Radio halos and relics are Mpc-scale diffuse radio sources in galaxy clusters, with a steep spectral index $alpha>1$ ($Spropto u^{-alpha}$). It has been proposed that they arise from particle acceleration induced by turbulence and weak shocks, injected in the intracluster medium (ICM) during mergers. MACS J1149.5+2223 (MACS J1149) is a high redshift ($z=0.544$) galaxy cluster possibly hosting a radio halo and a relic. We analysed LOFAR, GMRT, and JVLA radio data at 144, 323, 1500 MHz, and Chandra X-ray data to characterise the thermal and non-thermal properties of the cluster. We obtained radio images at different frequencies to investigate the spectral properties of the radio halo. We used Chandra X-ray images to constrain the thermal properties of the cluster. We measured a steep spectrum of the halo, with $alpha=1.49pm 0.12$ between 144 and 1500 MHz. The radio surface brightness distribution across the halo is found to correlate with the X-ray brightness of the ICM, with a sub-linear slope in the range 0.4 to 0.6. We also report two possible cold fronts in north-east and north-west, but deeper X-ray observations are required to firmly constrain the properties of the upstream emission. We show that the combination of high redshift, steep radio spectrum, and sub-linear radio-X scaling of the halo rules out hadronic models. An old ($sim 1 $ Gyr ago) major merger likely induced the formation of the halo through stochastic re-acceleration of relativistic electrons. We suggest that the two possible X-ray discontinuities may actually be part of the same cold front. In this case, the coolest gas pushed towards the north-west might be associated with the cool core of a sub-cluster involved in the major merger. The peculiar orientation of the south-east relic might indicate a different nature of this source and requires further investigation.
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