The time for a DNA sequence to find its homologous counterpart depends on a long random search inside the cell nucleus. Using polymer models, we compute here the mean first encounter time (MFET) between two sites located on two different polymer chains and confined locally by potential wells. We find that reducing tethering forces acting on the polymers results in local decondensation, and numerical simulations of the polymer model show that these changes are associated with a reduction of the MFET by several orders of magnitude. We derive here new asymptotic formula for the MFET, confirmed by Brownian simulations. We conclude from the present modeling approach that the fast search for homology is mediated by a local chromatin decondensation due to the release of multiple chromatin tethering forces. The present scenario could explain how the homologous recombination pathway for double-stranded DNA repair is controlled by its random search step. DOI: 10.1103/PhysRevE.97.032417 Repairing DNA double-strand breaks (DSBs) is a key step for cell survival. However, the underlying physical mechanism remains difficult to describe, mostly because it involves multiple molecular steps involving small (nanometer) and large (micrometer) scales. During the homologous recombination (HR) pathway, broken strands perform inside a large portion of the cell nucleus a random search for a homologous DNA template. Once this template is found, it will be used to copy the missing base pairs before repair [1]. As revealed by single-particle trajectories of chromatin [2,3], following a DSB, the broken locus dynamics is modified so that it can scan a larger area of the nucleus. This modification was attributed in part to chromatin decondensation and the release of tethering forces acting locally on the chromatin [4]. These changes could have consequences on the search for a homologous template. We present here polymer modeling and analytical tools to further characterize this search step.We recall that search processes involving two loci located on the same polymers have been investigated in the context of polymer looping [5][6][7][8]. However, much less is known about the mean time for two monomers belonging to two different polymers. The multiple relaxation times associated with the polymer dynamics [9] shows that computing the looping time cannot be obtained by the classical activation escape from a potential well (representing the end-to-end distance energy) [10]. For a long polymer, the mean encounter time is influenced by the slowest internal relaxation times of the polymer [9]. However, it is not clear how these times contribute to the mean encounter time for two monomers located on two different polymers. In addition, in a confined environment, the probability distribution function of monomers varies along the polymer chain [11,12], which again can influence the search time.To account for chromatin reorganization following DSB [4], we study here the random search of two monomers that belongs to two different monomers using the Ro...