# ${{\boldsymbol H}^{0}}$ SPIN AND $\boldsymbol CP$ PROPERTIES INSPIRE search

The observation of the signal in the ${{\mathit \gamma}}{{\mathit \gamma}}$ final state rules out the possibility that the discovered particle has spin 1, as a consequence of the Landau-Yang theorem. This argument relies on the assumptions that the decaying particle is an on-shell resonance and that the decay products are indeed two photons rather than two pairs of boosted photons, which each could in principle be misidentified as a single photon.

Concerning distinguishing the spin 0 hypothesis from a spin 2 hypothesis, some care has to be taken in modelling the latter in order to ensure that the discriminating power is actually based on the spin properties rather than on unphysical behavior that may affect the model of the spin 2 state.

Under the assumption that the observed signal consists of a single state rather than an overlap of more than one resonance, it is sufficient to discriminate between distinct hypotheses in the spin analyses. On the other hand, the determination of the $\mathit CP$ properties is in general much more difficult since in principle the observed state could consist of any admixture of $\mathit CP$-even and $\mathit CP$-odd components. As a first step, the compatibility of the data with distinct hypotheses of pure $\mathit CP$-even and pure $\mathit CP$-odd states with different spin assignments has been investigated. In order to treat the case of a possible mixing of different $\mathit CP$ states, certain cross section ratios are considered. Those cross section ratios need to be distinguished from the amount of mixing between a $\mathit CP$-even and a $\mathit CP$-odd state, as the cross section ratios depend in addition also on the coupling strengths of the $\mathit CP$-even and $\mathit CP$-odd components to the involved particles. A small relative coupling implies a small sensitivity of the corresponding cross section ratio to effects of $\mathit CP$ mixing.

VALUE DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
1
 2017 AM
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}$ +${}\geq{}$ 2 ${{\mathit j}}$ , ${{\mathit H}^{0}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ ( ${{\mathit \ell}}$ = ${{\mathit e}}$ , ${{\mathit \mu}}$ )
2
 2016
ATLS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$
3
 2016 BL
ATLS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit H}^{0}}{{\mathit j}}{{\mathit j}}{{\mathit X}}$ (VBF), ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \tau}}$ , 8 TeV
4
 2016 AB
CMS ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit W}}{{\mathit H}^{0}}$ , ${{\mathit Z}}{{\mathit H}^{0}}$ , ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ , 8 TeV
5
 2015 AX
ATLS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}^{*}}$
6
 2015 CI
ATLS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{*}}$ , ${{\mathit W}}{{\mathit W}^{*}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$
7
 2015
TEVA ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit W}}{{\mathit H}^{0}}$ , ${{\mathit Z}}{{\mathit H}^{0}}$ , ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$
8
 2015 B
CDF ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit W}}{{\mathit H}^{0}}$ , ${{\mathit Z}}{{\mathit H}^{0}}$ , ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$
9
 2015 Y
CMS ${{\mathit H}^{0}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ , ${{\mathit W}}{{\mathit W}^{*}}$ , ${{\mathit \gamma}}{{\mathit \gamma}}$
10
 2014 F
D0 ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit W}}{{\mathit H}^{0}}$ , ${{\mathit Z}}{{\mathit H}^{0}}$ , ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$
11
 2014 AA
CMS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{*}}$
12
 2014 G
CMS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}^{*}}$
13
 2014 P
CMS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$
14
 2013 AJ
ATLS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit Z}}$ ${{\mathit Z}^{*}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ , ${{\mathit W}}$ ${{\mathit W}^{*}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$
15
 2013 J
CMS ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{*}}$ $\rightarrow$ 4 ${{\mathit \ell}}$
1  SIRUNYAN 2017AM constrain anomalous couplings of the Higgs boson with 5.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV, 19.7 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV, and 38.6 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 13 TeV. See their Table 3 and Fig. 3, which show 68$\%$ CL and 95$\%$ CL intervals. A $\mathit CP$ violation parameter ${{\mathit f}_{{a3}}}$ is set to be ${{\mathit f}_{{a3}}}$cos $(\phi _{a3})$ = [$-0.38$, $0.46$] at 95$\%$ CL ($\phi _{a3}$ = 0 or ${{\mathit \pi}}$).
2  AAD 2016 study ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ with an effective Lagrangian including $\mathit CP$ even and odd terms in 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The data is consistent with the expectations for the Higgs boson of the Standard Model. Limits on anomalous couplings are also given.
3  AAD 2016BL study VBF ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \tau}}{{\mathit \tau}}$ with an effective Lagrangian including a $\mathit CP$ odd term in 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. The measurement is consistent with the expectation of the Standard Model. The $\mathit CP$-mixing parameter $\tilde{{\mathit d}}$ (a dimensionless coupling ${{\widetilde{\mathit d}}}=−({{\mathit m}^{2}_{{W}}}/\Lambda {}^{2}){{\mathit f}}_{ {{\widetilde{\mathit W}}} {{\mathit W}} }$) is constrained to the interval of ($-0.11$, $0.05$) at 68$\%$ CL under the assumption of ${{\widetilde{\mathit d}}}$ = ${{\widetilde{\mathit d}}_{{B}}}$.
4  KHACHATRYAN 2016AB search for anomalous pseudoscalar couplings of the Higgs boson to ${{\mathit W}}$ and ${{\mathit Z}}$ with 18.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. See their Table 5 and Figs 5 and 6 for limits on possible anomalous pseudoscalar coupling parameters.
5  AAD 2015AX compare the $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{+}$ Standard Model assignment with other $\mathit J{}^{\mathit CP}$ hypotheses in 20.3 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV, using the process ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}^{*}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit \mu}}{{\mathit \nu}}$ . ${}^{}2{}^{+}$ hypotheses are excluded at $84.5 - 99.4\%$CL, ${}^{}0{}^{-}$ at 96.5$\%$CL, ${}^{}0{}^{+}$ (field strength coupling) at 70.8$\%$CL. See their Fig. 19 for limits on possible $\mathit CP$ mixture parameters.
6  AAD 2015CI compare the $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{+}$ Standard Model assignment with other $\mathit J{}^{\mathit CP}$ hypotheses in 4.5 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and 20.3 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV, using the processes ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{*}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ . ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ and combine with AAD 2015AX data. ${}^{}0{}^{+}$ (field strength coupling), ${}^{}0{}^{-}$ and several ${}^{}2{}^{+}$ hypotheses are excluded at more than 99.9$\%$ CL. See their Tables $7 - 9$ for limits on possible $\mathit CP$ mixture parameters.
7  AALTONEN 2015 combine AALTONEN 2015B and ABAZOV 2014F data. An upper limit of 0.36 of the Standard Model production rate at 95$\%$ CL is obtained both for a ${}^{}0{}^{-}$ and a ${}^{}2{}^{+}$ state. Assuming the SM event rate, the $\mathit J{}^{\mathit CP}$ = ${}^{}0{}^{-}$ (${}^{}2{}^{+}$) hypothesis is excluded at the 5.0$\sigma$ (4.9$\sigma$) level.
8  AALTONEN 2015B compare the $\mathit J{}^{\mathit CP}$ = ${}^{}0{}^{+}$ Standard Model assignment with other $\mathit J{}^{\mathit CP}$ hypotheses in 9.45 fb${}^{-1}$ of ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 1.96 TeV, using the processes ${{\mathit Z}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \ell}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit W}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit b}}{{\overline{\mathit b}}}$ , and ${{\mathit Z}}$ ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \nu}}{{\mathit \nu}}{{\mathit b}}{{\overline{\mathit b}}}$ . Bounds on the production rates of ${}^{}0{}^{-}$ and ${}^{}2{}^{+}$ (graviton-like) states are set, see their tables II and III.
9  KHACHATRYAN 2015Y compare the $\mathit J{}^{\mathit CP}$ = ${}^{}0{}^{+}$ Standard Model assignment with other $\mathit J{}^{\mathit CP}$ hypotheses in up to 5.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and up to 19.7 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV, using the processes ${{\mathit H}^{0}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ , ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}^{*}}$ , and ${{\mathit H}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ . ${}^{}0{}^{-}$ is excluded at 99.98$\%$ CL, and several ${}^{}2{}^{+}$ hypotheses are excluded at more than 99$\%$ CL. Spin 1 models are excluded at more than 99.999$\%$ CL in ${{\mathit Z}}{{\mathit Z}^{*}}$ and ${{\mathit W}}{{\mathit W}^{*}}$ modes. Limits on anomalous couplings and several cross section fractions, treating the case of $\mathit CP$-mixed states, are also given.
10  ABAZOV 2014F compare the $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{+}$ Standard Model assignment with $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{-}$ and ${}^{}2{}^{+}$ (graviton-like coupling) hypotheses in up to 9.7 fb${}^{-1}$ of ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 1.96 TeV. They use kinematic correlations between the decay products of the vector boson and the Higgs boson in the final states ${{\mathit Z}}$ ${{\mathit H}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \ell}}{{\mathit b}}{{\overline{\mathit b}}}$ , ${{\mathit W}}$ ${{\mathit H}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit b}}{{\overline{\mathit b}}}$ , and ${{\mathit Z}}$ ${{\mathit H}}$ $\rightarrow$ ${{\mathit \nu}}{{\mathit \nu}}{{\mathit b}}{{\overline{\mathit b}}}$ . The ${}^{}0{}^{-}$ (${}^{}2{}^{+}$) hypothesis is excluded at 97.6$\%$ CL (99.0$\%$ CL). In order to treat the case of a possible mixture of a $0{}^{+}{}^{}$ state with another $\mathit J{}^{\mathit CP}$ state, the cross section fractions ${{\mathit f}_{{X}}}$ = ${{\mathit \sigma}_{{X}}}/({{\mathit \sigma}}_{0{}^{+}{}^{}}$ + ${{\mathit \sigma}_{{X}}}$) are considered, where ${{\mathit X}}$ = $0{}^{-}{}^{}$, $2{}^{+}{}^{}$. Values for ${{\mathit f}}_{0{}^{-}{}^{}}$ (${{\mathit f}}_{2{}^{+}{}^{}}$) above 0.80 (0.67) are excluded at 95$\%$ CL under the assumption that the total cross section is that of the SM Higgs boson.
11  CHATRCHYAN 2014AA compare the $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{+}$ Standard Model assignment with various $\mathit J{}^{\mathit CP}$ hypotheses in 5.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and 19.7 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{-}$ and 1${}^{\pm{}}$ hypotheses are excluded at 99$\%$ CL, and several $\mathit J = 2$ hypotheses are excluded at 95$\%$ CL. In order to treat the case of a possible mixture of a ${}^{}0{}^{+}$ state with another $\mathit J{}^{\mathit CP}$ state, the cross section fraction ${{\mathit f}_{{a3}}}$ = $\vert {{\mathit a}_{{3}}}\vert ^2$ ${{\mathit \sigma}_{{3}}}$ $/$ ($\vert {{\mathit a}_{{1}}}\vert ^2$ ${{\mathit \sigma}_{{1}}}$ + $\vert {{\mathit a}_{{2}}}\vert ^2$ ${{\mathit \sigma}_{{2}}}$ + $\vert {{\mathit a}_{{3}}}\vert ^2$ ${{\mathit \sigma}_{{3}}}$) is considered, where the case ${{\mathit a}_{{3}}}$ = 1, ${{\mathit a}_{{1}}}$ = ${{\mathit a}_{{2}}}$ = 0 corresponds to a pure $\mathit CP$-odd state. Assuming ${{\mathit a}_{{2}}}$ = 0, a value for ${{\mathit f}_{{a3}}}$ above 0.51 is excluded at 95$\%$ CL.
12  CHATRCHYAN 2014G compare the $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{+}$ Standard Model assignment with $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{-}$ and ${}^{}2{}^{+}$ (graviton-like coupling) hypotheses in 4.9 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and 19.4 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. Varying the fraction of the production of the ${}^{}2{}^{+}$ state via ${{\mathit g}}{{\mathit g}}$ and ${{\mathit q}}{{\overline{\mathit q}}}$ , ${}^{}2{}^{+}$ hypotheses are disfavored at CL between 83.7 and 99.8$\%$. The ${}^{}0{}^{-}$ hypothesis is disfavored against ${}^{}0{}^{+}$ at the 65.3$\%$ CL.
13  KHACHATRYAN 2014P compare the $\mathit J{}^{\mathit CP}$= ${}^{}0{}^{+}$ Standard Model assignment with a ${}^{}2{}^{+}$ (graviton-like coupling) hypothesis in 5.1 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ collisions at $\mathit E_{{\mathrm {cm}}}$ = 7 TeV and 19.7 fb${}^{-1}$ at $\mathit E_{{\mathrm {cm}}}$ = 8 TeV. Varying the fraction of the production of the ${}^{}2{}^{+}$ state via ${{\mathit g}}{{\mathit g}}$ and ${{\mathit q}}{{\overline{\mathit q}}}$ , ${}^{}2{}^{+}$ hypotheses are disfavored at CL between 71 and 94$\%$.
14  AAD 2013AJ compare the spin 0, $\mathit CP$-even hypothesis with specific alternative hypotheses of spin 0, $\mathit CP$-odd, spin 1, $\mathit CP$-even and $\mathit CP$-odd, and spin 2, $\mathit CP$-even models using the Higgs boson decays ${{\mathit H}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ , ${{\mathit H}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}^{*}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ and ${{\mathit H}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}^{*}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}}{{\mathit \nu}}$ and combinations thereof. The data are compatible with the spin 0, $\mathit CP$-even hypothesis, while all other tested hypotheses are excluded at confidence levels above 97.8$\%$.
15  CHATRCHYAN 2013J study angular distributions of the lepton pairs in the ${{\mathit Z}}{{\mathit Z}^{*}}$ channel where both ${{\mathit Z}}$ bosons decay to ${{\mathit e}}$ or ${{\mathit \mu}}$ pairs. Under the assumption that the observed particle has spin 0, the data are found to be consistent with the pure $\mathit CP$-even hypothesis, while the pure $\mathit CP$-odd hypothesis is disfavored.
References:
 SIRUNYAN 2017AM
PL B775 1 Constraints on Anomalous Higgs boson Couplings using Production and Decay Information in the Four-Lepton Final State
EPJ C76 658 Test of $\mathit CP$ Invariance in Vector-Boson Fusion Production of the Higgs Boson using the Optimal Observable Method in the Ditau Decay Channel with the ATLAS Detector
PL B753 69 Constraints on non-Standard Model Higgs Boson Interactions in an Effective Lagrangian using Differential Cross Sections Measured in the ${{\mathit H}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ Decay Channel at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
 KHACHATRYAN 2016AB
PL B759 672 Combined Search for Anomalous Pseudoscalar HVV Couplings in VH( ${{\mathit H}}$ $\rightarrow$ ${{\mathit b}}{{\overline{\mathit b}}}$ ) Production and ${{\mathit H}}$ $\rightarrow$ ${{\mathit V}}{{\mathit V}}$ decay
EPJ C75 231 Determination of Spin and Parity of the Higgs Boson in the ${{\mathit W}}$ ${{\mathit W}^{*}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit \mu}}{{\mathit \nu}}$ Decay Channel with the ATLAS Detector
EPJ C75 476 Study of the Spin and Parity of the Higgs Boson in Diboson Decays with the ATLAS Detector
 AALTONEN 2015B
PRL 114 141802 Constraints on Models of the Higgs Boson with Exotic Spin and Parity using Decays to Bottom-Antibottom Quarks in the Full CDF Data Set
 AALTONEN 2015
PRL 114 151802 evatron Constraints on Models of the Higgs Boson with Exotic Spin and Parity using Decays to Bottom-Antibottom Quark Pairs
 KHACHATRYAN 2015Y
PR D92 012004 Constraints on the Spin-Parity and Anomalous HVV Couplings of the Higgs Boson in Proton Collisions at 7 and 8 TeV
 ABAZOV 2014F
PRL 113 161802 Constraints on Spin and Parity of the Higgs Boson ${{\mathit V}}{{\mathit H}}\rightarrow{{\mathit V}}{\mathit {\mathit b}}{\mathit {\overline{\mathit b}}}$ Final States
 CHATRCHYAN 2014G
JHEP 1401 096 Measurement of Higgs Boson Production and Properties in the ${{\mathit W}}{{\mathit W}}$ Decay Channel with Leptonic Final States
 CHATRCHYAN 2014AA
PR D89 092007 Measurement of the Properties of a Higgs Boson in the Four-Lepton Final State
 KHACHATRYAN 2014P
EPJ C74 3076 Observation of the Diphoton Decay of the Higgs Boson and Measurement of its Properties
PRL 110 081803 On the Mass and Spin-Parity of the Higgs Boson Candidate via its Decays to ${{\mathit Z}}$ Boson Pairs