The SISCone Jet Algorithm

The split-merge variable issue:

Though the main IR difficulties are related to the search for stable cones, and are solved by a seedless procedure, it turns out that the split-merge phase of the algorithm is also non-trivial. The Tevatron run II split-merge procedure requires that "protojets" be considered in a sequence determined by some ordering variable. A change in the sequence can leads to a change in the final jets. When trying to find the best suited variable for the ordering of protojets in the split--merge process of SISCone, we met a couple of physical issues. Their history goes as follows:

• the E_t variable, suggested e.g. in the Tevatron Run II specification of the midpint algorithm, is not boost invariant.
• the p_t variable, used e.g. in practical midpoint implementations (except for MCFM), suffers from problems with two back-to-back protojets. Due to momentum conservation, they can have the same p_t. Their ordering is thus random and can be modified by the addition of a soft particle, leading to an IR unsafety problem.
• the m_t variable does not directly suffer from that problem: two back-to-back jets only overlap if they cover a region in the eta-phi plane. In that case, their values of m_t will differ and the ordering is safe. This choice (the default one for SISCone 1.1.0) suffers unfortunately from one remaining issue: though m_t works for pure QCD, in the case of two back-to-back narrow-decay-width unstable particles (e.g. a pair of Higgs bosons), both p_t and m_t will be the same.
• As of SISCone 1.1.1, we use pttilde: the p-scheme pt (the sum of the moduli of transverse momenta of all particles in the protojet ) that interpolates between p_t and m_t according to the decay plane of the unstable massive particle. This will lift the degeneracy between decays of identical pairs of unstable particles, since the phase space for them to have identical decay planes vanishes.