgs Boson Discovery

Abstract: The observation of a new boson of mass $\sim 125\gev$ at the CERN LHC may finally have revealed the existence of a Higgs boson. Now we have the opportunity to scrutinize its properties, determining its quantum numbers and couplings to the standard model particles, in order to confirm or not its discovery. We show that by the end of the 8 TeV run, combining the entire data sets of ATLAS and CMS, it will be possible to discriminate between the following discovery alternatives: a scalar $J^P=0^+$ or a tensor $J^P=2^+$ particle with minimal couplings to photons, at a $5σ$ statistical confidence level at least, using only diphotons events. Our results are based on the calculation of a center-edge asymmetry measure of the reconstructed {\it sPlot} scattering polar angle of the diphotons. The results based on asymmetries are shown to be rather robust against systematic uncertainties with comparable discrimination power to a log likelihood ratio statistic.

• The paper introduces a novel methodological approach using center-edge asymmetry and the sWeight technique to discriminate between scalar (0+) and tensor (2+) spin states in diphoton events.
• It demonstrates that, even with significant detector effects and a high background ratio, a 5σ discrimination can be achieved with 10–15 fb⁻¹ of data per experiment.
• The study shows that angular distribution analysis via center-edge asymmetry is largely insensitive to systematic uncertainties, reinforcing the exclusion of minimal coupling spin-2 scenarios.

Discriminating the Spin of the 125 GeV Resonance: Center-Edge Asymmetry and the sWeight Technique

Introduction

The identification of the quantum numbers of the newly discovered $~125$ GeV boson at the LHC is crucial for verifying whether the observed particle fulfills the properties required of the Higgs boson. While decays to pairs of vector bosons and fermions eliminate integer and odd-spin possibilities (notably, the Landau-Yang theorem excludes spin-1 for $\gamma\gamma$ decays), an explicit distinction between a scalar ($J^P=0^+$) and tensor ($J^P=2^+$) hypothesis is essential. The analysis in "Is the New Resonance Spin 0 or 2? Taking a Step Forward in the Higgs Boson Discovery" (1209.1037) addresses this discrimination using only inclusive diphoton ($\gamma\gamma$) channels.

Methodology: Kinematic Variables and the sWeight Technique

The core strategy involves the exploitation of the scattering polar angle $\theta^*$ of the photons in the resonance rest frame. At parton level, a scalar decays isotropically into two photons, yielding a flat distribution in $\cos\theta^*$. In contrast, a spin-2 resonance (with minimal couplings as in the Randall-Sundrum (RS) KK-graviton model) produces a highly anisotropic distribution parameterized as $$P_2(\cos\theta^*) = \frac{5}{32}(1 + 6\cos^2\theta^* + \cos^4\theta^*)$$. Detector effects and event selection induce significant distortions, increasing the resemblance of the two distributions, mandating optimal statistical inference tools.

Monte Carlo event generation (MadGraph5, Pythia 6.4, and ATLAS-like detector simulation via PGS) accurately models both irreducible and reducible $\gamma\gamma$ backgrounds, as well as the signal under both hypotheses, incorporating realistic kinematic/acceptance cuts and trigger efficiencies.

Given the dramatic signal-to-background ratio ($\sim 10^{-3}$ in the mass window $100$–$160$ GeV), classic cut-based shape analyses are suboptimal. Instead, the author utilizes the sWeight method [sPlot framework] for optimal unbinned maximum-likelihood separation of signal from background. This enables robust, background-subtracted angular distributions ("sPlots") for subsequent analysis.

Center-Edge Asymmetry as a Spin Discriminant

The central observable is the center-edge asymmetry, $A$,

$$A = \frac{\sigma(|\cos\theta^*| > 0.5) - \sigma(|\cos\theta^*| < 0.5)}{\sigma(|\cos\theta^*| > 0.5) + \sigma(|\cos\theta^*| < 0.5)}$$

which quantifies the prominence of the central (isotropic) versus edge (forward/backward) event populations in the background-subtracted $\cos\theta^*$ distribution.

The robustness of $A$ derives from its insensitivity to overall normalization uncertainties and its reduced vulnerability to shape distortion effects compared to likelihood-ratio statistics. This is crucial in high-background environments with significant systematic uncertainties (luminosity, selection efficiency, PDF and energy scale variations).

Monte Carlo pseudo-experiments are used to estimate the expected distribution of $A$ for each spin scenario, including detector and systematic effects. The author demonstrates that the mean and variance of $A$ are nearly unaffected by correlated normalization uncertainties up to 30%, while log-likelihood ratio (LLR) confidence levels degrade noticeably under the same conditions.

Quantitative Results

At parton level, the center-edge asymmetry sharply distinguishes scenarios: $A_{0^+} = 0$, $A_{2^+} = -0.207$. Detector effects shift these to $A_{0^+} \approx 0.32$ and $A_{2^+} \approx 0.005$ in sPlot distributions, reflecting migration of events due to detector geometries.

With 8 TeV ATLAS data alone, a $5\sigma$ discrimination between spin-0 and spin-2 minimal coupling is achievable with $\sim15$ fb$^{-1}$ using the asymmetry. Combining 7 and 8 TeV runs further improves power, and incorporating CMS data as well increases combined significance to $\sim9\sigma$ at $20$ fb$^{-1}$/experiment for SM-like signal strengths. Notably, a $5\sigma$ spin discrimination is possible with as little as $10$ fb$^{-1}$ per experiment if the observed diphoton excess surpasses SM rates.

LLR-based hypothesis testing, while more powerful in the absence of systematics, becomes less reliable as uncertainties increase. In contrast, the center-edge asymmetry remains nearly invariant—a strong argument for its adoption as a discovery statistic in this channel.

Implications and Outlook

These results establish the experimental viability of robust spin discrimination in high-background environments using inclusive diphoton measurements at the LHC, provided efficient sWeight techniques are applied. The minimal-coupling RS KK-graviton is adopted as a reference, but the methodology extends to other models with similar angular spectra.

From a practical perspective, this means that the $\gamma\gamma$ channel alone suffices for $J^P$ assignment, underlining the importance of the sPlot approach for future high-statistics LHC datasets and potentially motivating improved background modeling in this final state. The insensitivity to systematic errors for asymmetry-based observables suggests these should be prioritized in experimental combinations and fits, especially as data volume grows and systematic, not statistical, errors dominate.

Theoretically, this analysis reinforces the exclusion of spin-2 minimal coupling scenarios in favor of the Higgs hypothesis, supporting the completion of the quantum-number identification program for the observed resonance. Such approaches will remain essential as precision in Higgs studies continues to increase and as new heavy resonances are sought in LHC and future collider datasets.

Conclusion

This study rigorously demonstrates that, even within the highly contaminated $\gamma\gamma$ final state, the signal-background discrimination and subsequent spin measurement are possible at high significance using the center-edge asymmetry of the sPlot-extracted scattering polar angle distribution. The technique is robust against the leading sources of systematic uncertainty that compromise other inferential paradigms. Crucially, with datasets already accumulated by the ATLAS and CMS experiments, conclusive experimental differentiation between $J^P=0^+$ and $J^P=2^+$ minimal coupling scenarios is accessible. This work thus provides a blueprint for future precision quantum-number studies of resonances in hadron collider environments.