Study of the spin and parity of the Higgs boson in diboson decays with the ATLAS detector

Abstract

Studies of the spin, parity and tensor couplings of the Higgs boson in the [Formula: see text], [Formula: see text] and [Formula: see text] decay processes at the LHC are presented. The investigations are based on [Formula: see text] of pp collision data collected by the ATLAS experiment at [Formula: see text] TeV and [Formula: see text] TeV. The Standard Model (SM) Higgs boson hypothesis, corresponding to the quantum numbers [Formula: see text], is tested against several alternative spin scenarios, including non-SM spin-0 and spin-2 models with universal and non-universal couplings to fermions and vector bosons. All tested alternative models are excluded in favour of the SM Higgs boson hypothesis at more than 99.9 % confidence level. Using the [Formula: see text] and [Formula: see text] decays, the tensor structure of the interaction between the spin-0 boson and the SM vector bosons is also investigated. The observed distributions of variables sensitive to the non-SM tensor couplings are compatible with the SM predictions and constraints on the non-SM couplings are derived.

Fig. 1

Expected distributions of kinematic variables sensitive to the spin of the resonance considered in the $H\to \mathit{\gamma }\mathit{\gamma }$ analysis, a transverse momentum of the $\mathit{\gamma }\mathit{\gamma }$ system $p_{\text{T}}^{\mathit{\gamma }\mathit{\gamma }}$ and b the production angle of the two photons in the Collins–Soper frame $|cos{\mathit{\theta }}^{\ast }|$, for a SM Higgs boson and for spin-2 particles with three different choices of the QCD couplings

Fig. 2

Observed signal fraction per category for the $H\to \mathit{\gamma }\mathit{\gamma }$ analysis, and comparison to expected values for a SM Higgs boson and for a spin-2 particle with different choices of QCD couplings. a The 11 categories described in the text are displayed, corresponding to the $p_{\text{T}}^{\mathit{\gamma }\mathit{\gamma }}<300\text{GeV}$ selection; b the high-$p_{\text{T}}^{\mathit{\gamma }\mathit{\gamma }}$ category is discarded and the signal fractions are renormalised over the 10 remaining categories, corresponding to the $p_{\text{T}}^{\mathit{\gamma }\mathit{\gamma }}<125\text{GeV}$ selection

Fig. 3

Definitions of the angular observables sensitive to the spin and parity of the resonance in the $X\to Z{Z}^{\ast }\to 4\ell$ decay

Fig. 4

Distributions of some of the final-state observables sensitive to the spin and parity of the resonance in the $H\to Z{Z}^{\ast }\to 4\ell$ signal region $115\text{GeV}<m_{4\ell }<130\text{GeV}$ for data (points with errors), backgrounds (filled histograms) and predictions for two spin hypotheses (SM solid line and alternatives dashed lines). a–c Invariant masses $m_{12}$ , $m_{34}$ and decay $cos{\mathit{\theta }}_1$, respectively; d–f $\mathrm{\Phi }$, $cos{\mathit{\theta }}^{\ast }$ and ${\mathrm{\Phi }}_1$, respectively

Fig. 5

The distributions of the discriminant BDT${}_{ZZ}$ versus the $J^P$-MELA discriminant for the SM $J^P=0^{+}$ Higgs boson and for the backgrounds in the $H\to Z{Z}^{\ast }\to 4\ell$ signal region $115\text{GeV}<m_{4\ell }<130\text{GeV}$

Fig. 6

Distributions of the $J^P$-MELA and of the ${\mathrm{BDT}}_{ZZ}$ discriminants in the $H\to Z{Z}^{\ast }\to 4\ell$ signal region $115\text{GeV}<m_{4\ell }<130\text{GeV}$ for the data (points with errors), the backgrounds (filled histograms), and for predictions for several spin and parity hypotheses. The SM hypothesis is shown by the solid line while the alternative hypotheses are shown by the dashed lines. The signal distributions are normalised to the signal strength fitted in data. a–c $J^P$-MELA discriminants for $0^{+}$ SM vs $0^{-}$, $0^{+}$ SM vs $0_h^{+}$ and $0^{+}$ SM vs $2^{+}$, respectively; d–f ${\mathrm{BDT}}_{ZZ}$ discriminant for $0^{+}$ SM vs $0^{-}$, $0^{+}$ SM vs $0_h^{+}$ and $0^{+}$ SM vs $2^{+}$, respectively

Fig. 7

Examples of distributions of the test statistic $\tilde{q}$ defined in Sect. 5.1, for the combination of decay channels. a $0^{+}$ versus $0^{-}$; b $0^{+}$ versus $0_h^{+}$; c $0^{+}$ versus the spin-2 model with universal couplings (${\mathit{\kappa }}_q={\mathit{\kappa }}_g$); d $0^{+}$ versus the spin-2 model with ${\mathit{\kappa }}_q=2{\mathit{\kappa }}_g$ and the $p_{\text{T}}$ selection at 125 GeV. The observed values are indicated by the vertical solid line and the expected medians by the dashed lines. The shaded areas correspond to the integrals of the expected distributions used to compute the p-values for the rejection of each hypothesis

Fig. 8

Distributions of the observables used in the matrix-element-observable fit. a $T{O}_1({\tilde{\mathit{\kappa }}}_{HVV})+T{O}_2({\tilde{\mathit{\kappa }}}_{HVV})$, b $T{O}_1({\tilde{\mathit{\kappa }}}_{HVV})-T{O}_2({\tilde{\mathit{\kappa }}}_{HVV})$, for the Monte Carlo signal generated with $({\tilde{\mathit{\kappa }}}_{HVV}/{\mathit{\kappa }}_{\mathrm{SM}}=0,\pm 1;{\mathit{\kappa }}_{AVV}=0)$. c $T{O}_1({\tilde{\mathit{\kappa }}}_{AVV},\mathit{\alpha })$, d $T{O}_2({\tilde{\mathit{\kappa }}}_{AVV},\mathit{\alpha })$ for the Monte Carlo signal generated with $(({\tilde{\mathit{\kappa }}}_{AVV}/{\mathit{\kappa }}_{\mathrm{SM}})·tan\mathit{\alpha }=0,\pm 5;{\mathit{\kappa }}_{HVV}=0)$. e $\mathrm{BDT}(ZZ)$ for the Monte Carlo signal generated with $({\tilde{\mathit{\kappa }}}_{HVV}/{\mathit{\kappa }}_{\mathrm{SM}}=0,\pm 1;{\mathit{\kappa }}_{AVV}=0)$. The expected background contributions are shown as filled histograms on each plot

Fig. 9

Expected and observed distributions of the test statistic for fits of a ${\tilde{\mathit{\kappa }}}_{HVV}/{\mathit{\kappa }}_{\mathrm{SM}}$ and b $({\tilde{\mathit{\kappa }}}_{AVV}/{\mathit{\kappa }}_{\mathrm{SM}})·tan\mathit{\alpha }$ for the $H\to Z{Z}^{\ast }\to 4\ell$ analysis. The expected curves are calculated assuming the SM $J^P=0^{+}$ signal and produced with the SM signal strength $\mathit{\mu }=1$ and with the signal strengths fitted to data. The horizontal dotted black lines represent the levels of $-2ln\mathit{\lambda }$ above which the values of coupling ratios under study are excluded above $68\%$ and $95\%$ CL, respectively

Fig. 10

Expected distributions of the test statistic for the combination of $H\to W{W}^{\ast }\to e\mathit{\nu }\mathit{\mu }\mathit{\nu }$ and $H\to Z{Z}^{\ast }\to 4\ell$ analyses as a function of BSM coupling ratios a ${\tilde{\mathit{\kappa }}}_{HVV}/{\mathit{\kappa }}_{\mathrm{SM}}$ and b $({\tilde{\mathit{\kappa }}}_{AVV}/{\mathit{\kappa }}_{\mathrm{SM}})·tan\mathit{\alpha }$. The expected values are estimated for the signal strengths measured in data and assuming best-fit values for all other nuisance parameters. The 68 % and 95 % CL exclusion regions are indicated as lying above the corresponding horizontal lines. The individual distributions for $H\to W{W}^{\ast }\to e\mathit{\nu }\mathit{\mu }\mathit{\nu }$ and $H\to Z{Z}^{\ast }\to 4\ell$ channels are shown

Fig. 11

Expected and observed distributions of the test statistic for $H\to W{W}^{\ast }\to e\mathit{\nu }\mathit{\mu }\mathit{\nu }$ and $H\to Z{Z}^{\ast }\to 4\ell$ analyses and their combinations. The distributions are shown as a function of the BSM coupling ratios ${\tilde{\mathit{\kappa }}}_{HVV}/{\mathit{\kappa }}_{\mathrm{SM}}$ and $({\tilde{\mathit{\kappa }}}_{AVV}/{\mathit{\kappa }}_{\mathrm{SM}})·tan\mathit{\alpha }$. The 68 % and 95 % CL exclusion regions are indicated as lying above the corresponding horizontal lines. a, b Individual $H\to W{W}^{\ast }\to e\mathit{\nu }\mathit{\mu }\mathit{\nu }$ , $H\to Z{Z}^{\ast }\to 4\ell$ and combined observed distributions. c, d expected and observed combined distributions. The expected distributions are presented for the SM signal strength $\mathit{\mu }=1$ and for the signal strengths obtained from the fit to data