Models for Neutrino Masses and Physics Beyond Standard Model Salah - - PowerPoint PPT Presentation

Models for Neutrino Masses and Physics Beyond Standard Model

Salah Nasrj The 2nd Toyama International Workshop on ”Higgs as a Probe of New Physics 2015” (HPNP2015), Toyama, Japan February 12, 2015

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Introduction

. . The standard model is not the final theory

• Dark matter

. . [ ΩDMh2](obs) = 0.1199±0.0027 [Planck Collaboration (2013)]

• Matter- antimatter asymmetry of the universe

. . ηB : nB nγ = (6.047±0.074)×10−10 [Planck Collaboration (2013)]

• Neutrino Oscillations (masses and mixings)
• Hierarchy problem
• Strong CP problem
• Gauge coupling unification
• ect..

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Global Fit [Gonzalez-Garcia, Maltoni and Schwetz (2014)].

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Why me >> mν ̸= 0?

. . SM is an effective theory L = LSM + . . L (5)

ef f +L (6) ef f +..

[Weinberg(1979)] . . L (5)

ef f ∼ 1

ΛLΦLΦ ⇒ . . mν ∼ υ2 ΛNP ⇒ . . Λ ∼ 1014 GeV Can be written in . . 3 diff. forms : Type I = .......+ Cαβ 2ΛNP ( ¯ Lc

α iσ2 Φ)(LT β iσ2 Φ)+h.c

Type II = ....− Cαβ 4 ΛNP ( ¯ Lc

α iσ2 ⃗

σ Lβ)(ΦT iσ2 ⃗ σ Φ)+h.c Type III = ....+ Cαβ 2ΛNP ( ¯ Lc

α iσ2 ⃗

σ Φ)(LT

β iσ2 ⃗

σ Φ)+h.c

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. . Seesaw mechanisms . . Type I = ...+ ¯ L ˜ Φ Yν NR + 1 2 NT

R C MR NR +h.c ⇒

. .Cαβ ΛNP = Y T

ν M−1 Yν

[Minkowski; Yanagida; Ramond and Gell-Mann; Mohapatra and Senjanovic] . . Type II = ...+M2

∆Tr(∆†∆)+ µ∆ΦTiτ2∆†Φ+ hαβ

2 LTCiτ2∆ Lβ +h.c . .Cαβ ΛNP = hαβ µ∆ M2

∆

[Maag, Watterich, Shafi, Lazaridis; Mohapatra, Senjanovic; Schechter, Valle] . . Type III = ....+ 1 2 [ ΣRiMΣiΣc

Ri +Σc RM∗ ΣΣR

] + hαi ¯ Lα ΣRi ˜ Φ+h.c ⇒ . . mν = Cαβυ2 ΛNP [Foot, He, Lew, Joshi; Ma]

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• Leptogenesis. Ex: Type I
• Generate a B-L asymmetry through the

. .

• ut-of-equilibrium decays of NiR

into leptons and anti-leptons. ฀ [Fukugita and Yanagida (86)]

• The CP-asymmetry from the decay of Ni into lepton and anti-leptons:

εi = Γ(Ni → L Φ)−Γ(Ni → ¯ L ¯ Φ) Γ(Ni → L Φ)+Γ(Ni → ¯ L ¯ Φ) [Flanz et al,94;Covi, Roulet, Vissani,94]

• Part of it get converted to a baryon asymmetry via sphaleron transitions.

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• Leptogenesis. Ex: Type I
• Wash out effects (in addition to the inverse decay)
• 1. off-shell

. . ∆L = 1 scatterings involving top quark: N1 L ↔ t ¯ q, N1 ¯ L ↔ t ¯ q (s-channel) N1 t ↔ ¯ L q, N1 ¯ t ↔ L ¯ q (t-channel) 2. . . ∆L = 2 scatterings L Φ ↔ ¯ L ¯ Φ, L L ↔ ¯ Φ ¯ Φ, ¯ L ¯ L ↔ Φ Φ

• The final baryon asymmetry :

. . YB := nB s ≃ −4×10−3 ×ε1 ×κ f ×Cs Cs = 28 79 : [Conversion factor]; κf ( ˜ m1) [Efficiency factor]; . .˜ m1 = (YY †)11υ2 M1

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• Leptogenesis. Ex: Type I

After solving the Boltzmann equations: [Buchmuller, Di Bari, Plumacher(2004)] . . ε1 ≤ 3 16π M1 υ2 (m3 −m1) [Davidson and Ibarra(2002)] ⇒ . . M1 > 109 GeV Wash-out from ∆L = 2 processes → . .¯ m := √ m2

1 +m2 2 +m2 3 < 0.2 eV

⇒ ฀ . . mi < 0.11 eV

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Some remarques

• A super-heavy RHN is not accessible to collider experiments.
• If one take naturalness seriously, then a super-heavy RH neutrinos

distablises the EW scale (hierarchy problem): |δµ2| ≃ 1 4π2 ∑

α,i

|Yαi|2M2

i ;

1 4π2 mνM3 υ2 < υ2 ⇒ M < 107 GeV [De Gouvea, Hernandez and Tait (2014)]

• Super-heavy RHN could render the SM Higgs vacuum stability issue worse.
• M1 > 109 GeV ⇒ TRH > 109 GeV ⇒ Gravitino problem (if SUSY).
• No relation or correlation between ε1 and the low energy CP violation in

the ν-sector. ⇒ Need to reduce the number of parameters: Flavor Symmetries/Textures/Ansatz. [E.g: Frampton, Glashow, Yanagida; Branco, Felipe, Joaquim, Masina, Rebelo and Savoy; Mohapatra, S. N, Yu, ....]

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Radiative Neutrino Masses

. .

Mν at One loop

(a) Zee Model [(1980)] S(+) ∼ (1,1,+1), Φ2 ∼ (1,2,+1/2), Mν = A [ f m2

l +m2 l f T]

; A ∝ µ cotβ 16π2M2

2

sin2 2θ12 ≥ 1− 1 16 ( ∆m2

12

∆2m23 )2 [Koide; Frampton, Oh, Yoshikawa; He] ⇒ . . sin2 2θ12 > 0.999 Ruled out by solar neutrino oscillation data.

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.

Radiative Neutrino Masses

. .

Mν at One loop

(b) Scotogenic Model [Ma (2006)] SU(2)L ×U(1)Y×Z2 : Ni ∼ (1,0,−1), η ∼ (2,+1/2,−1) with < η0 >= 0, (Mν)αβ ≃ λ5 υ2 8π2 ∑

n

hαn Mn hβn m2

0 −M2 n

[ 1− M2

n

m2

0 −M2 n

ln m2 M2

n

] If λ5 << 1 . . For [ 1−

M2

n

m2

0−M2 n ln m2

M2

n

] ∼ 1 ⇒ λ5h2

i ∼ 10−10 ( Mi TeV

) The possible DM candidates:

• The lightest Ni if min (Mi) < mR,I,
• r
• ηR if mR < mI,min (Mi),
• r
• ηI if mI < mR,min (Mi).

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.

Radiative Neutrino Masses

. .

Mν at One loop

(c) Scotogenic Model [Ma (2013)] SU(2)L ×U(1)Y×U(1)D : η1 ∼ (2,+1/2,+1), η2 ∼ (2,+1/2,−1), Ni=1,2,3

L,R

∼ (1,0,+1). (Mν)αβ ∝ λ5∑

n

[ (h1)nαMn(h2)nβ +1 ↔ 2 ] 8π2 [ m2

1

m2

1 −M2 n

ln m2

1

M2

n

− m2

2

m2

2 −M2 n

ln m2

2

M2

n

] The possible DM candidates:

• The lightest Ni if U(1)D is unbroken,
• r
• The lightest neutral scalar mass eigenstate χ1 if

U(1)D is spontaneously broken and mχ1 < min (Mi).

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.

Radiative Neutrino Masses

. .

Mν at One loop

(c) Scotogenic Model II [Ma (2013)]

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4

∆T ∆S

100 200 300 400 500 600 700 800 900

mH±

1

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4

∆T ∆S

100 200 300 400 500 600 700 800 900

mχ1 mH±

1 ≥ 100 GeV ; mχ1 ≥ 90 GeV

[ Ahriche, Gaber, Ho, S.N, Tandean (2015)]

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.

Radiative Neutrino Masses

. .

Mν at One loop

(c) Scotogenic Model II [Ma (2013)]

100 200 300 400 500 600 700 800 900 100 200 300 400 500 600 700 800 900

mH1 (GeV) mχ1 (GeV)

200 300 400 500 600 700 800 900 200 300 400 500 600 700 800 900

mH2 (GeV) mχ2 (GeV)

The red (99%), green (95%), and blue (68%) CL ellipsoids in the (∆S,∆T) plane. [ Ahriche, Gaber, Ho, S.N, Tandean (2015)]

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.

Radiative Neutrino Masses

. .

Mν at two loops

Zee-Babu Model S+ ∼ (1,1,+1), k++ ∼ (1,1,+2) (Mν)αβ ≃ 3 2 J( m2

k

m2

h )

(4π2)2 µ m2

τ

M2 fατ h∗

ττ fβτ

J(x) = { 1+ 3

π2

[ (lnx)2 −1 ] x >> 1 1 x → 0 . .One of the neutrinos must be massless . .It excludes the possibility for a quasi-degenerate ν spectrum

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.

Radiative Neutrino Masses

. .

Mν at three loops

L ⊃ LSM + fαβ LT

αC iσ2Lβ S+ 1 +gαn NT n C lRα −1

2Mn Nc

i Nn +h.c−V(Φ,S1,S2)

Ni ∼ (1,1,0), S+

1,2 ∼ (1,1,+1);

Z2 : (Ni,S+

1 ,S+ 2 ) → (−Ni,S+ 1 ,−S+ 2 )

[L. Krauss, S. N, M. Trodden (2003)] [Other example: Aoki, Kanemura, Seto

(2004)]

. .Lightest of N′

is is a candidate for DM

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.

. .

Mν at three loops: Constraints

. .

• Fit the observed neutrino mass squared differences and mixings;
• Satisfy the bound on LFV processes; [→ Br(µ → e+γ) < 5×10−13];

. . ΩN1h2 ≃ 1.3×10−2 ∑α,β |g1αg∗

1β|2

( mN1 135 GeV )2 ( 1+m2

S2/m2 S1

)4 1+m4

S2/m4 S1

. . N1N1 → lαlβ (exchange of S±

2 )

. . .

mS1

. .

mS2

. . .Only 15% of the scanned points survive the µ → e+γ constraints

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.

. .

Mν at three loops: Type III

[Chen, McDonald, S. N (PLB 2014); Ahriche, McDonald, S. N (PRD 2014)] . . E0 = DM; M1 ∼ 2.7 TeV . . σ(E0 N → E0 N) ∼ 10−45 cm2; below the LUX bound.

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.

. .

KNT: Production of Ni at e+e− Colliders (ILC/CLIC)

. . If N2,3 decay inside the detector : e+e− → { N1N2,3 → . . E +lRlR N2N2,3 → . . E +lRlRlRlR . . If MN2,3 > 100 GeV : decay outside the detector : e+e− → NiNj + . . γ mN1 = 52.5GeV,mN2 = 122GeV,mN3 = 126GeV,mS2 = 144GeV; ge1 = −4×10−2,ge2 = 2×10−2,ge3 = −6.8×10−2. . . Background : e+e− → ν ¯ ν +γ (neutrino counting process) . . RH polarised e−and LH polarised e+ : . . Background ↘ whereas . . Signal ↗

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.

. .

KNT: Benchmark

+ Cuts

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.

. .

KNT: proton-proton Collider

← Benchmark

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.

. .

KNT: At LHC [ pp → l+

α l− β +Emiss

]

LHC-8 TeV LHC-14 TeV

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.

. .

KNT: At ILC/CLIC e±e− → e−µ+ +N us

Polarized Unpolarized [ Ahriche, S. N, Soualeh (PRD 2014)]

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.

Conclusion

• Neutrino masses and mixings can be a window to NP beyond the SM.
• If Mν is generated via the see-saw mechanism, then the origin of Ωb ∼ 5%

might be explained ( leptogenesis).

• If Mν is generated at loop-level, then
• The origin of ΩDM ∼ 27% might be explained if NP contain neutral particle(s).
• New degrees of freedom (particles) might be be accessible at low energy (e.g

Collider, EWPhT ...).

• Radiative Models with three loops are testable at high energy colliders (pp;

e+e−) and can be falsifiable (LFV) .

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.

Back-Up

. .

Mν at three loops: S1,2- Strongly First order EWPhT

V T=0(h,S1,S2) ⊃ λ1 2 |S1|2 h2 + λ2 2 |S2|2 h2 . .Requires λ1,2 to be order 1.

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.

. .

Mν at three loops: Variants

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.

. .

Mν at three loops: Cuts

LHC-8 TeV LHC-14 TeV

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