  In this work, we analysed new LOw Frequency ARray observations of the mini
halo in the cluster RBS797, together with archival Very Large Array
observations and the recent Chandra results. This cluster is known to host a
powerful active galactic nucleus (AGN) at its centre, with two pairs of jets
propagating in orthogonal directions. Recent X-ray observations have detected
three pairs of shock fronts, connected with the activity of the central AGN.
Our aim is to investigate the connection between the mini halo emission and the
activity of the central source. We find that the diffuse radio emission is
elongated in different directions at 144 MHz (east-west) with respect to 1.4
GHz (north-south), tracing the orientation of the two pairs of jets. The mini
halo emission is characterised by an average spectral index $\alpha=-1.02\pm
0.05$. The spectral index profile of the mini halo shows a gradual flattening
from the centre to the periphery. Such a trend is unique among the mini halos
studied to date, and resembles the spectral index trend typical of particles
re-accelerated by shocks. However, the estimated contribution to the radio
brightness profile coming from shock re-acceleration is found to be
insufficient to account for the radial brightness profile of the mini halo. We
propose three scenarios that could explain the observed trend: (i) the
AGN-driven shocks are propagating onto an already existing mini halo,
re-energising the electrons. We estimate that the polarisation induced by the
shocks could be detected at 6 GHz and above; (ii) we could be witnessing
turbulent re-acceleration in a high magnetic field cluster; and (iii) the mini
halo could have a hadronic origin, in which the particles are injected by
Future observations in polarisation would be fundamental to understand the role
of shocks and the magnetic field.
