1. ¡ (4S)B0B0 decays Measurement of EPR-type flavour entanglement in _
PRL 99 (2007)
Measurement of EPR-type flavour entanglement in
¡ (4S)B0B0 decays _
Bay Ecole Polytechnique Fédérale de Lausanne
Séminaire X 2007
LAPP X-2007

2. Summary Introduction: the EPR/Bohm argument and the J. Bell test
EPR correlations with neutral B mesons (and Kaons)
- production of entangled B0 B0 states
- is it possible to perform a Bell test ?
EPR correlation studies by the BELLE experiment
- test of two specific "local realistic" models
- "New Physics" searches: decoherence of entangled
states
LAPP X-2007

3. The EPR argument (1935)
A "complete theory" contain an element for each element of reality
EPR consider an entangled two particle system and the measurement
of two non-commuting observables (position and momentum)
Entanglement to transport the information from one sub-system
to the other
EPR identify a contradiction with the QM
rule for non-commuting observables. Y
LAPP X-2007

4. Bohm (1951), entangled states
Bohm analysis of the EPR : two spin 1/2 particles from singlet state
|Y1,2 ñ = (1/Ö2) ( |­ñ1 |¯ñ2 - |¯ñ1 |­ñ2 ) y
spin analyser I II z
Particle 1
Particle 2
Source x
* The two spin are entangled: a measurement Sx = +1/2 of the spin projection //x for particle 1 implies that we can predict the outcome of a measurement for 2:
Sx = -1/2.
* This will happen even if the decision to orient the polarizer for particle 1 is done at the very last moment => no causal connection.
How to explain this ?
with the introduction of a new instantaneous communication channel between the two sub-systems ...
or with the introduction of some new hidden information for particle 2, so that the particle knows how to behave.
=> QM is incomplete.
LAPP X-2007

5. J. S. Bell theorem (1964)
This problem was revitalized in 1964, when Bell suggested a way to distinguish QM from local models featuring hidden variables (J. S. Bell, Physics 1 (1964) 195 ).
The Bell theorem: Local hidden variable theories cannot reproduce all possible (statistical) results of QM.
Extended by J. Clauser, M. Horne, A. Shimony, and R. Holt, Phys. Lett. 23 (1969) 880.
Several experiments have been done with photon pairs, atoms,...
LAPP X-2007

6. Bell-CHSH a, b (and b',c) : orientations of the two analyzers
J. Clauser, M. Horne, A. Shimony, and R. Holt, Phys. Lett. 23 (1969) 880
a, b (and b',c) : orientations of the two analyzers
l : additional information, i. e. hidden variables
A(a,l), B(b,l) : results of the measurements (+1 or -1)
Correlation function :
r(l) is the normalized probability distribution
. . .
with products like B(b,l)B(c,l)
gives
can be violated by QM
If E(a,b) depends only on a = a - b, with b = c - b, g = b - b'
LAPP X-2007

7. Bell-CHSH experiment by Aspect et al.
Experiment by A. Aspect, P. Grangier, G. Roger, PRL 49 (1981) 91:
measurement of the correlations of the linear polarization of two photons
from a Ca40 source:
the probabilities of obtaining a ±1 result along direction a (particle 1)
and b (particle 2).
is the correlation coefficient of the measurements on the two photons with
the directions of the two analyzers
QM predicts E(d) = cos(2d), with d the angle between the two directions
where
Assuming local realism we have
LAPP X-2007

8. Aspect et al. apparatus
Two polarimeters with orientations a and b perform dichotomic measurements
of linear polarization of the 2 photons (n1, n2) from a Ca40 source.
The apparatus registers single rates and coincidence rates.
LAPP X-2007

9. Bell-CHSH test by Aspect et al.
22.50
They choose the following optimal configuration S
giving S(f) = 3E(f) - E(3f) QM
LR limit
The QM maximal value is S(22.5o) = 2√2=2.83
The LR limit is |S|  2
f [deg]
Needs to account for detection efficiency:
Aspect et al. estimate the correlations for a given angle (d=f or d=3f):
The experiment gives: S(f=22.5o)=3E(22.5o)-E(67.5o) = 2.6970.015 > 2
LAPP X-2007

10. EPR correlations in high energy experiments
In the '60 Lee and Yang recognized the EPR behaviour of the neutral Kaon doublet in a JPC = -1 state: here the "strangeness" S=+1 or S=-1 of the two Kaons plays the role of spin up or down.
* Tests have been carried out on correlated
Apostolakis et al., CPLEAR collab., Phys. Lett. B 422 (1998) 339
Ambrosino et al., KLOE collab., Phys. Lett. B 642 (2006) 315.
In B factories we have the opportunity to study the flavour entanglement in B0 pairs from ¡(4S) ® B0 B0
LAPP X-2007

11. K0 and B0 m~0.5 GeV/c2 m~5 GeV/c2 ~ ~ ~
e is the CP violating parameter ~10-3
lifetime K0Short t = s
K0Long t = s
~identical lifetimes t = s
ct ~ 500 mm
flavour oscillation parameter:
quite fast oscillation:
~ /ps
~ 0.5 1/ps
LAPP X-2007

12. B0 B0 oscillation d b t W+ W+ d t b
Suppose to produce a pure beam of B0 at t=0, then
LAPP X-2007

13. Analogy with spin measurement
The analogy proposed (by many authors) is
K or B
Differences with photons: K and B are unstable,
and we cannot test for an arbitrary superposition state
LAPP X-2007

14. Production of flavour entangled states (1/2)
24% Y(4S)
76% continuum
Interaction Point extension:
sx77 µm sy  2 µm sz  4 mm
8 GeV
electrons
3.5GeV positrons
KEK-B
 production of
(4S) (10.58GeV/c2)
 = 0.425
(4S)  B0 B0
 B+ B-
LAPP X-2007

15. Production of flavour entangled states (2/2)
From
Y(4S) is a resonance JCP = The strong decay conserves C which is transferred to the final state:
|Yñ = (1/Ö2) ( |B0ñ1 |B0ñ2 - |B0ñ1 |B0ñ2 )
Because of this a measurement of the flavour (B0 or B0) of particle 1,
tells with 100% probability that, at the same proper time, particle 2 is of
the opposite flavour (B0 or B0).
Experimentally, the flavour of a B can only be determined when it decays, and only if it decays into a “flavour-specific” mode, like d b c W+
the sign of the lepton
tells us the neutral B
flavour
LAPP X-2007

16. Experiment with of correlated B0 B0
(4S) produced with  = 0.425
by the asymmetric collider
e, m
(4S)
QM: region of
B0 & B0
coherent
evolution Dz D z0 z1 z2 z
B0 and B0 oscillate coherently. When the first decays, the other is known to be of the opposite flavour, at the same proper time
Than the other B0 oscillates
freely before decaying
after a time given by
Δt Δz /cβγ
N.B. : production vertex position z0 not very well known : only Dz is available !
LAPP X-2007

17. QM predictions for entangled pairs
Time (Dt)-dependent decay rate into two Opposite Flavour (OF) states
Dmd is the
mass difference of the two mass eigenstates
idem, into two Same Flavour (SF) states
=> we obtain the
time-dependent asymmetry
( ignoring CP violation effects O(10-4), and taking GH = GL )
LAPP X-2007

18. Bell-CHSH testing with mesons ?
Bramon and Nowakowsi, Bertlmann and Hiesmayr, Gisin and Go:
oscillation plays the role of rotating the polarizer...
The time-dependent asymmetry is formally equivalent to the expression for
the EPR correlation experiment with spin 1/2 particles: S
Then Gisin and Go (Am. J. Phys. 69 (2001) 3) suggest
to Bell-CHSH test with
S(f) = 3E(f) - E(3f)
- QM maximum for f = DmdDt = 45o, corresponding
to Dt~2.6 ps
- local realism limit is |S|  2
The experimental result (A. Go, Journal of Modern Optics 51 (2004) 991)
2.73 ± 0.19 was >3s above the Local Realism . QM
LR limit f
LAPP X-2007

19. Bell-CHSH testing with mesons ? No...
* Bertlmann, Bramon, Garbarino, and Hiesmayr, Phys. Lett. A 332 (2004) 355
the measurement is passive => cannot enforce locality;
non unitary evolution of the system because of decay.
Bell-CHSH inequalities refer to dichotomic measurements,
"Are you a B0 or a B0?" and "Are you a B0 or not ?" are two different
questions.
* Bramon, Escribano, and Garbarino, Journ. of Modern Optics 12 (2005) 1681
Published results are a "convincing proof of quantum entanglement" but "the test
is not a genuine Bell's inequality and thus cannot discriminate between QM and
local realistic approaches".
Proof : a local realistic model is considered which contains the information
(i. e. hidden variables) needed to "deterministically specifying ab ovo the
future decay times and decay modes of its two members".
(Only know implementation so far is a quite artificial model by E. Santos in
quant-ph/ ).
In addition to these arguments, let's consider what happen when we apply the proposed test to a simple model with locality ...
LAPP X-2007

20. Gisin&Go "Bell test" applied to a model with Spontaneous & immediate Disentanglement (SD)
SD: just after the decay into opposite flavor states, we considers an independent evolution for the B0 pair
non-QM !
Only Dt is known:
need to integrate
over t1+ t2 , for fixed
Dt values
LAPP X-2007

21. Gisin&Go "Bell test" applied to SD
~ experiment with
photons
SD prediction
S(Dt)
After integration over t1+ t2 ,
for fixed Dt, we can compute S: Dt
[ps]
=> We have found a local realistic model
which has a region with |S| 2 !
this implementation of the Bell-CHSH test does not work.
At which level is all this wrong ? Is E not appropriate ?
Is the analogy flavour oscillation  rotation of the polarization angle OK ?
LAPP X-2007

22. ... so, what can be tested ?
All this suggests to forget the Bell-CHSH test, and look for some more modest goal:
We decided to to check if specific local realistic models are compatible with our experimental results at Y(4S).
We didn't find too many local realistic models on the market (QM is difficult to imitate !)
one of them is our SD model, seen before,
the second is a model from Pompili and Selleri
LAPP X-2007

23. Spontaneous immediate Disentanglement (SD)
SD: just after the decay into opposite flavor states, we considers an independent evolution for the B0 pair
 QM
Only Dt is known:
need to integrate
over t1+ t2
LAPP X-2007

24. Local Realism by Pompili & Selleri (PS) (1/2)
F. Selleri, Phys. Rev. A 56 (1997) 3493
A. Pompili, and F. Selleri, Eur. Phys. J. C 14 (2000) 469
Local Realism, each B has "elements of reality” (hidden variables)
l1 : CP = +1 or -1
l2 : Flavour = +1 or indexed by i = 1, , , _
B0H, B0H, B0L, B0L
=> 4 basic states
* Mass states are stable in time, simultaneous anti-correlated
flavor jumps.
The model works with probabilities pij(t|0) = prob for a B to be
in the state j at proper time t=t, conditional of having been in state i at t=0.
* pij set to be consistent with single B0 evolution ~ exp{(G/2 + im)t}.
* PS build a model with a minimal amount of assumptions
They only determine upper and lower limits for combined
probabilities ...
LAPP X-2007

25. Local Realism by Pompili & Selleri 2/2
=> analytical expressions for A corresponding to the limits. The Amax is
 QM
Only Dt is known:
need to integrate
over tmin
PSmin
AQM>APS in the Dt region below ~5 ps
LAPP X-2007

26. Analysis goals and methods
We want to provide FULLY CORRECTED time-dependent
flavour asymmetry for the events
For this, we will
subtract all backgrounds
correct for events with wrong flavour associations
correct for the detector effects (resolution in Dt) by a deconvolution procedure
=> the result can then be directly compared to the models:
We will use our data to test
the Pompili and Selleri, and the Spontaneous Disentanglement models
against QM predictions
we will check for possible decoherence effects from New Physics
LAPP X-2007

27. The Belle Detector . 152 106 B0B0 pairs this study considers ~ 8 m
Silicon Vertex Detector SVD
resolution on Dz ~ 100 mm
Central Drift Chamber CDC
(Pt/Pt)2 = ( Pt)2 + (0.0030)2
K/ separation :
dE/dx in CDC dE/dx =6.9%
TOF TOF = 95ps
Aerogel Cerenkov ACC
Efficiency = ~90%,
Fake rate = ~6% 3.5GeV/c
, e : ECL (CsI crystals)
E/E ~ E=1GeV
e : efficiency > 90%
~0.3% fake for p > 1GeV/c
KL and  : KLM (RPC)
 : efficiency > 90%
<2% fake at p > 1GeV/c
The Belle Detector .
ACC
this study considers
B0B0 pairs
~ 8 m
LAPP X-2007

28. Event selection and tagging
* First B measured via
GeV/c2
M(D*)-M(D0)
Signal Sideband
* Remaining tracks are used to guess the flavour of second B, from the standard Belle flavour tagging procedure
Nevents/ps
From a total of B0B0 pairs:
OF and 1847 SF events after selection.
- Dz is obtained from track fit of the two vertices
and converted into a Dt value OF OF
Dt [ps] SF SF
LAPP X-2007

29. Background and wrong flavour tags
We correct bin by bin the OF and SF distributions for the following
sources of background:
- Fake D*
Uncorrelated D*-leptons, mainly D* from one B0 and the
lepton from the other
B  D** l v -
We also correct for
a ~1.5% fraction
of wrong flavour
associations - -
LAPP X-2007

30. Time-dependent asymmetry
We correct bin by bin the OF and SF distributions for
 Fake D* background
 Uncorrelated D*-leptons, mainly D* and leptons from different B0
 B  D** l v background
 ~1.5% fraction of wrong flavour associations
A(Dt) 1
0.5
after events selection
background subtracted
stat
syst
-0.5 -1
Dt [ps]
LAPP X-2007

31. Data deconvolution
Deconvolution is performed using response matrices for OF and SF distributions. The two 11x11 matrices are build from GEANT MC events. We use a procedure based on singular value decomposition, from H. Höcker and V. Kartvelishvili, NIM A 372, 469 (1996).
Toy MC of the 3 models (QM, PS and SD) have been used to study the method and to estimate the associated systematic error.
The result is given here:
Window Asymmetry
LAPP X-2007

32. Toy MC study of deconvolution
Toy MC with parametrized resolution in Dz
Simulate 400 “runs”, each consists of
~35000 “MC” events based on QM
~7000 “Data” events based on QM, LR or SD
Produce 2 unfolding matrices for SF and OF events from “MC”
Deconvolution performed on “Data” separately for SF and OF.
Correct for residual systematic effects.
A(unfolded)-A(generated)
LAPP X-2007

33. Before to compare with the models, a cross check with the B0 lifetime...
Add OF+SF distributions and fit for tB0
+ data
- fit
tB0 = 1.532±0.017(stat) ps
c2 = 3/11 bins
=> consistent with PDG value
LAPP X-2007

34. Sensitivity to Dm
Fitted Dm vs generated
LAPP X-2007

35. Comparison with QM
Least-square fits including a term taking the world-average Dmd into account. To avoid bias we discard BaBar and BELLE measurements, giving <Dmd> = ( ± ) ps-1
fitted value:
Dmd = (0.501±0.009) ps-1
c2 = 5.2 (11 dof)
QM (error from Dmd)
Data
=> Data fits QM
LAPP X-2007

36. Comparison with PS model
Fit data to PS model, using the closest boundary. We conservatively assign a null deviation when data falls between boundaries
fitted value:
Dmd=(0.447±0.010)ps-1
c2=31.3
PS (error from Dmd)
Data PS
=> Data favors QM over PS at the level of 5.1s
LAPP X-2007

37. Comparison with SD model
fitted value:
Dmd=(0.419±0.008)ps-1
c2=174
c2=74/11 bins LR
SD (error from Dmd)
Data
=> Data favors QM over
SD model by 13s.
LAPP X-2007

38. Search for New Physics: Decoherence
S. W. Hawking Commun. math. Phys., 87 (1982) 395
J. Ellis and J. S. Hagelin Nucl. Phys. B 241 (1984) 381
J. Ellis and J. L. Lopez, E. Navromatos, D.V. Nanopoulos Phys.Rev. D 53 (1984) 3846
R. A. Bertlmann: Lect. Notes. Phys. 689 (2006) 1
"Entanglement, Belle Inequalities, and Decoherence in Particle Physics"
. . .
Example: Decoherence can originate from the "interaction" with a foamy space-time => a modified Liouville equation describes the time evolution of the system state, represented by a density matrix r(t):
Simplest parametrization: D[r] = lD[r] with the decoherence parameter l
O(l) = m2/mPl (at the best) => time dependent decoherence
=> amplitude reduction of the time dependent asymmetry
A(Dt) ~ (1-z)AQM(Dt)
LAPP X-2007

39. Decoherence measurement at BELLE
Our setup does not permit time-dependent analysis.
In practice, we limit our decoherence studies to the two simplest
possibilities:
- the system can disentangle into the two mass eigenstates or
- into the two flavour eigenstates.
LAPP X-2007

40. Decoherence results zBB= 0.029 ± 0.057
1) Decoherence in BH, BL : A ~ (1 - zBHBL)AQM
zBHBL = ± (preliminary)
Measurements in K0 system:
CPLEAR zKLKS =
KLOE zKLKS = 0.018±0.040±0.007
2) Decoherence in B0, B0: A ~ (1 - zBB)AQM + zBBASD
zBB= ± 0.057
Measurements in K0 system:
From CPLEAR measurement, PLB 339 (1998) 422, Bertlmann et al. PRD 60 (1999) has deduced zKK = 0.4 ± 0.7
KLOE zKK = (0.10 ± 0.22 ± 0.04 ) 10-5
sic
LAPP X-2007

41. CONCLUSION
We have performed an experimental study of the EPR-type flavour entanglement in ¡ (4S)B0B0 decays. -
We have measured the time-dependent asymmetry due to flavour oscillation. The asymmetry has been corrected for the experimental effects and can be used directly to compare with the different theoretical models.
* The time dependent asymmetry is consistent with QM predictions, while the local realistic model of Pompili and Selleri is disfavoured at the level of 5.1s. A model with immediate disentanglement into flavour eigenstates is excluded by 13s.
This EPR state can be used for searches of New Physics, by the
measurement of the decoherence.
* The time dependent asymmetry measured by us is consistent with no decoherence.
LAPP X-2007

42. BACK UP
SLIDES
LAPP X-2007

43. Event selection Semileptonic B side:
All other tracks are used to identify the flavor of the accompanying B.
LAPP X-2007

44. After event selection: MC vs Data
Total of 6718 (OF)
and 1847 (SF) events selected
Data and MC (OF+SF)(Dt) distributions MC
LAPP X-2007

45. An example: background from fake D*
N/ps
from M(D*)-M(D0) sideband.
Cross-check and systematics from control sideband.
Check with MC truth.
Sideband
Control sideband
OF:126
SF:54
OF:128
SF:54
Dt [ps]
Dt [ps]
N/ps
MC truth
OF:126
SF:50
Control
sideband
Dt [ps]
[GeV/c2]
M(D*)-M(D0)
LAPP X-2007

46. Background: wrong D*lepton combination
Mainly due to lepton & D* coming from different B0.
Estimated by reversed lepton momentum
Systematics: moving the OF(SF) to +1(-1) s and calculate the asymmetry variation.
OF:78
SF:237
=78
=237
LAPP X-2007

47. Wrong D*lepton: consistency checks
Check: compare MC reversed lepton distributions with D*l not from same B (using MC truth info)
=> we get consistent
results.
The effect on the asymmetry is similar for MC and data.
MC reversed lepton
MC true
LAPP X-2007

48. Background: B±D** l n
B0D**- l +n (one p0 is lost) has flavor mixing => signal
B+D**0 l+ n (one p+ is lost) background
angle
fit cos(qB,D*l) distribution using MC shapes for D*ln and D**ln
Systematics:
7% error on the fit
20% error on the ratio of the fractions
of B0D**ln and B±D**ln
c2=1.21/dof (46 dof)
LAPP X-2007

49. Background: B± D**ln
OF:254
SF:1
=254 =1
LAPP X-2007

50. Wrong Flavor Use MC to estimate the wrong flavor
High purity events: w=0.015±0.006
Expect attenuation on the asymmetry:
A(Dt) = (1-2w) cos(DmDt)
= cos(DmDt)
=> ~3% attenuation
OF:22
SF:86
- data (+syst error) MC
~3% attenuation
LAPP X-2007

51. Cross check: Forward Test
Compare data with MC prediction for QM, LR and SD results
without unfolding.
Since our MC is generated with QM correlation, we re-weight each event to produce the prediction of PS and SD models.
Dm is fixed. The result favors QM
LAPP X-2007

52. Cross check: extra Dz resolution cut
Select events with better Dz resolution by adding a cut s(Vz) < 100 mm cut on both B decay vertices. This discards ~18% of the events.
+ with cut
+ without cut
=> results are consistent
LAPP X-2007

53. Sensitivity to decoherence (SD fraction)
Toy MC study of sensitivity to decoherence. Fit of
z from fit vs z generated
zfit
zfit z z
using corrected data using raw data
LAPP X-2007

54. First Bell-CHSH test S. J. Freedman and J. Clauser, PRL 28 (1972) 938
They use the entanglement of the polarization of two photons from a cascade
Needs to account for (very) low detection efficiency and analyzer precision.
Normalize by coincidence rates R1, R2, R0, with analyzer 2, 1, or both removed.
Then the "inequality" becomes:
Max violations occur at f = 22.5o (D(f)>0) and f = 67.5o (D(f)<-1)
The experiment gives: D(22.5o) = 0.104 D(67.5o) = 0.018
LAPP X-2007