Collaboration with Kang Young Lee, C.S.KIM The work is in progress now.

1. Light pseudoscalarη and ain Simplest Little Higgs model (SLHm)and Next-to-Minimal SuperSymmetric Model(NMSSM) 2010. 8. 11 Jubin Park LHC Physics Workshop at Korea, 10-12, August 2010 Konkuk University, Seoul

2. Collaboration with Kang Young Lee, C.S.KIM • The work is in progress now. • This talk is mainly based onK. Cheung, J. Song - PRD76,035007K. Cheung, J. Song, P. Tseng and Q. Yan - PRD78,2008 • R.Dermisek, J. F. Gunion and B. McElart - RD76,2007F. Domingo, U. Ellwanger, E. Fullana, C. Hugonie and M. Sanchis-Lozano - JHEP 01(2009)061 2010 LHC Physics Workshop at Korea, Jubin Park

3. From Florian Domingo’s talk, Recontre de Moriond 2010 2010 LHC Physics Workshop at Korea, Jubin Park

4. Goal : How to distinguish these two pseudoscalars at the LHC in these scenarios. 2010 LHC Physics Workshop at Korea, Jubin Park

5. Light pseudoscalarηin Simplest Little Higgs model (SLHm) 2010 LHC Physics Workshop at Korea, Jubin Park

6. Gauge groups and scalar particles inSLHm E UV completion ??? Sigma model cut-off Scale 10 TeV Non-linear sigma fields Global Sym. Gauge Sym. 1 TeV 10 = 5 + (4 + 1) Massive Heavy gauge bosons W’and Z’, Y,Y’ 200 GeV EW symmetry breaking scale SU(2)ⅹU(1) SM massive W and Z bosons Pseudo scalar η SM Higgs U(1) 2010 LHC Physics Workshop at Korea, Jubin Park EW

7. Non-linear sigma fields and global symmetry breaking. Two non-linear sigma fields Two VEVs Ratio between two VEVs !!! Pseudo scalar SM Higgs 2010 LHC Physics Workshop at Korea, Jubin Park

8. Kinetic terms and gauge symmetry. Heavy gauge bosons SU(3)w U(1)x g is equal to SM SU(2)w coupling. Note: tangnt from weakmixing angle 2010 LHC Physics Workshop at Korea, Jubin Park

9. Kinetic Lagrangian Compact form of two Phis Note: No mass term of eta particle 2010 LHC Physics Workshop at Korea, Jubin Park

10. This eta can make some problems for eta production : rare K and B decays. B-B bar mixing. Upsilon to eta gamma decay. Cosmological axion limit. 2010 LHC Physics Workshop at Korea, Jubin Park

11. Mu term Note: This mu term breaks explictly global symmetry !!! But this term is numerically small. therefore it is negligible !!! 2010 LHC Physics Workshop at Korea, Jubin Park

12. Yukawa terms and mixing : : Mixing angle Mixing 2010 LHC Physics Workshop at Korea, Jubin Park

13. Masses for fermions including heavy quarks (T,D,S) Q=(T,D,S) q=(t,d,s) 2010 LHC Physics Workshop at Korea, Jubin Park

14. Yukawa terms of eta particle and Yukawa couplings. Note: There are no differences (absolute value) of couplings between top, bottom type quakrs and leptons except heavy quarks(T,D,S). 2010 LHC Physics Workshop at Korea, Jubin Park

15. Supersymmetry models 2010 LHC Physics Workshop at Korea, Jubin Park

16. About supersymmetric models(MSSM vs NMSSM) • In MSSM there must be two Higgs doublets (Hu,Hd) because I. the Yukawa terms which consist of only one Higgs doublet and matter field break explictly SUSY. II. By SUSY, if we introduce only one Higgs field then its superpartner causes the anomaly of given gauge group. • In MSSM, 2010 LHC Physics Workshop at Korea, Jubin Park

17. However, • 3. From many studies and precise experiments, It is well known that the valid space of parameters are very narrow so that we need to modify or extend the MSSM. • 4. Roughly speaking, Next-to-Minimal Supersymmetric Standard Model (NMSSM) appears because of mu term • and axion problem. Helps avoiding the axion problem like Peccei-Quinn U(1), that is, there is known no PQ-type axion in Nature from experiments 2010 LHC Physics Workshop at Korea, Jubin Park

18. 5. What are new ingredients of NMSSM? 2010 LHC Physics Workshop at Korea, Jubin Park

19. Brief summary of known facts of NMSSM MSSN NMSSN 2010 LHC Physics Workshop at Korea, Jubin Park

20. Yukawa terms of a particle and Yukawa couplings in NMSSM. Note: There is the difference between top, bottom type quakrs . Mixing 2010 LHC Physics Workshop at Korea, Jubin Park

21. Decay widths of eta in SLHm η 2010 LHC Physics Workshop at Korea, Jubin Park

22. Decay widths of a particle in NMSSM. For up type quarks For down type quarks In fact, we need to check these values due to the complicated correlations among free parameters of the NMSSM 2010 LHC Physics Workshop at Korea, Jubin Park

23. Comparison of the ratios between decay widths of eta in SLHmand a in NMSSM I. X to f anti-f 2010 LHC Physics Workshop at Korea, Jubin Park

24. II. X to gamma gamma For the explicit study of gamma gamma decay and above ratio we should also consider full parameter regions which satisfy well known constraints. Nmhdecayfortran code 2010 LHC Physics Workshop at Korea, Jubin Park

25. Numerical results 2010 LHC Physics Workshop at Korea, Jubin Park

26. 2010 LHC Physics Workshop at Korea, Jubin Park

27. 2010 LHC Physics Workshop at Korea, Jubin Park

28. Summary • We calculated various decay widths of pseudo scalar particles eta and a. • We find there are some differences between ratios of decay widths of eta and a. • In the decay to two gammas we can also expect that there is a difference due to different couplings for each eta and a in triangle loop diagrams. • Since NMSSM has complicated correlations among parameters , we had better use NMHDECAY program package to study the ratios. • Now the program coding and running are in progress. 2010 LHC Physics Workshop at Korea, Jubin Park