Galaxy Clusters are considered to be efficient containers of cosmic rays (CRs). In their formation history, CRs are accelerated by active galactic nuclei (AGNs) and cosmological shocks and turbulence and accumulated in the intra-cluster space. Diffuse radio emission found in massive clusters is important to probe the magnetic field and cosmic ray electrons, while the content of cosmic ray protons is highly uncertain. The variety seen in the radio emission suggests that the CR acceleration is closely related to the formation processes such as cluster mergers and mass accretion. We study the CR acceleration in galaxy clusters by modeling the multi-wavelength emission in various clusters with different formation histories. We use the so-called merger tree method to simulate the merger history of clusters. We particularly focus on the re-acceleration by merger-induced turbulence, since it is considered to be the dominant mechanism of the diffuse radio emission. We find that the combination of radio surveys and the stacking analysis of neutrino background can constrain the parameters in the re-acceleration model for the radio halos in galaxy clusters.