Jet analysis by Deterministic Annealing

TL;DR

The paper compares the standard Durham jet clustering algorithm with Deterministic Annealing (DA), a variational, globally optimizing approach to jet identification in $e^+e^-$ collisions producing $W$ pairs. DA minimizes a Helmholtz free-energy-like objective and uses a deterministic cooling schedule, with a tailored modification to reflect jet momenta and fix a jet count. The study finds that DA yields clustering results and $W$-mass reconstructions that are broadly consistent with Durham, while offering substantially better computational scaling (approximately $t \propto N^{1.83}$ vs $N^{2.97}$ for Durham), suggesting practical benefits for high-multiplicity jet environments such as the LHC. Overall, DA emerges as a viable, more scalable alternative for jet physics analyses without sacrificing accuracy in the tested WW scenario.

Abstract

We perform a comparison of two jet clusterization algorithms. The first one is the standard Durham algorithm and the second one is a global optimization scheme, Deterministic Annealing, often used in clusterization problems, and adapted to the problem of jet identification in particle production by high energy collisions; in particular we study hadronic jets in WW production by high energy electron positron scattering. Our results are as follows. First, we find that the two procedures give basically the same output as far as the particle clusterization is concerned. Second, we find that the increase of CPU time with the particle multiplicity is much faster for the Durham jet clustering algorithm in comparison with Deterministic Annealing. Since this result follows from the higher computational complexity of the Durham scheme, it should not depend on the particular process studied here and might be significant for jet physics at LHC as well.

Figures (4)

• Figure 1: The $W$-mass distribution of the actual data; $m_W$ in GeV/c$^2$.
• Figure 2: The $W$-mass (in GeV/c$^2$) distributions as reconstructed by the Durham jet algorithm (left) and Deterministic Annealing (right).
• Figure 3: The distribution of the similarity $S$.
• Figure 4: CPU time (in seconds), vs. particle multiplicity for the Deterministic Annealing algorithm (lower curve) and the Durham algorithm (upper curve).