B中間子による量子もつれの検証
( submitted to PRL
quant-ph/0702267 )
物理的背景と解析・結果
One of “Exotic” topics of Belle Results
Y.Sakai KEK
金茶会 6-July-2007
1
KEKB
Integrated Luminosity
Mt. Tsukuba
KEKB
~700 fb-1
KEKB
for Belle
Belle
~1 km in diameter
Belle detector
PEP-II
~440 fb-1 for BaBar
8 GeV e- x 3.5 GeV e+
Ares RF
cavity
e+ source
Lpeak = 1.71x1034
Integ. Lum. ~700 fb-1
2
Belle Detector
, p0 reconstruction
e+-, KL identification
Electromagnetic Calorimeter
CsI(Tl) 16X0
K/p separation
Aerogel Cherenkov Counter
n = 1.015~1.030
3.5 GeV e+
TOF counter
K/p separation
8.0 GeV e-
B vertex
Si Vertex Detector
4-layer DSSD
charged particle tracking
Central Drift Chamber
momentum, dE/dx
50-layers + He/C2H6
Muon / KL identification
KL m detector
14/15 layer RPC+Fe
13 countries, 55 institutes, ~400 collaborators
3
EPR Entanglement
EPR Paradox:
Quantum Mechanics:
Entangled state  non-separable wave function even for
far apart particles
can not be a “complete” theory
A
B
Local realistic theory with “hidden” parameters
“an element corresponding to each element of reality”
4
Bohm: Entangled states
[Gedanken experiment]
[D.Bohm., Quantum Theory, p614(1951)]
two spin ½ particles from singlet state
QM
Measurement: Sx=+1/2 for a  predict Sx = -1/2 for b
Decision of orientation of polarizer at very last moment
 still above happen  No causal connection
Instantaneous communication ? ( Quantum communication)
Hidden parameters (Local Realistic Theory) ?
5
Bell Inequality
Key for experimental check !
J.S.Bell, Physics 1, 195(1964);
Clauser,Horene, Shimony, Holt, PRL 23, 880(1969)
Any Local realistic theory with “hidden” parameters
S = |E(a,b)-E(a’,b)| + |E(a,b’)+E(a’,b’)| < 2
(Bell-CHSH Inequality)
E(a,b): correlation function between
measurements a and b
A
Violation  Reject LRT, Confirm QM
Many experiments performed: loopholes
- Locality: need space-like measurements of A and B
- Detection efficiency: sub-sample  all
B
Bell Inequality Violation = QM: ~established
6
Bell Inequality: exp.
• Entangled photons
(1)
[e.g. G.Weihs et al., PRL 81, 5039(1998)]
(Locality loophole)
A,B: 400m away, measurements <<1.3ms
7
C++ + C---C+--C-+
E(a,b)=
Ntot
Cxx: # of coincidence
SQM:max
A: a,a’= 0, 45 deg
B: b,b’= 22.5, 67.5 deg
S = 2.73  0.02
14700 coincidence
Bell Ineq. is violated !
Efficiency ~5%
8
Bell Inequality: exp.
• Entangled 9Be+ ions
(2)
[e.g. M.A.Rowe et al., Nature 409, 791(2001)]
(Detection efficiency loophole)  ~98%
(f1, f2)
E(f1,f2)
Nsam-Ndif
= N +N
sam
dif
9
Detect photons by PMT
f1 = 3p/8, f2= 3p/8
E = -0.55
f1 = 3p/8, f2= -p/8
E = 0.56
S
= 2.25  0.03
Bell Ineq. is violated !
10
Why Y(4S)  B0B0 System
_
• One of few entangled systems in HEP
• Highest energy scale (~10 GeV)
breakdown of QM at high energy ?
[C= -1]
QM:
_
+ B0B0 mixing
Initial: B0
B0
_
B0
ー0
B
B0
11
Y(4S)  B0B0 System
_
QM:
Joint Probability at t1=t2 , B0B0 or B0B0 only
_
_
Same Flavor (B0B0, B0B0): ∝ e-G|Dt| [1 + cos(DmDt)]
Opposite Flavor (B0B0) : ∝ e-G|Dt| [1 - cos(DmDt)]
_
_ _
(Dt=t1-t2)
OF-SF
AQM(Dt) =
OF+SF
= cos(DmDt)
12
Y(4S)  B0B0 System
_
Bell Inequality Test ?
AQM(Dt) = cos(DmDt)
E(a,b) = cos(DmDt) ?
curve a: same as “Entangled photons”
or E(a,b) = - e-2Gt’ e-GDt cos(DmDt) ? [includes decay rate]
( t’ = Min(ta-tb) )
curve b
a
b
13
Y(4S)  B0B0 System
_
[A.Bertlmann et al., PL A332, 355(2004)]
Curve b should be taken
Bell Inequality Test : intrinsically impossible
• QM to violate Bell Inequality ;
x = Dm/G > 2.6  xd = 0.78
• Active measurement needed
 Flavor measurement via decay reconstruction = passive
[ some arguments may exist against above ]
Any way to test QM at Y(4S) ?
14
Belle’s Approach
Precise measurement of
Time-dependent Flavor Correlation
Quantitative proof of QM Entanglement
Quantitative Comparison with Non-QM model
Fully corrected (= true) A(Dt)
 Direct comparison with (any) theories
QM:
OF-SF
AQM(Dt) =
OF+SF
= cos(DmDt)
15
Non-QM models
(example 1)
• Local Realism: Pompili & Selleri (PS)
[EPJ C14,469(2004)]
“elements of reality” (hidden variables) _ _
= Flavor & mass (BH, BL, BH, BL)
Mass states: stable
random jump of Flavor within pair
Single B0: oscillation ~ 1  cos(Dmt)
only determine upper/lower limits of A(t1,t2)
16
A(Dt): PS model
Integrated
over tmin
Note) Local realistic model with same A(Dt) as QM is possible [quant-ph/0703206]
17
Non-QM models
(example 2)
• Spontaneous immediate Disentanglement (SD)
_
separates into B0 & B0 evolve independently
[e.g. PR 49,393(1936)]
Integrated
over t1+t2
18
Analysis Method
B0  D*-l+n + Lepton-tag
~Same as Dm measurement
[PRL,89,251,803(02),PRD 71,972003(05)]
Reconstruction
Vertexing: Dt = Dz/cb
( high quality lepton-tag only)
OF & SF
Dt distribution
• Background subtraction
• Unfolding (detector resolution)
Fully corrected (= true) A(Dt)
 Quantitative Test for non-QM model
19
Signal Reconstruction
152M BB
signal
background
Background
subtraction
of fake D*
6718 OF
1847 SF
20
Background Subtraction
Bin-by-bin (Dt ) for OF & SF
• Continuum: use off-Res. (negligible)
• Fake D*: M(D*)-M(D0) sideband
• Combinatoric D*l : “reversed l” method
• B+  D**0 ln : MC
• Wrong-tag correction : 1.5 0.5% (MC,data)
OF SF
126 54
78 237
254
2
22 86
6324 1490
152M BB
Dt (ps)
21
Unfolding (Deconvolution)
Singular Value Decomposition (SVD) method
[A.Hoecker, V.KKartvelishvile NIM A372, 469(1996)]
Measured Dt distribution
OF, SF separately
True Dt distribution
Detector effect
11 Dt bins: 11 x 11 Response Matrix
(measured) = R x (true) (using MC)
Dt Resolution
Matrix inversion
Data/MC difference included
 Robustness against input:
checked by Toy MC  Sys. error
22
Cross Check: Lifetime
Fully corrected OF+SF: fit with e-Dt/t
c2 = 3/11 bins
t = 1.532 0.017(stat) ps  consistent with PDG
(1.530 0.009 ps)
23
Results & Sys. errors
Fully corrected A(Dt)
Systematic Errors
stat. ~ sys.
24
Results & fit with QM
Fully corrected A(Dt): fit with QM
[quant-ph/0702267,
submitted to PRL]
152M BB
Dm = (0.501  0.009) ps-1
c2 = 5.2 (11 dof)
Good !
[ fit including WA Dm = (0.496  0.014) ps-1 (excl. Belle/BaBar)]
25
Result: PS model
152M BB
difference btw. Data/Fit
(points not used if
PSmin < Data < PSmax )
PS Best Fit
(error from Dm)
Dm = (0.447  0.010) ps-1
c2 = 31.3
disfavored 5.1s
over QM
26
Result: SD model
152M BB
difference btw. Data/Fit
SD Best Fit
(error from Dm)
Dm = (0.419  0.008) ps-1
c2 = 174
disfavored 13s
over QM
_
Decoherence fraction:
Fit (1-z)AQM + zASD : z = 0.029  0.057
cf) K0K0 system
[CPLEAR, PLB 422, 339(1998)
KLOE, PLB 642, 315 (2006)]
27
Summary
Quantitative study of EPR-type Flavor entanglement
in Y(4S)  B0B0 decays has been performed
_
Fully corrected A(Dt) measurement
 allow Direct comparison with any theory
• QM Entanglement : confirmed
• Pompili-Selleri type (Local Realism) model :
disfavored by 5.1s
• Spontaneous Disentanglement: rejected by 13s
Bell Inequality Test might be reconsidered ?
28
K0 system EPR: CPLEAR
[PLB 422,339 (1998)]
Dt=0
p p  K0K0 at rest (JPC~1- -)
_
_
Dt=5cm
Decoherence fraction in
K0K0 basis
z = 0.40  0.7
_
[PRD 60,114032 (1999)]
L + K (K-id by dE/dx)
Dt=0
OF
SF
Dt=5cm
OF-SF
A=
OS+SF
OF
SF
29
K0 system EPR: KLOE
[PLB 642,315(2006)]
KLOE at DAPHNE (f Factory)
CPV decay
380pb-1
Fit to Dt distribution
including regeneration
Decoherence fraction in
K0K0 basis
_
f  KSKL (p+p-)(p+p-)
z = (0.10 0.21 0.04)x10-5
Decoherence:
CP allowed decay
f  KSKS
30
Time-dependent Asymmetry
31