We have measured the muon flux at the underground Gran Sasso National Laboratory ( 3800 m w.e . )
to be ( 3.41 \pm 0.01 ) \cdot 10 ^ { -4 } m ^ { -2 } s ^ { -1 } using four years of Borexino data .
A modulation of this signal is observed with a period of ( 366 \pm 3 ) days and a relative amplitude of ( 1.29 \pm 0.07 ) % .
The measured phase is ( 179 \pm 6 ) days , corresponding to a maximum on the 28 ^ { th } of June .
Using the most complete atmospheric data models available , muon rate fluctuations are shown to be positively correlated with atmospheric temperature , with an effective coefficient \alpha _ { T } = 0.93 \pm 0.04 .
This result represents the most precise study of the muon flux modulation for this site and is in good agreement with expectations .