  Context. It is well-established that shock waves in the intracluster medium
launched by galaxy cluster mergers can produce synchrotron emission, which is
visible to us at radio frequencies as radio relics. However, the particle
acceleration mechanism producing these relics is still not fully understood. It
is also unclear how relics relate to radio halos, which trace merger-induced
turbulence in the intracluster medium. Aims. We aim to perform the first
statistical analysis of radio relics in a mass-selected sample of galaxy
clusters, using homogeneous observations. Methods. We analysed all relics
observed by the Low Frequency Array Two Metre Sky Survey Data Release 2 (LoTSS
DR2) at 144 MHz, hosted by galaxy clusters in the second Planck catalogue of SZ
sources (PSZ2). We measured and compared the relic properties in a uniform,
unbiased way. In particular, we developed a method to describe the
characteristic downstream width in a statistical manner. Additionally, we
searched for differences between radio relic-hosting clusters with and without
radio halos. Results. We find that, in our sample, $\sim$ 10% of galaxy
clusters host at least one radio relic. We confirm previous findings, at higher
frequencies, of a correlation between the relic-cluster centre distance and the
longest linear size, as well as the radio relic power and cluster mass.
However, our findings suggest that we are still missing a population of
low-power relics. We also find that relics are wider than theoretically
expected, even with optimistic downstream conditions. Finally, we do not find
evidence of a single property that separates relic-hosting clusters with and
without radio halos.
