CP violation in charged Higgs production and decays in the Complex 2HDM

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1 CP violation in charged Higgs production and decays in the Complex 2HDM Abdesslam Arhrib National Cheung Keung University (NCKU), Faculté des Sciences et Techniques Tangier, Morocco Based on: A.A, H. Eberl, E. Ginina, K. Christova, JHEP 11 NCTS, 24th May 2011 p.1/30

2 Plan Complex 2HDM: Motivations parametrization of C2HDM and constraints CP violation in charged Higgs production bg th and decays H ± tb, W ± h 1,2 CP violation in neutral Higgs decays h 1 τ + τ,... Conclusions NCTS, 24th May 2011 p.2/30

3 Complex 2HDM: Motivations In the SM, the amount of CP in CKM, may be enough to explain the observed size of CP in B and K meson system. NCTS, 24th May 2011 p.3/30

4 Complex 2HDM: Motivations In the SM, the amount of CP in CKM, may be enough to explain the observed size of CP in B and K meson system. However, it is too small to generate the observable Baryon Asymmetry in the Universe. [A.D. Sakharov 67] NCTS, 24th May 2011 p.3/30

5 Complex 2HDM: Motivations In the SM, the amount of CP in CKM, may be enough to explain the observed size of CP in B and K meson system. However, it is too small to generate the observable Baryon Asymmetry in the Universe. [A.D. Sakharov 67] Therefore, models with extra CP violating phases are welcome (SUSY, SM4, extended Higgs sector...) NCTS, 24th May 2011 p.3/30

6 Complex 2HDM: Motivations In the SM, the amount of CP in CKM, may be enough to explain the observed size of CP in B and K meson system. However, it is too small to generate the observable Baryon Asymmetry in the Universe. [A.D. Sakharov 67] Therefore, models with extra CP violating phases are welcome (SUSY, SM4, extended Higgs sector...) Those large CP violating phases can give contributions to the EDM which exceed the experimental upper bound. NCTS, 24th May 2011 p.3/30

7 With 2HDM Φ 1,2, CP can be violated either explicitly or spontaneously in the Higgs sector [T.D.Lee 73, Weinberg 76, G. Branco 85, Liu, Wolfstein 87] NCTS, 24th May 2011 p.4/30

8 With 2HDM Φ 1,2, CP can be violated either explicitly or spontaneously in the Higgs sector [T.D.Lee 73, Weinberg 76, G. Branco 85, Liu, Wolfstein 87] Scalar sector of the MSSM is a special case of the 2HDM scalar sector NCTS, 24th May 2011 p.4/30

9 With 2HDM Φ 1,2, CP can be violated either explicitly or spontaneously in the Higgs sector [T.D.Lee 73, Weinberg 76, G. Branco 85, Liu, Wolfstein 87] Scalar sector of the MSSM is a special case of the 2HDM scalar sector Some models of dynamical electroweak symmetry breaking yields the 2HDM as their low-energy effective theory [H. J. He et al, PRD65, (2002) hep-ph/ ]. NCTS, 24th May 2011 p.4/30

10 With 2HDM Φ 1,2, CP can be violated either explicitly or spontaneously in the Higgs sector [T.D.Lee 73, Weinberg 76, G. Branco 85, Liu, Wolfstein 87] Scalar sector of the MSSM is a special case of the 2HDM scalar sector Some models of dynamical electroweak symmetry breaking yields the 2HDM as their low-energy effective theory [H. J. He et al, PRD65, (2002) hep-ph/ ]. EW phase transition with 4th generation requires 2 SU(2) doublet Higgs fields [Y.Kikukawa, M. Kohda, J.Yasuda, Prog.Theor.Phys 09] NCTS, 24th May 2011 p.4/30

11 rameterization of C2HDM and constraint V = m 2 11(Φ + 1 Φ 1) + m 2 22(Φ + 2 Φ 2) + λ 1 (Φ + 1 Φ 1) 2 + λ 2 (Φ + 1 Φ 1) 2 + λ 3 (Φ + 1 Φ 1)(Φ + 2 Φ 2) + λ 4 Φ + 1 Φ 2 2 +{m 2 12(Φ + 1 Φ 2) + h.c} + [λ 5 (Φ + 1 Φ 2) 2 + h.c] NCTS, 24th May 2011 p.5/30

12 rameterization of C2HDM and constraint V = m 2 11(Φ + 1 Φ 1) + m 2 22(Φ + 2 Φ 2) + λ 1 (Φ + 1 Φ 1) 2 + λ 2 (Φ + 1 Φ 1) 2 + λ 3 (Φ + 1 Φ 1)(Φ + 2 Φ 2) + λ 4 Φ + 1 Φ 2 2 +{m 2 12(Φ + 1 Φ 2) + h.c} + [λ 5 (Φ + 1 Φ 2) 2 + h.c] One can have: Explicit CP if I(m 4 12 λ 5 ) 0 NCTS, 24th May 2011 p.5/30

13 rameterization of C2HDM and constraint V = m 2 11(Φ + 1 Φ 1) + m 2 22(Φ + 2 Φ 2) + λ 1 (Φ + 1 Φ 1) 2 + λ 2 (Φ + 1 Φ 1) 2 + λ 3 (Φ + 1 Φ 1)(Φ + 2 Φ 2) + λ 4 Φ + 1 Φ 2 2 +{m 2 12(Φ + 1 Φ 2) + h.c} + [λ 5 (Φ + 1 Φ 2) 2 + h.c] One can have: Explicit CP if I(m 4 12 λ 5 ) 0 For I(m 4 12 λ 5 ) = 0: we can have Spontaneous CP if: m2 12 λ 5 v 1 v 2 < 1; < Φ 1 >= v 1, < Φ 2 >= v 2 e iθ, the minimum occurs for: cos θ = m2 12 λ 5 v 1 v 2 ; λ 5 0 Stability condition 2 V θ > 0 λ 2 5 > 0, NCTS, 24th May 2011 p.5/30

14 parameterization of C2HDM Φ 1 = ϕ + 1 (v 1 + η 1 + iχ 1 )/ 2, Φ 2 = ϕ + 2 (v 2 + η 2 + iχ 2 )/ 2. The physical Higgs eigenstates are obtained as follows. The charged Higgs H ± and the charged Goldstone fields G ± are a mixture of ϕ ± 1,2 : tan β = v 2 /v 1. H ± = sin βϕ ± 1 + cosβϕ± 2, G ± = cosβϕ ± 1 + sin βϕ± 2, NCTS, 24th May 2011 p.6/30

15 The neutral physical Higgs states are obtained: One rotates the imaginary parts of: (χ 1,χ 2 ) into (G 0,η 3 ): G 0 = cos βχ 1 + sin βχ 2, η 3 = sin βχ 1 + cosβχ 2, G 0 is the Goldstone boson. The CP-odd η 3 mixes with the neutral CP-even components η 1,2. M 2 ij = 2 V Higgs /( η i η j ), i,j = 1, 2, 3 RM 2 R T = diag(m 2, M H 2, M 1 0 H 2 ),M 2 0 H3 0 H 0 1 M H 0 2 M H 0 3 with (H1 0,H0 2,H0 3 )T = R (η 1,η 2,η 3 ) T The mass eigenstates Hi 0 have a mixed CP structure. NCTS, 24th May 2011 p.7/30

16 R is parametrized by three rotation angles α i, i = 1, 2, 3: R = = c 2 0 s 2 c 1 s c 3 s s 1 c s 3 c 3 s 2 0 c c 1 c 2 s 1 c 2 s 2 (c 1 s 2 s 3 + s 1 c 3 ) c 1 c 3 s 1 s 2 s 3 c 2 s 3, c 1 s 2 c 3 + s 1 s 3 (c 1 s 3 + s 1 s 2 c 3 ) c 2 c 3 with s i = sin α i and c i = cosα i, π 2 < α 1 π 2 ; π 2 < α 2 π 2 ; 0 α 3 π 2. NCTS, 24th May 2011 p.8/30

17 Scalar potentiel parameters The potential has 12 real parameters: 2 real masses: m 2 11,22, 2 VEVs, 4 reals: λ 1, 2,3, 4, 2 complex: λ 5,m NCTS, 24th May 2011 p.9/30

18 Scalar potentiel parameters The potential has 12 real parameters: 2 real masses: m 2 11,22, 2 VEVs, 4 reals: λ 1, 2,3, 4, 2 complex: λ 5,m minimization conditions eliminates m 2 11,22 and also relates Im (m 2 12 ) and Im (λ 5): Im (m 2 12 ) = v 1 v 2 Im (λ 5 ). NCTS, 24th May 2011 p.9/30

19 Scalar potentiel parameters The potential has 12 real parameters: 2 real masses: m 2 11,22, 2 VEVs, 4 reals: λ 1, 2,3, 4, 2 complex: λ 5,m minimization conditions eliminates m 2 11,22 and also relates Im (m 2 12 ) and Im (λ 5): Im (m 2 12 ) = v 1 v 2 Im (λ 5 ). v v2 2 is fixed at the EW scale v = ( 2G F ) 1/2 = 246 GeV. NCTS, 24th May 2011 p.9/30

20 Scalar potentiel parameters The potential has 12 real parameters: 2 real masses: m 2 11,22, 2 VEVs, 4 reals: λ 1, 2,3, 4, 2 complex: λ 5,m minimization conditions eliminates m 2 11,22 and also relates Im (m 2 12 ) and Im (λ 5): Im (m 2 12 ) = v 1 v 2 Im (λ 5 ). v v2 2 is fixed at the EW scale v = ( 2G F ) 1/2 = 246 GeV. remains: 8 real independent parameters: λ 1,2,3,4, Re (λ 5 ), Re (m 2 12 ), tan β, Im (m2 12 ). or M H 0 1, M H 0 2, M H +, α 1, α 2, α 3, tan β, Re (m 12 ). M 2 H 0 3 = M2 H 0 1 R 13 (R 12 tan β R 11 )+M 2 H 0 2R 23 (R 22 tan β R 21 ) R 33 (R 31 R 32 tanβ), NCTS, 24th May 2011 p.9/30

21 Higgs couplings to gauge bosons The interactions relevant to our study are: C(H 0 iww) = cosβr i1 + sinβr i2, C(H 0 i W ± H ) = i(sinβr i1 cos βr i2 ) ± R i3. NCTS, 24th May 2011 p.10/30

22 Higgs couplings to gauge bosons The interactions relevant to our study are: C(H 0 iww) = cosβr i1 + sinβr i2, C(H 0 i W ± H ) = i(sinβr i1 cos βr i2 ) ± R i3. One can derives the following sum rules: C(H 0 iww) 2 + C(H 0 i W + H ) 2 = 1 for each i = 1, 2, 3 3 C(H 0 iww) 2 = 1 i=1 NCTS, 24th May 2011 p.10/30

23 Higgs couplings to gauge bosons The interactions relevant to our study are: C(H 0 iww) = cosβr i1 + sinβr i2, C(H 0 i W ± H ) = i(sinβr i1 cos βr i2 ) ± R i3. One can derives the following sum rules: C(H 0 iww) 2 + C(H 0 i W + H ) 2 = 1 for each i = 1, 2, 3 3 C(H 0 iww) 2 = 1 i=1 For a fixed i, if C(H 0 i W+ H ) 2 is suppressed, then (sinβr i1 cosβr i2 ) 2 0 and R 2 i3 0 H 0 i is dominantly a CP-even state. NCTS, 24th May 2011 p.10/30

24 C(H 0 iww) 2 + C(H 0 i W + H ) 2 = 1 for each i = 1, 2, 3 3 C(H 0 iww) 2 = 1 i=1 For a fixed i, if C(H 0 i W+ H ) 2 is suppressed, the second sum rule C(H 0 j WW)2 0 for j i. NCTS, 24th May 2011 p.11/30

25 Higgs couplings to fermions if Φ 1 and Φ 2 couple to all fermions L 2HDM Y ukawa = hd,1 ij (ΨL q ) i Φ 1 d R j h u,1 ij (ΨL q ) i Φ1 u R j + (Φ 1 Φ 2 ) The mass term is: M q ij = hq,1 ij v 1 + h q,2 ij v 2 NCTS, 24th May 2011 p.12/30

26 Higgs couplings to fermions if Φ 1 and Φ 2 couple to all fermions L 2HDM Y ukawa = hd,1 ij (ΨL q ) i Φ 1 d R j h u,1 ij (ΨL q ) i Φ1 u R j + (Φ 1 Φ 2 ) The mass term is: M q ij = hq,1 ij v 1 + h q,2 ij v 2 Diagonalization of M q ij does not diagonalize hq,k ij. NCTS, 24th May 2011 p.12/30

27 Higgs couplings to fermions if Φ 1 and Φ 2 couple to all fermions L 2HDM Y ukawa = hd,1 ij (ΨL q ) i Φ 1 d R j h u,1 ij (ΨL q ) i Φ1 u R j + (Φ 1 Φ 2 ) The mass term is: M q ij = hq,1 ij v 1 + h q,2 ij v 2 Diagonalization of M q ij does not diagonalize hq,k ij. We would have FCNC at tree level! NCTS, 24th May 2011 p.12/30

28 To avoid FCNC at tree level, several solutions : NCTS, 24th May 2011 p.13/30

29 To avoid FCNC at tree level, several solutions : Symétrie Z 2 (Théorème de Glashow-Weinberg): Φ 2 Φ 2,u ir u ir : 2HDM-II (pareil qu au MSSM) NCTS, 24th May 2011 p.13/30

30 To avoid FCNC at tree level, several solutions : Symétrie Z 2 (Théorème de Glashow-Weinberg): Φ 2 Φ 2,u ir u ir : 2HDM-II (pareil qu au MSSM) 2HDM-I 2HDM-II 2HDM-III 2HDM-(IV) (2HDM-L) up Φ 2 Φ 2 Φ 2 Φ 2 down Φ 2 Φ 1 Φ 1 Φ 2 lepton Φ 2 Φ 1 Φ 2 Φ 1 2HDM-IV ou 2HDM-L: (Lepton-specific model) NCTS, 24th May 2011 p.13/30

31 To avoid FCNC at tree level, several solutions : Symétrie Z 2 (Théorème de Glashow-Weinberg): Φ 2 Φ 2,u ir u ir : 2HDM-II (pareil qu au MSSM) 2HDM-I 2HDM-II 2HDM-III 2HDM-(IV) (2HDM-L) up Φ 2 Φ 2 Φ 2 Φ 2 down Φ 2 Φ 1 Φ 1 Φ 2 lepton Φ 2 Φ 1 Φ 2 Φ 1 2HDM-IV ou 2HDM-L: (Lepton-specific model) H i b b = i gm b 2m W ( R i1 cos β ir i3 tan βγ 5 ) H i t t = i gm t 2m W ( R i2 sin β ir i3 cotβγ 5 ) NCTS, 24th May 2011 p.13/30

32 Feynman Diagrams NCTS, 24th May 2011 p.14/30

33 Feynman Diagrams H ± tb NCTS, 24th May 2011 p.14/30

34 Feynman Diagrams: H ± W ± H i NCTS, 24th May 2011 p.15/30

35 Feynman Diagrams: vetex & selfenergies NCTS, 24th May 2011 p.16/30

36 Feynman Diagrams: vetex & selfenergies NCTS, 24th May 2011 p.16/30

37 Feynman Diagrams: boxes NCTS, 24th May 2011 p.17/30

38 CP violating asymmetries Decay rate asymmetries A CP D,f, defined by: A CP D,f (H± f) = Γ(H+ f) Γ(H f) 2Γ tree (H + f), f = t b; W ± Hi 0 NCTS, 24th May 2011 p.18/30

39 CP violating asymmetries Decay rate asymmetries A CP D,f, defined by: A CP D,f (H± f) = Γ(H+ f) Γ(H f) 2Γ tree (H + f), f = t b; W ± Hi 0 Production rate asymmetry A CP P A CP P = σ(pp H+ t) σ(pp H t) 2σ tree (pp H + t), defined by: NCTS, 24th May 2011 p.18/30

40 CP violating asymmetries Decay rate asymmetries A CP D,f, defined by: A CP D,f (H± f) = Γ(H+ f) Γ(H f) 2Γ tree (H + f), f = t b; W ± Hi 0 Production rate asymmetry A CP P A CP P = σ(pp H+ t) σ(pp H t) 2σ tree (pp H + t), defined by: Asymmetries A CP f A CP f for production and subsequent decays: = σ(pp th + tf) σ(pp th t f) 2σ tree (pp th + tf). NCTS, 24th May 2011 p.18/30

41 CP violating asymmetries Decay rate asymmetries A CP D,f, defined by: A CP D,f (H± f) = Γ(H+ f) Γ(H f) 2Γ tree (H + f), f = t b; W ± Hi 0 Production rate asymmetry A CP P A CP P = σ(pp H+ t) σ(pp H t) 2σ tree (pp H + t), defined by: Asymmetries A CP f A CP f for production and subsequent decays: = σ(pp th + tf) σ(pp th t f) 2σ tree (pp th + tf). In the narow width approximation: A CP f = A CP P + ACP D,f NCTS, 24th May 2011 p.18/30

42 m H± > 290 GeV: (b sγ) Constraints NCTS, 24th May 2011 p.19/30

43 m H± > 290 GeV: (b sγ) Constraints ρ parameter: extra-contribution: ρ NCTS, 24th May 2011 p.19/30

44 m H± > 290 GeV: (b sγ) Constraints ρ parameter: extra-contribution: ρ Theoretical constraints: Potential bounded from bellow: λ 1 > 0, λ 2 > 0, λ 3 + λ 1 λ 2 > 0, λ 4 +λ 4 λ 5 + λ 1 λ 2 > 0 NCTS, 24th May 2011 p.19/30

45 m H± > 290 GeV: (b sγ) Constraints ρ parameter: extra-contribution: ρ Theoretical constraints: Potential bounded from bellow: λ 1 > 0, λ 2 > 0, λ 3 + λ 1 λ 2 > 0, λ 4 +λ 4 λ 5 + λ 1 λ 2 > 0 Perturbative unitarity constraints: ( λ 1 + λ 2 ± ) (λ 1 λ 2 ) λ 5 2 < 16π, ( λ 1 + λ 2 ± (λ 1 λ 2 ) 2 + 4λ4) 2 < 16π, 3(λ 1 + λ 2 ) ± 9(λ 1 λ (λ 3 + λ 4 ) 2 ) < 16π, λ 3 ± λ 4 < 8π, λ 3 ± λ 5 < 8π, λ 3 + 2λ 4 ± λ 5 < 8π. Only λ 5 is constrained not the CP phase NCTS, 24th May 2011 p.19/30

46 Numerics: H ± tb Figure 1: Left: A CP D,tb as a function of M H +. M H 0 1,H0 2 = 120, 220 GeV, Re(m 12 ) = 170 GeV, α 1 = 0.8, α 2 = 0.9 and α 3 = π/3. Right: Cancellation for tan β = 1.5. NCTS, 24th May 2011 p.20/30

47 Numerics: H ± W ± H 1 Figure 2: Left: A CP as a function of M D,WH1 0 H +. Right: Cancellation in A CP for tan β = 1.5. D,WH1 0 NCTS, 24th May 2011 p.21/30

48 Figure 3: The allowed regions in (α 1,α 2 ) plan together with A CP D,tb. M H 0 1,H0 2,H± = 120, 220, 350 GeV, Re(m 12) = 170 GeV, and α 3 = π/3. On the top left plot tan β = 1.5 and tanβ = 3 NCTS, 24th May 2011 p.22/30

49 Figure 4: The BR(H + W + H 0 1) as a function of α 1 with α 2 in the allowed parameter range, tan β = 1.5 (left), tan β = 3 (right) NCTS, 24th May 2011 p.23/30

50 Production: pp th + Figure 5: A CP P as a function of m H± with M H 0 1,H 0 2 = 120, 220 GeV, Re(m 12 ) = 170 GeV, α 1 = 0.8, α 2 = 0.9 and α 3 = π/3; Right: cancellation in A CP P as a function of M H + for tanβ = 1.5 NCTS, 24th May 2011 p.24/30

51 Production: pp th + Figure 6: The allowed parameter regions in the (α 1,α 2 ) plan in the C2HDM together with A CP P. NCTS, 24th May 2011 p.25/30

52 Production and decays NCTS, 24th May 2011 p.26/30

53 PV in neutral Higgs decays into fermion At the LHC, the expected accuracy for h τ + τ is about 20%. NCTS, 24th May 2011 p.27/30

54 PV in neutral Higgs decays into fermion At the LHC, the expected accuracy for h τ + τ is about 20%. A CP = Γ1 (H 1 f L fl ) Γ 1 (H 1 f R fr ) Γ 0 (H 1 f L fl ) + Γ 0 (H 1 f R fr ) NCTS, 24th May 2011 p.27/30

55 PV in neutral Higgs decays into fermion At the LHC, the expected accuracy for h τ + τ is about 20%. A CP = Γ1 (H 1 f L fl ) Γ 1 (H 1 f R fr ) Γ 0 (H 1 f L fl ) + Γ 0 (H 1 f R fr ) Br(H 1 τ + τ &b b) suppressed for α 2 0 and α 1 ±π/2 H 1 b b = i gm b 2m W c β (cosα 1 cos α 2 isin α 2 sin βγ 5 ) NCTS, 24th May 2011 p.27/30

56 H 1 τ + τ A CP tanβ=2 tanβ=1 -π/4 0 π/4 A CP x Br(H 1 τ + τ - ) tanβ=2 tanβ=1 -π/4 0 π/4 α 1 (rad) α 1 (rad) NCTS, 24th May 2011 p.28/30

57 H 2 t t A CP 0.1 tanβ= Br(H 1 -->tt) A CP x Br(H 2 tt) tanβ= Br(H 2 -->tt) NCTS, 24th May 2011 p.29/30

58 Production: pp th + In C2HDM with softly broken Z 2, the complex m 2 12 parameter of the tree-level potential gives CPV in pp H ± t + X, and H ± to tb, and to WH i, i=1,2 The parameters space of C2HDM is severely constrained by vacuum stability, perturbative unitarity... CPA cannot be greater than 3 %. In the CMSSM, the CPVA can reach more than 20%. However, at the LHC they will have roughly same statistical significance. Not enough for a clear observation at the LHC. need for SLHC! Calculations have been done with FeynArts & FormCalc. A new model file has been created and corresponding fortran drivers have been written and NCTS, 24th May 2011 p.30/30