  In this work, we investigated the interplay between the X-ray and radio
emission of the cluster PSZ2G113.91-37.01 (z = 0.371) using the high-quality
XMM-Newton observations of the CHEX-MATE project, and the images of the
LoTSS-DR2. The cluster is undergoing a merger along the north-south axis, and
shows a central radio halo and two radio relics, one in the southern and one in
the northern regions. The analysis of the intracluster medium distribution
revealed the presence of a northern surface brightness jump associated to the
merger event. By extracting spectra across this discontinuity, we classified
the edge as a cold front. Furthermore, we made use of upgraded Giant Metrewave
Radio Telescope observations that allowed us to perform a spectral analysis of
the G113 radio emission. We found evidence of re-acceleration of particles in
the northern relic, and we measured an associated Mach number of M = 1.95 $\pm$
0.01, as inferred from radio observations. We then performed a point-to-point
analysis of the X-ray and radio emission both in the halo and in the northern
relic regions. We found a strong correlation for the halo and an
anti-correlation for the relic. The former behaviour is in agreement with
previous studies. The relic anti-correlation is likely related to the reverse
radial distribution of the X-ray (increasing towards the cluster centre) and
radio (decreasing towards the cluster centre) emissions. Finally, we performed
a point-to-point analysis of the radio emission and the residuals obtained by
subtracting a double beta model to the X-ray emission. We found a strong
correlation between the two quantities. This behaviour suggests the presence of
a connection between the process responsible for the radio emission and the one
that leaves fluctuations in the X-ray observations.
