  Gravitational lensing has long been considered as a valuable tool to
determine the total mass of galaxy clusters. The shear profile as inferred from
the statistics of ellipticity of background galaxies allows to probe the
cluster intermediate and outer regions thus determining the virial mass
estimate. However, the mass sheet degeneracy and the need for a large number of
background galaxies motivate the search for alternative tracers which can break
the degeneracy among model parameters and hence improve the accuracy of the
mass estimate. Lensing flexion, i.e. the third derivative of the lensing
potential, has been suggested as a good answer to the above quest since it
probes the details of the mass profile. We investigate here whether this is
indeed the case considering jointly using weak lensing, magnification and
flexion. We use a Fisher matrix analysis to forecast the relative improvement
in the mass accuracy for different assumptions on the shear and flexion signal
- to - noise (S/N) ratio also varying the cluster mass, redshift, and
ellipticity. It turns out that the error on the cluster mass may be reduced up
to a factor 2 for reasonable values of the flexion S/N ratio. As a general
result, we get that the improvement in mass accuracy is larger for more
flattened haloes, but extracting general trends is a difficult because of the
many parameters at play. We nevertheless find that flexion is as efficient as
magnification to increase the accuracy in both mass and concentration
determination.
