D-term Dynamical SUSY Breaking

Transcript

1 D-term Dynamical SUSY Breaking Nobuhito Maru (Keio University) with H. Itoyama (Osaka City University) arxiv: [hep-ph] ITP workshop on Field Theory & String Theory

2 Introduction

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

4 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 level is well known, but no known explicit model of D-term DSB as far as we know

5 Tree 1-loop

6 Plan! Introduction! Basic Idea! V Gap equation & nontrivial solution F 0 0 D0 0! induced by! Comments on model building! Summary

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 θ Im 1 τ ab Φa W a a α = iλ α ( y) + δ β α D a y Φ a = φ a ( y) + θψ a y ( )W aα W b α + d θw Φ a ( ) α β Fµν a ( ) i σ µ σ ν ( y) θ β ( ) +θθf a ( y) y µ = x µ + iθσ µ θ ( ) + h.c. L U N N= N=1 partial breaking models naturally applicable ( ) F Φ ( ) = Im d 4 θtrφe V Φ + d θ 1 ( ) = Tr eφ + m F ( Φ) W Φ Φ Antoniadis, Partrouche & Taylor (1996) Fujiwara, Itoyama & Sakaguchi (005) F ( Φ) Φ a Φ W aα b W b α + ( d θw ( Φ) + h.c. ) Electric & Magnetic FI terms

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

10 ( ψ a ) 1 λ a Fermion mass terms Mixed Majorana-Dirac type masses (<F>=0 assumed) 0 4 τ abc Db 4 τ abc Db ac c W λ c ψ c + h.c. Mass matrix M F 0 4 τ 0aaD 0 4 τ 0aa D0 ac a W <D 0 >: U(1) part of D-term

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

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

13 V

14 1-loop effective potential for D-term V 1 loop = a = d 4 k ( ) 4 ln 1 3π π a m a ( m a λ ( + ) k iε )( m a λ ( ) k iε ) ( m a k iε )( k iε ) 4 A d ( ) Δ Δ4 SUSY counterterm added A( d) = 3 4 γ + 1 d λ ( + )4 logλ ( + ) λ ( )4 logλ ( ) m a g aa a a W,λ ( ± ) 1 d=4 1± 1+ Δ,Δ τ D 0aa m a V c.t. = Im Λ d θw α 0 W α 0 = Im Λ ( ) D0

15 1-loop effective potential for D-term ( D) V 1 loop a Tree level D-term pot. + 1-loop CW pot. + counter term 1 m a 4 4 = m a c + 1 a 64π 1 3π λ + ( D) V 1 loop = c ( Δ) Δ=0 Δ 4 Δ + Λ res 8 ( )4 ( logλ + ) ( + λ )4 ( logλ ) Λ res c + β + Λ res π = 1 3π A( d), β g 00 a a W a m a 4 τ 0aa, Λ res Im Λ ( ) a a W a m a 4 τ 0aa

16 Gap equation & Nontrivial solution

17 0 = V ( D) 1 loop Δ = Δ c π + Gap equation Trivial solution Δ=0 is NOT lifted unlike NJL Λ res 4 Δ 1 λ ( + )3 logλ ( + ) 64π 1+ Δ +1 λ ( ± ) 1 ( 1± 1+ ) Δ { ( ) λ ( )3 ( logλ ( ) +1 )} Approximate form Δ 1: Δ ' Λ res 4c Δ 1:c π + Λ ' res ( ) 5 64π Δ ( c < 0) 1 3π Δ log Δ ( ' Λ res > 0)

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

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

20 Metastability of our false vacuum <D> = 0 tree vacuum is not lifted check if our vacuum <D> 0 is sufficiently long-lived 15 V(φ) 10 Long-lived for m a << ΔV (m a Λ) Decay rate of the false vacuum 5 our vac Δφ Λ φ 4 Δφ exp ΔV exp Λ Coleman & De Luccia(1980) m a 1 m: mass of Φ, Λ: cutoff scale

21 F 0 0 induced by D 0 0 $ Fermion mass

22 D 0 0 induces nonvanishing F 0 Effective potenital up to 1-loop V = g ab a W b W 1 g abd a D b + V 1 loop + V c.t. Stationary condition δv = 0 F 0 + m 0 g 00 0 g 00 F D0 + g 00 V 1 loop = 0 with δ V = 0 we further obtain m 0 g 00 0 g 00 F 0 = m 0 g 00 0 g 00 F 0 These determine the value of nonvanishing F-term

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

24 Comments on Model Building

25 Following the model of Fox, Nelson & Weiner (00), consider a N= gauge sector & N=1 matter sector in MSSM Chirality, Asymptotic freedom Take the gauge group G G SM (G =U(1):hidden sector) D=5 gauge kinetic term provides Dirac gaugino mass term d θτ ( c abc Φ)Φ W SM αa W b τ αsm abc Φ ( ) D a c b ψ SM λ SM Scalar gluon: distinct from the other proposals Gaugino masses are generated at tree level

26 Once gaugino masses are generated at tree level, sfermion masses are generated by RGE effects Sfermion M sf C ( i R)α i π M λi log m a M λi (i = SU(3)C, SU()L, U(1)Y) Fox, Nelson & Weiner, JHEP08 (00) 035 Flavor blind No SUSY flavor & CP problems

27 Summary! New mechanism of DDSB proposed! Shown a nontrivial solution of the gap eq. with nonzero <D> in a self-consistent H-F approx. Our vacuum is metastable & can be made long-lived Phenomenological Application briefly discussed