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 2009.10.22 国立清华大学

NMSSM SUSY nMSSM MSSM SUSY arXiv: 0810.0751 , in JHEP , Cao, Yang arXiv: 0810.0989 , in PRD , Cao, Yang   SUSY arXiv: 0901.1437, in PRD(R), Cao, Logan, Yang  arXiv: 0901.3818, in PLB, Wang, Xiong, Yang MSSM nMSSM arXiv: 0908.0486, in JHEP,  Wang, Xiong, Yang, Yu arXiv: 0801.1169, in PRD, Heng, Oakes, Wang, Xiong, Yang  SUSY

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

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

SUSY |B |F

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

MSSM NMSSM, nMSSM CMSSM -problem little hierarchy

-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

little hierarchy in MSSM: Experimental lower bound need sizable loop effects ! mh  114 GeV (95 GeV) Theoretical upper bound mh  90 GeV (tree-level) ~ 500 GeV  135 GeV (loop-level) 100 GeV

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 )

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)

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

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

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

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

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 )

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

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

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

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

(6)  g-2   

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 ?

2.2 Allowed Parameter Space NMSSM Higgs Dark Matter arXiv: 0810.0989 , in PRD , Cao, Yang  

nMSSM Dark Matter Higgs Decays arXiv: 0901.1437, in PRD(R), Cao, Logan, Yang 

2.3 Zbb anomaly arXiv: 0810.0751 , in JHEP , Cao, Yang  

2.4 FCNC B -Decays SUSY SUSY arXiv: 0801.1169, in PRD, Heng, Oakes, Wang, Xiong, Yang 

expt data no expt data

 NMSSM Sky-blue points excluded by

 NMSSM Sky-blue points excluded by

2.5 Residual Effects of Heavy SUSY Heavy sparticles can leave over sizable quantum effects in the light Higgs sector arXiv: 0901.3818, in PLB, Wang, Xiong, Yang

NMSSM

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 !

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

h ~ GeV , a < 0.5 GeV arXiv: 0908.0486, in JHEP,  Wang, Xiong, Yang, Yu

Sommerfeld enhancement

PAMELA arXiv: 0906.0362 Hooper, Tait

Implication on SM-like Higgs decay:

other visible modes (like ) are supressed

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

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