Borexino is an organic liquid scintillator detector located in the underground Gran Sasso National Laboratory (Italy). It is devoted mainly to the real time spectroscopy of low energy solar neutrinos via the elastic scattering on electrons in the target mass. The data taking campaign started in 2007 and led to key measurements of 7}Be and 8B solar neutrinos as well as antineutrinos from the earth (geo-neutrinos) and from nuclear power reactors. Borexino is also a powerful tool for the study of cosmic muons that penetrate the Gran Sasso rock coverage and thereby induced signals such as neutrons and radioactive isotopes which are today of critical importance for upcoming dark matter and neutrino physics experiments. Having reached 4y of continuous data taking we analyze here the muon signal and its possible modulation. The muon flux is measured to be (3.41+-0.01)E-4/m2/s. A modulation of this signal with a yearly period is observed with an amplitude of (1.29+-0.07)% and a phase of (179+-6) d, corresponding to June 28th. Muon rate fluctuations are compared to fluctuations in the atmospheric temperature on a daily base, exploiting the most complete atmospheric data and models available. The distributions are shown to be positively correlated and the effective temperature coefficient is measured to be alpha_T = 0.93 +- 0.04. This result is in good agreement with the expectations of the kaon-inclusive model at the laboratory site and represents an improvement over previous measurements performed at the same depth.
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