A local hidden variables model for the measured EPR-type flavour entanglement in upsilon(4S.pdf

arXiv:quant-ph/0703206v1 22 Mar 2007
gemn ihteqatmoe o h eeteprmn by experiment recent the for ones (2007) quant-ph/0702267 quantum the with agreement
Abstract
esrdERtp aoretnlmn in entanglement flavour EPR-type measured
oa idnvralsmdli xiie hc ie pred gives which exhibited is model variables hidden local A
oa idnvralsmdlfrthe for model variables hidden local A
Y
(4
S
)
mloSantos Emilio
→
B
1
0
B
0
decays
ac,1,2007 15, March,
oe al., et Go
cin in ictions
The aim of this note is to show that the results of the recent experiment
measuring EPR-type flavour entanglement in Y (4S) → B0B0 decays1 are
compatible with local realism. It is known that a Bell inequality test cannot
be performed2 but this does not prove that the experiment patible
with local realism. I shall prove patibility by exhibiting a local hidden
variables (LHV) model which reproduces the quantum prediction (and agrees
with the obtained results within experimental errors). The time-dependent
rate for decay into two flavour-specific states are1
1 i
Ri (△t) = exp(−△t/τ) 1 + (−1) cos (△m△t) , △t = |t2 − t1| , (1)
4τ 
where △m is the mass difference between the two B0 − B0 mass eigenstates,
i = 1 corresponds to the decays B0B0 or B0B0 and i = 2 to the decays B0B0
0 0
or B B . Actually Ri are the probability densities of decay at time t2 of
the second particle (say