Nils A. Törnqvist University of Helsinki Talk at Frascati, January 2006 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist + L e - e L + p 10000 events at Daphne2? p Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist In c.m.s. of L The L-> pp decay works as a spin analyser! Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Resonance decay into Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist 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. Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist 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 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist 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 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist 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 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist 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 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist = i.e. it factorizes and one has no interesting EPR corellations On the other hand for l=0 or longitudinal polarization one has Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Thus in e+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. Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist A more general formula for the correlations: Uninteresting factorized piece Interesting EPR correlations at 2.5 GeV k /E = 0.46 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Up til now only one experiment by the DM2 collaboration: M. H. Tixier et al. Physics Letters B212 (1988) 523 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist 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 Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist

EPR Lambda anti-Lambda N.A. Törnqvist Frascati. 19-20 January 2006 EPR Lambda anti-Lambda N.A. Törnqvist