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: gτ = coupling (τντW) In Standard Model → lepton universality: ge = gµ = gτ

• Radiative corrections in 2HDM –Rosiek ’90
• A τ puzzle ’92: Data on leptonic branching ratio too low by 2.5σ 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:

V = 1

2λ1(φ† 1φ1)2 + 1 2λ2(φ† 2φ2)2 + λ3(φ† 1φ1)(φ† 2φ2) + λ4(φ† 1φ2)(φ† 2φ1)

+1

2

• λ5(φ†

1φ2)2 + h.c.

• +
• (λ6(φ†

1φ1) + λ7(φ† 2φ2))(φ† 1φ2) + h.c.

• hard

−1

2

• m2

11(φ† 1φ1) +

• m2

12(φ† 1φ2) + h.c.

• soft + m2

22(φ† 2φ2)

• In general 14 parameters: λ1, λ2, λ3, λ4, λ5, λ6, λ7, m2

11, m2 22, m2 12

The (φ1, φ2) mixing ↔ Z2 symmetry: φ1 → −φ1, φ2 → φ2 (or 1 ↔ 2) Z2-symmetry if ⇒ λ6 = λ7 = m2

12 = 0

soft violation of Z2 symmetry governed by µ2 ∼ Re m12

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, φ1 and φ2, 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
• f 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 Z2 symmetry, that is the invariance of the Lagrangian under the interchange (φ1 ↔ φ1, φ2 ↔ −φ2)

• r

(φ1 ↔ −φ1, φ2 ↔ φ2). This symmetry forbids the φ1 ↔ φ2 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):

• φ′

1

φ′

2

• = e−iρ0
• cos θ eiρ/2

sin θ ei(τ−ρ/2) − sin θ e−i(τ−ρ/2) cos θ e−iρ/2 φ1 φ2

• This transformation induces changes in parameters of L:

λi → λ′

i and m2 ij → (m′)2 ij

A space of Lagrangians with coordinates given by parameters of L...

• A reparametrization transformation (RPaT) λi → λ′

i and m2 ij → (m′)2 ij

• 3 parametrical group with parameters: ρ, θ, τ
• A reparametrization invariance → a reparametrization equivalent space
• f 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 Z2 symmetry The violation of the Z2 symmetry allows for the φ1 ↔ φ2 transitions.

• Exact Z2 symmetry. λ6 = λ7 = m2

12 = 0. Only λ5 can be complex, by

rephasing → λ5 real.

• A soft violation of Z2 symmetry. Adding to the Z2 symmetric

Lagrangian the term m2

12(φ† 1φ2) + h.c., with a generally complex m2 12; as

before λ5 can be made real by rephasing.

• A hard violation of Z2 symmetry. (Operator dimension 4) with

generally complex parameters λ6, λ7 are added to V with a softly broken Z2 symmetry. The true hard violation of Z2 - if V cannot be transformed to the case of Z2 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 φ1,2 ∂V ∂φ1

• φ1=φ1,

φ2=φ2

= 0, ∂V ∂φ2

• φ1=φ1,

φ2=φ2

= 0. (1) The U(1)QED symmetric one corresponds to the lower energy than the charged one (Diaz-Cruz, Mendez; Santos, Barroso, Velhinho, GK) φ1 = 1 √ 2

• v1
• , φ2 = 1

√ 2

 

v2eiξ

  .

(2)

• 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 = v2

v1

depends on reparametrization!

• 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 µ2 (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:

φ1 → u-type fermions φ2 → d-type fermions The relative “basic couplings”:

χi

j = gi

j

gSM

j i = h, H, A; j = V, u, d Relations between relative couplings:

• eg. Σi(χi

j)2 = 1, for j = V, u, d

• 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 Z2 symmetry (µ2 term): ⇒ five Higgs bosons: h,H,A,H± ⇒ 7 parameters: Mh, MH, MA, MH±, α, β, and µ2 MODEL II (as in MSSM) Couplings (relative to SM): h A to W/Z: χV = sin(β − α) to down quarks/leptons: χd = χV −

• 1 − χ2

V tan β

−iγ5 tan β to up quarks: χu = χV +

• 1 − χ2

V / tan β −iγ5/ 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)! χh

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 MH± leptonic tau decay → g-2 data , → upper limit for χd 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 → Xsγ The weighted average for BRγ ≡BR[ ¯ B → Xsγ] BRexp

γ

= (3.23 ± 0.42) × 10−4 NLO prediction (Misiak, Gambino’01): MH+ above 490 GeV (95%)

100 200 300 400 500 10 20 30 40 50 60 70 MH+ [GeV] tan β

TYPE II 2HDM

B→ Xs γ Rb B->τ ν B->X τ ν DIRECT

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)

10

• 2

10

• 1

1 10 20 30 40 50 60 70 80 90 100

OPAL

√s



= 91, 183-209 GeV

10-6

Observed Expected

(CL=95%)

mS0 (GeV) Limit on k 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100

mh [GeV] mA [GeV]

OPAL

mh [GeV] mA [GeV]

10 20 30 40 50 60 70 80 90 100

0.4 ≤ tanβ ≤ 58 0.4 ≤ tanβ ≤ 1.0 1.0 < tanβ ≤ 58 expected ΓZ constraint

Light scalar h → small k = sin2(β − α) !

• M. Krawczyk

13 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Upper (95%) limits for Yukawa couplings χd (tan β)in 2HDM (II)

10 20 30 40 50 60 70 80 90 100 5 10 15 20 25 30 10 20 30 40 50 60 70 80 90 100 mh (GeV/c2) Cττ(h→ττ)

Delphi 94-95 ττh → ττττ

10 20 30 40 50 60 70 80 90 100 5 10 15 20 25 30 10 20 30 40 50 60 70 80 90 100 mA (GeV/c2) Cττ(A→ττ)

Delphi 94-95 ττA → ττττ

Yukawa coupling (tan β) up to 20 allowed mass larger than 35 GeV!

10 20 30 40 50 60 70 80 90 100 15 20 25 30 35 40 45 50 10 20 30 40 50 60 70 80 90 100 mA (GeV/c2) Cbb(A→ττ)

Delphi 94-95 bbA → bbττ

• M. Krawczyk

14 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

DATA and SM prediction for g − 2 for muon aµ ≡ (g−2)µ

2 Summer 2004 Summary

140 150 160 170 180 190 200 210

aµ – 11 659 000 (10–10)

BNL-E821 04

DEHZ 03 (e+e–-based) DEHZ 03 (τ-based) HMNT 03 (e+e–-based) J 03 (e+e–-based) TY 04 (e+e–-based) DEHZ 04 (e+e–-based) BNL-E821 04

180.9 ± 8.0 195.6 ± 6.8 176.3 ± 7.4 179.4 ± 9.3 (preliminary) 180.6 ± 5.9 (preliminary) 182.8 ± 7.2 (preliminary) 208 ± 5.8

Average: aµ(exp) = 11 659 208(6) × 10−10(0.5 ppm)

• M. Krawczyk

15 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

SM and data

SM contribution [in 10−11] QED 116 584 705.7 (2.9) had[FJ02] 6 869.0 (70.7) EW 152.0 (4.0) tot 116 591 726.7 (70.9) ∆aµ(σ) 303.3 (106.9) lim(95%) 93.8 ≤ δaµ ≤ 512.8 In hadronic part data for e+e− are used

• using hadronic tau decay problematic...

Jegerlehner, Talk at Marseille, March 2002 Hagiwara et al (hep-ph/0209187v2) Davier et al (hep-ph/0208177) Hocker (e+e− Oct. 2004) ∆aµ(σ) = 252(92) → 96.96 ≤ δaµ ≤ 505 δaµ (positive only) can be used to constrain parameters of models at 95% CL

• M. Krawczyk

16 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

2HDM contribution to aµ: a2HDM

µ

= ah

µ + aA µ + aH µ + aH± µ

• light h scenario : a2HDM

µ

≈ ah

µ

• light A scenario : a2HDM

µ

≈ aA

µ

• ne loop

two loop Zochowski,MK’96,MK’01;Dedes,Haber’01 Chang at al.,Cheung at al, Wu,Zhou, MK’01,’02..

Two loop contributions larger than one-loop for mass ∼ few GeV!

MK, hep-ph/0103223v3, Acta Phys. Pol. B 33 (2002) 2621 (hep-ph/020807)

• M. Krawczyk

17 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Various 2HDM(II) contributions for couplings = 1

1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000 0.1 1 10 100 delta a_mu M_h(A,H+), GeV contribution to (g-2)/2 for muon h ___ A - - - H+:

• ne-loop

in 10^{-11} h&A: one-loop h&A: two-loop 3 2 1

1– no H+ 2– MH±=800GeV 3– MH±=400GeV light h

• contr. positive

for mass below 3 GeV β − α = 0, µ2 = 0 light A

• contr. positive

for mass above 5 GeV

• M. Krawczyk

18 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Combined 95% CL constraints for h and A in 2HDM(II) ’2004

scalar h for β − α = 0, µ2 = 0

0.1 1 10 100 0.1 1 10 100 tan(beta) M_h, GeV Exclusion 95%C.L. for h in 2HDM(II) Z->h gamma Opal Delphi Upsilon K Tevatron allowed by g-2 N eta

pseudoscalar A

0.1 1 10 100 0.1 1 10 100 tan(beta) M_A, GeV Exclusion 95%C.L. for A in 2HDM(II) Z->A gamma Aleph Delphi Upsilon K Tevatron Opal N allowed by g-2

thick lines : upper & lower limits from g-2

plus LEP data, etc

If all existing data are taken into account → allowed regions for A only A with mass 25-70 GeV and 25 < tan β < 115 in agreement with data

• M. Krawczyk

19 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Leptonic tau decays In SM - tree-level W exchange, in 2HDM: tree-level charged Higgs

• ✁

• ✁

In 2HDM loop corrections involve also neutral Higgs bosons → dominant contributions at large tan β (φ0 = h, H, A)

• M. Krawczyk

20 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

The branching ratios for leptonic decays

• We consider

τ → e¯ νeντ and τ → µ¯ νµντ.

• The ’04 world av. data for the leptonic τ decays and τ lifetime:

Bre|exp = (17.84 ± 0.06)%, Brµ|exp = (17.37 ± 0.06)% ττ = (290.6 ± 1.1) × 10−15s.

• The SM prediction defined as

Brl|SM = Γl|SM Γtot

exp

= Γl|SMττ

• A possible beyond the SM contribution → ∆l

Brl = Brl|SM(1 + ∆l)

• M. Krawczyk

21 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

95% CL extra contributions The lowest order of SM Bre|SM = (17.80 ± 0.07)%, Brµ|SM = (17.32 ± 0.07)%. Together with the experimental data we get ∆e = (0.20 ± 0.51)%, ∆µ = (0.26 ± 0.52)%. 95% C.L. bounds on ∆l, for the electron and muon decay mode: (−0.80 ≤ ∆e ≤ 1.21)%, (−0.76 ≤ ∆µ ≤ 1.27)%.

The negative contributions are constrained more strongly..

• M. Krawczyk

22 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Partial widths or leptonic τ decays: SM vs 2HDM

SM at tree-level = the W ± exchange ( with leading order corrections

to the W propagator, and dominant QED one-loop contributions)

2HDM extra tree contribution due to the exchange of H+

ΓH±

tree = Γ0

 m2

τ m2 l tan4 β

4M4

H±

− 2mlmτtan2 β M2

H±

ml mτ κ

m2

l

m2

τ

  ,

where κ(x) = g(x)

f(x),

g(x) = 1 + 9x − 9x2 − x3 + 6x(1 + x) ln(x).

The second term - from the interference with the SM - much more

• important. It gives negative contribution to Br:

−m2

l /M2 H± tan β2

• M. Krawczyk

23 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Calculation of one-loop 2HDM(II) corrections

• Evaluation in the ’t Hooft-Feynman’s gauge using definitions and

conventions for one-loop integrals of Hollik.

• H± and W ± masses are very large compared to the leptonic masses

and external momenta so ∆µ

• neloop = ∆e
• neloop = ∆oneloop.
• large tan β enhanced contributions
• Self-energies: Two-point diagrams (χo = h, H, A, Go and χ+ = H+, G+).
• ✁✄✂
• ✁✆☎

• Three-point contribution ( (V, φ) = (G+, Z), (W +, h), (W +, h)/(Z, G+))

W ±τντ vertex corrections, similar diagrams for the W ±lνl vertex

• M. Krawczyk

24 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

• Charged lepton self-energies. Contributions involving the exchange of

a charged boson proportional to m2

l /M2 W and m2 l /M2 H± (for χ+ = G+and

H+, respectively) - negligible. Neutral Higgs and Goldstone bosons contr only for τ self-energy.

• Neutrino self-energies for tau neutrino only

δZL νe = δZL νµ = 0 δZL ντ = ∆H+

ντ

+ ∆G+

ντ

∆H+

ν

= − GFm2

τ

4 √ 2π2 tan2 β[B0 + B1](0; M2

H±, m2 τ ).

∆G+

ν

= GFm2

τ

4 √ 2π2[B0 + B1](0; M2

W, m2 τ ) ≃ 0.

(4)

• One-loop three-point contribution

Only the radiative contributions to the W ±τντ vertex important.

• M. Krawczyk

25 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

• χ+ − χ0 − τ Loops.

∆H+h

loops = GFm2 τ

2 √ 2π2 tan β sin α cos β cos(α − β)C20(m2

τ , m2 ντ; M2 h, m2 τ , M2 H±) + . . .

∆H+A

loops = GFm2 τ

2 √ 2π2 tan2 βC20(m2

τ , m2 ντ; M2 A, m2 τ , M2 H±) + . . .

∆H+H

loops = − GFm2 τ

2 √ 2π2 tan βcos α cos β sin(α − β)C20(m2

τ , m2 ντ; M2 H, m2 τ , M2 H±) + . . .

∆G+h

loops = − GFm2 τ

2 √ 2π2 sin α cos β sin(α − β)C20(m2

τ , m2 ντ; M2 h, m2 τ , M2 W ) + · · · ≃ 0

∆G+H

loops = − GFm2 τ

2 √ 2π2 cos α cos β cos(α − β)C20(m2

τ , m2 ντ; M2 H, m2 τ , M2 W) + · · · ≃ 0

∆G+Go

loops = − GFm2 τ

2 √ 2π2C20(m2

τ , m2 ντ; M2 Z, m2 τ , M2 W) + · · · ≃ 0

(5)

V − φ − l Loops -neglected τ − ντ − χ+ Loops -neglected

One-loop box diagrams can be neglected

One loop contribution for large tan β ∆oneloop ≈ GFm2

τ

8 √ 2π2 tan2 β ˜ ∆ ˜ ∆ =

 −  ln  M2

H+

m2

τ

  + F(RH±)  

+1 2

• ln

M2

A

m2

τ

• + F(RA)
• +1

2cos2(β − α)

• ln

M2

h

m2

τ

• + F(Rh)
• +1

2sin2(β − α)

• ln

M2

H

m2

τ

• + F(RH)
• ,

(6) where Rφ ≡ Mφ/MH± and F(R) = −1 + 2 R2lnR2/(1 − R2) NOTE, ˜ ∆ does not depend on mτ! Loop corrections are the same for e and µ channels

The exact and approximated expressions can not be distinguished

• M. Krawczyk

26 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Loop corrections for some scenarios Interesting scenarios: sin2(β − α)=0,any,1

• light h and sin2(β − α) = 0, → ˜

∆ does not depend on MH: MA = MH± → ˜ ∆ = ln Mh MH± +1 or MA ≪ MH± → ˜ ∆ = ln Mh MH± +ln MA MH± +2. h does not couple to gauge bosons and the Higgsstrahlung process at LEP is not sensitive to such Higgs boson. The leptonic tau decays have maximal sensitivity to h!

• For arbitrary sin2(β − α) and degenerate H, A, H± (with mass M):

˜ ∆ = cos2(β − α) [ln Mh M + 1].

• SM-like scenario, with light h, sin2(β − α) = 1 and very heavy

degenerate additional Higgs bosons: ˜ ∆ → 0 (decoupling)

• M. Krawczyk

27 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Mass charged Higgs boson If the tree level H+ exchange only (as in PDG04, Dova98, Stahl’97..): we obtain the 95% CL deviation from the SM prediction MH± > ∼ 1.71 tan β GeV

coefficient to be compared to 1.86 (1.4) from Dova at al (Stahl)

(the Michel parameter η in the 2HDM (II)) However loop effects large...

• M. Krawczyk

28 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Limits for mass of H+: One-loop and tree contr.

100 1000 100 M_H+, GeV tan beta Mass of H+ from tau decay loop only -excluded Mh= MA=MH+ sba2=0 20 b->s gam tree only -excluded

dotted: MA = 100 GeV; µ (red), e (green)

• M. Krawczyk

29 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

100 1000 100 M_H+, GeV tan beta Mass of H+ from tau decay loop only -excluded Mh= MA=MH+ sba2=0 5 20 100 b->s gam tree only -excluded

The upper limits: for Mh = 5, 20, 100 GeV and sin2(β − α) = 0, assuming MA = M+

H

• M. Krawczyk

30 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Combining limits for A Upper limits for tan β from the leptonic τ decay (degenerate masses of h, H, H+) and the allowed region from the newest g − 2 for muon data

1 10 100 10 100 tan(beta) MA, GeV Exclusion 95%C.L. for A in 2HDM(II) Delphi Upsilon K Opal g-2 tau sba2=0

1/4 TeV (upper/lower green line)

• M. Krawczyk

31 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Conclusion

• The one-loop contributions to the branching ratios for leptonic τ

decays are calculated in the CP conserving 2HDM(II) at large tan β - agreement with previous results by Guth & Kuhn, Rosiek, Chankowski et al, extension of Hollik & Sack.

• One-loop contributions, involving both neutral and charged Higgs

bosons, dominate over the tree-level H± exchange (the latter one being totally negligible for e).

• We show that the leptonic branching ratios of τ are complementary to

the Higgsstrahlung processes for h(H)

• We got upper limits on Yukawa couplings for both light h and light A

scenarios

• New lower limit on mass of MH± as a function of tan β, which differs

significantly from what was considered as standard constraint (based on the tree-level H± exchange only)

• We obtain also a upper limit on MH± !
• M. Krawczyk

32 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Constraints for h and A We also derive constraits for neutral Higgs bosons. For light h:

1 10 100 10 100 tan(beta) M_h, GeV Exclusion 95%C.L. for h in 2HDM(II) Opal Delphi Upsilon K tau decay

sin(β − α) = 0, MA = 100 GeV, MH± = 500 GeV and 4 TeV, upper and lower green lines; degenerate A and H+ (mass 4 TeV) -thick green line

• M. Krawczyk

33 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006

Constraints for pseudoscalar A Upper limits for Yukawa coupling (tan β) for light A

1 10 100 10 100 tan(beta) MA, GeV Exclusion 95%C.L. for A in 2HDM(II) Delphi Upsilon K Opal tau sba2=0

Limits from tau decay: Mh = 100 GeV, MH± = 500 GeV and 4 TeV, upper and lower green line The degenerate h and H± with mass 4 TeV - thick green line

• M. Krawczyk

34 Leptonic tau decay in 2HDM • Flavour at LHC era • CERN, 07.03.2006