Machine learning fully hadronic events with spectral functions
Characterising fully hadronic events is a difficult task at hadron colliders. Signal jets from the hard process are mingled with an arbitrary number of ISR and FSR jets, leading to a large combinatorial background. This also poses a challenge for machine-learning analyses, where the number of input features is fixed while the jet multiplicity fluctuates from event to event due to QCD radiation. In this work, we explore the use of the two-point correlation spectral function as an input feature for machine-learning analyses of such events. The spectral function maps the transverse-momentum data of an event into a one-dimensional function of the angular distance, encoding the event information modulo collider isometries and jet permutations, and is defined independently of the jet multiplicity. As a concrete benchmark we apply the method to discriminate gluino-pair production followed by $\tilde{g} \to t \bar{t} \tilde{\chi}_1^0$ against the fully hadronic $t \bar{t}$ background. With $139~{\rm fb}^{-1}$ of $\sqrt{s} = 13$ TeV $pp$ collision data, a dense neural network supplied with spectral-function features improves the expected reach in gluino-mass by roughly 150 GeV relative to a recent ATLAS analysis, and by roughly 250 GeV relative to the same network trained on jet kinematics alone.