Both components of the transverse electron polarization emitted in the beta decay of polarized, free neutron have been measured at cold neutron spallation source SINQ (PSI, Villigen) in a search for a new source of T- or (via CPT theorem equivalent) CP- symmetry violation.
The T-odd, P-odd correlation coefficient associated with polarization
component perpendicular to the neutron polarization and
electron momentum, was found to be R= 0.008+/-0.015.
This value is consistent with time reversal invariance, and significantly
improves limits on the relative strength of imaginary scalar couplings in the weak interaction.
The value obtained for the T-even correlation coefficient connected with the second polarization component, N=$ 0.056$\pm$0.011$, agrees with
the Standard Model expectation, providing an important sensitivity test
of the experimental setup.
This is the first determination of the R correlation coefficient in neutron decay and first determination of the coefficient N in nuclear decay.

Presented will be perspectives for significant improvement (almost by a factor of two) of the achieved accuracy of the correlation coefficient, resulting from the analysis of a new class of events and the application of a new method of the analysis which, taking advantage from the symmetry of the detector, decouples the determination of R and N coefficients.