Probing the Majorana Nature and CP Properties of Neutralinos

Yeong Gyun Kim (Korea University)

In collaboration with S.Y.Choi, B.C.Chung, J.Kalinoswski and K.Rolbiecki

reference, hep-ph/0504122

• Introduction • Neutralino mixing• Three-body leptonic neutralino decays• Numerical Analyses

Contents

0 02 1ˆ( ) in its rest framen l l

Lepton energy distribution Lepton angular distribution Lepton invariant mass and opening-angle distribution CP-odd triple spin/momentum product

Conclusions

I. Introduction

Neutralinos

spin-1/2 Majorana superpartners of neutral gauge bosons and Higgs bosons expected to be among the light SUSY particles that can be produced copiously at future high energy colliders

In this talk, we focus on probingIn this talk, we focus on probingthe Majorana nature and CP properties of neutralinos through

the charge self-conjugate three-body decays of polarized neutralinos

Supersymmetry (SUSY) one of the most interesting and natural extension of the Standard Model the search for SUSY is one of main goals at the LHC and ILC

0 01ˆ( )i n l l

Neutralinos produced in decays are 100 % polarized

The rest frame of the neutralino can be reconstructedin some cascade processes, e.g.

0 0 0 01 2 1 1L Le e e e e e e e

Le

02Le e

02Le e

02

Netagive helicity

Positive helicity

if CM energy and neutralino masses are known.

0 02 1

We provide a systematic combined analysis ofthe polarized neutralino decay in its rest frame

[Aguilar-Saavedra,04]

[Aguilar-Saavedra and Teixeira ,03]

II. Neutralino mass matrix In the basis

0 0 01 2( , , , )B W H H

1

2

0 cos sin sin sin

0 cos cos sin cos

cos sin cos cos 0

sin sin sin cos 0

Z W Z W

Z W Z W

Z W Z W

Z W Z W

M M M

M M M

M M

M M

0 0 0 01 2 3 1 4 2i i i i iN B N W N H N H

Two non-trivial phases may be attributed to M1 and mu ,

11 1| | , | | iiM M e e

and render the matrix N complex, violating CP.

All are purely real or purely imaginary in the CP invariant case.iN

III. Three-body leptonic neutralino decays

Decay matrix elements

0 0 0 02 1 1 2( ) [ ( ) ( )][ ( ) ( )]D l l D u P u u l P v l

with bilinear charges ( , , )D L R

Differential decay distribution

0 1 2 3ˆ ˆ ˆ ˆ ˆ ˆ ˆ( , ) ( ) ( , ) ( ) ( , ) ( ) ( , )d F x x q n F x x q n F x x n q q F x x

22 /x E m

02 2 ˆ( , ) ( ) ( ) ( )m n q l q l q

( , )( 0 3)iF x x i with four kinematic funtions

n̂ : neutralino spin 3-vector

where

Implications of CP and CPT invariance for the neutralino decay~

1 2

1 2

( )

( )LR RR

RL LL

D D t u

D D t u

CP invariance leads to the relations

0 0

1 2

3 3

( , ) ( , )

( , ) ( , )

( , ) ( , )

F x x F x x

F x x F x x

F x x F x x

CPT invariance (satisfied if Z-boson and slepton widths are neglected)

*

*

( )

( )

LR RR

RL LL

D D t u

D D t u

0 0

1 2

3 3

( , ) ( , )

( , ) ( , )

( , ) ( , )

F x x F x x

F x x F x x

F x x F x x

where are the intrinsic CP parities of

~

1,2 i 01,2

Since neutralinos are the Since neutralinos are the MajoranaMajorana particles, particles,

CP & CPT invariance : etc. LRDpure real forpure imaginary for

1 2 1 2

~

(T : naïve time reversal transformation)~

IV. Numerical Analyses We adopt an mSUGRA scenario

m0 = 150 GeV, m1/2 = 200 GeV, A0 =-650 GeV, tan(beta) = 10, sgn(mu) > 0

0 0 02 2 1( ) 28.4%, ( ) 4.6%LBr e e Br

Production cross sections with unpolarized e+e- beams at sqrt(s)=500 GeV

{ } 80.7 fb, { } 113.5 fbL L R Le e e e

Branching Ratios

With integrated luminosity of 1000 fb^-1, a sufficient number of events for the decay are expected to be selected. In MC simulation, we assume 1000 neutralino decay events are selected.

0 01 2

78.1 GeV, 148.5 GeVm m

Particle Masses

1 2( 80 GeV, 158 GeV, 415 GeV)M M

207.7 GeV, 173.1 GeVL Re em m

4.14.1 Lepton energy distribution

0 0( , ) ( , )F x x F x x to a good approximation ( exactly in CP-invariant case)

2

0 ( , )d

F x xdx dx

Symmetric distribution of events on (x-,x+) Dalitz plane

Majorana nature of neutralinos

sign( )x x ev 24N is within the expected error 1000 32

where 22 /x E m

4.24.2 Lepton angular distribution

1 1(1 cos )

cos 2

d

d

ˆ ˆcos q n

Lepton angle distribution w.r.t neutralino polarization vector

with

1 2( , ) ( , )F x x F x x

Majorana nature of neutralino the slope of the angle distribution

1 0

4.34.3 Lepton invariant mass and opening-angle distribution

Near the end point of the lepton invariant mass distribution01

22 1 1 2( ) , s m m t u m m

is produced nearly at rest,

Mandelstam variables

2 2 2 2 221 21| | (1 ) {[Re( )] [Re( )] } ( )LL RRD r r D D O

Invarinat mass distribution decreases

steeply if are purely real

slowly if are purely imaginary

1 2 1when ( 0 case)

1 2 1when ( case)

2 11 /( )llm m m

21 1 2( / )r m m

etc.LLD

etc.LLD

Selection rule of the orbital angular momentum by CP symmetry

2 1( 1)L ( L : orbital angular momentum of the final system )

Decay distribution w.r.t. the opening angle between two leptons

22 2 (1 cos )

2ll

mm x x

: maximum for for given x- and x+

cos 1

L=0 ( steep S-wave) for L=1 ( slow P-wave) for

1 2 1 ( 0 case) 1 2 1 ( case)

Angular momentum conservation forces L=0 for cos 1

ˆ ˆcos q q

4.44.4 CP-odd triple spin / momentum product

3 3

1( , ) [ ( , ) ( , )]

2CPF x x F x x F x x

ˆ ˆ ˆ( )CPO n q q

0

(sin / 2) ( , )( 0) ( 0)

( 0) ( 0) ( , )

CPCP CPCP

CP CP

F x x dx dxN O N OA

N O N O F x x dx dx

A CP-odd (CPT-even) distribution

A CP-odd quantity related to the above CP-odd distribution

~

(with 0) CPA

1

V. Conclusions

We have performed a systematic analysis of the polarized neutralino decay for probing the Majorana nature and CP properties of neutralinos

The Marorana nature of the neutralinos can be checked thorough lepton energy distribution, lepton angle distribution w.r.t neutralino polarization vector to a good approximation in CP non-invariant case (exactly in CP invariant case)

The relative CP parity of two neutralinos can be identified by measuring threshold behavior of the lepton invariant mass distribution and/or the opening angle distribution of lepton pairs. The CP violation in the neutralino system could be detected by measuring the asymmetry on the CP-odd quantity

0 02 1ˆ( )n l l

ˆ ˆ ˆ( )CPO n q q