  Several recent spectrophotometric studies failed to detect significant global
magnetic fields in late-B HgMn chemically peculiar stars, but some
investigations have suggested the presence of strong unstructured or tangled
fields in these objects. We used detailed spectrum synthesis analysis to search
for evidence of tangled magnetic fields in high-quality observed spectra of 8
slowly rotating HgMn stars and one normal late-B star. We also evaluated recent
sporadic detections of weak longitudinal magnetic fields in HgMn stars based on
the moment technique. Our analysis of the Zeeman broadening of magnetically
sensitive spectral lines reveals no evidence of tangled magnetic fields in any
of the studied HgMn or normal stars. We infer upper limits of 200-700 G for the
mean magnetic field modulus -- much smaller than the field strengths implied by
studies based on differential magnetic line intensification and quadratic field
diagnostics. The new HARPSpol longitudinal field measurements for the extreme
HgMn star HD 65949 and the normal late-B star 21 Peg are consistent with zero
at a precision of 3-6 G. Re-analysis of our Stokes V spectra of the spotted
HgMn star HD 11753 shows that the recent moment technique measurements
retrieved from the same data are incompatible with the lack of circular
polarization signatures in the spectrum of this star. We conclude that there is
no evidence for substantial tangled magnetic fields on the surfaces of studied
HgMn stars. We cannot independently confirm the presence of very strong
quadratic or marginal longitudinal fields for these stars, so results from the
moment technique are likely to be spurious.
