2006-6-28 Haibo Li 1
Clean Prediction of KSKS, KLKL Production Rates in Vector Quarkonium Decay to K0K0
PRL 96, 192001 (2006)
Haibo Li
Institute of High Energy Physics, Beijing.
International Workshop on Heavy Quarkonium
QWG4
– June 27-30 2006, BNL, USA
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CPV Established in Both K and B Decays
CKMV u
c
t
d s b
ud us ub
cd cs cb
td ts tb
V V V
V V V
V V V
CP Violation(Im[...] 0)
arg(...)
arg(...)
3 3 3
0ud ub cd cb td tbV V V V V V
A A A
,
0 0
mixingB B
and )B b c (
( )b u
0,1
2
3 0,0
1
ud ub
cd cb
V V
V V
td tb
cd cb
V V
V V
Results on the CKM angles:
1.3 1.
13 8
15 12
2.7
63
21
99
20 15184
Search for CPV in various reactions, probe possible new source of CPV.
I am going to talk about possible CP observation in quarkonium decays which may be correlated
with K, D, and B system .
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Vector Quarkonium Decay to K0K0 System
Q
Q
K0
K0
K0
K0
K0
K0W
Strong EM Weak 10-9
Assume QQ is pure QQ system, the possible strong multiquark effects that involve seaquarks play no rule here.
The K0K0 system is in a state with charge parity C =1:The reason is that the relative orbital angular momentum of the K0K0
pair must be in L = 1 because of angular momentum conservation. A boson-pair with L = 1 must be in an antisymmetric state, the antisymmetric
state of particleantiparticle pair must be in a state C = 1:
00001
00
2
1KKKKKK
C
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CPV Processes 1 Quarkonium Decay to KSKS , KLKL
Within Standard Model, the possible CPV processesVector QQbar KSKS, KLKL are due to K0K0 oscillation!
KSKL
KLKS
KSKS
KLKL
K0
K0
CPV processes
Time evolution of the K0K0 system produced in vector QQ decay can tell us the possibilities to find KSKL, KLKS, KSKS and KLKL
t1
t2t0
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TimeEvolution of K0K0 System The weak eigenstates of the K0 are:
,00 KqKpKS .00 KqKpKL
with eigenvalues : LLLSSS
im
im
2,
2
Then the time evolution of K0K0 system :
Following the 1 Quarkonium decay, the K0 and K0 will go separately and the time evolution of the particle states is:
,2
1)(,
2
1)( 00
Lti
Sti
Lti
Sti KeKe
qtKKeKe
ptK LSLS
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Time Dependent Amplitudes
1,22 LLsSSLLS KKKKqpKKKK
Since the states <KS| and |KL> are unorthogonal, we have :
Then the amplitudes to find KSKS, KSKL, KLKS, KLKL pairs are:
A1(t1, t2) = A4(t1, t2)A2(t1,t2) = A2 (t2,t1)
If CP is conserved, |p/q|=1, orthe two particles are observed at the same time, namely, t1=t2, thenA1(t1, t2) = A4(t1, t2)=0 for KSKS and KLKL cases because Bose-Einstein statistics prevents two identical bosons from being in an antisymmetric state. In other words, only KS and KL can be see at the same time in 1 K0K0 decay.
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Time-integrated Possibilities The time integrated possibilities to observe KSKS, KSKL and KLKL pairs, which are normalized by the widths of KS and KL are:
ym
xLS ,,2
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The Decay Widths The Partial widths of the KSKS, KLKL, KSKL are:
where C is the phase space factor.
The ratio RSS and RLL are defined as:
LLLS
LL
LS
SS RKK
KK
KK
KK
)(
),(
)(
),(
,, PP
PP
In the ratios, the phase space factor C and the strong matrix element square are completely canceled, which insure that the ratios are completely free from uncertainty caused by strong interaction in the decay.
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Correlation with KL Semileptonic Decays
RSS and RLL can be determined by using experimental measuredValues of x, y and |p|2 - |q|2, where |p|2 - |q|2 is related to CP
asymmetry parameters L in semileptonic KL decay:
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The Predicated Results for RSS and RLL
The results can be extended to all 1-- heavy quarkonia:
From PDG 2004, one gets:
= (0.327 0.012)%
8% relative error!
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Current Experimental Status for KSKL
BES: 58M, J/ KSKL
PRD, 69, 012003(2004)
BES: 14M, (2S)KSKL
PRL, 92, 052001(2004)
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The Predicted Results for CPV QQ(1) KSKS Processes
We got the following predicted branching factions for CPV processes :
From PDG 2004
BESII: PRD 69, 012003 (2004)BESII: PRL, 92, 052001 (2004)
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Search for CPV QQ(1) KSKS Processes (1) BESII 58M J/ , J/ KSKS
BESII 14M (2S), (2S) KSKS
BESII: PLB 589 (2004) 7
At BESIII, 1010 J/ sample can be produced per year !
The main backgrounds are due to J/ KSKS which will dilute the CP of KSKS final states.
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Search for CPV QQ(1) KSKS Processes (2)
2.3 fb-1 data collected at peak at DA NE, which correspond to 6 109 decay events. These data can be used to probe KSKS and KLKL precisely with statistic error about 1% level according to the prediction Br( KSKS ) = (3.59 0.27)10-6
The precise RSS will be obtained at 1% level, then, it can be used to constrain the KL semileptonic decay parameter L [ 4% 1%] by using the correlation between KSKS decay and KL semileptonic decay .
(nS) KSKS will be reached at future Super-B factory.
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Background from K Regeneration --Dissipation and Decoherence
One has to take care of the possibility of neutral K regeneration in detectors (KLOE, BES-III, Super-Belle). The beam pipe or material in Draft Chamber will be the target to make K regeneration. In this case, KSKL final states may become KSKS or KLKL, which will dilute the CP measurements. Especially, it is more dangerous at phi factory since the momentum of K is very low.
00
2
1KKKL SL KffKffKfKf
2
1
2
1
2
1 001 ff
We are working on this possible dilution at BES-III.
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Isospin Relation in QQ(1) KK DecaysBecause of isospin symmetry, we have then, it is straightforward to obtain the following relation by neglecting the phase space difference:
//00 JHKKJHKK
Where A is the correction factor due to K0-K0bar mixing:
One get A is not exactly equal to 1, even isospin symmetry is an exact symmetry :
One has to consider K0 mixing effect when test isospin symmetry which is violated mostly due to Electromagnetic effects.
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Summary(1)
• We have studied the CPV decay processes of J/, (2S), and (nS) Quarkonia to KSKS and KLKL.• The ratio of RSS (RLL) of KSKS (KLKL and KSKL production rates has been constructed in a model-independent way:
• Simultaneous measurements of vector quarkonium decays to both KSKS
and KSKL pairs are suggested at higher luminosity e+e machines (BEPC-II, DA NE-II, and Super-B). So many systematic errors can be canceled in the ratio RSS measurements.
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Summary(2)
• With current experimental information, the absolute branching fractions of the CPV processes are first predicted:
The results had been published at Phys. Rev. Lett. 96 (2006) 192001 By Haibo Li and Mao-Zhi Yang
