We present the first amplitude analysis of the CERN data on \pi ^ { - } p \to \pi ^ { - } \pi ^ { + } n on polarized target at 17.2 GeV/c for dipion masses 580-1080 MeV at low momentum transfers using the spin mixing mechanism .
The analysis of the S - and P -wave subsystem determines a unique solution for the spin mixing transversity amplitudes S _ { \tau } ,L _ { \tau } , the corresponding S -matrix amplitudes S ^ { 0 } _ { \tau } ,L ^ { 0 } _ { \tau } and the \rho ^ { 0 } ( 770 ) - f _ { 0 } ( 980 ) spin mixing parameters .
The spin mixing mechanism allows to extract D -wave observables from the CERN data .
Analysis of the full D -wave subsystem for transversity \tau = u reveals \rho ^ { 0 } ( 770 ) mixing in the amplitudes |D ^ { U } _ { u } | ^ { 2 } and |D ^ { N } _ { u } | ^ { 2 } and a violation of cosine conditions by the amplitudes D ^ { 2 U } _ { u } and D ^ { 2 N } _ { u } .
We determine spin mixing and S -matrix helicity amplitudes from which we calculate \pi \pi phase-shifts \delta ^ { 0 } _ { S } and \delta _ { P } below K \bar { K } threshold .
For spin mixing amplitudes the two Solutions for \delta ^ { 0 } _ { S } pass through 90 ^ { \circ } near \rho ^ { 0 } ( 770 ) mass .
There is no evidence for \rho ^ { 0 } ( 770 ) - f _ { 0 } ( 980 ) mixing in the two Solutions for \delta ^ { 0 } _ { S } for the S -matrix amplitudes .
The near equality of these Solutions suggests that a unique Solution for \delta ^ { 0 } _ { S } is attainable in phase-shift analysis of polarized target data .

The spin mixing and the violation of the cosine conditions arise from a non-standard pure dephasing interaction of the produced final S -matrix state \rho _ { f } ( S ) with a quantum state \rho ( E ) of a quantum environment to produce the observed state \rho _ { f } ( O ) .
Our analysis determines that the number of interacting degrees of freedom of the environment is M = 4 .
We identify the four eigenstates |e _ { k } > that define the density matrices \rho ( E ) with the four neutrino mass eigenstes |m _ { k } > with |m _ { 4 } > due to light sterile neutrino .
We call the mixed quantum states \rho ( E ) dark neutrinos and propose to identify them with particles of a distinct component of dark matter .
In the early Universe active neutrinos were converted in dephasing interactions into hot dark neutrinos which were redshifted by cosmic expansion to form the cold dark neutrinos of the quantum environment today .
Dark neutrinos can contribute to the structure formation and evolution because their free streaming length \lambda _ { fs } ( z ) is shortened by a large number of effective degrees of freedom identified with their entropy states .
With an estimated present \lambda _ { fs } ( 0 ) \sim 5 pc or \sim 5 mpc they can contribute to cool or cold dark matter or even to both .
Dephasing interactions involving thermal dark neutrinos and active neutrinos background are not rare events but they require high statistics accelerator experiments with polarized targets for their detection .
The presented amplitude analysis illustrates this new kind of search for dark matter .