  In this paper, we investigate the effects of helical primordial magnetic
fields (PMFs) on the cosmic microwave background (CMB) reduced bispectrum. We
derive the full three-point statistics of helical magnetic fields and
numerically calculate the even contribution in the collinear configuration. We
then numerically compute the CMB reduced bispectrum induced by passive and
compensated PMF modes on large angular scales. There is a negative signal on
the bispectrum due to the helical terms of the fields and we also observe that
the biggest contribution to the bispectrum comes from the non-zero IR cut-off
for causal fields, unlike the two-point correlation case. For negative spectral
indices, the reduced bispectrum is enhanced by the passive modes. This gives a
lower value of the upper limit for the mean amplitude of the magnetic field on
a given characteristic scale. However, high values of IR cut-off in the
bispectrum, and the helical terms of the magnetic field relaxes this bound.
This demonstrates the importance of the IR cut-off and helicity in the study of
the nature of PMFs from CMB observations.
