  We develop a renormalization group approach for analyzing Fr\"ohlich polarons
and apply it to a problem of impurity atoms immersed in a Bose-Einstein
condensate of ultra cold atoms. Polaron energies obtained by our method are in
excellent agreement with recent diagrammatic Monte Carlo calculations for a
wide range of interaction strengths. We calculate the effective mass of
polarons and find a smooth crossover from weak to strong coupling regimes.
Possible experimental tests of our results in current experiments with ultra
cold atoms are discussed.
