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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 contextof the THDM III1
Hector Bello Martınez
O. Felix BeltranJ. E. Barradas Guevara
FCFM-BUAP, Mexico
8 june 2012
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III2Resume
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.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III3Introduction
Introduction
1 The Higgs boson: hypothetical elementary particle, hisexistence is given by the SSB. It gives the mass of theparticles of the SM.
2 It was theorized in 1964 by Peter Higgs, Francois Englert yRobert Brout (in base to ideas of Philip Anderson), andindependently by G. S. Guralnik, C. R. Hagen and T. W. B.Kibble [1].
3 The Higgs field has a vacuum expectation value (VEV 6= 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 Planckscale(1016 TeV).
6 An extention of the SM is the Two Higgs Doblet Model(THDMIII).
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III4Introduction
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 upquarks, while the other one couples to down quarks.2
3 Type III. Higgs-fermions couplings are indistinc to anyone ofthe two doublets3.
1J.F. Gunion, S. Dawson, H.E. Haber, G.Kane. The Higgs Hunter’s Guide Addison Wesley Publishing (1990)
pag 6.2
R. A. Diaz Sanchez. Phenomenological analysis of the Two Higgs Doublet Model. PhD. Tesis arXiv:hep-
ph/0212237.3
J.L. Dıaz-Cruz, A. Dıaz-Furlong, and J.H. Montes de Oca Y.The general Two-Higgs doublet eXtensions of the
SM: a saucerful of secrets.arXiv:1010.0950v2 [hep-ph] 5 Feb 2011
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III5Standar Model
Standar Model
Figure 1:
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III6Standar 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 YukawaLagrangian and LC is the current Lagrangian.This includes 5 sectors: fermionic, Yang Mills, Higgs, Yukawa,and currents sectors.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III7Standar 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 conjugateof Higgs field; the isodoblet φc (φ) hypercharge is Y = 1.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III8Standar Model
General Yukawa’s Lagrangian is:
LYW = −∑a,k
Y ka ψ
kLφ
raψ
kR + h.c., (3)
k = l , u, d is the fermion type, a = 1, 2, 3, ...n where n is the numberof Higgs fields in the model (THDM, n = 2) and r is the isodoubletHiggs field φc or the Higgs field φ, if fermions are type up or down,ψL are left doublet fermions of SU(2)L:
1 l iL =
(νlili
)L
, with li leptons (e−, µ−, τ−), and
2 Q iL =
(ui
d i
)L
, with ui up quarks (u, c, t), and d i down
quarks (d , s, b).
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III9Standar 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|2
)2= −µ
2
2|φ|2 + λ
4
(|φ|2
)2, (5)
where µ = −m2 and λ > 0.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III10Standar Model
Figure 2: Higgs potential for real and imaginary mass.
Figure 3: Higgs potential for n = 2, note that red region is given by 246Gev’s.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III11THDM
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 inthe third generation of quarks (mt/mb ≈ 173.1/4.67 ≈ 37), this ismaking by letting the bottom quark mass given by one doublet andthe top one’s for the other.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III12THDM
The Higgs potential of THDM. We introduce two SU(2)Y dou-blets φ1, φ2, with hypercharge Y = ±1. This is a renormalizablepotential, compatible with gauge invariance, is obtained introducingthe hermitian gauge invariants operators:
A = φ†1φ1, (6)
B = φ†2φ2,
C =1
2
(φ†1φ2 + φ†2φ1
)= Re(φ†1φ2), (8)
D = − i
2
(φ†1φ2 − φ†2φ1
)= Im(φ†1φ2). (9)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III13THDM
The renormalizable and reparameterized Higgs potential for the THDMis:
V (φ1, φ2) = m211
(φ†1φ1
)+m2
22
(φ†2φ2
)−[m2
12
(φ†1φ2
)+ h.c.
]+λ12
(φ†1φ1
)2+λ22
(φ†2φ2
)2+ λ3
(φ†1φ1
)(φ†2φ2
)+λ4
(φ†1φ2
)(φ†2φ1
)+
{λ52
(φ†1φ2
)2+[λ6
(φ†1φ1
)+λ7
(φ†2φ2
)](φ†1φ2
)+ h.c.
}, (10)
14 new, 6 real (m211,m
222, λ1, λ2, λ3, λ4) and 4 complex
(m212, (m
212)
∗, λ5, λ∗5, λ6, λ
∗6, λ7, λ
∗7) parameters.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III14THDM
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 = m212 = 0 then V is symmetric under Z2.
Then:
φ1 =
(φ+1
φ01R+iφ0
1I√2
), φ2 =
(φ+2
φ02R+iφ0
2I√2
), (11)
4J.F. Gunion and H.E. Haber Conditions for CP-Violation in the General Two-Higgs-Doublet Model. arXiv:hep-
ph/0506227v2 26 Oct 2005.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III15THDM
Now we can calculate the mass matrix given by:
M2ij =
1
2
∂2V
∂φi∂φj=
(M2
C 00 M2
N
)8×8
, (12)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III16THDM
with M2C ,M
2N the 4× 4 charged and neutral matrices, where:
M2N =
(m212 + (m2
12)∗) v2e
iξ
4v1−(m2
12 + (m212)
∗) 14 (λ∗5 − λ5)
iv22 e
i2ξ
8
+λ1v212 +
(λ3 + λ4 +
λ5+λ∗5
2
)v1v2e iξ
2 +(λ∗6 − λ6)iv1v2e iξ
4 (λ5 − λ∗5)iv1v2e iξ
8
+(λ6 + λ∗6)3v1v2e iξ
8 − (λ7 + λ∗7)v32 e
i3ξ
8v1+(λ6 + λ∗6)
3v218 + (λ7 + λ∗7)
3v22 e
i2ξ
8
−(m2
12 + (m212)
∗) 14 (m2
12 + (m212)
∗) v1e−iξ
4v2−(λ5 − λ∗5)
(iv1v2e iξ)8 (λ5 − λ∗5)
iv218
+(λ3 + λ4 +
λ5+λ∗5
2
)v1v2e iξ
2 −λ2v22 e
i2ξ
2 − (λ6 + λ∗6)v31 e
−iξ
8v2−(λ7 − λ∗7)
iv22 e
i2ξ
4 +(λ7 − λ∗7)iv1v2e iξ
4
+(λ6 + λ∗6)3v2
18 + (λ7 + λ∗7)
3v22 e
i2ξ
8 +(λ7 + λ∗7)3v1v2e iξ
8
(λ∗5 − λ5)iv22 e
i2ξ
8 −(λ5 − λ∗5)(iv1v2e iξ)
8 (m212 + (m2
12)∗) v2e
iξ
4v1−m2
12+(m212)
∗
4
+(λ∗6 − λ6)iv1v2e iξ
4 −(λ7 − λ∗7)iv22 e
i2ξ
4 −(λ6 + λ∗6)v1v2e iξ
8 +(λ5 + λ∗5)v1v2e iξ
4
−(λ7 + λ∗7)v32 e
i3ξ
8v1+(λ6 + λ∗6)
v218 + (λ7 + λ∗7)
v22 e
i2ξ
8
(λ5 − λ∗5)iv218 −m2
12+(m212)
∗
4 + (λ5 + λ∗5)v1v2e iξ
4 (m212 + (m2
12)∗) v1e
−iξ
4v2
(λ5 − λ∗5)iv1v2e iξ
8 +(λ7 − λ∗7)iv1v2e iξ
4 +(λ6 + λ∗6)v218 −(λ7 + λ∗7)
v1v2e iξ
8
+(λ7 + λ∗7)v22 e
i2ξ
8
.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III17THDM
m2H0,h0 =
(λ∗1 +
1
2λ+
)v21 − 1
2µ22
±
√[(λ∗1 −
1
2λ+
)v21 +
1
2µ22
]2+
(1
2λ∗6v
21
)2
. (13)
(cosαsenα
)↔ m2
H0 ,
(−senαcosα
)↔ m2
h0 , (14)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III18THDM
where:
tan 2α =λ∗6v
21
(2λ∗1 − λ+)v21 + µ22, λ+ ≡ 1
2(λ3 + λ5), (15)
and λ∗i , µ2 are given as the reparametrization. Thus, the diagonal-ization process makes the rotation:(
cosα senα−senα cosα
)( √2φ01R − v1√2φ02R − v2
)=
(H0
h0
)(16)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III19Yukawa’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).
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III20Yukawa’s Lagrangian in THDM
Yukawa’s Lagrangian for the quark fields is:
LqY = q0LY
D1 φ1d
0R + q0LY
D2 φ2d
0R + q0LY
U1 φ1u
0R
+ q0LYU2 φ2u
0R + h.c., (17)
with Y U,D1,2 the 3× 3 Yukawa’s matrices, qL left quark doublets, uR ,
dR right singlets.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III21Yukawa’s Lagrangian in THDM
Before a correct SSB
The Higgs doublets are descomposed as:
φ1 =
(φ+1
v1+φ1+iχ1√2
), φ2 =
(φ+2
e iξv2+φ2+iχ2√2
), (18)
where v1, v2 εR+.By expresing q0L using (18), and transforming the quark fields tothe mass eigenstate basis through uL,R = UL,Ru
0L,R and dL,R =
DL,Rd0L,R ,
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III22Yukawa’s Lagrangian in THDM
using quirality operators of the matrix:
MQ = QLYQ1 Q†
R
v1√2+ QLY
Q2 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)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III23Yukawa’s Lagrangian in THDM
where qra are written as combination of θij ,these are given by:
r qr1 qr21 cos θ12 cos θ13 −senθ12 − i cos θ12senθ132 senθ12 cos θ13 cos θ12 − isenθ12senθ133 senθ13 i cos θ134 i 0
Table 1: Values of qra in terms of the mixing angles of the rotationmatrix.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III24Yukawa’s Lagrangian in THDM
We can rewrite the Lagrangian for neutral Higgs couplings to up anddown quarks:
Lneutralup,down = ¯(u, d)i
[Su,dijr + γ5Pu,d
ijr
](u, d)jHr + ¯(u, d)iM
u,Dij (u, d)j .
(21)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III25Yukawa’s Lagrangian in THDM
Su,dijr and Pu,d
ijr are given by:
Su,dijr =
Mu,D
2v
(q∗r1 + qr1 − tanβ
(q∗r2e
i(θ+ξ) + qr2e−i(θ+ξ)
))+
1
2√2cosβ
(q∗r2e
iθY u,D†2 + qr2e
−iθY u†,D2
), (22)
Pu,dijr = −∗M
u,D
2v
(q∗r1 − qr1 − tanβ
(q∗r2e
i(θ+ξ) − qr2e−i(θ+ξ)
))+
1
2√2cosβ
(q∗r2e
iθY u,D†2 − qr2e
−iθY u†,D2
). (23)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III26Yukawa’s Lagrangian in THDM
In THDM III we considere up y down sector the values of S y Pfor each of the Hi (i = 1, 2, 3) as follows:
1 For H1 = h0: S 6= 0 and P = 0.
2 For H2 = H0: S 6= 0 and P = 0.
3 For H3 = A0: S = 0 and P 6= 0.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III27Yukawa’s Lagrangian in THDM
The texture formalism started by Bjorken proposing:
Mf +∆Mf mf 0m∗
f Mf +∆Mf mf
0 m∗f Mf +∆Mf
, (24)
which reproduce the quarks mass and the elements of VCKM withgood aproximation.
1 It reproduces fermionic mass and mixing angles.
2 It supress FCNC.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III28Yukawa’s Lagrangian in THDM
The 4 textures Yukawa’s hermitic matrix fulfill:
1 Hierarchy |Aq| � |Bq|, |Bq|, |Cq|, Aq and Bq εR.
2 Phases of Cq and Bq (ΦBq and ΦCq) removed by Mq = P†qMqPq,
with Pq = diag(1, e iΦCq , e i(ΦCq+ΦBq )),
3 Mq = OTq MqOq, where M is:
Mq =
0 Cq 0
C ∗q Bq Bq
0 B∗q Aq
. (25)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III29Yukawa’s Lagrangian in THDM
The corrections to FC and FV depend of the diagonal matrix Y q2 =
OTq PqY
q2 P
†qOq. For Y q
2 , we asumme that Y q2 has the form of 4
textures. So with Cheng-Sher anzats:
(Y q2 )ij =
√mq
i mqj
vχqij =
√mq
i mqj
vχqije
iϑqij , (26)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III30Yukawa’s Lagrangian in THDM
considering the ansatz Yu,d2ij = χij
√mimj
v and taking no CPV and
using e−iθ23 = 1, cos θ12 = sen(β − α) y senθ12 = cos(β − α):
Lneutralupint =
g
2mwui
[mui
cosα
senβδij −
cos(α− β)√2senβ
√muimuj χ
uij
]ujh
0
+g
2mwui
[mui
senα
senβδij −
sen(α− β)√2senβ
√muimuj χ
uij
]ujH
0
− ig
2mwui
[−mui cotβδij +
√muimuj√2senβ
χuij
]γ5ujA
0,
(27)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III31Yukawa’s Lagrangian in THDM
Lneutraldownint =
g
2mwdi
[−mdi
senα
cosβδij +
cos(α− β)√2 cosβ
√mdimdj χ
dij
]djh
0
+g
2mwdi
[mdi
cosα
cosβδij +
sen(α− β)√2 cosβ
√mdimdj χ
dij
]djH
0
+ig
2mwdi
[−mdi tanβδij +
√mdimdj√2 cosβ
χdij
]γ5djA
0,
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III32Yukawa’s Lagrangian in THDM
Lneutralleptonesint =
g
2mwli
[−mli
senα
cosβδij +
cos(α− β)√2 cosβ
√mlimlj χ
lij
]ljh
0
+g
2mwui
[mli
cosα
cosβδij +
sen(α− β)√2 cosβ
√mlimlj χ
lij
]ujH
0
+ig
2mwui
[−mdi tanβδij +
√mdimdj√2 cosβ
χdij
]γ5ujA
0,
(28)
From this, we have the vertex for Feynman diagrams!
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III33Phenomenology
Production and posible Decays of neutral Higgs. Neutral Higgsbosons can be produced by:
Figure 4: a) Gluon fusion, b) vectorial bosons fusion, c) e-p collisions,d) p-p collisions.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III34Phenomenology
Neutral Higgs Decays in THDM III
We considered fermionic (with FCNC) and bosonic decays,
1 two fermions: (φ0 → fi fj), 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 formV < mh < 2mV .
4 two Higgs bosons: H0 → h0h0,H0 → A0A0.
5 one gauge boson and a light Higgs (just allowed A0 → Zh0).
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III35Phenomenology
We calculate to tree level
Figure 5: Feynman diagrams of neutral Higgs decaying to: a) 2 fermionswith FCNC, b) 2 gauge bosons, c) 2 neutral Higgs, d) a vectorial gaugeboson and a neutral Higgs.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III36Phenomenology
Higgs decaying to two fermions
In THDMIII: 18 posible decays (twice that in SM).
Γfi fj(mi ,mj ,mφ
0,Nc , n, ξij)=(
Nc
8π(mφ0)3
)(g
2mw
)2
ξ2ij((mφ0)2 − (mi +mj(−1)n)2
)·((m2
i −m2j − (mφ0)2)2 − 4m2
j (mφ0)2)1/2
. (29)
where Nc = 1(3) for leptons (quarks), n even for h0, H0; n odd forA0 and φ0 = h0,H0,A0.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III37Phenomenology
And ξij are given by:
Process THDMIII THDMII SM
h0 → ui uj muicosαsenβ δij −
cos(α−β)√2senβ
√muimuj χ
uij mui
cosαsenβ δij mui δij
h0 → di dj −mdisenαcosβ δij +
cos(α−β)√2 cosβ
√mdimdj χ
dij −mdi
senαcosβ δij mdi δij
H0 → ui uj muisenαsenβ δij −
sen(α−β)√2senβ
√muimuj χ
uij mui
senαsenβ δij −
H0 → di dj mdicosαcosβ δij +
sen(α−β)√2 cosβ
√mdimdj χ
dij mdi
cosαcosβ δij −
A0 → ui uj −mui cotβδij +
√mui
muj√2senβ
χuij −mui cotβδij −
A0 → di dj −mdi tanβδij +
√mdi
mdj√2 cosβ
χdij −mdi tanβδij −
Table 2: Values of ξij according to decay and model.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III38Phenomenology
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 64πm2W
sen2(β − α)√
1− x(V )
×(1− x(V ) +3
4x2(V )), (30)
Γ(H0 → VV ) =g2m3
h0
kV 64πm2W
cos2(β − α)√
1− x(V )
×(1− x(V ) +3
4x2(V )), (31)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III39Phenomenology
where kV = 1 for V = W , kV = 2 for V = Z and x(V ) = 4m2v
m2h.
Constrain: mhiggs > 2mV .
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III40Phenomenology
Higgs decaying to two gauge boson and one virtual
Γ(h0 → WW ∗) = 4g4mh0
512π3sen2(α− β)F (mW /mh0), (32)
Γ(h0 → ZZ ∗) = 4g4mh0
2048π3sen2(α− β)F (mZ/mh0)×[
7− (40/3)sen2θW + (160/9)sen4θWcos4 θW
],(33)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III41Phenomenology
where F (x) = −(1−x2)(47x
2 − 132 + 1
x2
)−3(1−6x2+4x4)ln(x)+
3(1−8x2+20x4√
4x2−1
)arccos
(3x2−12x3
). And for H0:
Γ(H0 → WW ∗,ZZ ∗) = Γ(h0 → WW ∗,ZZ ∗) cot2(α− β). (34)
Note that √4m2
W
m2h0
− 1 ε R, (35)
then4m2
W
m2h0
− 1 > 0 and so mh0 <√
4m2W , (mh0 < 160.78 GeV’s for
mW = 80.39 GeV).
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III42Phenomenology
A0 → Z 0h0 decay
The only way that A0 decays to two bosons.
Γ(A0 → Z 0h0) =g2λ1/2cos2(β − α)
64πm3A0cos2θW(
m2Z − 2(m2
A0 + 2m2h0) +
(m2A0 −m2
h0)2
m2Z
),(36)
with λ1/2 =((m2
Z0 +m2h0 −m2
A0)2 − 4m2
Z0m2h0
)1/2. No tree level
coupling to a pair of vectorial bosons because CPC.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III43Phenomenology
Higgs decaying to 2 Higgs
H0 → h (h = h0,A0).
Γ(H0 → hh) =g2m2
Z f2h
128πmH0 cos2 θW
(1−
4m2h
m2H0
)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.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III44Phenomenology
Branching Ratios
To calculate Neutral Higgs bosons BR, we need to calculate the totalwidth 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)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III45Phenomenology
Constraints
We have several constraints:
CUSTODIAL SIMMETRY SU(2)c .
ρ =M2
W
M2Z cos2 θW
=
∑k 2(Tk(Tk + 1)− Y 2
k /4)ν2k +
∑i 2Ti (Ti + 1)ν2i∑
k ν2kY
2,
TRIVIALITY COSTRAINTS.λ 6= 0 and finite.
STABILITY CONSTRAINT OF THE VACUUM. Stablevacuum requires λ > 0 so (Mh & 130 GeV) but vacuum must bemetastable so Mh & 115GeV .
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III46Phenomenology
Bounds of SM Higgs boson mass in november of 2011.
Figure 6: Combination of ATLAS data [4].
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III47Results
Results
We build a program in Mathematica R© which we compute the nextdecay 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).
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III48Results
In 3 scenarios:
1 scenario A: α− β = −π2 (for h0 this is SM scenario).
2 scenario B: α− β = 0.
3 scenario C: α− β = −π3 .
With:tanβ = 5, 10, 15, 20, 30, 50; thus also values of χij = 1, 0.5, 0,−0.2,−0.5,−1,in the 4 Yukawa’s textures context, (χ11 = χ13 = χ31 = 0).
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III49Results
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 = 1.776GeV, mAfijo = 250 GeV, g =
√4πα GeV, mt = 173.1 GeV, mw =
80.39 GeV, mz = 91.1876 GeV, sw =√0.2254, cw =
√1− s2w .
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III50Results
Branching Ratios of h0
For the h0 decays (SM Higgs boson), we considered for numericalanalysis 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 tanβ = 5, 15, 50.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III51Results
100 200 300 400 50010-5
10-4
10-3
10-2
10-1
100
100 200 300 400 500 100 200 300 400 500
tan
BR
(h°
XY
)
tan
tan
cc ss tt bb
ww* zz* ww zz
BR h° en escenario A:
Figure 7: BR(h0) with O > 10−5 scenario A.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III52Results
40 60 80 100 120 140 160 180 200 2201E-5
1E-4
1E-3
0.01
0.1
1
tan ij
BR h° en escenario A:
cc ss tt bb
WW* ZZ* WW ZZBR
(h°
XY)
mh° (GeV)
Figure 8: BR(h0) with O > 10−5 in SM.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III53Results
100 200 300 400 50010-5
10-4
10-3
10-2
10-1
100
100 200 300 400 500 100 200 300 400 500
tan
BR
( h°
XY
)
tan
BR h° en escenario B:
tan
cc ss tt bb ct sb ww zz
Figure 9: BR(h0) with O > 10−5 scenario B.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III54Results
100 200 300 400 50010-5
10-4
10-3
10-2
10-1
100
100 200 300 400 500 100 200 300 400 500
BR h° en escenario C:
tan
BR
( h°
XY
)
tan
tan
cc ss tt bb ct sb ww* zz* ww zz
Figure 10: BR(h0) with O > 10−5 scenario C.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III55Results
Branching Ratios of H0
For H0 decays (the neutral Higgs boson heavier than SM ones), weconsidered for the numerical analisis we considered a range for Higgsmass 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.tanβ and χij values, for first region dominant decays is to pair ofb-quarks (bb) and WW pairs.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III56Results
Proceso ξij en escenario A ξij en escenario B
h0 → ui uj mui δij mui cotβδij −√
muimuj√
2senβχuij
h0 → di dj −mdi δij −mdi tanβδij +
√mdi
mdj√2 cosβ
χdij
H0 → ui uj −mui cotβδij +
√mui
muj√2senβ
χuij mui δij
H0 → di dj mdi tanβδij −√
mdimdj√
2 cosβχdij mdi δij
A0 → ui uj −mui cotβδij +
√mui
muj√2senβ
χuij −mui cotβδij +
√mui
muj√2senβ
χuij
A0 → di dj −mdi tanβδij +
√mdi
mdj√2 cosβ
χdij −mdi tanβδij +
√mdi
mdj√2 cosβ
χdij
Table 3: ξij values according to decays and scenario[3].
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III57Results
200 300 400 500 600 700 80010-5
10-4
10-3
10-2
10-1
100
200 300 400 500 600 700 800 200 300 400 500 600 700 800
tan
BR
(H°
XY
)
tan
BR H° en escenario A:
tan
cc ss tt bb ct sb h°h° A°A°
Figure 11: BR(H0) with O > 10−5 in scenario A.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III58Results
200 300 400 500 600 700 80010-5
10-4
10-3
10-2
10-1
100
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 ww zz h°h° A°A°
Figure 12: BR(H0) with O > 10−5 in scenario B.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III59Results
200 300 400 500 600 700 80010-5
10-4
10-3
10-2
10-1
100
200 300 400 500 600 700 800 200 300 400 500 600 700 800
BR H° en escenario C:
tan
BR
( H
° X
Y)
tan
tan cc ss tt bb ct sb WW ZZ h°h° A°A°
Figure 13: BR(H0) with O > 10−5 scenario C.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III60Results
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 tanβand χij . For the first, the dominant decay is to bb, this becomedominant in second region for tanβ ≈ 50. It is important to saythat variations in BR are given the variation of BR(h0 → Z 0h0) aswell as the fermionic decays don’t depend on α.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III61Results
200 300 400 500 600 700 80010-5
10-4
10-3
10-2
10-1
100
200 300 400 500 600 700 800 200 300 400 500 600 700 800
tan
BR
(A
° X
Y)
tan
BR A° en escenario A:
tan 15
cc ss tt bb ct sb
Figure 14: BR(A0) with O > 10−5 scenario A.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III62Results
200 300 400 500 600 700 80010-5
10-4
10-3
10-2
10-1
100
200 300 400 500 600 700 800 200 300 400 500 600 700 800
tan
BR A° en escenario B: B
R (
A°
XY
)
tan
tan
cc ss tt bb ct sb Z°h°
Figure 15: BR(A0) with O > 10−5 scenario B.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III63Results
200 300 400 500 600 700 80010-5
10-4
10-3
10-2
10-1
100
200 300 400 500 600 700 800 200 300 400 500 600 700 800
tan
BR A° en escenario C: B
R (
A°
XY
)
tan
tan
cc ss tt bb ct sb Z°h°
Figure 16: BR(A0) with O > 10−5 scenario C.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III64Results
Events Number
Finally, to calculate the (ideal) events number that can occur inthese decays, we have:
Neventos = L × σ × BR, (40)
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III65Results
Figure 17: Cross sections in SM [5].
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III66Results
Figure 18: Cross sections in MSSM [5].
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III67Results
Figure 19: Luminosity reached at LHC in november 2011 [4].
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III68Results
We can calculate a prediction for the events number in LHC in theMSSM, like we show in chart 20. We take account the scenario Aand scenario B with mh = 120 GeV, mH = 200 GeV, mA = 250GeV, tanβ = 5, althoug, this calculation of events number wasdone for data of november of 2011 and for integrated luminosity of10 fb−1 that probably LHC will reach after 2012 ends.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III69Results
Figure 20: Prediction for events number in LHC using MSSM.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III70Results
From this data we observe that the events number for h0 → bb orh0 → ZZ ∗ is O(104 ) that could give the viability the detection ofthe SM Higgs boson, since there is a relevant number of events. Alsowe need to considere the eficience and aceptance of the detectors.Detections for A0 searches require a higher number of events (ofcourse more luminosity or energy) reached in another years.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III71Conclusions
Conclusions
I studied THDM type III, I calculate Yukawa’s Lagrangian.
We use the 4-textures matrices like a form of the Yukawa’smatrices and using the Cheng-Sher “anzats” we obtain thevertex for the neutral Higgs bosons decays.
We build a program where we can calculate the width decaysand the BR in three scenarios, for several tanβ and χij values.
We obtain dominant decays like the modes bb, ZZ ∗, WW ∗.
We calculate the number of events for luminosities of ≈ 1.6fb−1 and 10 fb−1 in LHC.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III72
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Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III83Render thanks
Gratefully
To the International Advisory Board and the Local Organizing Com-mittee for PASCOS.To Dra. Myriam Mondragon Ceballos for organizeTo Dra. Olga Felix, and Drs J.E Barradas, J.L Diaz, Melina GomezBock.For their knowledge.To VIEP-BUAP COCL-ING11-G for the grant.To Dr. Humberto Salazar and Dr. Jaime Hernandez for the financialsupport.
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III83Render thanks
Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III83Render thanks