  Within the Standard Model, the weak interaction of quarks and leptons is
characterized by certain symmetry properties, such as maximal breaking of
parity and favored helicity. These are related to the $V-A$ structure of the
weak interaction. These characteristics were discovered by studying
correlations in the directions of the outgoing leptons in nuclear beta decays.
These days, correlation measurements in nuclear beta decays are intensively
studied to probe for signatures for deviations from these symmetries, which are
an indication of Beyond Standard Model physics. We show that the structure of
the energy spectrum of emitted electrons in unique first-forbidden
$\beta$-decays is sensitive to the symmetries of the weak interaction, and thus
can be used as a novel probe of physics beyond the standard model. Furthermore,
the energy spectrum gives constraints both in the case of right and left
coupling of the new symmetry currents. We show that a measurement with modest
energy resolution of about 20 keV is expected to lead to new constraints on
beyond the standard model interactions with tensor symmetry.
