Study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>N</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>π</mml:mi><mml:mi>π</mml:mi><mml:mi>N</mml:mi></mml:math>processes on polarized targets: Quantum environment and its dephasing interaction with particle scattering

Unitary evolution law describes isolated particle scattering processes in an empty Minkowski spacetime. We put forward a hypothesis that the physical Universe includes a quantum environment that interacts with some particle scattering and decay processes. While the scattering process is governed by the $S$-matrix dynamics and its conservation laws and unitarity, the interaction with the environment evolves the produced final state ${\ensuremath{\rho}}_{f}(S)$ to the observed state ${\ensuremath{\rho}}_{f}(O)$. To be consistent with the Standard Model this new interaction must be a pure dephasing interaction. Governed by a nonunitary evolution law, it modifies the phases of the $S$-matrix amplitudes and can give rise to mixing of such amplitudes to form observed amplitudes. We present the first test of unitary evolution law in particle scattering. Conservation of $P$-parity in strong interactions imposes constraints on partial wave helicity and nucleon transversity amplitudes in $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$ processes. An independent set of constraints on these amplitudes is imposed by the $S$-matrix unitary evolution law. The unitary evolution evolves pure initial states into pure final states leading to 9 independent constraints on 16 components of angular intensities in $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$ processes. When expressed in terms of parity conserving transversity amplitudes, all 9 constraints are identities provided a single constraint on the transversity amplitudes holds true. The constraint implies that relative phases between transversity amplitudes of the same naturality and transversity must be 0 or $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$. Assuming a self-consistent set of these unitary phases we use the CERN data on spin observables ${R}_{u}^{0}$ and ${R}_{y}^{0}$ to determine a unique solution for the $S$- and $P$-wave moduli below 1080 MeV. The data require ${\ensuremath{\rho}}^{0}(770)\ensuremath{-}{f}_{0}(980)$ mixing in the $S$-wave but this unitary solution is excluded by data on observables ${R}_{x}^{0}$ within at least 5 standard deviations. All previous amplitude analyses of $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$ processes found nonunitary relative phases in an apparent violation of the unitary evolution law. The contrast between the predicted unitary relative phases and the observed nonunitary phases presents unambiguous evidence for the nonunitary evolution of the produced final state and supports the hypothesis of the existence of a quantum environment and its pure dephasing interaction with particle scattering processes.

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