Constraints on Multi-Higgs-Doublet Models: Flavour Alignment Antonio Pich IFIC, Univ. Valencia - CSIC A. Pich, P. Tuzón, Phys. Rev. D80 (009) 09170 M. Jung, A. Pich, P. Tuzón, JHEP 1011 (010) 003 M. Jung, A. Pich, P. Tuzón, Phys. Rev. D83 (011) 074011 A. Pich, arxiv:1010.517 [hep-ph]
Lepton-Photon, Mumbai, August 011: Excluded: M H (GeV) [145, 88] [96, 466] A-HDM A. Pich Paris 011
H. Bachacou, Lepton-Photon 011 A-HDM A. Pich Paris 011 3
A-HDM A. Pich Paris 011 4
Possible Scenarios: 1 Light SM Higgs. Favoured by EW precision tests Alternative perturbative EW SSB. Scalar Doublets and singlets (ρ) 3 Heavy Higgs. Non-perturbative EW SSB 4 No Higgs. Dynamical EW SSB A-HDM A. Pich Paris 011 5
Standard Model ( ) φ (+) One Higgs Doublet Φ = φ (0) Q L (ū L, d L ), Φ iτ Φ, 0 Φ 0 = ( 0 v ) L Y = Q il Γ ij Φd jr Q il ij Φu jr L il Π ijφl jr + h.c. SSB M d = v Γ, M u = v, M l = v Π Diagonalization { GIM Mechanism (Unitarity) Yukawas proportional to masses No Flavour-Changing Neutral Currents A-HDM A. Pich Paris 011 6
Two Higgs Doublets: φ a (a = 1,) 0 φ T a (x) 0 = 1 (0,v a e iθa ), θ 1 = 0, θ θ θ 1 Higgs basis: v v 1 +v, tanβ v /v 1 ( Φ1 Φ ) [ cosβ sinβ sinβ cosβ ] ( φ1 e iθ φ ) Φ 1 = [ ] ( G + 1 v +S1 +ig 0), Φ = [ 1 H + (S +is 3 ) ] Mass eigenstates: H ±, ϕ 0 i (x) {h(x),h(x),a(x)} = R ij S j (x) A-HDM A. Pich Paris 011 7
Yukawa Interactions in HDMs L Y = Q L (Γ 1φ 1 +Γ φ )d R Q L ( 1 φ 1 + φ )u R L L (Π 1φ 1 +Π φ )l R + h.c. L Y = v SSB { Q L (M d Φ 1 +Y d Φ )d R + Q L (M u Φ 1 +Y u Φ )u R + L L (M l Φ 1 +Y l Φ )l R + h.c. } M f and Y f unrelated M d = v 1 Γ 1 +v Γ e iθ, FCNCs M u = v 1 1 +v e iθ Y d = v 1 Γ e iθ v Γ 1, Y u = v 1 e iθ v 1 A-HDM A. Pich Paris 011 8
Avoiding FCNCs Very large scalar masses THDM irrelevant at low energies Very small scalar couplings Type III model: (Y f ) ij m i m j Yukawa textures (Cheng - Sher 87) Discrete Z symmetries: only one φ a (x) couples to a given f R (x) (Glashow - Weinberg 77) Z : φ 1 φ 1, φ φ, Q L Q L, L L L L, f R ±f R CP conserved in the scalar sector A-HDM A. Pich Paris 011 9
Aligned HDM (Pich - Tuzón 09) Require alignment in Flavour Space of Yukawa couplings: Γ = ξ d e iθ Γ 1, = ξ u eiθ 1, Π = ξ l e iθ Π 1 Y d,l = ς d,l M d,l, Y u = ς u M u, ς f ξ f tanβ 1+ξ f tanβ L Y = 1 v v H+{ ū [ ς d V CKM M d P R ς u M u V P ] CKM L d + ςl ( νm l P R l)} y ϕ 0 i f ϕ 0 i ϕ 0 i,f ( f Mf P R f ) + h.c. A-HDM A. Pich Paris 011 10
Fermionic couplings proportional to fermion masses. Neutral Yukawas are diagonal in flavour y ϕ0 i d,l = R i1 +(R i +i R i3 )ς d,l, y ϕ0 i u = R i1 +(R i i R i3 )ς u V CKM is the only source of flavour-changing phenomena All leptonic couplings are diagonal in flavour Only three new (universal) couplings ς f. The usual Z models are recovered in the limits ξ f 0, The inert doublet model corresponds to ς f = 0 (ξ f = tanβ) ς f are arbitrary complex numbers New sources of CP violation without tree-level FCNCs A-HDM A. Pich Paris 011 11
AHDM: General phenomenological setting without tree-level FCNCs L Y = 1 v v H+{ ū [ ς d V CKM M d P R ς u M u V P ] CKM L d + ςl ( νm l P R l)} y ϕ 0 i f ϕ 0 i ϕ 0 i,f ( f Mf P R f ) + h.c. Z models: Model ς d ς u ς l Type I cotβ cotβ cotβ Type II tanβ cotβ tanβ Type X cotβ cotβ tanβ Type Y tanβ cotβ cotβ Inert 0 0 0 A-HDM A. Pich Paris 011 1
Quantum Corrections L AHDM invariant under the phase transformation: [α ν i = α l i ] fl i (x) eiαf,l i fl i(x), f R i (x) eiαf,r i f i R (x) V ij CKM eiαu,l i V ij e iαd,l j, M CKM f,ij e iαf,l i M f,ij e iαf,r j Leptonic FCNCs absent to all orders in perturbation theory Loop-induced FCNCs local terms take the form: ū L V CKM (M d M d )n V CKM (M um u) m M u u R d L V CKM (M um u) n V CKM (M d M d )m M d d R MFV structure (D Ambrosio et al, Chivukula-Georgi, Hall-Randall, Buras et al, Cirigliano et al) A-HDM A. Pich Paris 011 13
Minimal Flavour Violation in HDMs SU(N G ) 5 Flavour Symmetry in the Gauge Sector (Q L, u R, d R, L L, l R ) Spurion Formalism: (D Ambrosio et al 0, Buras et al 10) Γ 1 ( N G,1,N G,1,1 ) 1 ( N G,N G,1,1,1 ) Π 1 ( 1,1,1,N G,N G ) Aligned Yukawas are also invariant Allowed Operators: Q L (Γ 1 Γ 1 )n ( 1 1 )m 1 u R Q L ( 1 1 )n (Γ 1 Γ 1 )m Γ 1 d R A-HDM A. Pich Paris 011 14
FCNCs at one Loop General HDM 1-loop Renormalization Group Eqs. known (Cvetic et al, Ferreira et al) (Jung-Pich-Tuzón) L FCNC = C(µ) 4π v 3 (1+ς uς d ) ϕ 0 i (x) i { ] (R i +i R i3 ) (ς d ς u ) [ d L V M CKM u M u V M CKM d d R ]} (R i i R i3 ) (ςd ς u) [ū L V CKM M d M d V CKM M uu R + h.c. C(µ) = C(µ 0 ) log(µ/µ 0 ) Vanish in all Z models as it should Suppressed by m q m q /(4π v 3 ) and V qq CKM s L b R, c L t R A-HDM A. Pich Paris 011 15
Phenomenological Constraints Jung-Pich-Tuzón τ µ/e: g µ /g e = 1.0036±0.009 ς l /M H ± < 0.40 GeV 1 (95% CL) Γ(P l ν l ) = m P 8π ( ) 1 m l mp G F m l f P V ij CKM 1 ij ij = m P M H ± ς l ς u m ui +ς d m dj m ui +m dj Γ(P P l ν l ) Scalar form factor: f0 (t) = f 0 (t) (1+δ ij t) δ ij ς l M H ± m i ς u m j ς d m i m j A-HDM A. Pich Paris 011 16
Global fit to P lν l, τ Pν τ, P P lν l (95% CL) Jung-Pich-Tuzón 0.15 0.1 Γ(K µν)/γ(π µν)+ Γ(τ Kν)/Γ(τ πν) M lν+b Dτν+ Z bb+τ µν 0.4 0.3 D µν M lν+b Dτν 0. Im(ζ d ζ * l/m H) 0.05 0-0.05 B τν Im(ζ u ζ * l/m H) 0.1 0-0.1 D s µ/τν(+b τν) -0. -0.1-0.15-0.1 0.0 0.1 0. Re(ζ d ζ * l/m H) C K M f i t t e r package -0.3 C K M f i t t e r R(B Dlν)(+B τν) package -0.4-0.1 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 Re(ζ u ζ * l/m H) (GeV units) A-HDM A. Pich Paris 011 17
Real Couplings: Jung-Pich-Tuzón 0.7 D s τν τ (B τν τ ) 0.7 D s µν µ (B τν τ ) 0.6 0.6 0.5 0.5 Re Ζ l Ζ u M H 0.4 0.3 0. 0.1 Re Ζ l Ζ u M H 0.4 0.3 0. 0.1 0.0 0.0 0.1 0.0 0. 0.4 0.6 Re Ζ l Ζ d M H 0.1 0.0 0. 0.4 0.6 Re Ζ l Ζ d M H 0.7 B Dτν τ Re Ζ l Ζ u M H 0.6 0.5 0.4 0.3 0. 0.1 0.0 (95% CL, GeV units) Type I/X: Dashed Line Types II/Y: Lighter grey area, tanβ [0.1,60] 0.1 0.0 0. 0.4 0.6 Re Ζ l Ζ d M H A-HDM A. Pich Paris 011 18
1-Loop Constraints on H ± Couplings q u, c, t b q W b B 0 B 0 Mixing W W u, c, t u, c, t b u, c, t q b W q Z b b b W t Z b b W t Z b Virtual H ± /W ±. Top-dominated contributions A-HDM A. Pich Paris 011 19
Constraints from Z b b and M Bs (95% CL) Jung-Pich-Tuzón 3 Z b b ( ς d < 50) 1 3.0 M Bs ( ς d < 50).5 0.9 0.8.5 0.7.0 0.6 ζ u 1.5 0.5 Ζu 1.5 1 0.5 0.4 0.3 0. 1.0 0.5 ς d = 0 0 C K M f i t t e r package 100 00 300 400 500 0 M H /GeV 0.1 0.0 100 00 300 400 500 M H GeV ς u /M H ± < 0.011 GeV 1 ς u ς l /M H ± < 0.005 GeV τ A-HDM A. Pich Paris 011 0
Constraints from ǫ K (95% CL) Jung-Pich-Tuzón A-HDM A. Pich Paris 011 1
Constraints from b sγ (95% CL) Jung-Pich-Tuzón Complex couplings Real couplings ς u = 0.5 ς u = 0.5 Ci eff (µ W ) = C i,sm + ς u C i,uu (ςu ς d ) C i,ud A-HDM A. Pich Paris 011
Global Constraints on Z Models (95% CL) Jung-Pich-Tuzón 3 Type I 3 Type X.8 b sγ.8 Log(M H /GeV).6.4. M/τ lν + B Dτν Log(M H /GeV).6.4. τ lν C K M f i t t e r package Z bb -1.0-0.5 0.0 0.5 1.0 1.5.0 Log(tan(β) ς u = ς d = ς l = cotβ C K M f i t t e r package Z bb b sγ -1.0-0.5 0.0 0.5 1.0 1.5.0 Log(tan(β) ς u = ς d = ς 1 l = cotβ A-HDM A. Pich Paris 011 3
Global Constraints on Z Models (95% CL) Jung-Pich-Tuzón 3 Type II 3 Type Y.8 b sγ.8 b sγ Log(M H /GeV).6.4. M/τ lν + B Dτν Z bb Log(M H /GeV).6.4. M/τ lν + B Dτν Z bb C K M f i t t e r package C K M f i t t e r package -1.0-0.5 0.0 0.5 1.0 1.5.0 Log(tan(β) -1.0-0.5 0.0 0.5 1.0 1.5.0 Log(tan(β) ς u = ς 1 d = ς 1 l = cotβ ς u = ς 1 d = ς l = cotβ M H ± > 77 GeV In agreement with previous analyses (Aoki et al, Wahab et al, Deschamps et al, Flacher at al, Bona et al, Mahmoudi-Stal, Misiak et al...) A-HDM A. Pich Paris 011 4
Constraints from b sγ (95% CL) Jung-Pich-Tuzón Important Correlations: C eff i (µ W ) = C i,sm + ς u C i,uu (ς uς d ) C i,ud 5 ς uς d vs. M H ± ς u ς d vs. arg(ς u ς d ) 0 Ζ u Ζd 15 10 5 0 100 00 300 400 500 MH Stronger constraint for small Scalar Masses For ϕ arg(ςu ς d ) = π (0) constructive (destructive) interference Important restriction on CP asymmetries A-HDM A. Pich Paris 011 5
Direct CP Asymmetry in b sγ Jung-Pich-Tuzón Small in the SM (Ali et al 98, Kagan-Neubert 98, Hurth et al 05) Potentially large in general HDMs (Borzumati-Greub 98) However, strongly constrained by Br(b sγ) a CP Γ Γ Γ+ Γ Compatible with measurement, but it could be sizeable A-HDM A. Pich Paris 011 6
D0: µ ± µ ± Asymmetry B 0 Mixing a s sl 0.0 0 SM A b sl N++ b N ++ b N b +N b -0.0-0.04 Standard Model B Factory W.A. DØ B s µd s X DØ Asl b DØ Asl b 95% C.L. DØ, 9.0 fb -1-0.04-0.0 0 0.0 a d sl a q sl Γ( B 0 q µ + X) Γ(B 0 q µ X) Γ( B 0 q µ+ X)+Γ(B 0 q µ X) = Γ q M q tanφ q LHCb does not confirm a large φ s in B s J/Ψφ (D0/CDF) D0 data seems to require new-physics contribution in Γ s A-HDM A. Pich Paris 011 7
LHCb-CONF-011-056 Average of Bs J/ψϕ and Bs J/ψf0 Simultaneous fit to both samples: LHCb Preliminary ϕs = 0.03 ± 0.16 ± 0.07 rad With present statistics, no evidence for deviation from the SM. Next steps: 1) Increase statistics (luminosity) ) Add same-side Kaon tagging 3) Break ambiguity by looking at relative S-wave phase vs. M(KK) in J/ψϕ G. Raven, Lepton-Photon 011 ] -1 [ps Γ s LL 0 18 16 14 1 10 8 6 4 0 0.5 0. 0.15 0.1 0.05 0-0.05-0.1-0.15-0. -0.5 LHCb Preliminary ΔΓs<0-4 -3 - -1 0 1 (rad) s LHCb Preliminary -1 s = 7 TeV, L 337 pb Bs J/ψ f0-4 - 0 68% C.L. 90% C.L. 95% C.L. ΔΓs>0 Bs J/ψϕ φ [rad] s A-HDM A. Pich Paris 011 8 33
B 0 s B 0 s Mixing Phase within the AHDM Jung-Pich-Tuzón Maximum possible enhancement from H ± exchanges: Sin Φs s Sin Φ s SM 6 4 a sl a sl SM = sinφ sinφ SM 4 1 3 4 5 6 Arg Ζ u Ζ d rad φ arg( M 1 /Γ 1 ) M 1 /M SM 1 H ± contributions to M are too small to explain the D0 asymmetry A-HDM A. Pich Paris 011 9
Electric Dipole Moments Highly sensitive to flavour-blind CP-violating phases Stringent experimental bounds: neutron, Thallium, Mercury... 1-loop H ± contributions very suppressed by light-quark masses Contributions from 4-fermion operators are small (also induced by φ 0 i exchange with 1-loop FCNC vertices) (Buras et al) Two-loop contributions dominate (Weinberg 89, Dicus 90, Barr-Zee 90) A-HDM A. Pich Paris 011 30
Neutron EDM dominated by H ± contribution to L W L W = C W 6 f abc ǫ µναβ G a µρg bρ ν G c αβ, C W Im(ς u ς d ) Jung-Pich-Tuzón, preliminary b sγ b sγ + d γ n d γ n M H ± = 80 GeV M H ± = 500 GeV M H ± = 500 GeV Im(ς u ςd ) strongly constrained, but not tiny A-HDM A. Pich Paris 011 31
Higgs Production (CP assumed) y h0 t = cos α+ς u sin α λ h0 W,Z = cos α y H0 t = sin α+ς u cos α λ H0 W,Z = sin α Charged Higgs: Z H + H, t H + b, W + H + h 0 (H 0 ) CP-odd A 0 : t t A 0, W + H + A 0, Z 0 A 0 h 0 (H 0 ) CP-violation: ϕ 0 i mixing (h 0, H 0, A 0 ), ς f A-HDM A. Pich Paris 011 3
Higgs Decay (CP assumed) λ h0 W,Z = cos α λ H0 W,Z = sin α y h0 t = cos α+ς u sin α y H0 t = sin α+ς u cos α h 0 (H 0 ) W ± H, h 0 (H 0 ) Z A 0, H 0 h 0 A 0 H + t b, H + W + h 0 (H 0 ) A 0 t t, A 0 W ± H, A 0 Z 0 h 0 (H 0 ), A 0 h 0 H 0 A-HDM A. Pich Paris 011 33
SUMMARY The Aligned THDM provides a general phenomenological setting Includes all Z models Tree-level FCNCs absent by construction Leptonic FCNCs forbidden to all orders Loop-induced quark FCNCs very constrained (MFV like) New sources of CP violation through ς f Satisfies flavour constraints with ς f O(1) Sizeable flavour-blind phases allowed by EDMs Interesting collider phenomenology A-HDM A. Pich Paris 011 34
Backup Slides A-HDM A. Pich Paris 011 35
CKM Fit within the AHDM Only the constraints from V ub /V cb and m s / m d survive γ from tree-level decays excludes the nd solution m s / m d = ( m s / m d ) SM + O[(m s m d )ς d /M W ] A-HDM A. Pich Paris 011 36
Parameter Value Comment f Bs (0.4±0.003±0.0) GeV f Bs /f Bd 1.3±0.016±0.033 f Ds (0.417±0.001±0.0053) GeV f Ds /f Dd 1.171±0.005±0.0 f K /f π 1.19±0.00±0.013 f Bs ˆB B 0 s (0.66±0.007±0.03) GeV f Bd ˆBB 0 s /(f Bs ˆBB 0 s ) 1.58±0.05±0.043 ˆB K 0.73±0.006±0.043 V ud 0.9745±0.000 ( λ 0.55 ± 0.0010 1 Vud ) 1/ V ub (3.8±0.1±0.4) 10 3 b ulν (excl. + incl.) A 0.80±0.01±0.01 b clν (excl. + incl.) ρ 0.15±0.0±0.05 Our fit η 0.38±0.01±0.06 Our fit ρ B Dlν 1.18±0.04±0.04 B Dlν 0.46±0.0 (0) 0.965±0.010 f Kπ + A-HDM A. Pich Paris 011 37
Φ 1 = [ ] ( G + 1 v +S1 +ig 0), Φ = [ 1 H + (S +is 3 ) ] Goldstones: G ±, G 0 Mass eigenstates: H ±, ϕ 0 i ϕ 0 i (x) = {h(x),h(x),a(x)} = R ij S j (x) (x) = {h(x),h(x),a(x)} CP-conserving scalar potential: ( H h ) = [ cos α sin α sin α cos α ] ( S1 A(x) = S 3 (x) S ) A-HDM A. Pich Paris 011 38