Bolotov et al. [14] have analyzed radiative pion decays
in flight (
events) in a
wider kinematical region than was explored in the
high-statistics experiment
of Bay et al. [15] (where 
events had been observed).
The theoretical branching ratio, calculated with the standard V-A coupling,
differs from the measured one by more than three standard deviations.
This discrepancy may be avoided by adding to the standard matrix element the
amplitude of a tensorial interaction [16].
Belyaev and Kogan [17] and Voloshin [18] have pointed
out, however, that in the standard model the induced
tensor coupling is too small to generate the rate observed in
ref. [14].
Gabrielli [19] has worked out the effect of tensor
couplings for 
decays. Using the above
quoted
values for the form factors A and V and a tensor coupling of a size
suggested to explain the data in Ref.
[14], he finds a 
effect
in the partial decay rates (the exact size depends on the chosen coupling,
channel, decay region,...). The author then suggests that these effects may be
accessible to detection at high precision experiments carried out at
DA
NE.
We wish to point out that this may be difficult for the
following reason. The calculation of the decays 
presented in this section is based on the one-loop formulae for the decay
matrix elements.
Higher-order effects may well be sizeable, see e.g.
figure 1.3.
There, it is explicitly seen that the effect of resonance exchange is
in particular regions of phase space. Therefore, in order to
identify effects due to tensor couplings, one first has to pin down
the contribution from higher-order effects in CHPT. This is not
an easy task to achieve to the accuracy required. On the other hand, it is of
course needless to say that the finding of a tensorial coupling of the size
suggested in Ref. [16] would be spectacular.