Optimisation of variables for studying dilepton transverse momentum distributions at hadron colliders

In future measurements of the dilepton (Z/γ^∗) transverse momentum, Q_T, at both the Tevatron and LHC, the achievable bin widths and the ultimate precision of the measurements will be limited by experimental resolution rather than by the available event statistics. In a recent paper the variable a_T, which corresponds to the component of Q_T that is transverse to the dilepton thrust axis, has been studied in this regard. In the region, Q_T < 30 GeV, a_T has been shown to be less susceptible to experimental resolution and efficiency effects than the Q_T. Extending over all Q_T, we now demonstrate that dividing a_T (or Q_T) by the measured dilepton invariant mass further improves the resolution. In addition, we propose a new variable, $\phi _{\rm \eta }^{*}$, that is determined exclusively from the measured lepton directions; this is even more precisely determined experimentally than the above variables and is similarly sensitive to the Q_T. The greater precision achievable using such variables will enable more stringent tests of QCD and tighter constraints on Monte Carlo event generator tunes.