Does the `Higgs' have Spin Zero?

TL;DR

The paper investigates whether the 125 GeV Higgs candidate could be a spin-2 particle by computing angular distributions in $gg\to X_2\to\gamma\gamma$ and $gg\to X_2\to WW^*\to \ell\ell\nu\nu$ under graviton-like couplings. It shows that the $\gamma\gamma$ channel yields a non-isotropic distribution $d\sigma/d\Omega \propto \tfrac14 + \tfrac32\cos^2\theta + \tfrac14\cos^4\theta$, while the leptonic $WW^*$ decays exhibit distinctive lepton-azimuthal and polar correlations that differ from the spin-0 Higgs expectations. The analysis highlights clear, testable discriminants between spin-0 and spin-2 hypotheses, albeit requiring detailed detector-level simulations to translate into experimental sensitivity. The work argues that angular observables in these channels could play a crucial role in spin determination given sufficient data, motivating continued simulation efforts with tools like PYTHIA and Delphes.

Abstract

The Higgs boson is predicted to have spin zero. The ATLAS and CMS experiments have recently reported of an excess of events with mass ~ 125 GeV that has some of the characteristics expected for a Higgs boson. We address the questions whether there is already any evidence that this excess has spin zero, and how this possibility could be confirmed in the near future. The excess observed in the gamma gamma final state could not have spin one, leaving zero and two as open possibilities. We calculate the angular distribution of gamma gamma pairs from the decays of a spin-two boson produced in gluon-gluon collisions, showing that is unique and distinct from the spin-zero case. We also calculate the distributions for lepton pairs that would be produced in the W W* decays of a spin-two boson, which are very different from those in Higgs decays, and note that the kinematics of the event selection used to produce the excess observed in the W W* final state have reduced efficiency for spin two.

Figures (7)

• Figure 1: (a) The vertex coupling $X_2$ to two gauge fields, (b) Feynman diagram and (c) the kinematics for the process $gg \to X_2 \to \gamma \gamma$.
• Figure 2: The $\gamma \gamma$ angular distribution of $d \sigma / d \Omega$ given in (\ref{['g10']}).
• Figure 3: The decay angular distribution functions $f(\theta)$ in $W^- \to \ell^- {\overline{\nu}}$ decays from the $W^-$ polarization states given by (a) $\epsilon^{+}$, (b) $\epsilon^{-}$, and (c) $\epsilon^{0}$.
• Figure 4: The angular distributions given by (a) (\ref{['wwplusplusmmsquare']}) $\times \sin{\theta_1}\, \sin{\theta_2}$ for decays of the $|JJ^z\rangle=|2+2\rangle$ state of $X_2 \to W^- W^+ \to \ell^- \ell^+ {\overline{\nu}} \nu$, (b) (\ref{['wwminusminusmmsquare']}) $\times \sin{\theta_1}\, \sin{\theta_2}$ for decays of the $|JJ^z\rangle=|2-2\rangle$ state of $X_2 \to W^- W^+ \to \ell^- \ell^+ {\overline{\nu}} \nu$, and (c) the sum of (a) and (b).
• Figure 5: The angular distributions for decays of $X_0 \to W^- W^+ \to \ell^- \ell^+ {\overline{\nu}} \nu$ given by (\ref{['J20a5J00']}) $\times \sin{\theta_1}\, \sin{\theta_2}$ for (a) $\phi =0$, (b) $\phi ={\pi}/2$, and (c) $\phi =\pi$.