Beyond the SM

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Higgs and physics

Beyond the SM

1.- Higgs

Oscar Vives

8th IDPASC School

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The Stardard Model

Gauge symmetry: SU(3)⊗SU(2)_L⊗U(1)_Y Particle content:

Repr. Q_L u^c_R d_R^c H

Q. numb. (3,2,¹₆) (¯3,1,−²₃) (¯3,1,¹₃) (1,2,−¹₂)

Spin ¹₂ ¹₂ ¹₂ 0

Repr. L_L e_R^c ν_R^c

Q. numb. (1,2,−¹₂) (1,1,1) (1,1,0)

Spin ¹₂ ¹₂ ¹₂

Plus scalar potential,V_H =µ²H^†H+λ H^†H₂

, and Yukawa couplings. . .

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4th July 2012

Higgs discovered. But, is it the SM Higgs??

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EW Global Fit

σmeas meas) /

fit - O (O

-3 -2 -1 0 1 2 3

2) (MZ (5) had

α

∆

2) (MZ

αs

mt b

R0 c

R0 0,b

AFB 0,c

AFB

Ab

Ac FB)

lept(Q

eff 2Θ sin

(SLD) Al

(LEP) Al

0,l

AFB lep

R0 0

σhad

ΓZ

MZ

ΓW

MW

MH 0.0(0.0)

-1.4(-1.3) 0.2(0.1) 0.2(0.2) 0.0(0.1) -1.5(-1.6) -1.0(-1.1) -0.8(-0.8) 0.2(0.2) -2.0(-2.0) -0.7(-0.7) 0.0(0.0) 0.6(0.6) 0.9(0.9) 2.5(2.5) 0.0(0.0) -0.8(-0.7) 0.5(0.4) 1.7(0.9) -0.2(-0.2) Full EW 2-loop

Z-partial widths at 1-loop GfitterSM

Jul ’14

σtot

- O) /

indirect

(O

-3 -2 -1 0 1 2 3

2) (MZ (5) αhad

∆ 2) (MZ αs

mt b R0 c R0 0,b AFB

0,c AFB

Ab Ac FB) lept(Q eff 2Θ sin

(SLD) Al

(LEP) Al

0,l AFB

lep R0

0 σhad ΓZ MZ ΓW MW MH

Global EW fit Indirect determination Measurement GfitterSM

Jul ’14

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⇒ Impresive SM success !!

Fixing the ∼ 25 parameters of the SM reproduces

(nearly) all experimental results obtained to date.

Have we nished with fundamental physics??

or can we expect Physics Beyond the SM???

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⇒ Impresive SM success !!

Fixing the ∼ 25 parameters of the SM reproduces (nearly) all experimental results obtained to date.

or can we expect Physics Beyond the SM???

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⇒ Impresive SM success !!

Fixing the ∼ 25 parameters of the SM reproduces (nearly) all experimental results obtained to date.

or can we expect Physics Beyond the SM???

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SM Theoretical Problems

•Assignment of matter Quantum Numbers

•Unication of Gauge Couplings

•Origin of Spontaneous Symmetry Breaking

•Accomodate Quantum Gravity

•Large number of Flavour Parameters

SM Observational Problems

•Need of non-baryonic Dark Matter

•CP violation source for Baryogenesis

•Mechanism of Ination

We DO need Physics Beyond the SM !!

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SM Observational Problems

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SM Observational Problems

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SM Observational Problems

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SM Observational Problems

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2 Higgs Doublet Models (2HDM)

Why a single scalar-doublet representation in SM??

Minimal possible extension of the SM:

addition of a second scalar doublet, Φ₁,Φ₂, with the same hypercharge.

But . . . is this phenomenologically allowed???

L_Y =Y_ij⁽¹⁾Qid_j^cΦ₁+Y_ij⁽²⁾Qid_j^cΦ₂

⇒ Tree-level FCNC!!!

(in general)

Theory and phenomenology of two-Higgs-doublet models G.C. Branco, et al., Phys.Rept. 516 (2012) 1-102

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⇒ Tree-level FCNC!!!

(in general)

Theory and phenomenology of two-Higgs-doublet models G.C. Branco, et al., Phys.Rept. 516 (2012) 1-102

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⇒ Tree-level FCNC!!!

(in general)

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However: Paschos-Glashow-Weinberg theorem: no tree-level FCNC iif all fermions with given charge and SU(2) representation receive contributions from a single source

⇒

In 2HDM can be enforced with discrete symmetries

• Type I 2HDM OnlyΦ₁ charged under Z₂

Φ₁→ −Φ₁, Φ₂ →Φ₂, Ψ_i →Ψ_i

L_Y =Y_ij^dQ_id_j^cΦ₂+Y_ij^uQ_iu_j^cΦ˜₂ Φ˜_i =iτ₂Φ^∗_i

• Type II 2HDM Φ₁ andd_R^c charged under Z2

Φ₁ → −Φ₁, Φ₂→Φ₂, d_R^c → −d_R^c, Ψ_i →Ψ_i L_Y =Y_ij^dQid_j^cΦ₁+Y_ij^uQiu^c_jΦ˜₂

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⇒

Φ₁→ −Φ₁, Φ₂ →Φ₂, Ψ_i →Ψ_i

• Type II 2HDM Φ₁ andd_R^c charged under Z2

Φ₁ → −Φ₁, Φ₂→Φ₂, d_R^c → −d_R^c, Ψ_i →Ψ_i L_Y =Y_ij^dQid_j^cΦ₁+Y_ij^uQiu^c_jΦ˜₂

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⇒

Φ₁→ −Φ₁, Φ₂ →Φ₂, Ψ_i →Ψ_i

• Type II 2HDM Φ₁ andd_R^c charged under Z₂

Φ₁ → −Φ₁, Φ₂ →Φ₂, d_R^c → −d_R^c, Ψ_i →Ψ_i L_Y =Y_ij^dQid_j^cΦ₁+Y_ij^uQiu^c_jΦ˜₂

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2HDM Scalar potential

Generalscalar potential (real, Z2 softly broken) with two doublets:

VH = m²₁₁Φ^†₁Φ₁+m²₂₂Φ^†₂Φ₂−m²₁₂

Φ^†₁Φ₂+ Φ^†₂Φ₁ +λ₁

2

Φ^†₁Φ₁2

+ λ₂ 2

Φ^†₂Φ₂2

+λ₃ Φ^†₁Φ₁Φ^†₂Φ₂+λ₄ Φ^†₁Φ₂Φ^†₂Φ₁ + λ₅

2

Φ^†₁Φ₂2

+

Φ^†₁Φ₂2

Minimization of the potential preserving electric charge:

Φ₁ =

φ⁺₁

(v1+ρ₁+iη1)/√ 2

−→ hΦ₁i=

0

v1

√2

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Wemust require stability of the scalar potential

⇒ potential bounded from below.

λ₁ ≥0, λ₂ ≥0, λ₃ ≥ −√ λ₁λ₂, λ₃+λ₄− |λ₅| ≥ −√

λ₁λ₂

On the other hand, quadratic terms can be negative for some values of the elds→ spontaneous symmetry breaking. This must be checked after loop corrections and for all scales (µ). . .

V(φ_i) =Vtree(φ_i) + 1 64π²

X

α

m⁴α(φ_i)

log

m²α(φ_i) µ²

−3 2

S. Coleman & E. Weinberg.

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λ₁ ≥0, λ₂ ≥0, λ₃ ≥ −√ λ₁λ₂, λ₃+λ₄− |λ₅| ≥ −√

λ₁λ₂

On the other hand, quadratic terms can be negative for some values of the elds→ spontaneous symmetry breaking.

This must be checked after loop corrections and for all scales (µ). . .

V(φ_i) =Vtree(φ_i) + 1 64π²

X

α

m⁴α(φ_i)

log

m²α(φ_i) µ²

−3 2

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λ₁ ≥0, λ₂ ≥0, λ₃ ≥ −√ λ₁λ₂, λ₃+λ₄− |λ₅| ≥ −√

λ₁λ₂

On the other hand, quadratic terms can be negative for some values of the elds→ spontaneous symmetry breaking.

This must be checked after loop corrections and for all scales (µ). . .

V(φ_i) =V_tree(φ_i) + 1 64π²

X

α

m⁴α(φ_i)

log

mα²(φ_i) µ²

−3 2

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In theminimumEW symmetry is broken: v² =v₁²+v₂² and tanβ = ^v_v¹

2, withv₁ andv₂ functions of the parametrers of the potential, m²_ij andλ_i.

⇒

Five physical scalars: H^±, H, h, A.

Charged scalars L_m^± = m+²

v² φ⁻₁ φ⁻₂

v₂² −v₁v₂

−v1v2 v₁²

φ⁺₁ φ⁺₂

,

with,m+² =

m²₁₂/(v₁v₂)−λ₄−λ₅

v₁²+v₂²

the mass of the charged HiggsH^±=−φ^±₁ sinβ + φ^±₂ cosβ, and a zero eigenvalue (Goldstone boson, G^±) eaten by W^±.

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In theminimumEW symmetry is broken: v² =v₁²+v₂² and tanβ = ^v_v¹

2, withv₁ andv₂ functions of the parametrers of the potential, m²_ij andλ_i.

⇒

Five physical scalars: H^±, H, h, A.

Charged scalars L_m± = m+²

v² φ⁻₁ φ⁻₂

v₂² −v₁v₂

−v1v2 v₁²

φ⁺₁ φ⁺₂

,

with,m+² =

m²₁₂/(v₁v₂)−λ₄−λ₅

v₁²+v₂²

the mass of the charged HiggsH^±=−φ^±₁ sinβ + φ^±₂ cosβ, and a zero eigenvalue (Goldstone boson, G^±) eaten by W^±.

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Pseudoscalar

L_A = m_A²

v² η₁ η₂

v₂² −v₁v₂

−v1v2 v₁²

η₁ η₂

,

with,m_A² =

m₁₂² /(v₁v₂)−2λ₅

v₁²+v₂²

the mass of the pseudoscalar, and a Goldstone boson, G⁰ eaten by Z⁰.

Neutral scalars L_H = − ρ₁ ρ₂

m²₁₂^v_v²₁ +λ₁v₁² −m₁₂² +λ₃₄₅v1v2

−m²₁₂+λ₃₄₅v₁v₂ m²₁₂^v_v¹₂ +λ₂v₂²

ρ₁ ρ₂

,

with,λ₃₄₅ =λ₃+λ₄+λ₅. Two physical neutral scalars: light Higgs, h =ρ₁sinα−ρ₂cosα and

heavy Higgs, H =−ρ₁cosα−ρ₂sinα

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Pseudoscalar

L_A = m_A²

v² η₁ η₂

v₂² −v₁v₂

−v1v2 v₁²

η₁ η₂

,

with,m_A² =

m₁₂² /(v₁v₂)−2λ₅

v₁²+v₂²

the mass of the pseudoscalar, and a Goldstone boson, G⁰ eaten by Z⁰.

Neutral scalars L_H = − ρ₁ ρ₂

m²₁₂^v_v²₁ +λ₁v₁² −m₁₂² +λ₃₄₅v1v2

−m²₁₂+λ₃₄₅v₁v₂ m²₁₂^v_v¹₂ +λ₂v₂²

ρ₁ ρ₂

,

with,λ₃₄₅=λ₃+λ₄+λ₅. Two physical neutral scalars:

light Higgs, h =ρ₁sinα−ρ₂cosα and

heavy Higgs, H cos sin

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Type-III 2HDM

Tree-level FCNCs can still be present if suciently small. . . L_Y =η^d_ijQ_id_j^cΦ₁+η_ij^uQ_iu_j^cΦ˜₁+ξ_ij^dQ_id_j^cΦ₂+ξ_ij^uQ_iu_j^cΦ˜₂

•Cheng-Sher ansatz: ξ_ij =λ_ij√

m_im_j ^√_v²,withλ_ij ∼ O(1).

•Minimal Flavour Violation (MFV) (∼Branco-Grimus-Lavoura):

⇒

All FC proportional toCKM matrix.

•Alignment models (Pich-Tuzon): Proportionality ofη andξ Yukawa matrices: ξ_ij^d =η_ij^d,ξ_ij^u=η^u_ij.

Somewhat ad hoc models, but can be motivated with avour symmetries . . .

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Type-III 2HDM

Tree-level FCNCs can still be present if suciently small. . . L_Y =η^d_ijQ_id_j^cΦ₁+η_ij^uQ_iu_j^cΦ˜₁+ξ_ij^dQ_id_j^cΦ₂+ξ_ij^uQ_iu_j^cΦ˜₂

•Cheng-Sher ansatz: ξ_ij =λ_ij√

m_im_j ^√_v²,withλ_ij ∼ O(1).

•Minimal Flavour Violation (MFV) (∼Branco-Grimus-Lavoura):

⇒

All FC proportional toCKM matrix.

•Alignment models (Pich-Tuzon): Proportionality ofη andξ Yukawa matrices: ξ_ij^d =η_ij^d,ξ_ij^u=η^u_ij.

Somewhat ad hoc models, but can be motivated with avour symmetries . . .

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2HDM phenomenology

B-physics constraints

From low-energy observables: B→τ ντ, B →Dτ ντ, Ds →τ ντ, B→X_sγ, B₀−B¯₀ mixing.

5.2 Results and Discussion 46

tanβ

10 20 30 40 50 60 70

[GeV]±HM

100 200 300 400 500 600 700

LEP 95% CL exclusion 68% CL exclusion from MC toy

95% CL exclusion from MC toy 99% CL exclusion from MC toy

dof=1) 2,n χ

∆ 95% CL for Prob(

dof=2) 2,n χ 95% CL for Prob(∆

tanβ

10 20 30 40 50 60 70

[GeV]±HM

100 200 300 400 500 600 700

tanβ

10 20 30 40 50 60 70

[GeV]±HM

100 200 300 400 500 600 700

LEP 95% CL exclusion 95% CL excluded regions

0 Rb

) sγ X

→ (B B

) ν τ

→ (B B

ν)

→ De (B B ν) / Dτ (B → B

) ν µ

→ π ( B ) / ν µ

→ (K B

) ν µ

→ (B B

Combined fit (toy MC)

tanβ

10 20 30 40 50 60 70

[GeV]±HM

100 200 300 400 500 600 700

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LHC bounds

Searches in pp→tH⁺→tτ⁺ν and pp →tH⁺→t tb.¯

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LHC bounds

Searches in pp→tH⁺→tτ⁺ν and pp →tH⁺→t tb.¯

Model independent bounds on Higgs production at LHC. No

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SM Theoretical Problems

SM Observational Problems

We DO need Physics Beyond the SM !!

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We DO need Physics Beyond the SM !!

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We DO need Physics Beyond the SM !!

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We DO need Physics Beyond the SM !!

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We DO need Physics Beyond the SM !!

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• Only possible extension of symmetry beyond Lie Symmetries (ColemanMandula Theorem).

• Correct Unication of Gauge couplings at MGUT,

GUT assignment of Quantum numbers (anomaly cancellation).

• Solution of the Hierarchy Problem, strong motivation for low-energy SUSY.

• Natural Mechanism of Electroweak Symmetry Breaking, Radiative Symmetry Breaking.

• SUSY is a necessary ingredient in String Theory.

Local Supersymmetry ⇔ Supergravity.

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ColemanMandula Theorem

In the 60's attempts to combine internal and Lorentz symmetries ...

The only conserved quantities that transform as tensors under Lorentz transformations in a theory with non-zero scattering amplitudes in 4D are the generators of the Poincare group and Lorentz invariant quantum numbers (scalar charges).

2×2 spinless particle scattering, bosonic conserved charge,Σ_µν, h1|Σ_µν|1i=αpµ¹p¹ν+βgµν

So, in the scattering process,

pµ¹p¹ν+pµ²p²ν =p³µpν³+pµ⁴pν⁴ & pµ¹+pµ² =p³µ+pµ⁴

Not possible in a theory with non-zero scattering.

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However: ColemanMandula theorem does not forbid conserved spinor charges, Qα (transforming like fermions under Lorentz)

Qα|Bosoni=|Fermioni Qα|Fermioni=|Bosoni [Qα,H] =0 [{Qα,Q¯β˙},H] =0

Supersymmetry Algebra {Qα,Q¯β˙}=2σ^µ

αβ˙Pµ {Qα,Qβ}=0 {Q¯α˙,Q¯β˙}=0 Supersymmetry relates particles of dierent spin with equal quantum numbers and identical masses.

₁ 02

∼

q (quark)

˜q (squark)

11 2

∼

g (gluon) g˜ (gluino)