¡ (4S)B0B0 decays Measurement of EPR-type flavour entanglement in _ PRL 99 (2007) 131802 Measurement of EPR-type flavour entanglement in ¡ (4S)B0B0 decays _ Bay Ecole Polytechnique Fédérale de Lausanne Séminaire 19 X 2007 LAPP X-2007

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

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

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

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

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

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

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

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

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

K0 and B0 m~0.5 GeV/c2 m~5 GeV/c2 ~ ~ ~ e is the CP violating parameter ~10-3 lifetime K0Short t = 0.9 10-10 s K0Long t = 5.2 10-8 s ~identical lifetimes t = 1.5 10-12 s ct ~ 500 mm flavour oscillation parameter: quite fast oscillation: ~ 0.005 1/ps ~ 0.5 1/ps LAPP X-2007

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

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

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

Production of flavour entangled states (2/2) From Y(4S) is a resonance JCP = 1- - . 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

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

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

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

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/0703206). 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

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

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

... 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

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

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 -1 indexed by i = 1, 2, 3, 4 _ 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

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

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

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 = (0.0019 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 ~ 1.8% @ 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 152 106 B0B0 pairs ~ 8 m LAPP X-2007

Event selection and tagging * First B measured via 0.14 0.15 0.16 0.17 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 152 106 B0B0 pairs: - 6718 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 0 5 10 15 20 LAPP X-2007

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

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] 0 2 4 6 8 10 12 14 16 18 20 LAPP X-2007

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

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

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

Sensitivity to Dm Fitted Dm vs generated LAPP X-2007

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> = ( 0.496 ± 0.013 ) 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

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

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

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

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

Decoherence results zBB= 0.029 ± 0.057 1) Decoherence in BH, BL : A ~ (1 - zBHBL)AQM zBHBL = 0.004 ± 0.017 (preliminary) Measurements in K0 system: CPLEAR zKLKS = 0.13+0.16-0.15 KLOE zKLKS = 0.018±0.040±0.007 2) Decoherence in B0, B0: A ~ (1 - zBB)AQM + zBBASD zBB= 0.029 ± 0.057 Measurements in K0 system: From CPLEAR measurement, PLB 339 (1998) 422, Bertlmann et al. PRD 60 (1999) 114032 has deduced zKK = 0.4 ± 0.7 KLOE zKK = (0.10 ± 0.22 ± 0.04 ) 10-5 sic LAPP X-2007

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

BACK UP SLIDES LAPP X-2007

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

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

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

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

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

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

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

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) = 0.970 cos(DmDt) => ~3% attenuation OF:22 SF:86 - data (+syst error) MC ~3% attenuation LAPP X-2007

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

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

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

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0.026 D(67.5o) = -1.0970.018 LAPP X-2007