ATLAS and CMS Higgs Mass and Spin/CP Measurement

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1 ATLAS and CMS Higgs Mass and Spin/CP Measurement These proceedings summarize the ATLAS and CMS collaboration measurement of Higgs properties. The properties discussed include mass, spin, parity and the coupling of the Higgs candidate to vector bosons. The combined measurement of the mass as measured by the experiments combined is mh = ± 0.21 (statistical uncertainty) ±0.11 (energy scale uncertainty) ±0.02 (other experimental uncertainty) ±0.01 (theoretical uncertainty) GeV. Both collaborations observe that the data are consistent with a Standard Model Higgs boson of spin/parity J P = 0+. Alternative spin-1 and spin-2 hypotheses are excluded by both collaborations at a greater than 99.9% confidence level. Within the spin-0 hypothesis the tensor structure of the coupling of the Higgs particle to vector gauge bosons is also investigated. 30 November 2015 ATL-PHYS-PROC N. Ilic on behalf of the ATLAS and CMS collaborations Department of Physics, 382 Via Pueblo Mall, Stanford, CA Introduction The discovery of a new boson was announced by the ATLAS and CMS collaborations on July 4th, In order to investigate the compatibility of the data with the Standard Model (SM), it is necessary to measure the new particle s properties such as mass and spin/cp. These measurements are performed on approximately 5 fb 1 of data collected at s = 7 TeV and 20 fb 1 collected at s = 8 TeV by each experiment. The profile likelihood approach 9 10 is used for quantifying the excess of data events over Monte Carlo at various masses and testing different spin hypotheses. 2 Mass Measurement The ATLAS and CMS analyses measure the mass of the Higgs boson candidate in the channels with the best mass resolution. These channels include the Higgs boson candidate decaying to two photons (H γγ), the Higgs decaying to two Z bosons, followed by two leptons (H ZZ 4e, 4µ, 2e2µ). The advantages of measuring the Higgs boson in the γγ include a narrow di-photon mass peak. However the disadvantage of this channel is that the ratio of the signal events to the background events is on the order of a few percent. This is in contrast to the H ZZ channel, which has a high ratio of signal to background events, but fewer events.

2 ATLAS and CMS Run 1 Total Stat. Syst. LHC Total Stat. Syst. ATLAS H γ γ ± 0.51 ( ± 0.43 ± 0.27) GeV CMS H γ γ ± 0.34 ( ± 0.31 ± 0.15) GeV ATLAS H ZZ 4l ± 0.52 ( ± 0.52 ± 0.04) GeV CMS H ZZ 4l ± 0.45 ( ± 0.42 ± 0.17) GeV ATLAS +CMS γ γ ± 0.29 ( ± 0.25 ± 0.14) GeV ATLAS +CMS 4l ± 0.40 ( ± 0.37 ± 0.15) GeV ATLAS +CMS γ γ +4l ± 0.24 ( ± 0.21 ± 0.11) GeV m H [GeV] Figure 1 The ATLAS and CMS mass measurements in the H γγ and H ZZ 4l channels 3. The statistical uncertainties are shown by the yellow band and denoted by Stat. The systematic uncertainties are shown by the pink band and denoted by Syst. 2.1 H γγ The two collaborations search for the H γγ signal using different techniques. ATLAS divides the search into ten categories based on the photon pseudorapidity, photon momentum, and whether the photon converts into an electron and positron pair. This increases the sensitivity of the analysis by exploiting different signal to background event ratios in the different categories. CMS splits the search into eleven categories which target different Higgs production processes. The CMS analysis is also optimized for a mass measurement since the effect of exclusive categories is very small. Both experiments then fit the data to the sum of signal estimations from Monte Carlo predictions and background estimations from data-driven techniques when possible, and Monte Carlo predictions otherwise. 2.2 H ZZ To separate the H ZZ process from its backgrounds, the ATLAS analysis uses a Multivariate Boosted Decision Tree (BDT) method. The final fit is performed to the invariant mass of the four lepton system (m 4l ), as well as the output of the BDT method. In contrast, CMS performs a three-dimensional fit using m 4l, the uncertainty on this value, and a variable calculated from the masses of di-lepton pairs and five angles that define the orientation of leptons 6. The latter CMS variable contains essentially the same information as the ATLAS BDT variable. 2.3 Results The summary of the ATLAS and CMS mass measurements are shown in Figure 1. The combined mass of the Higgs boson candidate, as determined by both experiments in all of the high resolution mass channels is m H = ± 0.21 (statistical uncertainty) ±0.11 (scale uncertainty) ±0.02 (other uncertainty) ±0.01 (theoretical uncertainty). The compatibility of the four measurements is tested using likelihood ratio (4 masses in numerator, common mass in denominator), and resulting pvalue is 10%. The detailed list of uncertainties is presented in Ref 3.

3 3 Spin/CP Measurement The Spin/CP measurement is performed in the H γγ, H ZZ 4µ/4e/2µ2e and H W W lνlν channels. In the H W W channel ATLAS uses only the eµ final state, while CMS considers the same-flavour lepton final states as well. To measure the spin and parity of the newly discovered particle ATLAS and CMS use different theoretical models. The ATLAS collaboration uses an Effective Field Theory (EFT) approach, in which an effective Lagrangian with all HV V terms compatible with Lorentz invariance is used to characterize SM and Beyond Standard Model (BSM) couplings 4. An example of an effective Lagrangian in the spin-0 hypothesis is shown in Equation 1. In Equation 1 the vector boson fields are represented by V µ (V = Z, W ± ), V µν represents the reduced field tensors, and Ṽ µν represents the dual tensor given by Ṽ µν = 1 2 ɛµνρσ V ρσ. The constants that correspond to SM, BSM CP-even and BSM CP-odd couplings of the spin-0 Higgs boson candidate (X 0 ) to di-bosons are given by κ SM, κ HV V and κ AV V respectively. Here, α is the mixing angle that allows for CP-mixed states. The notation used is s α = sin α and c α = cos α. Finally, Λ is the scale of BSM physics. Higher order terms are not shown in this equation. The equation for the spin-1 and spin-2 Lagrangian can be found in Ref 4. Only leading order electroweak calculations are performed using these Lagrangians. L = {c α κ SM [ 1 2 g HZZZ µ Z µ + g HW W W µ + W µ ] Λ [c ακ HZZ Z µν Z µν + s α κ AZZ Z Zµν µν ] (1) Λ [c ακ HW W W µνw + µν + s α κ AW W W µν + W µν ]}X 0 The CMS collaboration uses the anomalous couplings approach, in which the general amplitude compatible with Lorentz and gauge invariance is used to characterize SM and BSM couplings 5. An example of the scattering amplitude representing the interaction between and two vector gauge bosons, V V, is shown in Equation 2. In Equation 2, the m V 1 is the pole mass of the vector bosons, f (i)µν = ɛ µ V i qν V i ɛν V i qµ V i is the field strength vector of gauge bosons possessing momentum q V i and polarization ɛ V i, and f µν = 1 2 ɛ µνρσf (i),ρσ is the dual field strength (i) tensor. This equation does not show terms above qv 2. The equation for spin-1 and spin-2 models can be found in Ref 5. A(HV V ) [a V 1 V + κv 1 V qv kv 2 V qv 2 2 (Λ V 1 V ) 2 ]m 2 V 1ɛ V 1ɛ V 2 + a V 2 V fµν (1) f (2),µν + a V 3 V fµν (1) f (2),µν (2) 3.1 H γγ In the H γγ channel, a Higgs boson of spin-1 is forbidden by the Landau-Yang theorem. Thus in this channel only the spin-0 and spin-2 hypotheses are tested. The discriminating variable used in this channel by both the ATLAS and CMS experiments is the scattering angle distributions of the photons in the resonance rest frame H ZZ In the H ZZ channel, the kinematic variables used are the five angles that describe the direction of the decay products 6, the invariant mass of the di-lepton system and the invariant mass of the four lepton system. The angles and masses are relevant for the spin tests, while for parity only the angles enter. These variables are used in a Matrix Element Likelihood Analysis (MELA) which builds the final discriminating variable used in the analysis. MELA determines probabilities of events by calculating them from leading-order matrix elements

4 Table 1: The ATLAS results of the Higgs spin-0 and spin-1 hypotheses tested in the H ZZ and H W W channel, and spin-2 hypothesis tested in the same channels and in addition the H γγ one. The 2 + A notation refers to a spin-2 particle having negligible coupling to light quarks 4. The 2 + B notation refers to the spin-2 particle having enhanced coupling to quarks 4. A transverse momentum (p T ) cut off is also applied to the different spin-2 particles being tested 4. Hypothesis 0 + h B 2 + B p T < 125/300 p T < 125/300 p SM obs / /0.28 ALT excl at (%) / / Figure 2 The CMS spin and parity measurement results categorized by the Higgs production mechanism H W W The main discriminating variables used in the H W W channel is transverse mass of the dilepton system and the transverse mass of the final state. The transverse mass of the final state is defined differently by the ATLAS and CMS collaborations but using the same variables Results The ATLAS results of the spin measurement are shown in Table 1. The data are compatible with the SM prediction of a CP-even, spin-0 (J P = 0 + ) Higgs particle. Alternative spin-1 and many spin-2 hypotheses are excluded at a greater than 99.9% confidence level. The CMS results are shown in Figure 2. CMS tests several different spin-1 and spin-2 hypotheses against the spin-0 model. The models are described in more detail in Ref 5. The results are categorized by the type of Higgs production mechanism. The data are compatible with the J P = 0 + hypothesis, and disfavour all others at a > 99.9% confidence level. 3.5 Spin-0 couplings in HV V The couplings of the Higgs boson candidate to vector bosons are measured under the assumption of a spin-0 boson in the H ZZ and H W W channels. ATLAS measures the couplings using an effective Lagrangian, while CMS uses the effective coupling approach. An example of an ATLAS coupling measurement is shown on the left of Figure 3. This figure shows the value of the BSM CP-even coupling, given by κ HV V = ν κ HV V 4Λ, where ν is the vacuum expectation value. The data are compatible with a BSM CP-even coupling of zero, as predicted by the SM. Similarly BSM-CP odd couplings were tested and found to be compatible with the SM expectations of zero 4. The measurement in the H ZZ and H W W channels is combined assuming that κ HV V /κ SM and κ AV V /κ SM tan α are the same for the two processes. This measurement excludes couplings outside the region 0.73 < κ HV V /κ SM < 0.63 and 2.18 < κ AV V /κ SM tan α < 0.83 at a 95% confidence level. The exclusion limits for individual channels can be found in Ref 4. An example of a CMS coupling measurement is shown on the right of Figure 3. This figure shows the BSM CP-odd coupling characterized by Equations 3 and 4. The σ i terms are cross sections of processes corresponding to the a i terms defined in Equation 2. The σ Λ1 term is the effective cross section of the process corresponding to Λ 1 > 0, a j Λ1 =0. f a3 = a 3 σ 3 a 1 2 σ 1 + a 2 2 σ 2 + a 3 2 σ 3 + σ Λ1 /(Λ 1 ) 4 (3)

5 Figure 3 The value of the BSM CP-even coupling measured by ATLAS using EFT (left) 4. The value of the BSM CP-odd coupling measured by CMS using anomalous couplings 5. φ a3 = arg ( ) a3 The right plot of Figure 3 shows that the CMS measurement of a BSM CP-odd coupling is consistent with the SM expectation of zero. CMS performed a similar measurement of the BSM CP-even couplings as well as mixtures of BSM CP-even and CP-odd couplings and found them to be consistent with the SM values of zero 5. References 1. The ATLAS collaboration Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Physics Letters B Volume 716, Issue 1, 17, Pages 1-29 (2012). 2. The CMS Collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Physics Letters B Volume 716, Issue 1, 17, Pages (2012). 3. The ATLAS and CMS Collaborations, Combined Measurement of the Higgs Boson Mass in pp Collisions at s = 7 TeV and s = 8 TeV with the ATLAS and CMS Experiments, CERN-PH-EP/ (2015). 4. The ATLAS Collaboration, Study of the spin and parity of the Higgs boson in di-boson decays with the ATLAS detector, CERN-PH-EP (2015). 5. The CMS Collaboration, Constraints on the spin-parity and anomalous HVV couplings of the Higgs boson in proton collisions at 7 and 8 TeV, CERN-PH-EP/ (2015). 6. Y. Gao et al., Spin determination of single-produced resonances at hadron colliders, Phys. Rev. D (2010). 7. S. Bolognesi et al., Spin and parity of a single-produced resonance at the LHC, Phys. Rev. D (2012). 8. I. Anderson et al., Constraining anomalous HVV interactions at proton and lepton colliders, Phys. Rev. D 89 (2014). 9. G. Cowan et al., Asymptotic formulae for likelihood-based tests of new physics, Eur. Phys. J. C (2011). 10. ATLAS and CMS Collaborations, Procedure for the LHC Higgs boson search combination in Summer 2011, ATL-PHYS-PUB , CMS NOTE 2011/005 (2011). a 1 (4)