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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 of the THDM III1 H´ ector Bello Mart´ ınez O. F´ elix Beltr´ an J. E. Barradas Guevara FCFM-BUAP, M´ exico 8 june 2012

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.

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 < m h < 180 GeV, so SM is valid through the Planck scale(10 16 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 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 doublets 3 .

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III5 Standar Model Standar Model Figure 1:

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: L SM = L F + L B + L SBS + L YW + L C , (1) L F is the fermionic Lagrangian, L B is the bosonic Lagrangian ( L B = L YM + L GF + L FP ), L SBS is the SSB Lagrangian, L YW is the Yukawa Lagrangian and L C 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 III7 Standar Model Yukawa’s sector (important) Yukawa’s Lagrangian give mass to fermions after SSB . We intro- duce a covariant object under SU L (2), defined by: � φ 0 ∗ � φ c ∼ i τ 2 φ ∗ = , (2) − φ − where τ 2 is the second Pauli’s matrix, φ ∗ is the complex conjugate of Higgs field; the isodoblet φ c ( � φ ) hypercharge is Y = 1.

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: � k Y k L φ r a ψ k L YW = − a ψ R + h . c ., (3) a , k k = l , u , d is the fermion type, a = 1 , 2 , 3 , ... n where n is the number of Higgs fields in the model (THDM, n = 2) and r is the isodoublet Higgs field φ c or the Higgs field φ , if fermions are type up or down, ψ L are left doublet fermions of SU (2) L : � ν l i � 1 l i , with l i leptons ( e − , µ − , τ − ), and L = l i L � u i � , with u i up quarks ( u , c , t ), and d i down 2 Q i L = d i L quarks ( d , s , b ).

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: L SSB = 1 2 | D µ φ | 2 − V ( φ ) − 1 4( F µν ) 2 . (4) � | φ | 2 � 2 m 2 2 | φ | 2 + λ V ( φ ) = 4 � | φ | 2 � 2 − µ 2 2 | φ | 2 + λ = , (5) 4 where µ = − m 2 and λ > 0.

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.

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 ( m t / m b ≈ 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.

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 φ 1 , φ 2 , with hypercharge Y = ± 1. This is a renormalizable potential, compatible with gauge invariance, is obtained introducing the hermitian gauge invariants operators: A = φ † ˆ 1 φ 1 , (6) B = φ † ˆ 2 φ 2 , � � C = 1 ˆ φ † 1 φ 2 + φ † = Re ( φ † 2 φ 1 1 φ 2 ) , (8) 2 � � D = − i ˆ φ † 1 φ 2 − φ † = Im ( φ † 2 φ 1 1 φ 2 ) . (9) 2

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: � � � � � � � � φ † φ † φ † m 2 + m 2 m 2 V ( φ 1 , φ 2 ) = 1 φ 1 2 φ 2 − 1 φ 2 + h . c . 11 22 12 � � 2 � � 2 � � � � + λ 1 + λ 2 φ † φ † φ † φ † 1 φ 1 2 φ 2 + λ 3 1 φ 1 2 φ 2 2 2 � λ 5 � � � � � � 2 � � � φ † φ † φ † φ † + λ 4 1 φ 2 2 φ 1 + 1 φ 2 + λ 6 1 φ 1 2 � � �� � � φ † φ † + λ 7 2 φ 2 1 φ 2 + h . c . , (10) 14 new, 6 real ( m 2 11 , m 2 22 , λ 1 , λ 2 , λ 3 , λ 4 ) and 4 complex ( m 2 12 , ( m 2 12 ) ∗ , λ 5 , λ ∗ 5 , λ 6 , λ ∗ 6 , λ 7 , λ ∗ 7 ) parameters.

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 CPC 4 , when m 12 , λ 5 , λ 6 , λ 7 are reals. 3 If λ 6 = λ 7 = m 2 12 = 0 then V is symmetric under Z 2 . Then: � � � � φ + φ + 1 2 φ 1 = , φ 2 = , (11) φ 0 1 R + i φ 0 φ 0 2 R + i φ 0 1 I 2 I √ √ 2 2

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: � M 2 � ∂ 2 V ij = 1 0 M 2 C = , (12) M 2 0 2 ∂φ i ∂φ j N 8 × 8

Implications of the Yukawa’s textures of the neutral Higgs bosons in the context of the THDM III16 THDM with M 2 C , M 2 N the 4 × 4 charged and neutral matrices, where:   � 12 ) ∗ � 1 5 − λ 5 ) iv 2 2 e i 2 ξ 12 ) ∗ ) v 2 e i ξ ( m 2 12 + ( m 2 − m 2 12 + ( m 2 ( λ ∗ 4 v 1 � � 4 8    v 2 λ 3 + λ 4 + λ 5 + λ ∗ v 1 v 2 e i ξ 6 − λ 6 ) iv 1 v 2 e i ξ 5 ) iv 1 v 2 e i ξ  + λ 1 1 + 5 +( λ ∗ ( λ 5 − λ ∗   2 2 2 4 8    6 ) 3 v 1 v 2 e i ξ 7 ) v 3 2 e i 3 ξ 6 ) 3 v 2 7 ) 3 v 2 2 e i 2 ξ  +( λ 6 + λ ∗ − ( λ 7 + λ ∗ +( λ 6 + λ ∗ 8 + ( λ 7 + λ ∗ 1   8 8 v 1 8       � 12 ) ∗ � 1 5 ) iv 2  12 ) ∗ ) v 1 e − i ξ 5 ) ( iv 1 v 2 e i ξ )  m 2 12 + ( m 2 ( m 2 12 + ( m 2 − ( λ 5 − λ ∗ ( λ 5 − λ ∗ − 1   � � 4 4 v 2 8 8   λ 3 + λ 4 + λ 5 + λ ∗ v 2 2 e i 2 ξ 6 ) v 3 1 e − i ξ 7 ) iv 2 2 e i 2 ξ v 1 v 2 e i ξ 7 ) iv 1 v 2 e i ξ  − ( λ 6 + λ ∗ − ( λ 7 − λ ∗ +( λ 7 − λ ∗  + 5 − λ 2   2 2 2 8 v 2 4 4   6 ) 3 v 2 7 ) 3 v 2 2 e i 2 ξ 7 ) 3 v 1 v 2 e i ξ  +( λ 6 + λ ∗ 8 + ( λ 7 + λ ∗ +( λ 7 + λ ∗  1 .   8 8 M 2 N =      5 − λ 5 ) iv 2 2 e i 2 ξ − m 2 12 +( m 2 12 ) ∗  5 ) ( iv 1 v 2 e i ξ ) 12 ) ∗ ) v 2 e i ξ ( λ ∗ − ( λ 5 − λ ∗ ( m 2 12 + ( m 2   8 8 4 v 1 4   7 ) iv 2 2 e i 2 ξ  6 − λ 6 ) iv 1 v 2 e i ξ 6 ) v 1 v 2 e i ξ 5 ) v 1 v 2 e i ξ  +( λ ∗ − ( λ 7 − λ ∗ − ( λ 6 + λ ∗ +( λ 5 + λ ∗   4 4 8 4   7 ) v 3 2 e i 3 ξ 6 ) v 2 7 ) v 2 2 e i 2 ξ  − ( λ 7 + λ ∗ +( λ 6 + λ ∗ 8 + ( λ 7 + λ ∗  1  8 v 1 8       5 ) iv 2 − m 2 12 +( m 2 12 ) ∗  5 ) v 1 v 2 e i ξ 12 ) ∗ ) v 1 e − i ξ ( λ 5 − λ ∗ + ( λ 5 + λ ∗ ( m 2 12 + ( m 2  1   8 4 4 4 v 2  6 ) v 2  5 ) iv 1 v 2 e i ξ 7 ) iv 1 v 2 e i ξ 7 ) v 1 v 2 e i ξ  ( λ 5 − λ ∗ +( λ 7 − λ ∗ +( λ 6 + λ ∗ − ( λ 7 + λ ∗ 1   8 4 8 8 7 ) v 2 2 e i 2 ξ +( λ 7 + λ ∗ 8