Calibrating b-tagging using Dijet Events

This note describes two strategies for data-based measurement of the semi-leptonic $b$-tagging efficiency of ATLAS lifetime $b$-tagging algorithms using jet data. The $p_{T,rel}$ method uses templates of the muon $p_T$ relative to the jet+muon axis for bottom, charm, and light jets to estimate the $b$-quark content of a jet sample. The $b$-tagging efficiency is btained by measuring the $b$-quark content before and after tagging a sample. The second method, System 8, uses two samples of jets of differing $b$-quark content and two uncorrelated tagging algorithms to form a system of 8 equations and 8 unknowns, one of which is the $b$-tagging efficiency. Both methods use a Monte Carlo scale factor to convert the measured semi-leptonic efficiency to an inclusive efficiency. Both methods give results binned in $p_T$ and $\eta$. Good agreement was found between the $b$-tagging efficiencies determined by both techniques and true Monte Carlo for $15 < p_T < 80$ GeV, however above 80 GeV both methods have difficulty. Initial systematics studies have been performed which indicate that it should be possible to control the absolute error on $b$-tagging efficiency to 6\% for both methods. This error does not include the error associated with converting the semi-leptonic efficiency to the inclusive efficiency.