(Upper panel) The K$^+$K$^-$ invariant mass distribution in $|y|$< 0.5, for the bin 0.5 $<  \pt < $ 0.6 GeV/$c$ (left) and 1.1 $<  \pt < $ 1.2 GeV/$c$ (right) in pp collisions at 7 TeV. The solid curve is the fit result (Eq. 2), while the dashed line describes the background. The background shape estimated using unlike-sign pairs from different events (event mixing) or like-sign pairs from the same event are shown as open red squares and full green squares, respectively (Lower panel). The K$^+$K$^-$ invariant mass distribution after mixed-event background subtraction for 0.5 $<  \pt < $ 0.6 GeV/$c$ (left) and 1.1 $<  \pt < $ 1.2 GeV/$c$ (right). The solid curve is the fit result (Eq. 2), while the dashed line describes the residual background.