This is the first of the series of papers which present a precision method of the day-by-day monitoring of the absolute LHC luminosity. This method is based on the measurement of the rate of coplanar lepton pairs produced in peripheral collisions of the beams' particles. In the present paper we evaluate the modeling precision of the lepton pair production processes in proton-proton collisions, optimise the measurement region to achieve better than 1 % accuracy of the predicted rates, and discuss the experimental challenges to filter out the luminosity monitoring lepton pairs at LHC.
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