Nils A. Törnqvist University of Helsinki
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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?
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p
In c.m.s. of
Thep decay works as a spin analyser!
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Resonance decay into
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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.
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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
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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
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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:
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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
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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
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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.
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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
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Up til now only one experiment by the DM2 collaboration:
M. H. Tixier et al. Physics Letters B212 (1988) 523
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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
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