Leptonic decays in 2HDM Maria Krawczyk, Warsaw U. with David Temes - PowerPoint PPT Presentation

Leptonic τ decays in 2HDM Maria Krawczyk, Warsaw U. with David Temes – hep-ph/0410248 [EPJC 44(2005)435] Outlook • The leptonic tau decays • Two Higgs Doublet Model (CP conservation) • Large loop corrections for leptonic tau decays • Constraints on masses and couplings for neutral and charged Higgs bosons M. Krawczyk 1 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

� ✁ ✂ ✁ ✄ ☎ The τ lepton A unique laboratory to test the Standard Model and beyond ✆✞✝ The coupling of the τ lepton to the W : g τ = coupling ( τν τ W ) In Standard Model → lepton universality: g e = g µ = g τ • Radiative corrections in 2HDM –Rosiek ’90 • A τ puzzle ’92: Data on leptonic branching ratio too low by 2 . 5 σ than expected in SM → “Tau decay in the two Higgs doublet model”: Guth, Hoang, Kuhn ’92 → “Can a second Higgs doublet diminish the leptonic tau decay width?” Hollik, Sack ’92, • Precise data in agreement with SM - can be used to constrain 2HDM M. Krawczyk 2 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

2HDM models without and with CP violation 2HDM Potential with quartic and quadratic terms separated: 2 λ 1 ( φ † 1 φ 1 ) 2 + 1 2 λ 2 ( φ † 2 φ 2 ) 2 + λ 3 ( φ † 1 φ 1 )( φ † 2 φ 2 ) + λ 4 ( φ † 1 φ 2 )( φ † V = 1 2 φ 1 ) 1 φ 2 ) 2 + h . c . λ 5 ( φ † ( λ 6 ( φ † 1 φ 1 ) + λ 7 ( φ † 2 φ 2 ))( φ † + 1 � � � � + 1 φ 2 ) + h . c . 2 hard 11 ( φ † 12 ( φ † 22 ( φ † − 1 � � � � m 2 m 2 soft + m 2 1 φ 1 ) + 1 φ 2 ) + h . c . 2 φ 2 ) 2 In general 14 parameters: λ 1 , λ 2 , λ 3 , λ 4 , λ 5 , λ 6 , λ 7 , m 2 11 , m 2 22 , m 2 12 The ( φ 1 , φ 2 ) mixing ↔ Z 2 symmetry: φ 1 → − φ 1 , φ 2 → φ 2 (or 1 ↔ 2) Z 2 -symmetry if ⇒ λ 6 = λ 7 = m 2 12 = 0 soft violation of Z 2 symmetry governed by µ 2 ∼ Re m 12 Lee, Diaz-Cruz, Mendez, Haber, Pomarol, Barroso, Santos, Hollik, Djouadi, Illana, Branco,Gunion, Grzadkowski,Akeroyd, Arhrib, Dubnin, Froggatt, Sher, Pilaftsis, Carena.. Kalinowski, Zerwas, Choi, Kanemura, Okada,. M. Krawczyk 3 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Symmetries of Two Higgs Doublet Model I. F. Ginzburg, M. Krawczyk, hep-ph/0408011 (PRD’05); I. F. Ginzburg at PLC2005 • 2HDM contains two fields, φ 1 and φ 2 , with identical quantum numbers: weak isodoublets ( T = 1 / 2) with hypercharges Y = +1 • Global transformations which mix these fields and change the relative phases are allowed without changing physical picture • One of the reason for introducing 2HDM was to describe phenomenon of CP violation Lee’ 73; Glashow and Weinberg’77- CP violation and the flavour changing neutral currents (FCNC) can be naturally suppressed by imposing in Lagrangian a Z 2 symmetry, that is the invariance of the Lagrangian under the interchange ( φ 1 ↔ φ 1 , φ 2 ↔ − φ 2 ) or ( φ 1 ↔ − φ 1 , φ 2 ↔ φ 2 ) . This symmetry forbids the φ 1 ↔ φ 2 transition. Branco, Rebelo’ 85 M. Krawczyk 4 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Symmetries of 2HDM Weinberg, Glashow, ’77; Branco, Rebelo ’85 - ’05; Botella, Silva ’94, Botella, Nebot, Vives, Lavoura 95,04..Ginzburg, MK ’04, Ivanov’05, Haber, Gunion’05 Two fields with identical quantum numbers → mixing A global unitary transformation U(1)x SU(2): cos θ e iρ/ 2 sin θ e i ( τ − ρ/ 2) � φ ′ � � � � � φ 1 = e − iρ 0 1 − sin θ e − i ( τ − ρ/ 2) cos θ e − iρ/ 2 φ ′ φ 2 2 This transformation induces changes in parameters of L: i and m 2 ij → ( m ′ ) 2 λ i → λ ′ ij A space of Lagrangians with coordinates given by parameters of L... i and m 2 ij → ( m ′ ) 2 • A reparametrization transformation (RPaT) λ i → λ ′ ij - 3 parametrical group with parameters: ρ , θ , τ • A reparametrization invariance → a reparametrization equivalent space of L (3-dim subspace in 14-dim space) Physical observables invariant of the RPaT like masses. But not tan β ! • The rephasing transformation group - one parameter only ρ . M. Krawczyk 5 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Reparametrization: Lagrangian and Z 2 symmetry The violation of the Z 2 symmetry allows for the φ 1 ↔ φ 2 transitions. • Exact Z 2 symmetry. λ 6 = λ 7 = m 2 12 = 0. Only λ 5 can be complex, by rephasing → λ 5 real. • A soft violation of Z 2 symmetry. Adding to the Z 2 symmetric 12 ( φ † Lagrangian the term m 2 1 φ 2 ) + h.c. , with a generally complex m 2 12 ; as before λ 5 can be made real by rephasing. • A hard violation of Z 2 symmetry. (Operator dimension 4) with generally complex parameters λ 6 , λ 7 are added to V with a softly broken Z 2 symmetry. The true hard violation of Z 2 - if V cannot be transformed to the case of Z 2 conservation, nor its weak violation. Remarks on CP The complex values of some of parameters in V provide a necessary condition for the CP violation in the Higgs sector. If V can be reparametrized so that all parameters became real - no CP violation is present. M. Krawczyk 6 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Vacuum The extremes of the potential define the vacuum expectation values (v.e.v.’s) of the fields φ 1 , 2 � � ∂V ∂V � � = 0 , = 0 . (1) � � ∂φ 1 � ∂φ 2 � � φ 1= � φ 1 � , � φ 1= � φ 1 � , φ 2= � φ 2 � φ 2= � φ 2 � The U(1) QED symmetric one corresponds to the lower energy than the charged one (Diaz-Cruz, Mendez; Santos, Barroso, Velhinho, GK)   0 � � 1 , � φ 2 � = 1 0  . √ √ � φ 1 � = (2)  v 1 2 2 v 2 e iξ • The rephasing of fields shifts the phase difference ξ as ξ → ξ − ρ . (3) so, the phase difference ξ has no physical sense (Branco). • The ratio tan β = v 2 depends on reparametrization! v 1 M. Krawczyk 7 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

CP conservation: Higgs masses and couplings Physical content of the Higgs potential: h, H, A, H ± • Higgs masses - Two cases: masses of H + , A, H can be large due large µ 2 (decoupling) or large λ ′ s (nondecoupling) • Higgs trilinear couplings • Higgs quartic couplings Independent of the form of Higgs potential are: • couplings to gauge bosons: hWW , HWW , while AWW = AZZ = 0 • couplings to fermions (Yukawa) e.g. Model II: φ 1 → u -type fermions φ 2 → d -type fermions The relative “basic couplings”: g i j χ i j = i = h, H, A ; j = V, u, d g SM j j ) 2 = 1, for j = V, u, d eg. Σ i ( χ i Relations between relative couplings: M. Krawczyk 8 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Existing constraints for 2HDM (II) CP conserv. 2HDM(II) with soft violation of Z 2 symmetry ( µ 2 term): ⇒ five Higgs bosons: h , H , A , H ± ⇒ 7 parameters: M h , M H , M A , M H ± , α, β , and µ 2 MODEL II (as in MSSM) Couplings (relative to SM): h A to W/Z: χ V = sin( β − α ) 0 � 1 − χ 2 to down quarks/leptons: χ d = χ V − V tan β − iγ 5 tan β � 1 − χ 2 to up quarks: χ u = χ V + V / tan β − iγ 5 / tan β For H couplings like for h with: sin( β − α ) ↔ cos( β − α ) and tan β → − tan β . For large tan β → enhanced couplings to d − type fermions (and τ, µ, e )! χ h V H + = cos( β − α ) - complementarity to hV V ! M. Krawczyk 9 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

DATA LEP • direct:( h ) Bjorken process Z → Zh , → sin( β − α ) ( hA ) pair prod. e + e − → hA , → cos( β − α ) ( h/A ) Yukawa process e + e − → bbh/A , ττh/A , → tan β ( H ± ) e + e − → H + H − via loop:( h/A, and H ± ) Z → h/Aγ Others exp. • via loop:( h/A ) Wilczek process Υ → h/Aγ loop: ( H ± ) b → sγ , → lower limit for M H ± leptonic tau decay → g-2 data , → upper limit for χ d Global fit • (all Higgses) Chankowski at al.,’99 (EPJC 11,661;PL B496,195) Cheung and Kong ’03 M. Krawczyk 10 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Constraints from b → sγ - Gambino, Misiak’01 Strong constraints on new physics from ¯ B → X s γ The weighted average for BR γ ≡ BR[ ¯ B → X s γ ] BR exp = (3 . 23 ± 0 . 42) × 10 − 4 γ NLO prediction (Misiak, Gambino’01): M H + above 490 GeV (95%) 500 B → X s γ R b B-> τ ν B->X τ ν 400 DIRECT M H + [GeV] 300 TYPE II 2HDM 200 100 10 20 30 40 50 60 70 tan β Here mass limit 350 GeV corresponds to 99 % CL ! M. Krawczyk 11 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Direct and undirect limits for charged Higgs boson - PDG2004 Tevatron and LEP limits (90 GeV) M. Krawczyk 12 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Neutral Higgs bosons - couplings to gauge boson, and mass exclusion Light h OR light A in agreement with current data hZZ: sin ( β − α ) and hAZ: cos ( β − α ) OPAL 100 100 m A [GeV] m A [GeV] Limit on k 0.4 ≤ tan β ≤ 58 90 90 OPAL 0.4 ≤ tan β ≤ 1.0  80 80 √ s = 91, 183-209 GeV 1.0 < tan β ≤ 58 70 70 1 expected 60 60 Γ Z constraint 50 50 Observed 40 40 -1 Expected 10 (CL=95%) 30 30 20 20 10 10 -2 10 0 0 10 -6 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 m h [GeV] m h [GeV] m S0 (GeV) Light scalar h → small k = sin 2 ( β − α ) ! M. Krawczyk 13 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006