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Testing the custodial symmetry in the Higgs sector of the Georgi-Machacek model at the LHC Kei Yagyu (National Central U) C.-W. Chiang, KY, arXiv: 1211.2658 [hep-ph], to be published in JHEP National Taiwan University, 17th December 2012 Plan of the talk • Introduction - Current status of the Higgs boson search at the LHC • Extended Higgs sectors - Motivation - The Georgi-Machacek model • Phenomenology - Higgs decays - Higgs productions - Simulation study at the LHC - Higgs to γγ and Zγ decay • Summary Current states of the Higgs search at the LHC ‣ The Higgs-like particle has been found at around 126 GeV at the LHC with 5σ. h → γγ h → ZZ* → 4 lepton Historic Milestone but only the Beginning. R. Heuer, July 4th, CERN Current states of the Higgs search at the LHC Signal strength (σobs/σSM) in each mode Hadron Collider Physics Symposium 2012, Hadron Collider Physics Symposium 2012, CMS ATLAS Current states of the Higgs search at the LHC Signal strength (σobs/σSM) in each mode Hadron Collider Physics Symposium 2012, Hadron Collider Physics Symposium 2012, CMS ATLAS H → ZZ and H→ WW modes are good agreement to the SM prediction. Current states of the Higgs search at the LHC Signal strength (σobs/σSM) in each mode Hadron Collider Physics Symposium 2012, Hadron Collider Physics Symposium 2012, CMS ATLAS Obs. H → γγ signal seems to be large compared to the SM prediction. Current states of the Higgs search at the LHC Signal strength (σobs/σSM) in each mode Hadron Collider Physics Symposium 2012, Hadron Collider Physics Symposium 2012, CMS ATLAS H → bb and H→ττ modes still have a large uncertainty. The SM-like Higgs boson? • At present, observed new resonance at 126 GeV looks like the SM -like Higgs boson. (-Consistent with the precision measurements at LEP, - Observed from expected events γγ and ZZ → H is spin 0 or 2) • Large deviation from the SM prediction in H→γγ mode • The central value for the H → ττ mode exceeds 0. We need to collect more data in order to clarify the property of the new particle w/126 GeV. Still there are possibilities to consider non-minimal Higgs sectors! Extended Higgs sector Why extended Higgs sector? • No principle in the Higgs sector - Negative μ2 term → Just an assumption - Higgs boson as an elementary scalar. → Cause for the quadratic div. in the Higgs mass correction. • Phenomena which cannot be explained in the SM - Neutrino masses - Dark matter - Baryon asymmetry of the Universe Why extended Higgs sector? • No principle in the Higgs sector → Supersymmetry, Dynamical symmetry breaking, Little Higgs models, … • Phenomena which cannot be explained in the SM - Neutrino masses → Rad. seesaw models, type-II seesaw mechanism - Dark matter → Discrete sym. in the Higgs sector e.g. Inert doublet - Baryon asymmetry of the Universe → Electroweak baryogenesis Predict How can sector Higgs Extended Higgswe know the true New physics models sector? O(100) GeV Determine higher than TeV scale Basic two constraints from experiments There are hints to determine the structure of the Higgs sector. +0.0017 1. Electroweak rho parameter ρexp = 1.0008 -0.0007 Additional doublets or singlets Additional triplets or higher isospin Reps. → ρtree = 1 → In general, ρtree ≠ 1 2. Flavor Changing Neutral Current (FCNC) Tree level FCNC processes should be suppressed. Models with multi-doublet structure → There appear tree level FCNCs. ★Additional doublet(s) → FCNC, ★Additional triplet(s) → Rho parameter In this talk, we focus on the possibility that the Higgs sector has triplets. The minimal Higgs Triplet Cheng, Li (1980); Schechter, Valle, (1980); Model Magg, Wetterich, (1980); Mohapatra, Senjanovic, (1981). SU(2)I U(1)Y U(1)L The Higgs triplet field Δ is added to the SM. Φ 2 1/2 0 ・Important new interaction terms: Δ 3 1 -2 Lepton number breaking parameter ・Neutrino mass matrix MΔ : Mass of triplet scalar boson. vΔ : VEV of the triplet Higgs O(0.1) eV 246 GeV O(0.1) eV The HTM can be O(1) O(100) GeV tested at colliders !! The minimal Higgs Triplet Cheng, Li (1980); Schechter, Valle, (1980); Model Magg, Wetterich, (1980); Mohapatra, Senjanovic, (1981). SU(2)I U(1)Y U(1)L The Higgs triplet field Δ is added to the SM. Φ 2 1/2 0 ・Important new interaction terms: Δ 3 1 -2 Lepton number breaking parameter ・Neutrino mass matrix MΔ : Mass of triplet scalar boson. vΔ : VEV of the triplet Higgs Non-zero vΔ breaks the custodial symmetry → ρ deviates from unity at the tree level. We discuss the extension of the HTM to keep the custodial symmetry. Georgi, Machacek (1985) The Georgi-Machacek (GM) Model ★ The minimal extension of the HTM. SU(2)I U(1)Y U(1)L HTM Φ 2 1/2 0 ★ Two isospin triplet Higgs fields GM χ 3 1 -2 are introduced to the SM. ξ 2 0 0 ★ The doublet field and the triplet fields can be expressed as SU(2)L×SU(2)R form: SU(2)R SU(2)L ★ If we take two triplet VEVs are the same: <χ0> = <ξ0> SU(2)L ×SU(2)R → SU(2)V (Custodial Symmetry) Decomposition Δ:3×3 Φ:2×2 Irreducible decomposition 5 +3 +1 3 +1 Mixing (angle β): Mixing (angle α) : 5-plet Higgs Goldston bosons SM-like Higgs + 3-plet Higgs + Singlet Higgs h, H1 The Higgs bosons belonging to the same multiplet are degenerate in mass because of the custodial symmetry. Interactions (Neutrino) Yukawa interaction l l l H5 H3 h, H1 ∝1/sinβ l l ∝cosβ/sinβ l ∝cosβ/sinβ (Usual) Yukawa interaction f f H3 h, H1 f f Gauge interaction ∝tanβ ∝cosα/cosβ, sinα/cosβ V V H5 ∝ sinβ h, H1 V V ∝ cosβ*cosα, cosβ*sinα Higgs potential ★ The most general SU(2)L×SU(2)R invariant potential: ★ There are 9 parameters in the potential: [m1, m2, μ1, μ2 : dimension full, λ1 – λ5 : dimension less] 2 VEVs : v, vΔ, 4 masses : mH5, mH3, mH1, mh, 1 mixing angle : α and reminding 2 parameters: μ1, μ2. Decoupling limit The mass formulae (α = 0) In the limit of vΔ →0 (β → 0, M22 → 0) ★ Triplet-like Higgs bosons are decoupled when M12 is taken to be large values. ★There is a relationship among the masses: Consequences of the custodial sym. 1. Electroweak rho parameter is unity at the tree level → Triplet VEV can be taken to be O(10) GeV. 2. Mass degeneracies among 5- and 3-plet Higgs bosons; mH5++ = mH5+ = mH50 = mH5, mH3+ = mH30 = mH3 3. Specific interactions; 5-plet Higgs can couple to gauge boson pairs. 3-plet Higgs can couple to fermion pairs . We focus on the features 2 and 3 in order to identify the custodial symmetric GM model at the LHC. Phenomenology Decay of the 5-plet Higgs bosons Δm = mH3 – mH5 mH3 = 150 GeV, Δm > 0 H5++ H 5+ H 50 The case of Δm > 0 is the same as the case of Δm=0. Decay of the 3-plet Higgs bosons mH3 = 150 GeV Δm > 0 Δm < 0 4 regions on the vΔ – mΔ plane ★Decays of the triplet-like Higgs bosons can be classified into 4 distinctive regions depending on the vΔ and Δm. 4 regions on the vΔ – mΔ plane ★Region I: small vΔ and small mΔ ・5-plet Higgs decays l H5 l ・3-plet Higgs decays l H3 l 4 regions on the vΔ – mΔ plane ★Region III: small vΔ and large mΔ ・5-plet Higgs decays l H3 H5 H5 l V ・3-plet Higgs decays H5 H1 H3 H3 V V 4 regions on the vΔ – mΔ plane ★Region IV: large vΔ and large mΔ ・5-plet Higgs decays V H3 H5 H5 V V ・3-plet Higgs decays H5 H1 H3 H3 V V 4 regions on the vΔ – mΔ plane ★Region II: large vΔ and small mΔ ・5-plet Higgs decays V H5 V ・3-plet Higgs decays f H3 f We discuss the phenomenology for Region II. Production modes for 5- and 3-plet Higgs Both 5-plet 3-plet 1. Drell-Yan Process: 3. Vector boson fusion Process 5. Yukawa Process H5 , H3 H3 + H5 H5 ’ , H 3 ’ 2. Mixed Drell-Yan Process: H5 4. Gauge boson associate Process H3 0 H5 H3 H3 0 , H 3 + V ,t Production modes for 5- and 3-plet Higgs Both 5-plet 3-plet 1. Drell-Yan Process: 3. Vector boson fusion Process 5. Yukawa Process H5 , H3 H3 + H5 H5 ’ , H 3 ’ 2. Mixed Drell-Yan Process: H5 4. Gauge boson associate Process H3 0 H5 H3 H3 0 , H 3 + V ,t Production cross sections H5++ H 5+ H 50 Production cross sections H5++ H 5+ VBF H 50 Production cross sections H5++ H 5+ VBF Associated H 50 Production cross sections H5++ H 5+ Mixed DY H 50 Strategy H5 The VBF and associated processes H5 2 forward jets tagging V H5++ may be detected. Transverse mass cut + b-jet veto H5+ and H50 may be detected. The mass degeneracy of the 5-plet may be tested. The mixed DY process H5 Transverse mass cut H3 The mass degeneracy of the 3-plet may be tested. Scenario • mH3 = 150 GeV, mH5 = 140 GeV, vΔ = 20 GeV, α = 0 → Concrete example for Region II • Branching fractions: BR(H5→VV) ~ 100 %, BR(H3+ → cs) ~ 30%, BR(H3+ → τν) ~ 70%, BR(H30 → bb) ~ 90% • We perform the signal & background analysis by using MadGraph5 with the parton level. We consider the hadronic decay of the 3-plet Higgs bosons 5-plet Higgs reconstructions ★ We use the VBF and associated production processes. Signal Background pp → W+W+jj, pp → W+Z jj, pp → W+W- / ZZ jj , tt Δη distributions Difference of the pseudo-rapidity: Δη distributions Difference of the pseudo-rapidity: Δη > 3.5, (Δη > 4.0 for event) MT distributions Transverse mass: MT distributions Transverse mass: 50 GeV < MT < 150 GeV Signal and background events (int. luminosity 100 fb-1) b-jet tagging efficiency: 0.6 3-plet Higgs reconstructions ★ We use the mixed DY production processes. 5-plet Higgs bosons → diboson decay, 3-plet Higgs bosons → dijet Distributions in the mixed DY process The Δη cut cannot be applied to the mixed DY process, while the MT cut can be used. Signal and background events (int. luminosity 100 fb-1) After taking the same MT cut, the signal significance can exceed 5 in both the events. Mjj distributions ★The dijet invariant mass distribution after taking the MT cut: The masses of H3+ and H30 may be measured by the peak in the dijet invariant mass distribution. Higgs decays into γγ and Zγ + RZγ Rγγ Higgs to γγ and Zγ decay RZγ Rγγ ★ Current LHC data of h→γγ mode can be explained when mH5 <~ 150 GeV and mH3 = 150 GeV. ★ Measuring the h→Zγ channel is also important to test the structure of the Higgs sector. (Chiang, KY, arXiv: 1207: 1065[hep-ph]) When Rγγ ~ 1.6, RZγ ~ 1.2. Summary • The Georgi-Machacek (GM) model is the minimal model included Higgs triplet fields whose Higgs sector is custodial symmetric. • In the GM model, there are the 5-plet, 3-plet and singlet Higgs bosons under the custodial SU(2)V symmetry. • The masses of the Higgs bosons belonging to the same SU(2)V multiplet are the same. • Testing mass degeneracy among the 5-plet Higgs bosons: → The VBF and weak boson associated processes are useful. • Testing mass degeneracy among the 3-plet Higgs bosons: → The mixied DY process is useful after the detection of the 5-plet. The custodial symmetry in the GM model may be tested by above the two steps at the LHC. Back up slides Constraint from Zbb vertex The electroweak rho parameter ★ The experimental value of the rho parameter is quite close to unity. ρexp ~ 1 Tree-level expression for the rho parameter （Kinetic term of Higgs fields） ρtree = 1 ρtree ≠ 1 ・ Standard Model ・ Models with Higgs fields ・Multi-doublet whose isospin is larger than ½ (with singlets) model e.g., the HTM. There is the custodial SU(2) sym. The custodial SU(2) sym. is in the kinetic term broken in the kinetic term. These sector affects the rho parameter by the Higgs Potential loop effects. Yukawa interaction 12/35 Custodial Symmetry The SM Lagrangian can be written by the 2×2 matrix form of the Higgs doublet: When we take g’ and yA → 0, Lagrangian is invariant under SU(2)L×SU(2)R ★ Kinetic term , After the Higgs field gets the VEV: ★ Higgs potential this symmetry is reduced to SU(2)L＝SU(2)R =SU(2)V (custodial symmetry). SU(2)V breaking by g’ is included in ★ Yukawa interaction (top-bottom sector) the definition of the rho parameter, while that by yA is not. There is a significant contribution to the deviation of rho = 1 from the top-bottom sector by the loop effect. 13/35 Testing an extended Higgs sector at colliders • Direct way：Discovery of extra Higgs bosons Ex. Charged Higgs boson, CP-odd Higgs boson, … • Indirect way: Precise measurement for the Higgs couplings Ex. hhh, hff, hVV Interactions Yukawa interaction f f H3 ∝tanβ h, H1 ∝ cosα/cosβ, sinα/cosβ f f Gauge interaction V V H5 ∝ sinβ h, H ∝ cosβ*cosα, cosβ*sinα V V 5-plet Higgs can (cannot) couple to the gauge boson (fermons). 3-plet Higgs can (cannot) couple to the fermions (gauge bosons).