Determination of S- and P-wave helicity amplitudes and non-unitary evolution of pion creation process pi(-)p -> pi(-)pi(+)n on polarized target

TL;DR

This paper provides a model-independent analysis of pion production amplitudes revealing non-unitary evolution and phase relations, offering new insights into quantum environment interactions in particle processes.

Contribution

It introduces an analytical solution for helicity amplitudes and phase relations, enabling a novel test of Kraus representation in pion creation processes.

Findings

Only the omega_ij=pi solution yields physical helicity amplitudes.

S- and P-wave amplitudes are consistent with rho^0(770)-f_0(980) mixing.

Probabilities p_ij can be measured via recoil hyperon polarization.

Abstract

We present the first model independent determination of S- and P-wave helicity amplitudes from CERN measurements of pi(-)p -> pi(-)pi(+)n on polarized target at small t and dipion masses 580-1080 MeV. The purely analytical determination of the helicity amplitudes is made possible by our finding analytical solution for relative phase omega_ij between S-wave amplitudes S_d and S_u of opposite transversity for each set of solutions for transversity amplitudes A_u(i), A_d(j),i,j=1,2. Of the six possible solutions for omega_ij only the solution with omega_ij=pi yields physical helicity amplitudes. Assigning rho^0(770) phase to the dominant P-wave helicity flip amplitude L_1(ij) necessitates a phase of the S-wave helicity flip amplitude S_1(ij) that is near to the rho^0(770) phase.These two amplitudes are consistent with rho^0(770)-f_0(980) mixing. The relative phases omega_ij=pi satisfy certain selfconsistency relation that must be satisfied in order for the four sets of solutions A_u(i),A_d(j),i,j=1,2 to be all physical solutions that can be identified with coevolution amplitudes describing the interaction of the pion creation process with a quantum environment. This test on phases omega_ij provides a new test of Kraus representation of the mixed final state density matrix. We show that the probabilities p_ij determining the final state rho_f in terms of solution states rho_f(ij) can be determined in measurements of recoil hyperon polarization in pi(-)p->pi(-)K(+)Lambda0 on polarized target.