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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III1 Implications of the Yukawa’s textures of the neutral Higgs bosons in the context

• f the THDM III1

H´ ector Bello Mart´ ınez

• O. F´

elix Beltr´ an

• J. E. Barradas Guevara

FCFM-BUAP, M´ exico 8 june 2012

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III2

Resume

Resume

In this work we studied the neutral Higgs bosons decays in the two Higgs doblet model type III (THDM-III) taking acount the implications of Yukawa’s

• textures. We calculate the decay widths (Γ) and the corresponding branch-

ing ratios (BR) of the main decay modes of such neutral Higgs bosons. We realized numerical analysis considering the analitic results in the permitted parameter space considering also different cases of the model. In addition, we bound the cases in concordance with the corresponding theoretical re-

• strictions. Finally we present the expected event number, which it give the

posibility of detection in current colliders.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III3

Introduction

Introduction

1 The Higgs boson: hypothetical elementary particle, his

existence is given by the SSB. It gives the mass of the particles of the SM.

2 It was theorized in 1964 by Peter Higgs, Francois Englert y

Robert Brout (in base to ideas of Philip Anderson), and independently by G. S. Guralnik, C. R. Hagen and T. W. B. Kibble [1].

3 The Higgs field has a vacuum expectation value (VEV = 0,

VEV = 246 GeV).

4 SM doesn’t predict the mass value of the Higgs boson[2]. 5 If 115 < mh < 180 GeV, so SM is valid through the Planck

scale(1016 TeV).

6 An extention of the SM is the Two Higgs Doblet Model

(THDMIII).

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III4

Introduction

THDM: This model is introduced by three types:

1 Type I. One Higgs doublet couples to fermions.1 2 Type II. One of the Higgs doublets couples just to the up

quarks, while the other one couples to down quarks.2

3 Type III. Higgs-fermions couplings are indistinc to anyone of

the two doublets3.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III5

Standar Model

Standar Model

Figure 1:

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III6

Standar Model

The SM Lagrangian density, is gauge simmetry invariant is: LSM = LF + LB + LSBS + LYW + LC, (1) LF is the fermionic Lagrangian, LB is the bosonic Lagrangian (LB = LYM+LGF +LFP), LSBS is the SSB Lagrangian, LYW is the Yukawa Lagrangian and LC is the current Lagrangian. This includes 5 sectors: fermionic, Yang Mills, Higgs, Yukawa, and currents sectors.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III7

Standar Model

Yukawa’s sector (important)

Yukawa’s Lagrangian give mass to fermions after SSB. We intro- duce a covariant object under SUL(2), defined by: φc ∼ iτ2φ∗ = φ0∗ −φ−

• ,

(2) where τ2 is the second Pauli’s matrix, φ∗ is the complex conjugate

• f Higgs field; the isodoblet φc (

φ) hypercharge is Y = 1.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III8

Standar Model

General Yukawa’s Lagrangian is: LYW = −

• a,k

Y k

a ψ k Lφr aψk R + h.c.,

(3) k = l, u, d is the fermion type, a = 1, 2, 3, ...n where n is the number

• f Higgs fields in the model (THDM, n = 2) and r is the isodoublet

Higgs field φc or the Higgs field φ, if fermions are type up or down, ψL are left doublet fermions of SU(2)L:

1 li L =

νli li

• L

, with li leptons (e−, µ−, τ −), and

2 Qi L =

ui di

• L

, with ui up quarks (u, c, t), and di down quarks (d, s, b).

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III9

Standar Model

The SSB Lagrangian density is: LSSB = 1 2 |Dµφ|2 − V (φ) − 1 4(Fµν)2. (4) V (φ) = m2 2 |φ|2 + λ 4

• |φ|22

= −µ2 2 |φ|2 + λ 4

• |φ|22

, (5) where µ = −m2 and λ > 0.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III10

Standar Model

Figure 2: Higgs potential for real and imaginary mass. Figure 3: Higgs potential for n = 2, note that red region is given by 246 Gev’s.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III11

THDM

THDM

Some motivations:

1 New phenomenology (appear charged Higgs bosons,FCNC.), 2 It allows to introduce ECPV. 3 It naturally solves the hierarchy from the Yukawa’s couplings in

the third generation of quarks (mt/mb ≈ 173.1/4.67 ≈ 37), this is making by letting the bottom quark mass given by one doublet and the top one’s for the other.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III12

THDM

The Higgs potential of THDM. We introduce two SU(2)Y dou- blets φ1, φ2, with hypercharge Y = ±1. This is a renormalizable potential, compatible with gauge invariance, is obtained introducing the hermitian gauge invariants operators: ˆ A = φ†

1φ1,

(6) ˆ B = φ†

2φ2,

ˆ C = 1 2

• φ†

1φ2 + φ† 2φ1

• = Re(φ†

1φ2),

(8) ˆ D = − i 2

• φ†

1φ2 − φ† 2φ1

• = Im(φ†

1φ2).

(9)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III13

THDM

The renormalizable and reparameterized Higgs potential for the THDM is: V (φ1, φ2) = m2

11

• φ†

1φ1

• + m2

22

• φ†

2φ2

• −
• m2

12

• φ†

1φ2

• + h.c.
• +λ1

2

• φ†

1φ1

2 + λ2 2

• φ†

2φ2

2 + λ3

• φ†

1φ1

φ†

2φ2

• +λ4
• φ†

1φ2

φ†

2φ1

• +

λ5 2

• φ†

1φ2

2 +

• λ6
• φ†

1φ1

• +λ7
• φ†

2φ2

φ†

1φ2

• + h.c.
• ,

(10) 14 new, 6 real (m2

11, m2 22, λ1, λ2, λ3, λ4) and 4 complex

(m2

12, (m2 12)∗, λ5, λ∗ 5, λ6, λ∗ 6, λ7, λ∗ 7) parameters.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III14

THDM

PROPERTIES OF THE POTENTIAL:

1 It’s renormalizable and hermitic V † = V . 2 It allows (ECPV), and just CPC4, when m12, λ5, λ6, λ7 are reals. 3 If λ6 = λ7 = m2 12 = 0 then V is symmetric under Z2.

Then: φ1 =

• φ+

1 φ0

1R+iφ0 1I

√ 2

• ,

φ2 =

• φ+

2 φ0

2R+iφ0 2I

√ 2

• ,

(11)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III15

THDM

Now we can calculate the mass matrix given by: M2

ij = 1

2 ∂2V ∂φi∂φj = M2

C

M2

N

• 8×8

, (12)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III16

THDM

with M2

C, M2 N the 4 × 4 charged and neutral matrices, where:

M2

N =

                                   (m2

12 + (m2 12)∗)v2eiξ 4v1

−

• m2

12 + (m2 12)∗ 1 4

(λ∗

5 − λ5)iv2

2 ei2ξ

8

+λ1

v2

1

2

+

• λ3 + λ4 + λ5+λ∗

5

2

• v1v2eiξ

2

+(λ∗

6 − λ6)iv1v2eiξ 4

(λ5 − λ∗

5)iv1v2eiξ 8

+(λ6 + λ∗

6)3v1v2eiξ 8

− (λ7 + λ∗

7)v3

2 ei3ξ

8v1

+(λ6 + λ∗

6)3v2

1

8 + (λ7 + λ∗ 7)3v2

2 ei2ξ

8

−

• m2

12 + (m2 12)∗ 1 4

(m2

12 + (m2 12)∗)v1e−iξ 4v2

−(λ5 − λ∗

5)(iv1v2eiξ) 8

(λ5 − λ∗

5)iv2

1

8

+

• λ3 + λ4 + λ5+λ∗

5

2

• v1v2eiξ

2

−λ2

v2

2 ei2ξ

2

− (λ6 + λ∗

6)v3

1 e−iξ

8v2

−(λ7 − λ∗

7)iv2

2 ei2ξ

4

+(λ7 − λ∗

7)iv1v2eiξ 4

+(λ6 + λ∗

6)3v2

1

8 + (λ7 + λ∗ 7)3v2

2 ei2ξ

8

+(λ7 + λ∗

7)3v1v2eiξ 8

(λ∗

5 − λ5)iv2

2 ei2ξ

8

−(λ5 − λ∗

5)(iv1v2eiξ) 8

(m2

12 + (m2 12)∗)v2eiξ 4v1

−m2

12+(m2 12)∗

4

+(λ∗

6 − λ6)iv1v2eiξ 4

−(λ7 − λ∗

7)iv2

2 ei2ξ

4

−(λ6 + λ∗

6)v1v2eiξ 8

+(λ5 + λ∗

5)v1v2eiξ 4

−(λ7 + λ∗

7)v3

2 ei3ξ

8v1

+(λ6 + λ∗

6)v2

1

8 + (λ7 + λ∗ 7)v2

2 ei2ξ

8

(λ5 − λ∗

5)iv2

1

8

−m2

12+(m2 12)∗

4

+ (λ5 + λ∗

5)v1v2eiξ 4

(m2

12 + (m2 12)∗)v1e−iξ 4v2

(λ5 − λ∗

5)iv1v2eiξ 8

+(λ7 − λ∗

7)iv1v2eiξ 4

+(λ6 + λ∗

6)v2

1

8

−(λ7 + λ∗

7)v1v2eiξ 8

+(λ7 + λ∗

7)v2

2 ei2ξ

8

                                  

.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III17

THDM

m2

H0,h0

=

• λ∗

1 + 1

2λ+

• v2

1 − 1

2µ2

2

±

• λ∗

1 − 1

2λ+

• v2

1 + 1

2µ2

2

2 + 1 2λ∗

6v2 1

2 . (13) cos α senα

• ↔ m2

H0,

−senα cos α

• ↔ m2

h0,

(14)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III18

THDM

where: tan 2α = λ∗

6v2 1

(2λ∗

1 − λ+)v2 1 + µ2 2

, λ+ ≡ 1 2(λ3 + λ5), (15) and λ∗

i , µ2 are given as the reparametrization. Thus, the diagonal-

ization process makes the rotation: cos α senα −senα cos α √ 2φ0

1R − v1

√ 2φ0

2R − v2

• =

H0 h0

• (16)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III19

Yukawa’s Lagrangian in THDM

Yukawa’s Lagrangian in THDM

Three diferent models according to the Yukawa’s Lagrangian cou- pling.

1 THDM-I One doublet couples to all fermions. 2 THDM-II Each doublet couples to one type of fermions. 3 THDM-III All doublets couples to all fermions (∃ FCNSI).

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Yukawa’s Lagrangian in THDM

Yukawa’s Lagrangian for the quark fields is: Lq

Y

= ¯ q0

LY D 1 φ1d0 R + ¯

q0

LY D 2 φ2d0 R + ¯

q0

LY U 1

φ1u0

R

+ ¯ q0

LY U 2

φ2u0

R + h.c.,

(17) with Y U,D

1,2

the 3 × 3 Yukawa’s matrices, qL left quark doublets, uR, dR right singlets.

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Yukawa’s Lagrangian in THDM

Before a correct SSB

The Higgs doublets are descomposed as: φ1 =

• φ+

1 v1+φ1+iχ1 √ 2

• ,

φ2 =

• φ+

2 eiξv2+φ2+iχ2 √ 2

• ,

(18) where v1, v2 ǫR+. By expresing ¯ q0

L using (18), and transforming the quark fields to

the mass eigenstate basis through uL,R = UL,Ru0

L,R and dL,R =

DL,Rd0

L,R,

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III22

Yukawa’s Lagrangian in THDM

using quirality operators of the matrix: MQ = QLY Q

1 Q† R

v1 √ 2 + QLY Q

2 Q† R

e−iξv2 √ 2 , (19) with Q = U, D, and φ1 + iχ1 =

• r

(qr1cosβ − qr2e−i(θ23+ξ)senβ)Hr, φ2 + iχ2 =

• r

(qr1eiξsenβ + qr2e−iθ23cosβ)Hr, (20)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III23

Yukawa’s Lagrangian in THDM

where qra are written as combination of θij,these are given by: r qr1 qr2 1 cos θ12 cos θ13 −senθ12 − i cos θ12senθ13 2 senθ12 cos θ13 cos θ12 − isenθ12senθ13 3 senθ13 i cos θ13 4 i

Table 1: Values of qra in terms of the mixing angles of the rotation matrix.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III24

Yukawa’s Lagrangian in THDM

We can rewrite the Lagrangian for neutral Higgs couplings to up and down quarks: Lneutral

up,down

= ¯ (u, d)i

• Su,d

ijr

+ γ5Pu,d

ijr

• (u, d)jHr +

¯ (u, d)iMu,D

ij

(u, d)j. (21)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III25

Yukawa’s Lagrangian in THDM

Su,d

ijr

and Pu,d

ijr

are given by: Su,d

ijr

= Mu,D 2v

• q∗

r1 + qr1 − tanβ

• q∗

r2ei(θ+ξ) + qr2e−i(θ+ξ)

+ 1 2 √ 2cosβ

• q∗

r2eiθ

Y u,D†

2

+ qr2e−iθ Y u†,D

2

• ,

(22) Pu,d

ijr

= −∗ Mu,D 2v

• q∗

r1 − qr1 − tanβ

• q∗

r2ei(θ+ξ) − qr2e−i(θ+ξ)

+ 1 2 √ 2cosβ

• q∗

r2eiθ

Y u,D†

2

− qr2e−iθ Y u†,D

2

• .

(23)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III26

Yukawa’s Lagrangian in THDM

In THDM III we considere up y down sector the values of S y P for each of the Hi (i = 1, 2, 3) as follows:

1 For H1 = h0: S = 0 and P = 0. 2 For H2 = H0: S = 0 and P = 0. 3 For H3 = A0: S = 0 and P = 0.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III27

Yukawa’s Lagrangian in THDM

The texture formalism started by Bjorken proposing:   Mf + ∆Mf mf m∗

f

Mf + ∆Mf mf m∗

f

Mf + ∆Mf   , (24) which reproduce the quarks mass and the elements of VCKM with good aproximation.

1 It reproduces fermionic mass and mixing angles. 2 It supress FCNC.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III28

Yukawa’s Lagrangian in THDM

The 4 textures Yukawa’s hermitic matrix fulfill:

1 Hierarchy |Aq| ≫ |

Bq|, |Bq|, |Cq|, Aq and Bq ǫR.

2 Phases of Cq and Bq (ΦBq and ΦCq) removed by Mq = P† q

MqPq, with Pq = diag(1, eiΦCq , ei(ΦCq +ΦBq )),

3 Mq = OT q

MqOq, where M is: Mq =   Cq C ∗

q

• Bq

Bq B∗

q

Aq   . (25)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III29

Yukawa’s Lagrangian in THDM

The corrections to FC and FV depend of the diagonal matrix Y q

2 =

OT

q PqY q 2 P†

• qOq. For

Y q

2 , we asumme that Y q 2 has the form of 4

• textures. So with Cheng-Sher anzats:

( Y q

2 )ij

=

• mq

i mq j

v

• χq

ij =

• mq

i mq j

v χq

ijeiϑq

ij,

(26)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III30

Yukawa’s Lagrangian in THDM

considering the ansatz Y

u,d 2ij

= χij

√mimj v

and taking no CPV and using e−iθ23 = 1, cos θ12 = sen(β − α) y senθ12 = cos(β − α): Lneutral

upint

= g 2mw ¯ ui

• mui

cos α senβ δij − cos(α − β) √ 2senβ muimuj χu

ij

• ujh0

+ g 2mw ¯ ui

• mui

senα senβ δij − sen(α − β) √ 2senβ muimuj χu

ij

• ujH0

− ig 2mw ¯ ui

• −mui cot βδij +

√muimuj √ 2senβ

• χu

ij

• γ5ujA0,

(27)

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Yukawa’s Lagrangian in THDM

Lneutral

downint

= g 2mw ¯ di

• −mdi

senα cos β δij + cos(α − β) √ 2 cos β mdimdj χd

ij

• djh0

+ g 2mw ¯ di

• mdi

cos α cos β δij + sen(α − β) √ 2 cos β mdimdj χd

ij

• djH0

+ ig 2mw ¯ di

• −mdi tan βδij +

√mdimdj √ 2 cos β

• χd

ij

• γ5djA0,

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III32

Yukawa’s Lagrangian in THDM

Lneutral

leptonesint

= g 2mw ¯ li

• −mli

senα cos β δij + cos(α − β) √ 2 cos β mlimlj χl

ij

• ljh0

+ g 2mw ¯ ui

• mli

cos α cos β δij + sen(α − β) √ 2 cos β mlimlj χl

ij

• ujH0

+ ig 2mw ¯ ui

• −mdi tan βδij +

√mdimdj √ 2 cos β

• χd

ij

• γ5ujA0,

(28) From this, we have the vertex for Feynman diagrams!

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III33

Phenomenology

Production and posible Decays of neutral Higgs. Neutral Higgs bosons can be produced by:

Figure 4: a) Gluon fusion, b) vectorial bosons fusion, c) e-p collisions, d) p-p collisions.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III34

Phenomenology

Neutral Higgs Decays in THDM III

We considered fermionic (with FCNC) and bosonic decays,

1 two fermions: (φ0 → ¯

fifj), φ0 = h0, H0, A0 and fi = li, qi.

2 two bosons: (H0 → ¯

ViVj), Vi = Z 0, W ±.

3 two bosons with one virtual: H0, h0 → V ∗V , allowed for

mV < mh < 2mV .

4 two Higgs bosons: H0 → h0h0, H0 → A0A0. 5 one gauge boson and a light Higgs (just allowed A0 → Zh0).

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III35

Phenomenology

We calculate to tree level

Figure 5: Feynman diagrams of neutral Higgs decaying to: a) 2 fermions with FCNC, b) 2 gauge bosons, c) 2 neutral Higgs, d) a vectorial gauge boson and a neutral Higgs.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III36

Phenomenology

Higgs decaying to two fermions

In THDMIII: 18 posible decays (twice that in SM). Γfi¯

fj

• mi, mj, mφ0, Nc, n, ξij
• =
• Nc

8π(mφ0)3 g 2mw 2 ξ2

ij

• (mφ0)2 − (mi + mj(−1)n)2

·

• (m2

i − m2 j − (mφ0)2)2 − 4m2 j (mφ0)21/2 .

(29) where Nc = 1(3) for leptons (quarks), n even for h0, H0; n odd for A0 and φ0 = h0, H0, A0.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III37

Phenomenology

And ξij are given by:

Process THDMIII THDMII SM h0 → ui¯ uj mui

cos α senβ δij − cos(α−β) √ 2senβ

√muimuj χu

ij

mui

cos α senβ δij

muiδij h0 → di ¯ dj −mdi

senα cos βδij + cos(α−β) √ 2 cos β

√mdimdj χd

ij

−mdi

senα cos βδij

mdiδij H0 → ui¯ uj mui

senα senβ δij − sen(α−β) √ 2senβ

√muimuj χu

ij

mui

senα senβ δij

− H0 → di ¯ dj mdi

cos α cos β δij + sen(α−β) √ 2 cos β

√mdimdj χd

ij

mdi

cos α cos β δij

− A0 → ui¯ uj −mui cot βδij + √mui muj

√ 2senβ

χu

ij

−mui cot βδij − A0 → di ¯ dj −mdi tan βδij + √mdi mdj

√ 2 cos β

χd

ij

−mdi tan βδij −

Table 2: Values of ξij according to decay and model.

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III38

Phenomenology

Higgs decaying to two gauge bosons

In THDM III: 11 decays to gauge bosons (7 more than in SM). Γ(h0 → VV ) = g2m3

h0

kV 64πm2

W

sen2(β − α)

• 1 − x(V )

×(1 − x(V ) + 3 4x2(V )), (30) Γ(H0 → VV ) = g2m3

h0

kV 64πm2

W

cos2(β − α)

• 1 − x(V )

×(1 − x(V ) + 3 4x2(V )), (31)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III39

Phenomenology

where kV = 1 for V = W , kV = 2 for V = Z and x(V ) = 4 m2

v

m2

h .

Constrain: mhiggs > 2mV .

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III40

Phenomenology

Higgs decaying to two gauge boson and one virtual

Γ(h0 → WW ∗) = 4g4mh0 512π3 sen2(α − β)F(mW /mh0), (32) Γ(h0 → ZZ ∗) = 4 g4mh0 2048π3 sen2(α − β)F(mZ/mh0) × 7 − (40/3)sen2θW + (160/9)sen4θW cos4 θW

• ,

(33)

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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III41

Phenomenology

where F(x) = −(1−x2)

• 47

x 2 − 13 2 + 1 x2

• −3(1−6x2 +4x4)ln(x)+

3

• 1−8x2+20x4

√ 4x2−1

• arccos
• 3x2−1

2x3

• . And for H0:

Γ(H0 → WW ∗, ZZ ∗) = Γ(h0 → WW ∗, ZZ ∗) cot2(α − β). (34) Note that

• 4m2

W

m2

h0

− 1 ǫ R, (35) then 4m2

W

m2

h0 − 1 > 0 and so mh0 <

• 4m2

W , (mh0 < 160.78 GeV’s for

mW = 80.39 GeV).

SLIDE 42

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III42

Phenomenology

A0 → Z 0h0 decay

The only way that A0 decays to two bosons. Γ(A0 → Z 0h0) = g2λ1/2cos2(β − α) 64πm3

A0cos2θW

• m2

Z − 2(m2 A0 + 2m2 h0) + (m2 A0 − m2 h0)2

m2

Z

• ,

(36) with λ1/2 =

• (m2

Z 0 + m2 h0 − m2 A0)2 − 4m2 Z 0m2 h0

1/2. No tree level coupling to a pair of vectorial bosons because CPC.

SLIDE 43

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III43

Phenomenology

Higgs decaying to 2 Higgs

H0 → h (h = h0, A0). Γ(H0 → hh) = g2m2

Zf 2 h

128πmH0 cos2 θW

• 1 − 4m2

h

m2

H0

1/2 , (37) where fh = cos 2α cos(β + α) − 2sen(2α)sen(β + α)ifh = h0, cos 2α cos(β + α)ifh = A0. Constrain: mH0 > 2mh.

SLIDE 44

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III44

Phenomenology

Branching Ratios

To calculate Neutral Higgs bosons BR, we need to calculate the total width decay: Γtot =

• X,Y

Γ(φ → XY ). (38) So the BR for the decay φ → ab is: BR(φ → ab) = Γ(φ → ab) Γtot . (39)

SLIDE 45

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III45

Phenomenology

Constraints

We have several constraints: CUSTODIAL SIMMETRY SU(2)c. ρ = M2

W

M2

Z cos2 θW

=

• k 2(Tk(Tk + 1) − Y 2

k /4)ν2 k + i 2Ti(Ti + 1)ν2 i

• k ν2

kY 2

, TRIVIALITY COSTRAINTS. λ = 0 and finite. STABILITY CONSTRAINT OF THE VACUUM. Stable vacuum requires λ > 0 so (Mh 130 GeV) but vacuum must be metastable so Mh 115GeV .

SLIDE 46

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III46

Phenomenology

Bounds of SM Higgs boson mass in november of 2011.

Figure 6: Combination of ATLAS data [4].

SLIDE 47

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III47

Results

Results

We build a program in Mathematica R which we compute the next decay widths:

1 18 to pair of fermions. 2 11 to pair of bosons. 3 4 to boson-virtual boson. 4 3 to pair of Higgs bosons (A0 → Z 0h0, H0 → hh, AA) 5 Total: 36 width decays (possibles BR).

SLIDE 48

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III48

Results

In 3 scenarios:

1 scenario A: α − β = − π 2 (for h0 this is SM scenario). 2 scenario B: α − β = 0. 3 scenario C: α − β = − π 3 .

With: tan β = 5, 10, 15, 20, 30, 50; thus also values of χij = 1, 0.5, 0, −0.2, −0.5, − in the 4 Yukawa’s textures context, (χ11 = χ13 = χ31 = 0).

SLIDE 49

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III49

Results

Imput parameters: mu = 0.0017 GeV, md = 0.004 GeV, ms = 0.1 GeV, mc = 1.3 GeV, mb = 4.67 GeV, me = 0.0005 GeV, mµ = 0.105 GeV, mτ = 1.776 GeV, mAfijo = 250 GeV, g = √ 4πα GeV, mt = 173.1 GeV, mw = 80.39 GeV, mz = 91.1876 GeV, sw = √ 0.2254, cw =

• 1 − s2

w.

SLIDE 50

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III50

Results

Branching Ratios of h0

For the h0 decays (SM Higgs boson), we considered for numerical analysis in range for the Higgs boson mass 500 ≥ mh0 ≥ 50 GeV, and we obtained the next graphics for BR. χij = 1, 0, −1 (χij = 0 THDM type II and χij = 1, −1; allow FCNC, this is THDM-III), thus we considered the values tan β = 5, 15, 50.

SLIDE 51

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III51

Results

100 200 300 400 500 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 100 200 300 400 500 100 200 300 400 500 tan B R (h X Y ) tan tan cc ss tt bb w w * zz* w w zz BR h en escenario A:

SLIDE 52

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III52

Results

40 60 80 100 120 140 160 180 200 220 1E-5 1E-4 1E-3 0.01 0.1 1 tan ij BR h en escenario A: cc ss tt bb W W * ZZ* W W ZZ BR (h XY) m h (GeV)

Figure 8: BR(h0) with O > 10−5 in SM.

SLIDE 53

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III53

Results

100 200 300 400 500 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 100 200 300 400 500 100 200 300 400 500 tan B R( h X Y ) tan BR h en escenario B: tan cc ss tt bb ct sb w w zz

SLIDE 54

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III54

Results

100 200 300 400 500 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 100 200 300 400 500 100 200 300 400 500 BR h en escenario C: tan B R( h X Y ) tan tan cc ss tt bb ct sb w w * z z * w w z z

SLIDE 55

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III55

Results

Branching Ratios of H0

For H0 decays (the neutral Higgs boson heavier than SM ones), we considered for the numerical analisis we considered a range for Higgs mass 800 ≥ mH0 ≥ 150 GeV. We considered 2 regions: 150 < mH0 < 350 GeV, 350 < mH0 < 800 GeV. For the second the dominant decays depend on scenario. tan β and χij values, for first region dominant decays is to pair of b-quarks (b¯ b) and WW pairs.

SLIDE 56

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III56

Results

Proceso ξij en escenario A ξij en escenario B h0 → ui¯ uj muiδij mui cot βδij − √mui muj

√ 2senβ

χu

ij

h0 → di ¯ dj −mdiδij −mdi tan βδij + √mdi mdj

√ 2 cos β

χd

ij

H0 → ui¯ uj −mui cot βδij + √mui muj

√ 2senβ

χu

ij

muiδij H0 → di ¯ dj mdi tan βδij − √mdi mdj

√ 2 cos β

χd

ij

mdiδij A0 → ui¯ uj −mui cot βδij + √mui muj

√ 2senβ

χu

ij

−mui cot βδij + √mui muj

√ 2senβ

χu

ij

A0 → di ¯ dj −mdi tan βδij + √mdi mdj

√ 2 cos β

χd

ij

−mdi tan βδij + √mdi mdj

√ 2 cos β

χd

ij

Table 3: ξij values according to decays and scenario[3].

SLIDE 57

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III57

Results

200 300 400 500 600 700 800 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 200 300 400 500 600 700 800 200 300 400 500 600 700 800 tan B R(H X Y ) tan BR H en escenario A: tan cc ss tt bb ct sb hh AA

SLIDE 58

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III58

Results

200 300 400 500 600 700 800 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 200 300 400 500 600 700 800 200 300 400 500 600 700 800 BR H en escenario B: B R(H X Y ) tan tan tan cc ss tt bb w w zz hh AA

SLIDE 59

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III59

Results

200 300 400 500 600 700 800 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 200 300 400 500 600 700 800 200 300 400 500 600 700 800 BR H en escenario C: tan B R( H X Y ) tan tan cc ss tt bb ct sb W W ZZ hh AA

SLIDE 60

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III60

Results

Branching Ratios of A0

For A0 decays we considered 800 ≥ mA0 ≥ 150 GeV. In 3 regions: 150 < mA0 < mz + mh0 ≈ 215 GeV (para mh0 = 120) 215 mA0 < mz + mh0 < 2mt ≈ 350 GeV, 350 < mA0 < 800. For the second and third region, dominant decays depend on tan β and χij. For the first, the dominant decay is to b¯ b, this become dominant in second region for tan β ≈ 50. It is important to say that variations in BR are given the variation of BR(h0 → Z 0h0) as well as the fermionic decays don’t depend on α.

SLIDE 61

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III61

Results

200 300 400 500 600 700 800 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 200 300 400 500 600 700 800 200 300 400 500 600 700 800 tan B R (A

• X Y )

tan BR A en escenario A: tan 15 cc ss tt b b ct sb

SLIDE 62

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III62

Results

200 300 400 500 600 700 800 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 200 300 400 500 600 700 800 200 300 400 500 600 700 800 tan BR A en escenario B: B R (A

• X Y )

tan tan cc ss tt b b ct sb Zh

SLIDE 63

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III63

Results

200 300 400 500 600 700 800 10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 200 300 400 500 600 700 800 200 300 400 500 600 700 800 tan BR A en escenario C: B R (A

• X Y )

tan tan cc ss tt bb ct sb Zh

SLIDE 64

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III64

Results

Events Number

Finally, to calculate the (ideal) events number that can occur in these decays, we have: Neventos = L × σ × BR, (40)

SLIDE 65

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III65

Results

Figure 17: Cross sections in SM [5].

SLIDE 66

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III66

Results

Figure 18: Cross sections in MSSM [5].

SLIDE 67

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III67

Results

Figure 19: Luminosity reached at LHC in november 2011 [4].

SLIDE 68

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III68

Results

We can calculate a prediction for the events number in LHC in the MSSM, like we show in chart 20. We take account the scenario A and scenario B with mh = 120 GeV, mH = 200 GeV, mA = 250 GeV, tan β = 5, althoug, this calculation of events number was done for data of november of 2011 and for integrated luminosity of 10 fb−1 that probably LHC will reach after 2012 ends.

SLIDE 69

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III69

Results

Figure 20: Prediction for events number in LHC using MSSM.

SLIDE 70

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III70

Results

From this data we observe that the events number for h0 → b¯ b or h0 → ZZ ∗ is O(10 4) that could give the viability the detection of the SM Higgs boson, since there is a relevant number of events. Also we need to considere the eficience and aceptance of the detectors. Detections for A0 searches require a higher number of events (of course more luminosity or energy) reached in another years.

SLIDE 71

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III71

Conclusions

Conclusions

I studied THDM type III, I calculate Yukawa’s Lagrangian. We use the 4-textures matrices like a form of the Yukawa’s matrices and using the Cheng-Sher “anzats” we obtain the vertex for the neutral Higgs bosons decays. We build a program where we can calculate the width decays and the BR in three scenarios, for several tan β and χij values. We obtain dominant decays like the modes b¯ b, ZZ ∗, WW ∗. We calculate the number of events for luminosities of ≈ 1.6 fb−1 and 10 fb−1 in LHC.

SLIDE 72

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III72

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http://indico.cern.ch/conferenceTimeTable.py?confId=142227#all. http://indico.in2p3.fr/conferenceOtherViews.py?view=standard&confId=6004. TeV4LHC Higgs Working Group. Tevatron-for-LHC Report: Higgs.arXiv:hep-ph/0612172v2 17 Dec 2007. http://arxiv.org/PS_cache/hep-ph/pdf/0612/0612172v2.pdf.

SLIDE 83

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III83

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Gratefully

To the International Advisory Board and the Local Organizing Com- mittee for PASCOS. To Dra. Myriam Mondragon Ceballos for organize To Dra. Olga Felix, and Drs J.E Barradas, J.L Diaz, Melina Gomez Bock. For their knowledge. To VIEP-BUAP COCL-ING11-G for the grant. To Dr. Humberto Salazar and Dr. Jaime Hernandez for the financial support.

SLIDE 84

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III83

Render thanks

SLIDE 85

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III83

Render thanks