Renormalization of the Higgs Triplet Model Kei Yagyu (National Central U) S. Kanemura, KY, arXiv: [hep-ph], accepted M. Aoki, S. Kanemura, M. Kikuchi. KY, arXiv: [hep-ph] National Taiwan University, 14 th May /35

Phenomenology of the Higgs Triplet Model at the LHC Kei YAGYU (Univ. of Toyama) 柳生 慶 富山大学 M. Aoki, S. Kanemura, KY, arXiv: [hep-ph] 2nd Jan National Taiwan University 2/35

Plan of the talk Introduction - The Higgs triplet model Renormalization of the Higgs Triplet Model - Radiative corrections to the EW parameters - Radiative corrections to the Higgs potential Phenomenology - Higgs → 2 photon decay - LHC physics Summary 3/35

Introduction ・ The Higgs sector has not been confirmed. - Minimal? or Non-minimal? - The Higgs boson search is underway at the LHC. The Higgs boson mass is constrained to be 115 GeV 600 GeV at 95% CL. - There is a “SM-like” Higgs boson at around 125 GeV. ・ There are phenomena which cannot be explained in the SM. - Tiny neutrino masses, dark matter and Baryon asymmetry of the Universe ・ New physics may explain these phenomena above the TeV scale. 100 GeV TeV or 100 TeV or GUT scale or … SM New physics model, where m ν, DM, BAU are explained. Energy scale 100 GeV SM with extended Higgs sectors, where m ν, DM, BAU are explained. TeV 4/35

Explanation by extended Higgs sectors Tiny neutrino masses - The type II seesaw model - Radiative seesaw models (e.g. Zee model) Dark matter - Higgs sector with an unbroken discrete symmetry Baryon asymmetry of the Universe - Electroweak baryogenesis Introduced extended Higgs sectors SU(2) doublet Higgs + Singlet [U(1) B-L model] + Doublet [Inert doublet model] + Triplet [Type II seesaw model], etc… Studying extended Higgs sectors is important to understand the phenomena beyond the SM. 5/35

How we can constrain various Higgs sectors? Higgs Potential ・ Higgs boson mass ・ Higgs self coupling Yukawa Interaction ・ Flavor changing neutral current EW Parameters ・ Rho parameter ・ Gauge boson masses Experimental Data LEP, LHC, ILC, … It is necessary to prepare precise calculations of observables in order to compare the experimental data and to distinguish various Higgs sectors. An Extended Higgs Sector Affects Compare 6/35

How we can constrain various Higgs sectors? Yukawa Interaction ・ Flavor changing neutral current Experimental Data LEP, LHC, ILC, … Affects Compare In this talk, we focus on the Higgs Triplet Model (HTM) and its renormalization of electroweak parameters and the Higgs potential. An Extended Higgs Sector Higgs Potential ・ Higgs boson mass ・ Higgs self coupling EW Parameters ・ Rho parameter ・ Gauge boson masses 7/35

The Higgs Triplet Model The Higgs triplet field Δ is added to the SM. M Δ : Mass of triplet scalar boson. v Δ : VEV of the triplet Higgs Cheng, Li (1980); Schechter, Valle, (1980); Magg, Wetterich, (1980); Mohapatra, Senjanovic, (1981). ・ Important new interaction terms: SU(2)IU(1) Y U(1) L Φ21/20 Δ31-2 Lepton number breaking parameter ・ Neutrino mass matrix When the lepton number breaking parameter μ is taken to be of O(eV) scale, we can take M Δ ~ O( ) GeV. In this case, the HTM can be tested at colliders. 8/35

Important predictions (Tree-Level) How these predictions are modified by the radiative corrections? 2. Characteristic relations among the masses of the Δ-like Higgs bosons are predicted. 1. Rho parameter deviates from unity. A, H H+H+ H ++ A, H H+H+ H ++ Case I Case II Mass 2 Under v Δ << v Φ (Required by ρ exp ~ 1) m H++ 2 － m H+ 2 ≃ m H+ 2 － m A 2 mA2 ≃ mH2mA2 ≃ mH2 Renormalization of the electroweak parameters Renormalization of the Higgs potential These relations are useful to test the model. ・ Mass eigenstates: (SM-like) h, (Triplet-like) H ±±, H ±, H, A 9/35

Strategy Renormalization of the EW parameters. We search allowed parameter regions by the EW precision data. Renormalization of the Higgs potential By using the constrained parameter space, we calculate one-loop corrected predictions of observables in the Higgs potential (e.g., the mass spectrum, hhh coupling). Phenomenology at the LHC 10/35

Renormalization of the EW parameters 11/35

Higgs Potential The electroweak rho parameter ★ The experimental value of the rho parameter is quite close to unity. There is the custodial SU(2) sym. in the kinetic term ρ exp ~ 1 Tree-level expression for the rho parameter （ Kinetic term of Higgs fields ） ・ Models with Higgs fields whose isospin is larger than ½ e.g., the HTM. ρ tree = 1 ρ tree ≠ 1 ・ Standard Model ・ Multi-doublet (with singlets) model The custodial SU(2) sym. is broken in the kinetic term. Yukawa interaction These sector affects the rho parameter by the loop effects. 12/35

Custodial Symmetry The SM Lagrangian can be written by the 2×2 matrix form of the Higgs doublet: ★ Kinetic term ★ Higgs potential ★ Yukawa interaction (top-bottom sector) SU(2) V breaking by g’ is included in the definition of the rho parameter, while that by y A is not. There is a significant contribution to the deviation of rho = 1 from the top-bottom sector by the loop effect. 13/35 After the Higgs field gets the VEV: this symmetry is reduced to SU(2) L ＝ SU(2) R =SU(2) V (custodial symmetry). When we take g’ and y A → 0, Lagrangian is invariant under SU(2) L ×SU(2) R,

Models with ρ = 1 at the tree level The electroweak observables are described by the 3 input parameters. There are 3 parameters: g, g’ and v in the kinetic term of Higgs fields. We can choose α em, G F and m Z as the 3 input parameters. α em (mz) = ± , G F = ± GeV -2, m z = ± GeV The weak angle sin 2 θ W = s W 2 and m W can be written in terms of the above 3 inputs. The counter term of δs W 2 is derived as ~ δρ = ρ-1 = α em T The quantity δρ (or T) measures the violation of the custodial symmetry. 14/35

Scalar boson and fermion loop contributions to δρ Peskin, Wells (2001); Grimus, Lavoura, Ogreid, Osland (2008); Kanemura, Okada, Taniguchi, Tsumura (2011). Dependence of the quadratic mass splitting among particles in the same isospin multiplet appears in the T (rho) parameter. The two Higgs doublet model case Custodial sym. breaking in the top-bottom sector Custodial sym. breaking in the scalar sector mh = 117 GeV 500 GeV 15/35 mH+ = 300 GeV mA = 200 – 300 GeV α em T =

Models without ρ = 1 at the tree level e e Z s W 2 is defined by the effective Zee vertex: ^ s W 2 = ± ^ There are 4 parameters (instead of 3 in the SM): g, g’, v and ρ 0 in the kinetic term of Higgs fields. The electroweak observables are described by the 4 input parameters. We can choose α em, G F, m Z and s W 2 as the input parameters. ^ Blank, Hollik (1997) In order to calculate the EW parameters at one-loop order, we shift the bare parameters and impose reno. conditions. This parameter causes ρ tree ≠ 1 at the tree level. Ex. the VEV of the triplet Higgs in the HTM. 16/35

On-shell renormalization scheme IPI diagram Counter term IPI diagram On-shell renormalization conditions From these 5 conditions, 5 counter terms (δg, δg’, δv, δZ W and δZ B ) are determined. 2-point function 3-point function = = + + Parameters shift: g → g + δg, g’ → g’ + δg’, v → v + δv, s W 2 → s W 2 + δ s W 2, W μ → Z W 1/2 W μ, B μ → Z B 1/2 B μ ^ ^ ^ 17/35

On-shell renormalization scheme IPI diagram Counter term IPI diagram On-shell renormalization conditions 2-point function 3-point function = = + + Parameters shift: g → g + δg, g’ → g’ + δg’, v → v + δv, s W 2 → s W 2 + δ s W 2, W μ → Z W 1/2 W μ, B μ → Z B 1/2 B μ How we can determine the counter term δ s W 2 ? ^ ^ ^ ^ 18/35

Radiative corrections to ρ in models w/o ρ = 1 at the tree level s W 2 is an independent parameter. → Additional renormalization condition is necessary. Blank, Hollik (1997) By the renormalization of δs W 2, quadratic dependence of mass splitting disappear. Model w/ ρ tree = 1 Model w/o ρ tree = 1 Effect of the custodial symmetry breaking = 0 1PI diagram Counter term ^ ^ 19/35 In models without ρ = 1 at the tree level, one-loop contribution to ρ dose not measure the violation of the custodial symmetry.

Radiative corrections to ρ in models w/o ρ = 1 at the tree level s W 2 is an independent parameter. → Additional renormalization condition is necessary. Blank, Hollik (1997) By the renormalization of δs W 2, quadratic dependence of mass splitting disappear. We apply this renormalization scheme to the HTM. Model w/ ρ tree = 1 Model w/o ρ tree = 1 Effect of the custodial symmetry breaking = 0 1PI diagram Counter term ^ ^ 19/35

Renormalized ρ and m W in model w/o ρ tree = 1, One-loop corrected ρ and m W are given by: Renormalization conditions + Vertex corrections and box diagram corrections = X Y p 20/35

Prediction of the W boson mass at the 1-loop level In Case I, by the effect of the mass splitting, there are allowed regions. Case II is highly constrained by the data. A, H H+H+ H ++ Case I mH ++ = 150 GeVmH ++ = 300 GeV Kanemura, KY, arXiv: [hep-ph] Δm = m H++ - m H+ A, H H+H+ H ++ Case II mA = 150 GeVmA = 300 GeV We fixed mh=125 GeV and mt=173 GeV. 21/35

One-loop corrected rho parameter in the HTM A, H H+H+ H ++ Case I A, H H+H+ H ++ Case II In Case I, mH ++ = 150 GeV, 100 GeV <|Δm| < 400 GeV, 3 GeV < vΔ < 8 GeV is favored, while Case II is highly constrained by the data. v Δ is calculated by the tree level formula: Kanemura, KY, arXiv: [hep-ph] Δm = m H++ - m H+ m H++ = 150 GeV, mh = 125 GeVm A = 150 GeV, mh = 125 GeV 22/35

Heavy mass limit When we take heavy mass limit, loop effects of the triplet-like scalar bosons disappear. Even in such a case, the prediction does not coincide with the SM prediction. ξ = m H++ 2 – m H+ 2 SM prediction Case I Case II Kanemura, KY, arXiv: [hep-ph] 23/35

Decoupling property of the HTM HTM with L# (μ ≠ 0) ・ ρ ≠ 1 at the tree level (v Δ ≠ 0) ・ 4 input parameters (α em, G F, m Z and s W 2 ) HTM with L# (μ = 0) ・ ρ = 1 at the tree level (v Δ = 0) ・ 3 input parameters (α em, G F and m Z ) with s W 2 = 1-m W 2 /m Z 2 SM ・ L# is conserved. ・ ρ = 1 at the tree level ・ 3 input parameters (α em, G F and m Z ) with s W 2 = 1-m W 2 /m Z 2 Heavy Δ-like fields limit 24/35

Renormalization of the Higgs potential 25/35

Higgs Potential Non-minimal Higgs sectors Discovery of extra Higgs bosons; i.e., Charged Higgs bosons H ±, … Deviation of (SM-like) Higgs couplings (hVV, hff, hhh) from those predicted values in the SM. Precise calculation of these physics quantities is very important to discriminate various Higgs sectors. ★ Once “SM-like” Higgs boson (h) is discovered, precise measurements for the Higgs mass and the triple Higgs coupling turns to be very important. Direct evidence Indirect signature ★ Measuring the mass spectrum, decay branching ratios of these extra Higgs bosons. 26/35

・ The most general form under the SU(2)×U(1) gauge sym. 10 scalar states can be translated to 3 NG bosons, 1 SM-like scalar boson and 6 Δ-like scalar bosons.. 6 Δ-like scalar bosons → H ±±, H ±, A and H Doubly-chargedSingly-charged CP-oddCP-even There are 10 degrees of freedom of scalar states. The Higgs potential in the HTM 27/35

・ The most general form under the SU(2)×U(1) gauge sym. 8 parameters in the potential 8 physical parameters v, v Δ, m H++, m H+, m A, m H, m h, αμ, m, M, λ 1, λ 2, λ 3, λ 4, λ 5 If the U(1) lepton number sym. is approximately restored (μ → 0, v Δ → 0 ), 5 parameters contribute to the masses 5 physical parameters v, M, m h, + 2 triplet Higgs massesm, M, λ 1, λ 4, λ 5 The Higgs potential in the HTM 2 of 4 triplet-like Higgs masses are not independent. → There must be 2 relations: m H++ 2 － m H+ 2 = m H+ 2 － m A 2 = -v 2 λ 5 /4 28/35

Renormalization of the Higgs potential 8 parameters in the potential 8 physical parameters v, v Δ, m H++, m H+, m A, m h, m H, αμ, m, M, λ 1, λ 2, λ 3, λ 4, λ 5 Vanishing 1-point function δT φ, δT Δ Tadpole ： δT φ, δT Δ, Wave function renormalization ： δZ H++, δZ H+, δZ A, δZ H, δZ h Counter terms δv, δv Δ, δm H++ 2, δm H+ 2, δm A 2, δm h 2, δm H 2, δα On-shell condition δm H++ 2, δm H+ 2, δm A 2, δm h 2, δm H 2 δZ H++, δZ H+, δZ A, δZ H, δZ h No-mixing condition δα where 2-point function is defined by Aoki, Kanemura, Kikuchi, KY, arXiv: Renormalization of G F and s w 2 δv, δv Δ ^ 29/35

Radiative corrections to the mass spectrum In favored parameter sets by EW precision data: m H++ = O(100)GeV, |Δm| ～ 100GeV, ΔR can be as large as O(10)%. Case I (m A 2 ) tree is determined by m H++ 2 and m H+ 2 : Ratio of the squared mass difference R Tree level: Less than Loop level : Loop correction Aoki, Kanemura, Kikuchi, KY, arXiv: /35

One-loop corrected hhh coupling On-shell renormalization of the hhh coupling: By measuring the mass spectrum as well as the hhh coupling, the HTM can be tested. For α = 0 and v Δ 2 << v 2 Quartic mass dependence of Δ-like Higgs bosons appears to the hhh coupling ⇒ Non-decoupling property of the Higgs sector. Results for the renormalization of the EW parameter suggests m H++ = O(100)GeV, |Δm| ～ 100GeV. In this set, deviation of hhh is predicted more than 25% Case I Unitarity is broken Aoki, Kanemura, Kikuchi, KY, arXiv: /35

Phenomenology 32/35

Higgs → two photon decay A, H H+H+ H ++ Case I SM contribution ＋ Triplet-like scalar loop contribution The decay rate of h → γγ is around half in the HTM compared with that in the SM. + Kanemura, KY, arXiv: [hep-ph] mH ++ = 150 GeV, mh = 125 GeV mH ++ = 300 GeV, mh = 125 GeV 33/35

Phenomenology at the LHC ★ From the results of the renormalization of the EW parameters Favored scenario by the precision data: 1. Case I (m H++ > m H+ > mA, mH) 2. Δm (=m H++ - m H+ ) = O(100) GeV 3. m H++ < GeV 4. vΔ = O(1) GeV ★ From the results of the renormalization of the Higgs potential ΔR ~ - 10% → (m H m H+ 2 )/(m H+ 2 – m A 2 ) ~ 0.9 ★ Decays of triplet-like Higgs bosons (Multi-W boson event may be expected): H ++ → W + W + H + → W - H ++ H, A → W ± H ∓ → W ± W ± H ∓ ∓ C.-W. Chiang, T. Nomura, K. Tsumura (2012) → Studied multi-W signature assuming Δm = 0. M. Aoki, S. Kanemura, KY (2011) → Studied the pheno. of the HTM with Δm ≠ 0. Cascade decay 34/35

Summary Precise calculations of EW parameters as well as Higgs couplings (hhh, hVV, hff) are important to discriminate various Higgs sectors. The important predictions in the Higgs Triplet Model: Renormalization of the EW parameters - 4 input parameters (not 3 as the SM) are necessary in to describe the EW parameters. ⇒ mA > mH+ > mH++ with Δm=O(100) GeV is favored. Renormalization of the Higgs potential - One-loop corrected mass spectrum: ΔR = O(10)% - One-loop corrected hhh coupling : deviation from the SM prediction can be as large as O(100) % The decay rate of h→γγ is half compared to that of the SM prediction. At the LHC, multi-W signatures can be expected. m H++ 2 － m H+ 2 ≃ m H+ 2 － m A 2 35/35

Back up slides

Transverse mass distribution ≃ Smith,Neerven,Vermaseren,PRL(1983)

Counter terms δv and δv Δ

Measurements of hhh coupling at colliders LHC gg → hh → W+W-W+W- → l+l+4j ILC Baur, Plehn, Rainwater, PRL89 (2002) e + e - → hhνν -mh < 140 GeV : It is difficult to detect the hhh coupling at the LHC. Yasui, Kanemura, Kiyoura, Odagiri, Okada, Senaha, Yamashita, hep-ph/ mh (GeV) e + e - → Zhh It can be expected around 10-30% accuracy. Detector level simulation is underway.

Mass reconstruction qq’ → H ++ H - → (l + l + ννbb)(jjbb) qq’ → H + H → (l + νbb)(bb)qq → HA → (bb)(bb) 8.0 fb (14 TeV) 2.8 fb (7 TeV) 33 fb 12 fb 130 fb 42 fb All the masses of the Δ-like scalar bosons may be reconstructed. v Δ = GeV MTMT MTMT M T, M inv mH++mH+ mH, mA Signal only h H, A H+H+ H GeV 119 GeV 130 GeV 140 GeV

Large mh and mH ++ case (Case I) m h = 125 GeV and mH ++ = 150 GeVm h = 125 GeV and mH ++ = 300 GeV m h = 700 GeV and mH ++ = 150 GeVm h = 700 GeV and mH ++ = 300 GeV

Approximately formulae of Δr Case I: Case II: mA > mH + > mH ++ mH ++ > mH + > mA By using Case I: Case II: with m lightest = mH ++ with m lightest = mA

Y=1 Higgs Triplet Model:Kinetic term Covariant Derivative VEVs Masses for Gauge bosons ρ parameter

Branching ratio of H ++ Δm = 0 Δm = 10 GeV v Δ = 0.1 MeV, m H++ = 200 GeV m H++ = 150 GeV m H++ = 300 GeV m H++ = 500 GeV Phenomenology of Δm ≠ 0 is drastically different from that of Δm = 0. m H++ = 150 GeV m H++ = 300 GeV m H++ = 500 GeV Chakrabarti, Choudhury, Godbole, Mukhopadhyaya, (1998); Chun, Lee, Park, (2003); Perez, Han, Huang, Li, Wang, (2008); Melfo, Nemevsek, Nesti, Senjanovic, (2011)

Branching ratios of H +, H and A ★ The H + →   W + mode can be dominant in the case of Δm ≠ 0. ★ The   → bb mode can be dominant when v Δ > MeV.

Renormalized hhh coupling in the 2HDM Kanemura, Okada, Senaha, Yuan (2004)