1. Phenomenology of Non-minimal SUSY Models
Jin Min Yang
杨 金 民
Institute of Theoretical Physics, Academia Sinica, Beijing
中国科学院 理论物理研究所
国立清华大学

2. NMSSM SUSY nMSSM MSSM SUSY arXiv: 0810.0751 , in JHEP , Cao, Yang
arXiv: , in PRD , Cao, Yang  
SUSY
arXiv: , in PRD(R), Cao, Logan, Yang 
arXiv: , in PLB, Wang, Xiong, Yang
MSSM
nMSSM
arXiv: , in JHEP,  Wang, Xiong, Yang, Yu
arXiv: , in PRD, Heng, Oakes, Wang, Xiong, Yang 
SUSY

3. Outline 1. Models: MSSM,NMSSM,nMSSM 2. Phenomenology Studies
2.1 Current expt constraints
2.2 Allowed parameter space
2.3 Zbb anomaly
2.4 B-meson FCNC decays
2.5 Residual effects of heavy SUSY
2.6 Explain PAMELA
3、Conclusion

4. 1. SUSY Models SUSY GUT Fine-Tuning Dark Matter Electroweak Inflation
Baryogenesis
Inflation
Affleck-Dine
Baryogenesis

6. SUSY
|B
|F

7. R-conserving SUSY Models
MSSM, CMSSM (mSUGRA, GMSB, AMSB)
NMSSM，nMSSM
Split-SUSY
· · ·
R-violating SUSY Models

8. MSSM
NMSSM, nMSSM
CMSSM
-problem
little hierarchy

9. -problem in MSSM: =0 dimensionful parameter conserving SUSY
should be at Planck scale or 0
chargino is too light
=0
only one Higgs-doublet gets vev

10. little hierarchy in MSSM:
Experimental lower bound
need sizable loop effects !
mh  114 GeV (95 GeV)
Theoretical upper bound
mh  GeV (tree-level)
~ 500 GeV
 GeV (loop-level)
100 GeV

11. MSSM + singlet NMSSM, nMSSM: Dynamical solution to -problem
Solve little hierarchy problem
Field Content:
MSSM +
singlet
no dimensionful parameter (NMSSM)
SUSY-conserving part:
naturally small dimensionful parameter (nMSSM)
SUSY breaking ( < TeV )
dimensionful soft
parameters (TeV)
SUSY-breaking part:
trigger EWSB ( < TeV )
generate -term ( < TeV )

12. motivated from top-down view ?
E6 models (superstring-inspired)
string scale
SO(10)  U(1)  …
at low energy: S, Hu, Hd + heavy particles
U(1) global PQ
cubic term
(NMSSM)
to break U(1) PQ
tadpole
(nMSSM)

13. NMSSM Superpotential：
U(1)B: Q(1/3), U(-1/3), D(-1/3), L(0), E(0), Hu(0), Hd(0), S(0)
U(1)L: Q(0), U(0), D(0), L(1), E(-1), Hu(0), Hd(0), S(0)
U(1)R: Q(1), U(1), D(1), L(1), E(1), Hu(1), Hd(1), S(1), W(3)
0
U(1)PQ: Q(-1), U(0), D(0), L(-1), E(0), Hu(1), Hd(1), S(-2)
Scalor Potential：
U(1)R  Z3 (non-R)
U(1)R ( A0, A0 )：PGB

14. Z3 ( X  ei2/3 X ) domain wall NMSSM domain wall：
SSB
domain wall
must disappear before BBN
So we need Z3-breaking term in Veff
impose discrete R-symmetry on W
introduce high-order non-renormalizable operator to W
multi-loop
large enough to break Z3
too small to upset gauge hierarchy

15. nMSSM Superpotential：
U(1)B: Q(1/3), U(-1/3), D(-1/3), L(0), E(0), Hu(0), Hd(0), S(0)
U(1)L: Q(0), U(0), D(0), L(1), E(-1), Hu(0), Hd(0), S(0)
U(1)R: Q(1), U(1), D(1), L(1), E(1), Hu(0), Hd(0), S(2), W(2)
 0
U(1)PQ: Q(-1), U(0), D(0), L(-1), E(0), Hu(1), Hd(1), S(-2)
U(1)R  Z2 matter parity

16. + MSSM Spectrum of NMSSM/nMSSM: One more CP-odd Higgs (A1 or a )
One more CP-even Higgs
One more neutralino

17. How to solve -problem ？ V Before SUSY breaking
SUSY vacuum: Vmin = 0
〈  〉 = 0 
EW not broken; no  term
With SUSY breaking (TeV)
dimensionful soft parameters (TeV) V
non-SUSY vacuum: Vmin < 0
〈  〉  0
SUSY breaking ( < TeV ) 
trigger EWSB ( < TeV )
generate -term ( < TeV )

18. How to solve little hierarchy ？
mh theoretical upper bound
MSSM:
NMSSM:
mh experimental lower bound
suppressed !
has singlet component
suppressed !

19. 2.Phenomenology Studies
2.1 Expt Constraints
(1) direct bounds:
LEP I
LEP II
Tevatron
LEP II

20. true (physical) vaccum
(2) Stability of Higgs Potential
true (physical) vaccum
local vaccum 
(3) Cosmic Dark Matter (WMAP)

21. (4) Precision Electroweak Data
1 , 2 , 3 (S, T, U) Rb
= (Zbb)/  (Zhadrons)
SUSY

22. (6)  g-2   

23. Under all above constraints
scan over parameter space
to find out the allowed part
display the allowed part
predict FCNC B-decay
can solve Zbb anomaly ?
residual SUSY effects
explain Pamela ?

24. 2.2 Allowed Parameter Space
NMSSM
Higgs
Dark Matter
arXiv: , in PRD , Cao, Yang  

25. nMSSM Dark Matter Higgs Decays
arXiv: , in PRD(R), Cao, Logan, Yang 

26. 2.3 Zbb anomaly
arXiv: , in JHEP , Cao, Yang  

27. 2.4 FCNC B -Decays
SUSY
SUSY
arXiv: , in PRD, Heng, Oakes, Wang, Xiong, Yang 

28. expt
data
no expt data

29. 
NMSSM
Sky-blue points excluded by

30. 
NMSSM
Sky-blue points excluded by

31. 2.5 Residual Effects of Heavy SUSY
Heavy sparticles can leave over sizable quantum effects
in the light Higgs sector
arXiv: , in PLB, Wang, Xiong, Yang

32. NMSSM

33. 2.6 To Explain PAMELA NMSSM No！ nMSSM OK !
--Pamela+Relic density via Sommerfeld Enhance
NMSSM
nMSSM
No！
LSP mass in a narrow range
No light particles to give SE
general singlet extension of MSSM:
OK !

34. General singlet extension of MSSM: 
Final states
h ~ GeV, a < 0.5 GeV
singlet-like
Sommerfeld enhancement

35. h ~ GeV , a < 0.5 GeV
arXiv: , in JHEP,  Wang, Xiong, Yang, Yu

37. Sommerfeld enhancement

38. PAMELA
arXiv: Hooper, Tait

39. Implication on SM-like Higgs decay:

40. other visible modes (like )
are supressed

41. 3. Conclusion NMSSM, nMSSM, General Singlet Extension
Precision Electroweak Data Rb
Zbb anomaly
B-meson FCNC decays
Residual effects of heavy SUSY
Higgs Decays
 g-2
Dark Matter Relic Density
PAMELA

42. 温家宝： 屈原： 天 问 一个民族有一些关注天空的人, 他们才有希望; 一个民族只是关心脚下的事情, 那是没有未来的。
一个民族有一些关注天空的人, 他们才有希望;
一个民族只是关心脚下的事情, 那是没有未来的。
屈原： 天 问
遂古之初 谁传道之 上下未形 何由考之
冥昭瞢暗 谁能极之 冯翼惟象 何以识之
明明暗暗 惟时何为 阴阳三合 何本何化。