Matrix element method at next-to-leading order for arbitrary jet algorithms

The matrix element method usually employs leading-order matrix elements. We discuss the generalization towards higher orders in perturbation theory and show how the matrix element method can be used at next-to-leading order for arbitrary infrared-safe jet algorithms. We discuss three variants at next-to-leading order. The first two variants work at the level of the jet momenta. The first variant adheres to strict fixed order in perturbation theory. We present a method for the required integration over the radiation phase space. The second variant is inspired by the POWHEG method and works as the first variant at the level of the jet momenta. The third variant is a more exclusive POWHEG version. Here we resolve exactly one jet into two subjets. If the two subjets are resolved above a scale $p_{\perp }^{\min }$, the likelihood is computed from the POWHEG-modified real emission part, otherwise it is given by the POWHEG-modified virtual part.

Figure 1

A sketch of the region, which maps under the jet algorithm to the same jet configuration. In the left figure we show the situation for the dedicated jet algorithm of [12]. The region is in the fiber above $\overrightarrow{x}$. On the right figure we show the situation for an arbitrary jet algorithm, using the same coordinate system as before. The region is now no longer within a single fiber. We may however still parametrize the three-dimensional manifold by ${\varphi }_{\text{unres}}$.