非最小超对称唯象研究： 工作汇报 杨 金 民 中科院 理论物理所 2009.9.25 南开大学

MSSM 超对称 NMSSM nMSSM arXiv: 0810.0989 (Cao, Yang) arXiv: 0901.1437 (Cao, Logan, Yang)  arXiv: 0901.3818 (Wang, Xiong, Yang) arXiv: 0908.0486  (Wang, Xiong, Yang, Yu) arXiv: 0801.1169 (Heng, Oakes, Wang, Xiong, Yang) 

目录 1. 模型介绍: MSSM,NMSSM,nMSSM 2. 唯象研究 3、结论 2.1 目前的实验限制 2.2 可允许的参数空间 2.1 目前的实验限制 2.2 可允许的参数空间 2.3 Zbb 反常 2.4 B-介子的双轻衰变 2.5 超对称粒子的残留效应 2.6 解释暗物质Pamela 3、结论

1. 模型 超对称 GUT Dark Matter Inflation Fine-Tuning Electroweak 1. 模型 Fine-Tuning GUT Dark Matter 超对称 Electroweak Baryogenesis Inflation Affleck-Dine Baryogenesis

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) 特点 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 超势： 标势： U(1)R  Z3 (non-R) U(1)R ( A0, A0 )：PGB 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) 标势： U(1)R  Z3 (non-R) U(1)R ( A0, A0 )：PGB

Z3 ( X  ei2/3 X ) domain wall NMSSM domain wall： 自发破却 domain wall must disappear before BBN 要求 Z3-breaking term in Veff impose discrete R-symmetry on W 引入high-order non-renormalizable operator to W multi-loop large enough to break Z3 too small to upset gauge hierarchy

nMSSM 超势： U(1)R  Z2 matter parity  0 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.唯象研究 2.1 实验限制 (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)  反常磁矩 a   

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 可存活的参数空间 NMSSM 暗物质 黑格斯

nMSSM 暗物质 黑格斯衰变

2.3 Zbb anomaly

2.4 FCNC B -Decays SUSY SUSY

expt data no expt data

 NMSSM Sky-blue points excluded by

 NMSSM Sky-blue points excluded by

2.5 超对称粒子的残留效应 重的 sparticles 会在轻的 Higgs部分 有大的残留效应

NMSSM

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

General singlet extension of MSSM:

DM Annihilation  h, a  Large Sommerfeld Enhancement Induced by h  Relic Density  DM Annihilation  h, a  Large Sommerfeld Enhancement Induced by h   Pamela  Hooper, Tait 0906.0362

Implication on SM-like Higgs Pheno:

3. 结论 except: Zbb anomaly is well motivated: can account for all current expt data: Precision Electroweak Data; Rb  g-2 FCNC B-decays Dark Matter Relic Density Pamela ? . . . . . . . . . except: Zbb anomaly LHC Super B-factory 暗物质实验 检验模型