nils a. törnqvist university of helsinki

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

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Nils A. Törnqvist University of Helsinki

Talk at Frascati, January 2006

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

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e

e

p

p10000 events at Daphne2?

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

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p

In c.m.s. of

Thep decay works as a spin analyser!

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

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Resonance decay into

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

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In words this means that ’s coming from a singlet anti- state are polarized just like ’s prepared to be polarized in a tagged direction given by the direction of the in the anti-decay.

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

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This is a demonstration of the conceptual peculiarities involved in the EPR problem: Knowledge of how one of the decayed, or will decay (time ordering is not relevant here) tells an observer that the second decayed, or will decay, as if it had a definite polarization.

p

In cms

+

p

In cms

c

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

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

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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 0spin 1/2 spin 1/2

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

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

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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,

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

Or equivalently:

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

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

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Spin 1 decay to

helicity =+1, transverse polarization

helicity = -1, transverse polarization

helicitylongitudinal polarization

Only thecase is interesting (entangled) from the point of view of EPR correlations

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

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i.e. it factorizes and one has no interesting EPR corellations

On the other hand for =0 or longitudinal polarization one has

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

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Thus ine+e- to

one should look for situations where the initial photon is longitudinally polarized with respect to the 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

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

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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

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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

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

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

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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

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