Problems in resumming interjet energy flows with k_t clustering

Abstract

We consider the energy flow into gaps between hard jets. It was previously believed that the accuracy of resummed predictions for such observables can be improved by employing the $k_t$ clustering procedure to define the gap energy in terms of a sum of energies of soft jets (rather than individual hadrons) in the gap. This significantly reduces the sensitivity to correlated soft large-angle radiation (non-global leading logs), numerically calculable only in the large $N_c$ limit. While this is the case, as we demonstrate here, the use of $k_t$ clustering spoils the straightforward single-gluon Sudakov exponentiation that multiplies the non-global resummation. We carry out an ${\mathcal{O}}(\alpha_s^2)$ calculation of the leading single-logarithmic terms and identify the piece that is omitted by straightforward exponentiation. We compare our results with the full ${\mathcal{O}} (\alpha_s^2)$ result from the program EVENT2 to confirm our conclusions. For $e^{+}e^{-} \to 2$ jets and DIS (1+1) jets one can numerically resum these additional contributions as we show, but for dijet photoproduction and hadron-hadron processes further studies are needed.