Resonant H/A Mixing in CP Noninvariant 2HDM and MSSM

Transcription

1 Resonant H/A Mixing Outline S.Y. Choi (Chonbuk, Korea) Resonant H/A Mixing in CP Noninvariant 2HDM and MSSM [SYC, J. Kalinowski, Y. Liao and P.M. Zerwas, to appear in EPJC] Outline. Introduction to CP violating 2HDM 2. CP Violating Higgs Mixing General structure and resonant H/A mixing MSSM Higgs sector with distinct phenomenology Complex/non-Hermitian Higgs Mixing 3. Signatures at PLC 4. Conclusions March 2, 25 of 5

2 Resonant H/A Mixing Introduction S.Y. Choi (Chonbuk, Korea) Introduction SUSY (MSSM) is the best motivated extension of the SM, (with two Higgs doublets). The tree level MSSM Higgs potential is severely constrained. Quartic couplings are gauge couplings No CP violation Loop corrections are important and the effective potential includes All possible quartic couplings All CP violating effects Therefore, the MSSM Higgs sector CP violation can be described in the context of the general 2 Higgs doublet model. [Gunion et al. 2, Ginzburg et al. 2/4, Dubinin et al. 2/4, S.Y. Choi et al. 4, Ginzburg and CPNSH] March 2, 25 2 of 5

3 Resonant H/A Mixing CP Violating Higgs Mixing S.Y. Choi (Chonbuk, Korea) CP Violating Higgs Mixing Loop corrected MSSM Higgs sector General 2 Higgs doublet model The most general gauge invariant 2 Higgs potential (m 2 assumed to be real) V = m 2 Φ Φ + m 2 22 Φ 2 Φ 2 [ ] m 2 2 Φ Φ 2 + h.c. + 2 λ (Φ Φ ) λ 2(Φ 2 Φ 2) 2 + λ 3 (Φ Φ )(Φ 2 Φ 2) + λ 4 (Φ 2 Φ 2)(Φ 2 Φ ) { [ ] } + 2 λ 5(Φ Φ 2) 2 + λ 6 (Φ Φ ) + λ 7 (Φ 2 Φ 2) (Φ Φ 2) + h.c. The imaginary parts of λ 5, λ 6 and λ 7, signalling CP violation, are developed at the loop level with complex parameters in the other SUSY sectors. In the CP conserving case we have two CP even h, H and one CP odd A mass eigenstates. In the MSSM, all terms could effectively be non zero the CP violating 2HDM. March 2, 25 3 of 5

4 Resonant H/A Mixing CP Violating Higgs Mixing S.Y. Choi (Chonbuk, Korea) Loop induced CP violating Higgs Mixing H a CP Mixing of H a = h, H, A t, b, t, b χ, τ,... Ah,AH 3m2 f 6π 2 Im(A f µ) m 2 f 2 m 2 f H b Large radiative corrections: m tree h < m Z m h < 35 GeV [Okada et al., 99;... ] Large CP mixing among CP even and CP odd states [Pilaftsis, 998; Demir, 999; Pilaftsis and Wagner, 999; SYC, Drees and J.S.Lee, 999; Carena et al., 2; S.W. Ham et al., 22] Higgs couplings to SM and MSSM particles are significantly modified. [CPsuperH: J.S. Lee et al., 24;... ] March 2, 25 4 of 5

5 Resonant H/A Mixing CP Violating Higgs Mixing S.Y. Choi (Chonbuk, Korea) The mass matrix M 2 in the (h, H, A) basis takes the form λ + (m 2 A /v2 λ A )c 2 γc 2γ ˆλ p s γ λ p c γ λ (m 2 A /v2 λ A )s 2 γc 2γ ˆλ p c γ + λ p s γ ˆλ p s γ λ p c γ ˆλ p c γ + λ p s γ m 2 A /v2 All h, H, A mix H, H 2, H 3 mass eigenstates w/o definite CP parities ˆλ p, λ p,(λ q ) are combinations of imaginary parts of λ 5, λ 6, λ 7 ˆλ p = Im(λ 5 )s β c β + Im(λ 6 )c 2 β + Im(λ 7)s 2 β λ p = 2 Im(λ 5)(c 2 β s2 β ) Im(λ 6 λ 7 )s β c β λ q = Im(λ 5 )s β c β Im(λ 6 )s 2 β Im(λ 7)c 2 β If ˆλ p = λ p =, but λ q CP violation via triple/quartic couplings March 2, 25 5 of 5

6 Resonant H/A Mixing Masses and Couplings S.Y. Choi (Chonbuk, Korea) M H, M H2 [ GeV ] g 2, g 2, g 2 HZZ H2ZZ H3ZZ arg (A t ) = arg (A b ) [ deg ] (a) - M H + = 5 GeV, tanβ = 4 µ = 2 TeV, A t = A b = TeV M SUSY =.5 TeV, m(gluino) = TeV m(wino) = m(bino) =.3 TeV g 2 HZZ g 2 H3ZZ g 2 HZZ SUSY Modes: M,2 = 5/5 GeV.35.3 B(H χ χ ) : GAMBRN(5,3,).9 H 2 : GAMBRN(,3,2).8.25 Φ =.7 H 3 : GAMBRN(,3,3).2 Φ = Φ = Φ =9.2 H ± : GAMBRC(5,3) Φ µ [ ] Φ µ [ ] -2 g 2 H2ZZ arg (A t ) = arg (A b ) [ deg ] (b) March 2, 25 6 of 5

7 Resonant H/A Mixing Branching Fractions S.Y. Choi (Chonbuk, Korea) Φ A = Φ 3 = o Φ A = Φ 3 = 9 o - -2 BR(H ) gg bb ττ cc WW - -2 BR(H 2 ) bb ττ H Z tt - -2 BR(H ) bb ττ WW gg - -2 BR(H 2 ) H H bb ττ WW ZZ gg H Z tt γγ M H BR(H 3 ) WW H H tt bb H H ττ ZZ gg cc M H3 2 Γ(H) H3 H2 H 2 H ± gg 5 2 M H2 5 2 M H -3 γγ cc M H BR(H 3 ) bb H H tt H H WW ZZ ττ H Z -2 gg M H3 cc 2 Γ(H) H3 H2 H 2 H H 5 2 M H2 H ± 5 2 M H March 2, 25 7 of 5

8 Resonant H/A Mixing Higgs Searches S.Y. Choi (Chonbuk, Korea) [P. Bechtle, hep ex/47] LEP GeV Preliminary OPAL preliminary tanβ m h -max tanβ MSSM CPX FeynHiggs.3 Excluded by LEP FeynHiggs 2. m +5 GeV t Excluded Theoretically inaccessible Theoretically Inaccessible Theoretically inaccessible m h (GeV/c 2 ) m H (GeV) March 2, 25 8 of 5

9 Resonant H/A Mixing Non Hermitian Mixing S.Y. Choi (Chonbuk, Korea) Non Hermitian Mixing The hermitian M 2 must be supplemented with anti hermitian imγ built up by loops!, particularly crucial for degenerate states [K K, B B, n n mixing] As a result of the complex mixing, the Higgs exchange process must include both diagonal and off diagonal H a H b complex transitions. [H a,b = h, H, A] X H a H b Y Diagonalize the complex/symmetric Weisskopf Wigner matrix cut M 2 c = M 2 imγ [SYC, Kalinowski, Liao, Zerwas, 4; Ellis, J.S. Lee, Pilaftsis, 4] March 2, 25 9 of 5

10 Resonant H/A Mixing Decoupling Limit S.Y. Choi (Chonbuk, Korea) Decoupling Limit: m 2 A λ i v 2 H becoms the CP even SM like and decouples from the H/A system. H and A almost degenerate The 2 state complex H/A mixing can be large. [ ] m 2 M 2 H im H Γ H δm 2 HA c = m 2 A im M 2 diag AΓ = CM2 cc T A δm 2 HA The rotation matrix C with a complex mixing angle θ is given by [ ] cos θ sin θ C =, X sin θ cos θ 2 tan2θ = δm 2 HA m 2 H m2 A i(m HΓ H m A Γ A ) H 2 and H 3 no longer orthogonal Need to use both bra and ket states! H 2 = cos θ H + sin θ A, H 2 = cos θ H + sin θ A H 3 = sin θ H + cos θ A, H 3 = sin θ H + cos θ A Correspondingly, the transition amplitudes for X H Y are given by Y H X = Y H i s m 2 H i X H i + im Hi Γ Hi i=2,3 March 2, 25 of 5

11 Resonant H/A Mixing CP violating MSSM S.Y. Choi (Chonbuk, Korea) Example: CP violating MSSM M S =.5 TeV, A t =. TeV, µ =. TeV, φ µ = ; tan β = 5 Turning on the phase φ A of A t with only t/ t and h in the loops 5 Re(X) Im(X) Mixing Parameter φ A [π] March 2, 25 of 5

12 Resonant H/A Mixing CP violating MSSM S.Y. Choi (Chonbuk, Korea) For φ A =, M H /M A = 5.3/5. GeV and Γ H /Γ A =.2/.5 GeV Mass and Width Shifts 6 (a) Mass Shift.6 (b) Width Shift M 3-3 Γ φ A [π] φ A [π] March 2, 25 2 of 5

13 Resonant H/A Mixing Signatures at PLC S.Y. Choi (Chonbuk, Korea) Signatures at the Photon LC () Higgs formation in polarized γγ collisions γγ H i Y [i = 2,3] with the following CP even and CP odd asymmetries A lin = σ σ σ + σ and A hel = σ ++ σ σ ++ + σ (2) Top polarization in (γγ )H i t t [φ angle between t and t decay planes] dγ = [ π2 (m 2 t ] 2m2 W )2 ( ) Γdφ 2π 6(m 2 t + C cos φ + C sin φ 2m2 W )2 with the following CP even and CP odd azimuthal correlators C = s s and C = ˆp t (s s ) March 2, 25 3 of 5

14 Resonant H/A Mixing Signatures at PLC S.Y. Choi (Chonbuk, Korea).5 H 2.5 H 2.5 H 2.5 H 3 A lin A hel C C H H 2 H φ A [π] φ A [π] H φ A [π] φ A [π].5 A hel.5 C -.5 A lin -.5 C E γγ E tt γγ H φ A = 3π/4 H t t March 2, 25 4 of 5

15 Resonant H/A Mixing Conclusions S.Y. Choi (Chonbuk, Korea) Conclusions A general CP violating two Higgs doublet model Need to include decay widths in the mixing formalism The complex mixing can be large for (nearly) degenerate states. An interesting case: the decoupling limit in the 2HDM MSSM Higgs bosons in the decoupling limit with M A > 2m Z The lightest H is a CP even SM like Higgs boson. Naturally, H and A become nearly degenerate in the limit. CP violating loop corrections lead to large complex H/A mixing. Complex mixing can be investigated in γγ H i t t with large CP effects. Encouraging results!! Do detailed expt l simulations! Extensions to NMSSM and Application to χχ H/A March 2, 25 5 of 5