Phenomenlogical Aspects of Mirage Mediation

Yeong Gyun Kim(Sejong University)

Neutralino Dark Matter in Mirage Mediation (thermal relic density, direct detection)

LHC signature of Mirage Mediation

Neutralino Dark Matterin Mirage Mediation

In collaboration with

K.Choi, K.Y.Lee, Y.Shimizu (KAIST)K.Okumura (Kyushu University)

JCAP 0612 (2006) 017

In KKLT-type moduli stabilization scenario

Modulus mediated contribution to SSB parameters at MGUT

Mirage Mediation

can be comparable to the anomaly mediated one O (m3/2 /42) when the gravitino mass m3/2 ~ 10 TeV.

Depending upon the anomaly to modulus mediation ratio

the model can lead to a highly distinctive pattern of superpaticle masses at low energy scale.

The soft parameters at MGUT are determined to be

where aijk = ai + aj + ak, and ci parameterize the patternof the pure modulus mediated soft masses.

ba and i : beta function and anomalous dim.

An interesting consequence of this mixed modulus-anomaly mediation is that soft masses are unified at a mirage messenger scale

For instance,

A Benchmark Model

The original KKLT compactification of IIB theory gives(T : Calabi-Yau volume modulus)

modulus Kahler potentialmodulus superpotential

matter Kahler metric

gauge kinetic function

uplifting potential

ni are rational numbers depending on the origin of matter superfield. (e.g, ni=0 for matter fields living on D7 brane)

(tanM0) plane Stau LSP in large tan Stop LSP in small M0

Neutralino LSP (Bino-like)

Magenta region gives thermal relic density

Stop-neutralino coannihil.Stau-neutralino coannihil.Higgs resonance channel

Mt=172.7 GeV

Masses vs. tan h2 vs. tan

(M0 = 800 GeV)

Low energy effective Lagrangian for neutralino-quark int.

scalar interaction

In most situations the dominant contribution to the spin-independent (scalar) amplitude is the exchange of the two neutral CP-even Higgs bosons.

Significant scalar couplings to nuclei arise if the neutralino is a mixed gaugino-higgsino state.

Heavy CP-even Higgs coupling to d-type quark is essentially proportional totan for 2tan 1

Smaller Higgs masses give larger amplitude.

5 5( ) ( ) ( ) ( )q qL f qq d q q

Direct detection ( SI vs. m )

Higgs and sparticlemass and B(b s)bounds are imposed

Bino-like LSPmA is rather largem > ~ 400 GeV

small SI

Red points satisfy WMAP bound on relic density

More general cases

It is possible to generalize the compactification to get different values of the mirage mediation parameters , ai and ci

Treat as a free parameter while focusing on = O (1),with various choices of ai and ci

ai=ci=1 ai=ci=1/2 aH=cH=0, ai=ci=1 aH=cH=0, ai=ci=1/2

(, M0) parameter space with ai=ci=1

tan=10 tan=35

small : Bino-like, large : Higgsino-likeseperated by stop/stau LSP region, >2 : No EWSB

When increases, the lightest neutralino is changed from Bino-like to Higgsino-like via Bino-Higgsino mixing region

larger smaller M3 (relative to M1) reduced

M3~M0 (1-0.3 ), while M1~M0 (1+0.7 ) at GUT scale

tan=10 tan=35

Direct detection ( SI vs. m )Red points satisfy WMAP bound on relic density

Varying with

So far, we assumed ai=ci=1. The sparticle specturm, however, depends on the choice of the parameters ai and ci.

The choice of ai and ci which decrease Xt implies that the reduction of soft masses by Xt becomes less significant,as evolved from the GUT to the EW scale.

where

When

m2tR and Xt decrease m2

t1 increases

(NO stop LSP)

m2R and X decrease m1 decreases

(stau LSP)

m2Hu and Xt decrease |m2

Hu| decreases (reduction of ) (reduction of mA)

At GUT scale RGE At EW scale

(, M0) parameter space with ai=ci=1/2

tan=10 tan=35

small : Bino-like, large : Higgsino-likeNO stop LSP region, >1.5 : No EWSB Bino-Higgsino Mixing Region appear !

When increases, the lightest neutralino is changed from Bino-like to Higgsino-like via Bino-Higgsino mixing region

~ M1 around ~ 1

tan=10 tan=35

tan=10 tan=35

Direct detection ( SI vs. m )Red points satisfy WMAP bound on relic density

m2tR remains the same m2

t1 increasesXt decrease (NO stop LSP)

m2R remains the same m1 increases

X decrease (NO stau LSP)

m2Hu and Xt decrease |m2

Hu| similar

m2Hd and X,b decrease m2

Hd decreases (Small mA)

At GUT scale RGE At EW scale

When aH=cH=0 and ai=ci=1

(, M0) parameter space with aH=cH=0 and ai=ci=1

tan=10 tan=35

small : Bino-like, large : Higgsino-likeNO stop LSP region, NO stau LSP regionBino-Higgsino Mixing Region appear

When increases, the lightest neutralino is changed from Bino-like to Higgsino-like via Bino-Higgsino mixing region

~ M1 around ~ 1.5

tan=10 tan=35

tan=10 tan=35

and

Direct detection ( SI vs. m )

m2tR and Xt decrease m2

t1 increases

(NO stop LSP)

m2R and X decrease m1 decreases

(stau LSP)

m2Hu and Xt decrease |m2

Hu| decreases (reduction of ) (reduction of mA)

At GUT scale RGE At EW scale

When aH=cH=0 and ai=ci=1/2

(, M0) parameter space with aH=cH=0 and ai=ci=1/2

tan=10 tan=35

small : Bino-like, large : Higgsino-likeNO stop LSP region, >~2 : No EWSB Bino-Higgsino Mixing Region appear

tan=10 tan=35

and

Direct detection ( SI vs. m )

Summary of neutralino DM

Depending upon the model parameters, especially the anomaly to modulus mediation ratio, the nature of the LSP is changed from Bino-like neutralino to Higgsino-like one via Bino-Higgsino mixing region. For the Bino-like LSP, the standard thermal production mechanism can give a right amount of relic DM density through pseudo-scalar Higgs resonance effect or the stau-neutralino or stop-neutralino coannihilation process.

Neutralino DM might be detected by near future direct detecting experiments, especially in the case of Bino-Higgsino mixed LSP.

LHC signature of Mirage Mediation

In collaboration with

W.Cho, K.Y.Lee, C.Park, Y.Shimizu (KAIST)

A benchmark point for collider study

alpha = 1M0 = 500 GeVaM=cM=1/2aH=cH=0tan(beta)=10

Mirage benchmark point alpha=1, M0=500 GeV, aM=cM=1/2, aH=cH=0, tanb=10(M1=367 GeV, M2=461 GeV, mu=475 GeV at EW scale)

m_gluino= 884 GeV, m_dL=776 GeV, m_t1=545 GeVm_N1 = 355 GeV, m_N2 = 416 GeV, m_eR = 382 GeV

0 02 1Rq e The cascade decay is open !

(m_N2 > m_eR)

Cross section for SUSY events ~ 6 pb

We generated SUSY events ( ~ 30 fb-1 luminosity)using PYTHIA (event generator) + PGS (detector simulation)

(cf. mSUGRA )

Precision measurements of sparticle masses at the LHC

When the cascade decay0 02 1Rq e is open,

a clean SUSY signal is l l + jets + missing TE events.

2q q

Re e

1e

jlm

llmjllm

• Di-lepton invariant mass distribution

for the mirage point1with 30 fb-1 lumi.

Mll (max) ~ 60 GeVwell matched withthe generated value

• Various distributions for the mirage point

m_squark, m_slepton, m_N2, and m_N1 can be determined.

Gluino and squark mass measurement

Di-jet invariant mass Stransverse mass

The mass ratio of gluino to LSP

which is quite distinctive from the predictionof GUT unification of gaugino masses.

‘Model-Independent’ Masses

Backup slides

Gluino, squark and slepton masses

M0, alpha and c_i

Neutralino masses

Mu (EW scale), tan(beta) c_H and tan(beta)

Determination of model parameters

(Bachacou, Hinchliffe, Paige 2000)

0 0 02 2 1

02

1/ 22 2 2 2

max2

( )( )Lq

jll

m m m mm

m

0 02 1

1/ 22 2 2 2

max2

( )( )R R

R

e e

lle

m m m mm

m

(for “point 5”, M=300 GeV and m=100 GeV)

etc.

• Moduli-induced gravitino problem

M.Endo,K.Hamaguchi,F.Takahashi (2006)N.Nakamura, M.Yamaguchi (2006)

Recently, it is shown that the branching ratio of the modulus decay into the gravitino is generically quite large.

which causes serious problems after the modulus decay.

In this work, we just assume that this problem is avoidedby some mechanism and the thermal production of DM isrealized. Then we investigate theraml relic density and directdetection rate of neutralino DM.