D-term Dynamical SUSY Breaking. Nobuhito Maru (Keio University)

Transcription

1 D-term Dynamical SUSY Breaking Nobuhito Maru (Keio University) with H. Itoyama (Osaka City University) Int. J. Mod. Phys. A27 (2012) [arxiv: [hep-ph]] 12/6/2012 University

2 Plan l Introduction l Basic Idea l Gap equation l Some Comments on Phenomenological Application l Summary

3 Introduction

4 SUPERSYMMETRY is one of the attractive scenarios solving the hierarchy problem, but it must be broken at low energy

5 Dynamical SUSY breaking(dsb) is most desirable to solve the hierarchy problem F-term DSB is induced by non-perturbative effects due to nonrenormalization theorem and well studied so far D-term SUSY breaking is NOT affected by the nonrenormalization theorem In principle, D-term DSB is possible, but no known explicit model as far as we know

6

7 Basic Idea

8 N=1 SUSY U(N) gauge theory with an adjoint chiral multiplet L = d 4 θk Φ a,φ a,v ( ) + d 2 θ Im 1 2 τ ( ) ab Φa W a a α = iλ α ( y) + δ β α D a y Φ a = φ a ( y) + 2θψ a y W aα W b α + d 2 θw Φ a ( ) α β Fµν a ( ) i 2 σ µ σ ν ( ) +θθf a ( y) ( y) θ β y µ = x µ + iθσ µ θ W(Φ a )/ Φ a = level assumed ( ) + h.c. Fermion masses Important dim 5 operator d 2 θτ ( ab Φ)W aα b W α τ ( abc Φ)ψ c λ a D b + τ ( abc Φ)F c λ a λ b d 2 θw ( Φ) Dirac mass term 1 2 W ( Φ a b )ψ a ψ b τ abc τ ab ( Φ) φ c

9 ( ψ a ) 1 2 λ a Fermion mass terms Mixed Majorana-Dirac type masses (<F>=0 assumed) τ abc Db 2 4 τ abc Db ac c W λ c ψ c + h.c. Mass matrix M F τ 0aaD τ 0aaD 0 ac a W Only U(1) part of D-term VEV is assumed

10 if D 0 & a a W 0 m = 1 ± 2 a W 1± 1+ a 2 D a a W 2 Gaugino becomes massive by nonzero <D> SUSY is broken D 2 4 τ 0aa D0

11 D-term equation of motion: D 0 = 1 ( ) 2 2 g00 τ 0cd ψ d λ c + τ 0cd ψ d λ c Dirac bilinear condensation The value of <D> will be determined by the gap equation

12 Gap equation

13 1-loop effective potential for D-term Tree level D-term pot. + 1-loop CW pot. + counter term (-Im Λ/2 d 2 Θ W α W α ) ( D) V 1 loop 4 = m a c + 1 a 64π π 2 λ + Δ 4 Δ 2 + Λ res 8 ( )4 ( logλ + )2 ( + λ )4 ( logλ )2 m a a a W, λ ( ± ) 1 2 a 1 m a 4 1± 1+ Δ2 2 V = 2c, β g 00 a a W 2 ( Δ) m Δ=0 a τ 0aa a, Δ τ 0aaD 0, Λ res c + β + Λ res + 1 2m a 64π, 2 (, Λ res Im Λ) W 2 a a a m a 4 τ 0aa 2

14 Gap equation 0 = V ( D) 1 loop Δ = Δ c π + 2 Λ res 4 Δ2 1 λ ( + )3 2logλ ( + )2 64π 2 1+ Δ +1 2 { ( ) λ ( )3 ( 2logλ ( )2 +1 )} 1! V 1-loop (D)! Nontrivial solution!! c +1 64π 2 = 1, Λ res 8 = Δ

15 E = D 2 /2 0 in SUSY Trivial solution Δ=0 is NOT lifted Our SUSY breaking vac. is a local min. V(φ) ! Δ=0 φ

16 Metastability of our false vacuum <D> = 0 tree vacuum is not lifted check if our vacuum <D> 0 is sufficiently long-lived V(φ) Long-lived for m a << Λ ΔV Decay rate of the false vacuum 5 our vac Δφ φ 4 Δφ exp ΔV exp Λ Coleman & De Luccia(1980) 2 m a 2 1 m a : mass of Φ, Λ: cutoff scale

17 Some Comments on Phenomenological Application

18 Following the model of Fox, Nelson & Weiner (2002), consider a N=2 gauge sector & N=1 matter sector in MSSM Chirality, Asymptotic freedom of QCD Take the gauge group U ( 1) G SM (U(1) :hidden gauge group) Dim 5 gauge kinetic term provides Dirac gaugino mass term d 2 θτ ( c abc Φ)Φ W SM αa W b τ αsm abc Φ ( ) D a c b ψ SM λ SM Gaugino masses are generated at tree level

19 Once gaugino masses are generated at tree level, sfermion masses are generated by RGE effects Sfermion M sf 2 C ( i R)α i π M λi 2 log m 2 a 2 M λi (i = SU(3)C, SU(2)L, U(1)Y) Fox, Nelson & Weiner, JHEP08 (2002) 035 Flavor blind No SUSY flavor & CP problems

20 Summary l A new dynamical mechanism of DDSB proposed l Shown a nontrivial solution of the gap eq. with nonzero <D> in a self-consistent Hartree-Fock approx. Our vacuum is metastable & can be made long-lived Phenomenological Application briefly discussed

21 Backup

22 D 0 0 F 0 0 Effective potenital up to 1-loop δv = 0 V = g ab a W b W 1 2 g ab Da D b + V 1 loop + V c.t. Stationary condition F m 0 g 00 0 g 00 F D g 00 V 1 loop = 0 This determines the value of nonvanishing <F>

23 Fermion masses Fermion masses are modified as follows SU(N) part: ( holo L ) mass = 1 2 g 0a,a F 0 ψ a ψ a + i 4 F 0aa F 0 λ a λ a 1 2 a a W ψ a ψ a F 0aa D 0 ψ a λ a U(1) part: NG fermion: admixture of λ 0 and ψ 0

24 Once SUSY is broken, the next issue we should consider is how to mediate its breaking to our world SUSY breaking mediation mechanism reflects the pattern of sparticle spectrum, which must satisfy severe constraints from experiments ex. K 0 K 0 mixing ( d δ ) 12 m 2 Q,12 LL 0.01 m 2 m 100 GeV Gauge mediation is one of the attractive scenarios SM gauge interaction loops SUSY SSM

25 Super-Higgs mechanism If we couple our theory to supergravity, a super-higgs mechanism works Gravitino mass e 1 L gravitino mass = e K 2 W ψ µ σ µν ψ ν +ψ µ σ µ g 2 D i aλ a + e K 2 2 D W a ψ a + h.c. can be diagonalized by the following redefinition of the gravitino ψ µ =ψ µ + i 2 e K 2 W σ µ g 2 D aλ a + e K 2 i 2 D W a ψ a e 1 L gravitino mass = e K 2 W ψ µ σ µν ψ ν + i 2 e K 2 g W 2 D aλ a + e K 2 i 2 D aw ψ a 2 + h.c.

26 Gravitino mass m 3 2 = e K 2 W M P 2 D a W e K 2 0 V 2 + g 2 2 Da 2 3M P 2

27 N = 2 N = 1 Model Fujiwara, Itoyama & Sakaguchi (2005, 2006) Take the following N=2 SYM L U N F ( Φ) ( ) = Im d 4 θtrφe V + d 2 θ 1 Φ 2 + d 2 θtr 2eΦ + m F Φ Φ ( ) + h.c. Electric & Magnetic FI terms F Φ 2 F ( Φ) Φ a Φ W αa b W b α ( ) :" prepotential" holomorphic function of Φ N=2 theory can be obtained from N=1 theory by imposing SU(2)R invariance ( λ a ψ a ) ( ψ a λ a )

28 SUSY transformation δ λ a ψ a 0 eδ 0 = 2 N g ab b + mf 0b eδ 0 b + mf 0b 0 0 = 2 N g ab ( e e )δ 0 b η 1 η 1 η 2 Vacuum condition chosen as eδ b 0 + mf 0b = 0 (F=0) from 0 = V φ a = g bd F ade g ec eδ b 0 + mf 0b eδ 0 c + mf 0c =0 N=2 SUSY is partially broken to N=1 NG fermion: ψ

29 In the present model, the gaugino masses are ( Λ ± ) ( = m λ ± ) (, λ ± ) 1 a a 2 ( ) 1± 1+ Δ2 ( ) 2 m 2N m g aa F, Δ 2 D0 a 0aa Adjoint scalar mass Mass 4Nm 2 N=2 N=1 m a Φ(φ, ψ) 0 V(A µ, λ), Φ(φ, ψ) V(A µ, λ)