  The $\beta$ Cephei pulsators are massive main-sequence stars, presenting low
radial-order modes. These modes probe in particular the chemical gradient at
the edge of the convective core. They hence give constraints on macroscopic
processes, such as hydrodynamic or magnetic instabilities. Yet, it is not clear
to what extent the seismic inferences depend on the physics employed for the
stellar modelling or on the observational dataset. We investigate the
observational constraints which are necessary to provide accurate constraints
on the mixing processes in $\beta$ Cephei stars. We explore the importance of
the identification of the angular degree of modes. Depending on the quality of
the seismic dataset and the classical constraints, we estimate the precision
achievable with asteroseismology. We propose a method extending the forward
approach classically used to model $\beta$ Cephei stars The probability
distributions of the asteroseismic-derived stellar parameters are obtained.
With these distributions, we provide a systemic way to estimate the errors of
the modelling. A particular effort is made to also include the theoretical
uncertainties of the models. We then estimate the accuracy and precision of
asteroseismology for $\beta$ Cephei stars in a series of hare and hound
exercises. The exercises show that a set of four to five oscillation
frequencies with an identified angular degree already leads to accurate
inferences on the stellar parameters. Without the identification of the modes,
the addition of other classical observational constraints allow to succeed the
seismic modelling. When the micro-physics of the star and stellar models used
for the modelling differ, the constraints derived on the internal structure
remain valid if expressed in terms of acoustic variables. The characterisation
of the mixing processes at the boundary of the convective core remain
model-dependent.
