EPR Entanglement and decoherence in B mesons Apollo

EPR Entanglement and decoherence in B mesons Apollo Go National Central University, Taiwan May 23, 2007 Apollo Go 1

Quantum Innovations QM forces us to modify our view on the reality of a physical system by new conceptual innovations: Superposition -- several possible outcomes exist ( or at least potentially) until the measurement. Probability -- reduction of wavefunction to a single outcome is purely by chance. Uncertainty Principle -- less precise knowledge of the physical system Wave-Particle duality -- How can an electron be both a particle (local) and a wave (non-local)? Entanglement -- Multi-particle wavefunction implies correlation even at a large distance. May 23, 2007 Apollo Go 2

Entanglement Peculiar two-particle QM system Two particles created in a singlet QM state are spatially separated yet belong to the same wavefunction: a single wavefunction Ya, b describes both particles a and b. ¯ Particle b Particle a ¯+¯ Source ¯+¯ |Ya, b ñ = (1/Ö 2) ( | ña |¯ñb + |¯ña | ñb ) QM: the outcome is not defined until measurement! Measurement on a will define the state of b instantaneously even without measuring it, first pointed out by Einstein, Podolski and Rosen (EPR). QUESTION: This seems to contradict Special Relativity! How can two separate particles knows about each other immediately? Does this violate locality? Or it was pre-determined by some factor, just we do not know? May 23, 2007 Apollo Go 3

Entanglement in Particle Physics A similar entangled system can be found in the decay of _ massive particle f(1020) ® K 0: The wavefunction (at t=0) has the same form as the two photon system. _ _ |Yñ = (1/Ö 2) ( |K 0ña |K 0ñb - |K 0ña |K 0ñb ) _ If one of them is measured to be K 0 Þ the other becomes K 0, However, they are NOT pre-determined. _ K 0 0 _ _ K 0 K 0 K K _ _ ¡ ¡ K 0 K 0 _ K 0 K 0 K 0 May 23, 2007 Apollo Go 4

Entanglement vs separability Entanglement: _ K 0 K _0 K 0 K 0 F _ K 0 K _0 K 0 K 0 _ K 0 F K 0 Pre-determined/separated: KL KS F F KL May 23, 2007 KS Apollo Go 5

EPR Test in Particle Physics I did such experiment at CPLEAR in 1996: - - 0 K 0 : pp®K - - |Yñ = (1/Ö 2) ( |K 0ña |K 0ñb - |K 0ña |K 0ñb ) Determine the strangeness/flavor of the two K 0 by their strong interaction products with two converters (K 0®K-, L; K 0®K+ ) • Same Flavor: K-L, LL • Opposite Flavor: K+L, K+ K- Copper, R~2 cm 0. 7 cm thick, 240° Carbon, R~7 cm 2. 5 cm thick, 120° Asymmetry: A(Dt) º IOF - ISF IOF + ISF -(g. L+gs)Dt/2 cos(Dm. Dt) 2 e = e-gs. Dt + e-g. LDt Physics Letters B 422 (1998) 339 -348 May 23, 2007 Apollo Go 6

Decoherence Instead of complete (100%) separation, one might have some fraction of the QM wavefunction undergo separation (decoherence). Bertlmann et. al. (PRD 60, 114032) made the fit to our CPLEAR data: extra parameter (1 -z) in the interference term. • Decoherence in KL_KS basis: +0. 16 z=0. 13 -0. 15 _ • Decoherence into K 0 K 0 basis: A=(1 -z)AQM z=0. 4± 0. 7 May 23, 2007 Apollo Go 7

Testing Decoherence in KLOE has done the same decoherence fit using f KLKS p+p-p+p • Decoherence in KLKS basis: z=0. 018± 0. 040 stat± 0. 007 syst • Decoherence into K 0 K 0 basis: z=(0. 10± 0. 21 stat± 0. 04 syst)10 -5 Phys. Lett. B 642(2006) 315 May 23, 2007 Apollo Go 8

¡(4 s) wavefunction - 0 has same entangled wavefunction: ¡(4 S)®B 0 B |Yñ = (1/Ö 2) ( |B 0ñ a -0 -0 |B ñb - |B ña |B 0ñb ) Single B 0 wavefunction: • Two eigenstates, just like K 0 • Can be written in 2 basis: - 0 : Flavor eigenstates (particle/anti-particle) B 0, B BL, BH : mass eigenstates (with small mass split: md= 0. 489*10 -12 hs-1 ) • Transform from one basis to the other: |BHñ = (1/Ö 2) ( |B 0ñ + |B 0ñ ) |B 0ñ = (1/Ö 2) ( |BHñ +|BLñ ) - 0ñ ) |BLñ = (1/Ö 2) ( |B 0ñ - |B |B-0ñ = (1/Ö 2) ( |BHñ - |BLñ ) • Unstable particle with a decay lifetime of 1/g=1. 542 ps: |BH (t)ñ = e-ia. Ht |BHñ Same decay with for BH and BL • Due to the BH, BL mass difference (Dmd), a B 0 can oscillate into B 0 and vice versa (flavor mixing). A B 0 at t=0 evolves as: |Y(t)ñ = (1/Ö 2) (e-ia. Ht |BH ñ + e-ia. Lt |BLñ ) Probability of finding B 0 at time t: P(B 0 (t) / B 0 (t=0)) =1/2 e-gt (1 - cos(Dmdt)) none-zero prob. for t>0! May 23, 2007 Apollo Go 9

Testing EPR entanglement in B mesons - 0: Look for particle/antiparticle correlation in ¡(4 S)®B 0 B 1. • 0 s by the charge of the decayed lepton: Identify the flavor of the two B _ -0 l+ B 0 l B First B 0: Fully reconstructed semileptonic decay _ B 0® D* l+n, _ (l+=e+, m+) Branching Ratio=4. 6% | ® D 0 p |®K+p_, K+p_p 0, K+p_p+p_ • Second B 0: only identify lepton to tag the flavor - 0® l-X where X is any (one or more) particles. Branching ratio=10. 5% B 2. Find decay time difference Dt: e- 3. ¡(4 S) Count and form: B 0 -0 B Dz @ bg Dt l- l+ D* - n e+ X N+-(Dt)+N-+(Dt)-N++(Dt)-N--(Dt) NOF(Dt)-NSF(Dt) N++(Dt)+N--(Dt)+N+-(Dt)+N-+(Dt) NOF(Dt)+NSF(Dt) A(Dt) = = In QM: (Dt) = cos(Dmd. Dt) May 23, 2007 Apollo Go 10

BELLE experiment Ingetral luminosity of 140 fb-1 (corresponding to 152*106 produced Bs) were used in this analysis. May 23, 2007 Apollo Go 11

QM vs. Spontaneous Disentanglement Two models can be tested against QM: _ 1. Spontaneous disentanglement (SD) into B 0 B 0 at t~0. Via the flavor asymmetry: ASD (average out t 1+t 2 ) May 23, 2007 Apollo Go 12

QM vs. Local Realism by PS 2. Local Realism model by Pompili & Selleri (PS): 4 definite _ _ particles at all times: B 0 H, B 0 L, B 0 H, B 0 L • Two hidden variables: l 1: CP=+1 or -1 l 2: Flavour=+1 or -1 • Mass states are stable in time • Simultaneous flavour jumps. • Individual B 0 follows QM time evolution QM Amax Amin This model gives two limits: Amax and Amin F. Selleri, Phys. Rev. A 56 (1997) 3493 A. Pompili and F. Selleri, Eur. Phys. J. C 14 (2000) 469 May 23, 2007 Apollo Go 13

Analysis Steps Total of 140 fb-1 (152 M) data were used. • • Event selection Background subtraction – – – • • • Wrong flavor tag correction Data deconvolution Checks of deconvolution – • Fake D* Uncorrelated D*l B+- D**ln B 0 lifetime. Comparison with models Decoherence test. Full Geant MC of about 5 times the data is used in background/wrong tag and data deconvolution. May 23, 2007 Apollo Go 14

Event selection Semileptonic B side: Once the B 0 is selected, all other tracks are used to identify the flavor of the accompanying B. Lepton tag only and r>0. 875 to obtain highest purity. May 23, 2007 Apollo Go 15

After event selection: MC vs Data Total of 6718 (OF) and 1847 (SF) events selected Consistence check: MC vs. data in Dt distribution for OF+SF (independent of QM entanglement assumption in MC) May 23, 2007 Apollo Go 16

Systematics We estimate the systematics after subtracting backgrounds (Fake D*, Uncorrelated D*l, charged B) and wrong flavor tag: May 23, 2007 Apollo Go 17

Cross Check: Forward Test At this stage, we compare data with MC prediction for QM, LR and SD results Since our MC is generated with QM correlation, we re-weight each event to produce the prediction of PS and SD models. The result favors QM and quite far from SD and PS models. In principle, we can stop here, the test it done! May 23, 2007 Apollo Go 18

Data Deconvolution To be able to compare results directly with different models, we need to correct for the detector resolution which damps the asymmetry, i. e. need to unfold data: use Singular Value Decomposition (SVD) response matrix constructed with MC events, with following notes: • • • MC imperfection: need to add extra (46± 40)um to the Dz resolution to reproduce data. SVD uses regularization/filtering to discard matrix elements with poor statistical significance. It also uses the MC shape as "a priori". can discard information and can introduce biases. MC with QM hypothesis were generated with a given Dm, B 0 lifetime. (Solution: mix OF and SF events, so that it is fair among the models) Toy MC of the 3 models (QM, LR and SD) were generated and used to study the method and to estimate systematics. May 23, 2007 Apollo Go 19

Deconvolution: Toy MC study • 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 A(unfolded)-A(generated) • Produce 2 unfolding matrices for SF and OF events from “MC” • Deconvolution performed on “Data” separately for SF and OF subsets. • Some residual systematics effects observed. Add correction and get systematic errors. May 23, 2007 Apollo Go 20

Cross Check: B 0 lifetime Add OF+SF and fit the lifetime of B 0: + data - fit value t=1. 532± 0. 017 ps c 2=3/11 bins May 23, 2007 Consistent with PDG value Apollo Go 21

Result: Comparison with QM We let Dmd float (but with the constraint Dmd=(0. 496± 0. 013)ps-1, from the best experimental value excluding entangled B pair measurements) and fit data to QM, we obtain: Dmd=(0. 501± 0. 009)ps-1 c 2=5 (for 11 bins) Data fits QM quite Well!! QM May 23, 2007 Apollo Go 22

Result: Comparison with SD model We let Dmd float (but with the constraint Dmd=(0. 496± 0. 013)ps-1) and fit data to SD model, we obtain: LR c 2=74/11 bins Dmd=(0. 419± 0. 008)ps-1 c 2=174 (for 11 bins) SD May 23, 2007 Apollo Go Hypothesis Test: Data favors QM over SD model by 13 s. Completely ruled out! 23

PS model vs. QM Fit data to PS model, using the closest boundary. We conservatively assign a null deviation when data falls between Amax and Amin LR c 2=74/11 bins SD PS (error from Dm) Data favors QM over PS model by 5. 1 s. Strongly ruled out! May 23, 2007 Apollo Go 24

Decoherence Check 0 One can construct a model where only a fraction (l) of the B _ pair disentangle into B 0, the asymmetry becomes: A=(1 -z)AQM+z. ASD Single parameter l fit gives: z=0. 029± 0. 057 Consistent with 0 (=> no decoherence) Previous estimate from CLEO and Argus data: z=-0. 06± 0. 10 (Bertlmann and Grimus: PRD 64 (2001) 056004) Similarly, one can fit decoherence in BHBLbasis: A=(1 -z)AQM May 23, 2007 z=0. 004± 0. 017 Apollo Go 25

Conclusion • EPR-type quantum entanglement has been observed both in K 0 and B 0 d mesons 1. K meson: PLB 422 (1998) 339 2. B meson: quant-ph/0702267 (submitted to PRL) • • B 0 system: Local Realism models can be tested: two specific models has been ruled out. Decoherence are measured in both systems, consistent with zero. May 23, 2007 Apollo Go 26

EPR Entanglement in Particle Physics At CPLEAR we can have the state: - - 0 K 0 : pp®K - - |Yñ = (1/Ö 2) ( |K 0ña |K 0ñb - |K 0ña |K 0ñb ) i. e. the strangeness of the neutral kaons are entangled, despite possible spacial separation. Similar to the spin ½ system of Bohm. Knowing the strangeness of the one K 0 will give us the information of the other K 0 at the same proper Asymmetry: A(Dt) º May 23, 2007 IOF - ISF IOF + ISF 2 e-(g. L+gs)Dt/2 cos(Dm. Dt) = e-gs. Dt + e-g. LDt Apollo Go 27

¡(4 S)®B 0 B 0 : |Yñ = (1/Ö 2) ( |B 0ña |B 0ñb - |B 0ña |B 0ñb ) is formally the same as the spin ½ system BUT… Differences compared to spin ½ system: – Instead of spin or polarization, the correlation is in the flavor (particleantiparticle quantum number), experiments are done by looking at the flavor specific interaction or decays. – Instead of rotating the polarizer, we look for flavor at different time Dt (similar to the spin rotation under magnetic field or birefringence in fibers), this is due to flavor mixing (B 0 «B 0). – Since B 0 are unstable particles, one need to deal with the loss of correlation due to decays (similar to PDL in fibers). More later. Gisin and I wrote a paper making detail comparisons between kaon and photon in fiber: Am. J. Phys. 69 (3), Mar. 2001, 264 -270 May 23, 2007 Apollo Go 28

Background: Fake D* • Due to fake D 0 and/or false ps It can be estimated from data using the sideband (0. 156 -0. 164 Ge. V/c 2) on the mass difference between D* and D 0 Control sideband • A control sidebands is used to estimate the systematics. • Consistency check: MC truth info on fake D 0 and/or fase ps. May 23, 2007 Apollo Go 29

Background: Wrong D*l combination Uncorrelated, random combinations of lepton & D*, mainly due to lepton & D* coming from different B 0. • To estimate and subtract it, reverse lepton momentum (l’) and select events which passes |Cos(q. B, D*l’ )|<1. 1 cut. • Systematics: moving the OF(SF) to +1(-1) s and calculate the asymmetry difference. May 23, 2007 Apollo Go 30

Background: B± D**ln Three types of events remain: • B 0 D*ln (signal) • B 0 D**ln (has flavor mixing, signal) • B± D**ln (background) To extract B± background: 2 parameter fit Ndata=(P 1*ND**+P 2*ND*) with ND**=NB 0 D**ln +NB± D**ln from MC. Systematics: • 6% error on the fit • ~20% error on the ratio BR(B 0 D**ln)/BR(B± D**ln) c 2=1. 21 May 23, 2007 Apollo Go 31

Wrong Flavor • Use MC to estimate the wrong flavor • High purity events: w=0. 015± 0. 001(stat) • Expect attenuation on the asymmetry: A(Dt)= (1 -2 w) cos(Dm. Dt)= 0. 970 cos(Dm. Dt) ~3% attenuation • Similar analysis for another Belle paper (PRD 71 072003 (2005)) gives w=0. 020± 0. 005 for r>0. 875 - data (+syst error) - MC • Systematics: • ± 1 sigma correction • extra ± 0. 010 to account for difference with sin(2 f 1) paper May 23, 2007 ~3% attenuation Apollo Go 32

Background Subtractions: 1. Fake D*: Due to fake D 0 and/or false ps. Estimated from data using the sideband (0. 156 -0. 164 Ge. V/c 2) on the mass difference between D* and D 0 2. Wrong D*l combination: Uncorrelated, random combinations of lepton & D*, mainly due to lepton & D* coming from different B 0. Reverse lepton momentum (l’) and select events which passes |Cos(q. B, D*l’ )|<1. 1 cut to estimate and subtract. 3. B± D**ln: May 23, 2007 Apollo Go 33

Testing Decoherence Strong believe in the community that the transition from QM to Classical world is not the size (microscopic vs. macroscopic) but the decoherence (loss of quantum correlation) In the correlated pair of B 0 s, decoherence can happen during the time evolution of the pair, before they decay… Decoherence can be introduced into the SF and OF intensities as a parameter 0£z£ 1: ISF µ e-g. Dt [1 - (1 - z(t))cos(Dm Dt)] IOF µ e-g. Dt [1+(1 - z(t))cos(Dm Dt)] z=0: no decoherence (i. e. QM) z=1: total decoherence (i. e. Separability) A(z, Dt=0)= (1 - z(t)) By measuring at different t (absolute decay time), A is constant if no decoherence, decreasing if there is decoherence. May 23, 2007 Apollo Go 34

Background: Fake D* sideband control sideband =128 OF: 128 =54 SF: 54 OF: 126 SF: 54 Sideband (+ syst) - MC truth =126 OF: 126 =50 SF: 50 May 23, 2007 Apollo Go 35

Background: B± D**ln OF: 254 =1 SF: 1 May 23, 2007 Apollo Go 36

2 nd Cross Check: extra Dz resolution cut Include extra s(Vz)<100 um cut on both B decay vertices improve Dz resolution but reduce ~18% number of events. Used to check for stability of deconvolution method. + with cut + without cut Consistent with no such cut: stability of our results May 23, 2007 Apollo Go 37

Experimental Tests: BELLE At KEK B collider at Tsukuba, Japan: CP violation in B 0 system May 23, 2007 Apollo Go 38

BELLE detector May 23, 2007 Apollo Go 39