This paper recalls the main achievements of the nTRV experiment which
measured two components of the transverse polarization
(\sigma_{T_{1}}σT1,
\sigma_{T_{2}}σT2)
of electrons emitted in the \betaβ-decay
of polarized, free neutrons and deduced two correlation coefficients,
RR
and NN,
that are sensitive to physics beyond the Standard Model. The value of
time-reversal odd coefficient RR,
0.004\pm±0.012\pm±0.005,
significantly improved limits on the relative strength of imaginary
scalar coupling constant in the weak interaction. The value obtained for
the time-reversal even correlation coefficient
NN,
0.067\pm±0.011\pm±0.004,
agrees with the Standard Model expectation, providing an important
sensitivity test of the electron polarimeter. One of the conclusions of
this pioneering experiment was that the transverse electron polarization
in the neutron \betaβ-decay
is worth more systematic exploring by measurements of yet experimentally
not attempted correlation coefficients such as
HH,
LL,
SS,
UU
and VV.
This article presents a brief outlook on that questions.