probing the majorana nature and cp properties of neutralinos yeong gyun kim (korea university) in...
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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