Hi Higgs Mass ss in in D- D-term Triggered Dy Dynamical SU - - PowerPoint PPT Presentation

Hi Higgs Mass ss in in D- D-term Triggered Dy Dynamical SU SUSY Br SY Breakin ing

No Nobuhito Maru

(Osa saka Ci City Universi sity) wi with H.

• H. It

Itoyama a

(Osa saka Ci City Universi sity)

3/5/2015 SCG CGT15@Nagoya Universi sity

Re Referenc nces

“D-Term Triggered Dynamical Supersymmetry Breaking”

• H. Itoyama and NM, PRD88 (2013) 025012

“D-Term Dynamical Supersymmetry Breaking Generating Split N=2 Gaugino Masses

• f Majorana-Dirac Type”
• H. Itoyama and NM, IJMPA27 (2012) 1250159

“126 GeV Higgs Boson Associated with D-Term Triggered Dynamical Supersymmetry Breaking”

• H. Itoyama and NM, Symmetry 2015 7 193

Pl Plan

In

Introduction n ! A New Mechanism sm of D-term Dy Dynamical SU SUSY Br SY Brea eakin king ! Higgs s Mass ss vi via D- D-term ef effects

Su

Summa mary

γγ

(GeV)

γ γ

m

110 120 130 140 150

S/(S+B) Weighted Events / 1.5 GeV

500 1000 1500

Data S+B Fit B Fit Component σ 1 ± σ 2 ±

• 1

= 8 TeV, L = 5.3 fb s

• 1

= 7 TeV, L = 5.1 fb s CMS (GeV)

γ γ

m

120 130

Events / 1.5 GeV

1000 1500

Unweighted

A Higgs boson was discovored, but…

In Introduction n

No No in indicatio ion

• f
• f SU

SUSY ( SY ($ BSM BSM)

Observed Higgs Mass 126 GeV Severe constraints on MSSM parameter space (MSSM + light sparticles)

MSSM + heavy sparticles Extension

• f

MSSM

Observed Higgs Mass 126 GeV Severe constraints on MSSM parameter space (MSSM + light sparticles)

MSSM + heavy sparticles

Dirac Gaugino scenario

Dira Dirac Ga Gaug ugin ino Sc Scenario io

Gauge sector: N=2 extension

• adj. chiral superfields added

Matter sector: N=1

Φa=SU 3

( ),SU 2 ( ),U 1 ( ) = ϕa,ψ a,F

a

( )

Dirac gaugino masses from if in hidden U(1)

Fox, Nelson & Weiner (2012)

L = d 2θ 2 W

α 0W a αΦa

Λ

∫

= D0 Λ λaψ a +…

D0 ≠ 0 ⊂ W

α 0 = θαD0

Once gaugino masses are generated at tree level, sfermion masses are generated by RGE effects

Sfermion masses @1-loop

Fl Flavor b r blind nd No SUSY flavor & CP problems

(a = SU(3)C, SU(2)L, U(1)Y)

Dirac gauginos Sfermions

4π/g

LHC bounds relaxed (gluino/squark production suppressed)

Kribs & Martin (2012)

M 

f 2 ≈ Ca f

( )α a

π M λa

2 log mϕa 2

M λa

2

⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥

A Ne New Mechanism sm

• f
• f D-

D-term Dy Dynamical SU SUSY Br SY Breakin ing

Itoyama & NM (2012,2013)

SUSY U(N) gauge theory with adjoint chiral supermultiplets Gauge kinetic function Superpotential

L = d 4θK Φa,Φa,V

( )

∫

+ d 2θ Im 1 2 Fab Φa

( )W aαW

α b +

d 2θW Φa

( )+ h.c.

∫

⎡ ⎣ ⎤ ⎦

∫

Kahler potential

SUSY U(N) gauge theory with adjoint chiral supermultiplets Gauge kinetic function Superpotential

L = d 4θK Φa,Φa,V

( )

∫

+ d 2θ Im 1 2 Fab Φa

( )W aαW

α b +

d 2θW Φa

( )+ h.c.

∫

⎡ ⎣ ⎤ ⎦

∫

Kahler potential

d 2θFab Φ

( )W aαW

α b

∫

⊃ Fa0c Φ

( )ψ cλ aD0 + Fab0 Φ ( )F0λ aλ b

d 2θW Φ

( )

∫

⊃ − 1 2 ∂a∂bW Φ

( )ψ aψ b

Dirac gaugino mass

Fermion mass terms

Fermion mass ss terms

Mixed Majorana-Dirac type masses

− 1 2 λ a ψ a

( )

− 2 4 FabcDb − 2 4 FabcDb ∂a

c∂cW

⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ λ c ψ c ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + h.c.

d 2θFab Φ

( )W aαW

α b

∫

⊃ Fa0c Φ

( )ψ cλ aD0 + Fab0 Φ ( )F0λ aλ b

d 2θW Φ

( )

∫

⊃ − 1 2 ∂a∂bW Φ

( )ψ aψ b

Dirac mass

<F>=0 assumed

m± = 1 2 gaa ∂a∂aW 1± 1+ 2 D ∂a∂aW ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥

D ≠ 0 & ∂a∂aW ≠ 0

if Ga Gaug ugin ino(m) becomes s massi ssive by by nonzero <D> SUSY is broken

D ≡ − 2 4 F0aaD0

D-term equation of motion:

Dirac bilinears s condensa sation

The value of <D0> will be determined by th the gap equation

D0 = − 1 2 2 g00 F0cdψ dλ c + F0cdψ dλ c

( )

Potential analysi sis

Work in the region where <F0> << <D0> and perturbative

∂V D,ϕ,ϕ,F = F = 0

( )

∂D = 0 ∂V D,ϕ,ϕ,F = F = 0

( )

∂ϕ = 0

D*,ϕ*,ϕ*

( )

Stationary values

gap equation

F

*,F *

( )

3 constant background fields:

ϕ ≡ ϕ 0, D ≡ D0, F ≡ F0

∂V D = D* F,F

( ),ϕ = ϕ* F,F ( ),ϕ = ϕ* F,F ( ),F,F

( )

∂F

D,ϕ,ϕ ,F fixed

= 0

D- D-term effective potential@1-loop

λ

±

( ) = 1

2 1± 1+ Δ0

2

( ), Δ0 ≈

′′′ F ′′ W D0 C2: constants

1-loop part = CW potential

gauge + adjoint chiral superfield contributions

V = N 2 mϕ

4 c1 ϕ,ϕ

( )Δ0

2

⎡ ⎣ + 1 32π 2 c2Δ0

4 − λ +

( ) 4 log λ

+

( ) 2 − λ

−

( ) 4 log λ

−

( ) 2

( )

⎤ ⎦ ⎥

Tree

Gap Gap e equa quatio ion

Itoyama & NM (2012)

0 = ∂V ∂D ϕ,ϕ = Δ0 c1 + 1 64π 2 4c2Δ0

2 −

1 1+ Δ0

2 λ +

( )3 2logλ

+

( )2 +1

( )− λ

−

( )3 2logλ

−

( )2 +1

( )

{ }

⎧ ⎨ ⎪ ⎩ ⎪ ⎫ ⎬ ⎪ ⎭ ⎪ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥

Trivial solution Δ0=0 is NOT lifted

5 10 15 20 25 30 1.0 0.5 0.5 1.0

Δ0

Nontrivial solution!!

1 ∆ 0 ∂V ∂D

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Δ0*,ϕ* = ϕ*

( )

determined as the intersection point

• f two real curves in the plane

Δ0*,ϕ = ϕ

( )

ϕ Λ

Δ0

Solution of the gap eq. ∂V/∂D=0

∂V/∂φ=0

E 0 in SUSY Trivial solution Δ0=0 is NOT lifted Our SUSY breaking vac. is a local min.

Δ0=0

1 2 3 4 5 5 10 15

V(φ)

φ

! 0 ≠ 0

Metastability of our false se vacuum

<D> = 0 vacuum is not lifted check if our vacuum <D> 0 is sufficiently long-lived

≠

Decay rate of

• ur vacuum

1 2 3 4 5 5 10 15

V(φ) φ

Coleman & De Luccia(1980)

Δφ Δ0Λ (Λ: cutoff scale) ΔV (mφ ΛΔ0)2

• ur vac.

Long-lived for mφ << ΔΛ

∝ exp − Δφ

4

ΔV ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ≈ exp − Δ0Λ

( )

2

mϕ

2

⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ≪1 Δ0Λ >> mφ

Numerical samples of solutions for the gap equation & the stationary condition for φ

Hi Higgs Mass ss vi via D- D-term Ef Effects ts

Itoyama & NM (2013)

LHiggs = d 4θ Hu

†e−gYV

1−g2V2−2qugV0Hu + Hd

†egYV

1−g2V2−2qdgV0Hd

⎡ ⎣ ⎤ ⎦

∫

+ d 2θµHuHd

∫

( )− BµHuHd + h.c.

⎡ ⎣ ⎤ ⎦

Higgs Lagrangian Hu,d with U(1) charges qu,d assumed µ-termqu + qd = 0 <V0> = θ <D0> additional Higgs mass@tree

VH = g2

2

2 1+ ImF0YY ϕ 0

( )

Hu

† σ a

2 Hu + Hd

† σ a

2 Hd ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

a

∑

2

+ gY

2

8 1+ ImF0YY ϕ 0

( )

Hu

2 − Hd 2

( )

2

+ 1 2 1+ ImF0YY ϕ 0

( )

qug Hu

2 + qdg Hd 2 − D0

( )

2

+ µ

2 Hu 2 + Hd 2

( )+ BµHuHd + h.c.

( )

! g2

2 + gY 2

8 Hu

0 2 − Hd 0 2

( )

2

+ 1 2 qug Hu

0 2 + qdg Hd 0 2 − D0

( )

2

+ µ

2 Hu 0 2 + Hd 0 2

( )− BµHu

0Hd 0 + h.c.

( )

ImF0YY ϕ 0 ≈ ϕ 0 Λ ≪1

Higgs potential

µ2 + M Z

2

2 = qug cos2β −qugv2 cos2β − 2 D0

( )

M A

2 ≡ 2Bµ

sin2β = 2µ2 = −M Z

2 −

qug cos2β −qugv2 cos2β − 2 D0

( )

mHiggs

2

= 1 2 ! M Z

2 + M A 2 −

! M Z

2 + M A 2

( )

2 − 4 !

M Z

2M A 2 cos2 2β

⎡ ⎣ ⎢ ⎤ ⎦ ⎥

! M Z

2 ≡ M Z 2 + qu 2g2v2 :qu = 0 ⇒ mHiggs 2

= mMSSM Higgs

2

mHiggs

2

= 1 2 − 2qug cos2β D0 − − 2qug cos2β D0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

2

+ 8qug D0 ! M Z

2 cos2β + 4 !

M Z

4 cos2 2β

⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥

Higgs mass

Minimization conditions

A plot for 126 GeV Higgs

Su Summa mary

! Dirac gaugino scenario is s

• ne of the interesting alternatives

s ! A new dynamical mechanism

sm of D- D-term DSB propose sed ! 126 GeV Higgs s mass ss possi ssible vi via D D-t

• term tr

m tree l ee level el e effects ts

Work in progress

(w/ Itoyama & Shindou)

Possi ssibility of 126 GeV Higgs s mass ss vi via t top-s

• stop l

loop e effects ts