Probing Majorana Phases and Neutrino Mass Spectrum in the Higgs Triplet Model at the LHC

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1 Probing Majorana Phases and Neutrino Mass Spectrum in the Higgs Triplet Model at the LHC Andrew Akeroyd National Cheng Kung University, Tainan, Taiwan TeV scale mechanisms ( testable ) for neutrino mass generation Higgs Triplet Model Production of H ±± at hadron colliders Precise measurements of H ±± l ± l ± at the LHC Testing HTM at the LHC A.A, Mayumi Aoki (ICRR, Kashiwa), Hiroaki Sugiyama (SISSA, Trieste), arxiv: [he IPMU Workshop on Neutrino Mass, Kashiwa, 19 March 2008

2 TeV scale models of neutrino mass generation Many models for neutrino mass generation! Models with a specific signature at High Energy Colliders (Tevatron/LHC) are phenomenologically appealing One such model is: Higgs Triplet Model (HTM) Schechter/Valle 80, Cheng/Li 80 Distinctive signature: H ±± with coupling to W, Z and leptons

3 Higgs Triplet Model (HTM) SM Lagrangian with one SU(2) L I = 1, Y = 2 Higgs triplet Higgs potential: = δ+ / 2 δ ++ δ 0 δ + / 2 V = m 2 (Φ Φ) + λ 1 (Φ Φ) 2 + M 2 Tr( ) +λ i (quarticterms) µ(φ T iτ 2 Φ) + h.c Triplet vacuum expectation value: < δ 0 >= v L µv 2 /M 2 (1 ev < v L < 8 GeV )

4 Higgs boson spectrum The HTM has 7 Higgs bosons: H ±±, H ±, H 0, A 0, h 0 H ±, H 0, A 0, h 0 are mixtures of doublet and triplet fields Mixing v L /v and v L << v h 0 plays role of SM Higgs boson (essentially I = 1/2 doublet) H ±± purely triplet and H ±, H 0, A 0 essentially triplet H ±±, H ±, H 0, A 0 close to degenerate M For H ±± in range at LHC require M < 1 TeV.

5 Neutrino mass in Higgs Triplet Model (HTM) No right-handed neutrino: Neutrino mass from triplet-lepton-lepton coupling (h ij ): h ij [ 2 l c i P Ll j H ++ + ( l c i P Lν j + l c j P Lν i )H + 2 ν c i P Lν j H 0] + h.c Light neutrinos receive a Majorana mass: M ν v L h ij h ij = 1 2vL V MNS diag(m 1, m 2, m 3 )V T MNS (V MNS = V l V ν; take V l = I and V ν = V MNS )

6 Limits on h ij Presence of H ±± would lead to lepton flavour violating decays Many limits exist for h ij (assuming m H ±± < 1 TeV): Cuypers/Davidson 98 BR(µ eee) < h µe h ee < 10 7 : 1988; no forthcoming experiment BR(τ l i l j l k ) < 10 8 h τi h jk < 10 4 Limits from ongoing B factories BR(µ eγ) < i h µi h ei < 10 6 sensitivity to BR> from 2008 All constraints can be respected with suitably chosen h ij Absolute values not so important for H ±± direct searches

7 Production of H ±± at Hadron Colliders (Tevatron and LHC)

8 Production of H ±± at Tevatron First searches at a Hadron collider in 2003 CDF,D0 L = i [ ( µ H ) H ++] ( gw3lµ + g B µ ) + h.c q q γ, Z H ++ H σ H ++ H is a simple function of m H ±± σ H ++ H has no dependence on h ij

9 Search strategy H ±± decays via h ij to same charge ee, µµ, ττ, eµ, eτ, µτ 4 leptons from pair produced H ++ H For e ± e ±,e ± µ ±,µ ± µ ±, sufficient to search for two leptons of high momentum and same charge Background almost negligible ( 1 event) Mass limits presented for BR(H ±± l i ± l± j ) = 100% in a given channel

10 Comparison of H ±± searches Coupling (h ll ) OPAL Exclusion Single Production ±± H ee L3, OPAL, DELPHI ll ±± H µµ ±± L DO H CDF: ±± HL µµ ±± HL ee ±± HL eµ ±± HR µµ ±± 2 H Mass (GeV/c ) CD Strongest mass limits for any Higgs boson!

11 Branching ratio for H ±± l ± l ± and testing HTM at LHC Akeroyd,Aoki,Sugiyama, arxiv: [hep-ph]

12 Light H ±± at LHC Simulations by Azuelos et al 05, Hebbeker et al 06, Hektor et al 07, Han et al 07 Discovery for m H ±± < 400 GeV with 1 fb 1 Precise measurements of BR(H ±± l ± l ± ) possible for l = e, µ Sensitivity to BR(H ±± l ± l ± ) 1% for l = e, µ Large Event Numbers for H ±± : m H ±± (GeV) N 4l (30 fb 1 ) N 4l (300 fb 1 )

13 Branching ratios of H ±± l ± l ± BR(H ±± l ± i l± j ) depends on relative values of h ij Γ(H ±± l ± i l± j ) m H ±± 8π h ij 2 In HTM h ij is directly related to neutrino mass matrix h ij = 1 2vL V MNS diag(m 1, m 2, m 3 )V T MNS Prediction for BR(H ±± l i ± l± j ) determined by: Chun,Lee,Park 03 Neutrino mass hierarchy (normal, inverted) Neutrino oscillation parameters (masses, mixing angles)

14 Explicit expressions for h ij All h ij are functions of nine parameters: h ee = 1 2v (m 1 c 2 12c m 2 s 2 12c 2 13e iϕ 1 + m 3 s 2 13e 2iδ e iϕ 2 ) Five parameters are experimentally constrained: m 2 21 m 2 2 m ev 2, m 2 31 m 2 3 m ev 2, sin 2 2θ , sin 2 2θ 23 1, sin 2 2θ 13 < Main uncertainty in h ij comes from: Absolute mass of lightest neutrino: 0 < m 0 < 1eV Majorana phases 0 < φ 1, φ 2 < 2π These three parameters are unconstrained by neutrino oscillation data

15 Testing the HTM at LHC via precise measurements of BR(H ±± l ± l ± ) There are several models of neutrino mass generation with possibly light H ±± l ± l ± : Left-Right Symmetric Model : I = 1, Y = 2 triplet Neutrino mass via seesaw mechanism, h ij arbitrary Zee-Babu Model I = 0, Y = 4 singlet Radiative neutrino mass; some correlation of h ij with neutrino mass matrix HTM predicts distinctive regions for BR(H ±± l ± l ± ) which can be tested at LHC for m H ±± < 400 GeV

16 Dependence of BR(H ±± l ± l ± ) on m 0,φ 1,φ 2 Neglect Majorana phases, φ 1 = φ 2 = 0 : BR(H ±± l ± l ± ) essentially determined by absolute neutrino mass m 0 Include Majorana phases, φ 1 0, φ 2 0 : Allowed regions for BR(H ±± l ± l ± ) considerably larger but still smaller than case of arbitrary h ij we quantify the prediction for BR(H ±± l ± l ± ) in the HTM (see also Garayoa et al,arxiv: [hep-ph] and Kadastik et al, [hep-ph]

17 BR(H ±± l ± i l± j ) against lightest neutrino mass (m 0): normal hierarchy

18 BR(H ±± l ± i l± j ) against lightest neutrino mass (m 0): inverted hierarchy

19 BR(H ±± l ± i l± j ) against Majorana phase and m 0 = 0: normal hierarchy NH µτ m 0 = µµ ττ 0.1 eτ 0 0 eµ ee ϕ rel = ϕ 1 ϕ

20 BR(H ±± l ± i l± j ) against Majorana phase and m 0 = 0: inverted hierarchy IH eµ m 0 = eτ µτ ττ ee µµ ϕ 1

21 HTM prediction in the plane [BR(H ±± e ± e ± ),BR(H ±± e ± µ ± )] normal, inverted (a) HTM HTM, normal HTM, inverted BR ee +BR eµ = 1 BR eµ BR ee

22 HTM prediction in the plane [BR(H ±± e ± e ± ),BR(H ±± µ ± µ ± )] normal, inverted (b) HTM HTM, normal HTM, inverted BR ee +BR µµ = 1 BR µµ BR ee

23 HTM prediction in the plane [BR(H ±± e ± µ ± ),BR(H ±± µ ± µ ± )] normal, inverted (c) HTM HTM, normal HTM, inverted BR eµ +BR µµ = 1 BR µµ BR eµ

24 HTM prediction in the plane [BR(H ±± e ± e ± ),BR(H ±± e ± µ ± )] with/without CP violation from Majorana phases true BR eµ (a) CPV 90%CL HTM Case I Case II Case III Case IV BRtrue ee +BReµ true = true BR ee

25 Conclusions Higgs Triplet Model generates neutrino mass h ij v T H ±± l ± l ± is a distinctive signal with BRs determined by h ij LHC can produce thousands of H ±± l ± l ± events if M H ±± < 400 GeV HTM predicts specific regions for BR(H ±± l ± l ± ) which can be tested at LHC Majorana phases/neutrino mass determine the allowed regions of BR(H ±± l ± l ± ) Collider information on such parameters

26 Other production mechanisms/decay channels for H ±± Several production mechanisms : Barenboim et al 96,Maalampi et al 02 qq W ± H ±± W, qq q q W ± W ± q q H ±± WWH ±± v L ; appreciable rates only for v L > 1 GeV Several decay channels : H ±± W ± W ± ; small for v L < 0.1 MeV H ±± H ± W ± ; not open for m H ± m H ±± Hereafter we assume the sole decay channel is H ±± l ± l ±

27 Tevatron search for pp H ++ H, H ±± e ± e ±, e ± µ ±, µ ± µ ± Cross section BR (pb) eµ ee Theory (L) µµ Theory (R) H ±± Mass (GeV/c 2 )

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