Nils A. Törnqvist University of Helsinki

1. Nils A. Törnqvist University of Helsinki Talk at Frascati, January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

2. - p p + L e - e L + p 10000 events at Daphne2? p EPR Lambda anti-Lambda N.A. Törnqvist

3. q p L p In c.m.s. of L The L-> pp decay works as a spin analyser! EPR Lambda anti-Lambda N.A. Törnqvist

4. Resonance decay into EPR Lambda anti-Lambda N.A. Törnqvist

5. In words this means that L’s coming from a singlet L anti-L state are polarized just like L’s prepared to be polarized in a tagged direction given by the direction of the p in the anti-L decay. EPR Lambda anti-Lambda N.A. Törnqvist

6. This is a demonstration of the conceptual peculiarities involved in the EPR problem: Knowledge of how one of the L decayed, or will decay (time ordering is not relevant here) tells an observer that the second L decayed, or will decay, as if it had a definite polarization. p + p L L h c p p In L cms In L cms EPR Lambda anti-Lambda N.A. Törnqvist

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8. Bell’s inequalities The violation of Bell’s inequalities by quantum mechanics has been historically of great importance in removing any doubt that a local theory, in the EPR sense, is incompatible with quantum mechanics. These inequalities are usually written in terms of correlations, such that for the case of a spin 0 state decaying into two spin ½ particles the spin corellation function E obeys the inequality Here denote unit vectors along which the spin components are measured in the classic Bohm variant of the EPR spin 0 decay to two spin ½ particles. spin 0 spin 1/2 spin 1/2 EPR Lambda anti-Lambda N.A. Törnqvist

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10. However quantum mechanics deals with relations between amplitudes, and the amplitudes related to the cross sections in these inequalities form a triangle in the complex plane. Thus QM implies triangle inequalities for the square roots of the cross sections, Or equivalently: and not for the cross sections as in the Bell inequalities. It is instructive to plot the domains separated by these inequalities in a barycentric coordinate system (Figure 4) in which ine plots the normalized ratios EPR Lambda anti-Lambda N.A. Törnqvist

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12. Spin 1 decay to helicity l=+1, transverse polarization helicity l= -1, transverse polarization ( ) + helicity l= 0, longitudinal polarization Only the l=0 case is interesting (entangled) from the point of view of EPR correlations EPR Lambda anti-Lambda N.A. Törnqvist

13. = i.e. it factorizes and one has no interesting EPR corellations On the other hand for l=0 or longitudinal polarization one has EPR Lambda anti-Lambda N.A. Törnqvist

14. Thus ine+e- to one should look for situations where the initial photon is longitudinally polarized with respect to the LL axis. This means not in the forward direction, but near 90 degrees in the center of mass. EPR Lambda anti-Lambda N.A. Törnqvist

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16. A more general formula for the correlations: Uninteresting factorized piece Interesting EPR correlations at 2.5 GeV k /E = 0.46 EPR Lambda anti-Lambda N.A. Törnqvist

17. Up til now only one experiment by the DM2 collaboration: M. H. Tixier et al. Physics Letters B212 (1988) 523 EPR Lambda anti-Lambda N.A. Törnqvist

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20. Concluding remarks EPR correlations can be tested at in e+e- -> It would be a test involving weak interactions Strongest effects with lambda pair at near 90 degrees and highest possible cms energy EPR Lambda anti-Lambda N.A. Törnqvist

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