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) arxiv: [hep-ph] 4/3/2012 Progress in QFT $ String City University

2 Plan! Introduction! General Discussion! Gap equation! Some Comments on Phenomenological Application! 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 General Discussion

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 ( ) + h.c. N=2 N=1 partial breaking models naturally applicable Antoniadis, Partrouche & Taylor (1996); Fujiwara, Itoyama & Sakaguchi (2005) Fermion masses Important D=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 a b W ( Φ)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 abcd b 2 4 τ abcd b ac c W λ c ψ c + h.c. Mass matrix M F τ 0aaD τ 0aa D0 ac a W

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 bilinears 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 (Λ/2 W α W α ) ( V D) 1 loop = 4 m c + 1 a 64π 2 a Δ 2 Δ 4 + Λ res π 2 λ ( + )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, Λ res c + β + Λ res + 1 2m a 64π, 2 (, Λ res Im Λ) a a W 2 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 15 V(φ) 10 Long-lived for m<< ΔV Decay rate of the false vacuum 5 our vac Δφ 4 Δφ exp ΔV φ exp Λ Coleman & De Luccia(1980) 2 m 2 1 m: 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 Take the gauge group G G SM (G :hidden gauge group) D=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 2 C ( R)α i i sf 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! A new dynamical mechanism of DDSB proposed! 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 Thank you very much for your attention!!