Light pseudoscalarη and a

in 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

2010 LHC Physics Workshop at Korea, Jubin Park

Collaboration with Kang Young Lee, C.S.KIM

The work is in progress now.

This talk is mainly based on K. 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

From Florian Domingo’s talk, Recontre de Moriond 2010

2010 LHC Physics Workshop at Korea, Jubin Park

Goal : How to distinguish these two pseudoscalars at the LHC in these scenarios.

2010 LHC Physics Workshop at Korea, Jubin Park

Light pseudoscalar η in Simplest Little Higgs model

(SLHm)

2010 LHC Physics Workshop at Korea, Jubin Park

Gauge groups and scalar particles in SLHm

E

200 GeV

10 TeV

UV completion ???

Sigma model cut-off Scale

EW symmetry breaking scale

SM massive W and Z bosons

EWU(1)

SU(2)ⅹU(1)

Massive Heavy gauge bosons W’ and Z’, Y,Y’

SM Higgs

Pseudo scalar η

Global Sym.Gauge Sym.Non-linear sigma fields

1 TeV10 = 5 + (4 + 1)

2010 LHC Physics Workshop at Korea, Jubin Park

Two non-linear sigma fields

Two VEVs

SM Higgs

Ratio between two VEVs !!!

Pseudo scalar

Non-linear sigma fields and global sym-metry breaking.

2010 LHC Physics Workshop at Korea, Jubin Park

Kinetic terms and gauge symmetry.

SU(3)w U(1)x

NOTE: g is equal to SM SU(2)w coupling.

tangnt from weakmixing angle

Heavy gauge bosons

2010 LHC Physics Workshop at Korea, Jubin Park

Kinetic Lagrangian

NOTE: NO MASS TERM OF ETA PARTICLE

Com

pact

form

of

two

Phis

2010 LHC Physics Workshop at Korea, Jubin Park

This eta can make some problems for eta production :

1. RARE K AND B DECAYS.2. B-B BAR MIXING.

3. UPSILON TO ETA GAMMA DECAY.4. COSMOLOGICAL AXION LIMIT.

2010 LHC Physics Workshop at Korea, Jubin Park

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

Yukawa terms and mixing

: :

MIXINGMIXING ANGLE

2010 LHC Physics Workshop at Korea, Jubin Park

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

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

Supersymmetry models

2010 LHC Physics Workshop at Korea, Jubin Park

About supersymmetric models(MSSM vs NMSSM)

1. In MSSM there must be two Higgs doublets (Hu,Hd) be-cause 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.

2. In MSSM,2 2 2 2 22 2

,sin 2 sin 2C W A C W

A AM M M M M

2 2 2 2 2 2 2 2 21,2

1 ( ) 4 cos 22S A Z A Z A ZM M M M M M M

1 2

1

2 2 2

S Z S

S A

W C

W A C

M M MM MM M

M M M

2010 LHC Physics Workshop at Korea, Jubin Park

However,3. From many studies and precise experiments, It is well

known that the valid space of parameters are very nar-row 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.3

1 21[ ] . . , [ ] . .3

TF FH H H c H H c

Helps avoiding the axion problem like Peccei-Quinn U(1),

that is, there is known no PQ-type axion in Nature from experiments

S

2010 LHC Physics Workshop at Korea, Jubin Park

5. What are new ingredients of NMSSM?

2010 LHC Physics Workshop at Korea, Jubin Park

Brief summary of known facts of NMSSM

MSSN NMSSN

2010 LHC Physics Workshop at Korea, Jubin Park

Yukawa terms of a particle and Yukawa couplings in NMSSM.

Mixing

NOTE: THERE IS THE DIFFERENCE BETWEEN TOP, BOTTOM TYPE QUAKRS .

2010 LHC Physics Workshop at Korea, Jubin Park

Decay widths of eta in SLHm

η

2010 LHC Physics Workshop at Korea, Jubin Park

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

Comparison of the ratios between decay widths of eta in SLHm

and a in NMSSMI. X to f anti-f

2010 LHC Physics Workshop at Korea, Jubin Park

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.NMHDECAY FORTRAN CODE

2010 LHC Physics Workshop at Korea, Jubin Park

NUMERICAL RESULTS

2010 LHC Physics Workshop at Korea, Jubin Park

2010 LHC Physics Workshop at Korea, Jubin Park

2010 LHC Physics Workshop at Korea, Jubin Park

Summary1. We calculated various decay widths of pseudo scalar

particles eta and a.

2. We find there are some differences between ratios of decay widths of eta and a.

3. 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.

4. Since NMSSM has complicated correlations among pa-rameters , we had better use NMHDECAY program package to study the ratios.

5. Now the program coding and running are in progress.