Spin determination of single-produced resonances at hadron colliders

TL;DR

The paper develops a model-independent framework to determine the spin and parity of a single resonance produced at the LHC by exploiting the full angular information in the decay X→ZZ→4l. It provides a general parameterization for X couplings to SM fields across spins 0, 1, and 2, derives the complete helicity amplitudes, and presents five-angle angular distributions that encode production and decay dynamics. A dedicated Monte Carlo with detector-like effects and a multivariate maximum-likelihood analysis demonstrates that, with tens to a few hundred fully reconstructed events, one can distinguish between spin hypotheses and measure helicity fractions and phases, thereby constraining the resonance’s couplings to vector bosons, fermions, and gluons. The results indicate substantial separation power (up to ~4σ) for plausible event samples and mass points, and the approach is readily extensible to other final states beyond ZZ→4ℓ.

Abstract

We study the production of a single resonance at the LHC and its decay into a pair of Z bosons. We demonstrate how full reconstruction of the final states allows us to determine the spin and parity of the resonance and restricts its coupling to vector gauge bosons. Full angular analysis is illustrated with the simulation of the production and decay chain including all spin correlations and the most general couplings of spin-zero, -one, and -two resonances to Standard Model matter and gauge fields. We note implications for analysis of a resonance decaying to other final states.

Figures (5)

• Figure 1: Illustration of an exotic $X$ particle production and decay in $pp$ collision $gg$ or $q\bar{q}\to X\to ZZ\to 4l^\pm$. Six angles fully characterize orientation of the decay chain: $\theta^*$ and $\Phi^*$ of the first $Z$ boson in the $X$ rest frame, two azimuthal angles $\Phi$ and $\Phi_1$ between the three planes defined in the $X$ rest frame, and two $Z$-boson helicity angles $\theta_1$ and $\theta_2$ defined in the corresponding $Z$ rest frames. The offset of angle $\Phi^*$ is arbitrarily defined and therefore this angle is not shown.
• Figure 2: Distribution of the $\cos\theta^*$ (left), $\Phi_1$ (second from the left), $\cos\theta_1$ and $\cos\theta_2$ (second from the right), and $\Phi$ (right) generated for $m_{ X}=250$ GeV with the program discussed in the text (unweighted events shown as points with error bars) and projections of the ideal angular distributions given in the text (smooth lines). The four sets of plots from top to bottom show the models discussed in Table \ref{['table-scenarios']} for spin-zero $0^+$ and $0^-$ (top), spin-one $1^+$ and $1^-$ (second row from top), spin-two $2_m^+$, $2_L^+$, and $2^-$ (third row from top), and the bottom row shows distributions in background generated with Madgraph (points with error bars) and empirical shape (smooth lines). The $J^+$ distributions are shown with solid red points and $J^-$ distributions are shown with open blue points, while the $2_m^+$ and $2_L^+$ are shown with red circles and green squares, respectively.
• Figure 3: Distribution of the $\cos\theta^*$ (left) and $\Phi_1$ (right) for the case of spin-zero resonance production $gg\to X\to ZZ$. The mass of the resonance is $m_{ X}=250$ GeV (solid points) and 1 TeV (open points). Detector acceptance effects are taken into account, see text for details. Lines show empirical parameterization.
• Figure 4: Distribution of ${2\ln({\cal L}_1/{\cal L}_2)}$ with the likelihood ${\cal L}$ evaluated for two models $k=1,2$ and shown for 1000 generated experiments with the MC events generated according to model one ($k=1$, open dots) and model two ($k=2$, solid dots). Left plot: $0^+$ vs. $0^-$; right plot: $0^+$ vs. $2_m^+$. Effective signal hypothesis separation power ${\cal S}$ is 4.1 (left plot) and 2.8 (right plot).
• Figure 5: Top: distribution of the number of fitted signal events $n_{\rm sig}$ (left) and the fraction of transverse component in the decay amplitude $(f_{++}+f_{--})$ (right) in 1000 generated experiments with $0^+$ hypothesis corresponding to Table \ref{['table-fit-test1']}. Bottom: distribution of the above parameters normalized by the fit errors.