Jet energy calibration hands each stage to a neural network: residual pile-up dependence falls to about a tenth of the parametric baseline
Synopsis
Hadronic jet energy calibration at the Large Hadron Collider has relied on fitting parametric functional forms to selected observables, correcting pile-up, detector response and data–simulation differences in sequence. A prototype pipeline instead trains a neural network for each stage directly against the quantity that stage removes, imposes no functional form, and extends by adding inputs. On simulated dijet and large-radius jet samples it matches or exceeds the parametric baseline at nearly every stage, with residual pile-up dependence averaging about a tenth of the baseline's.
Interpretation
Each stage of jet energy calibration can be learned by a neural network instead of being designed as a parametric functional form. Current ATLAS and CMS schemes apply several sequential corrections whose parameters come from fits of parametric functional forms to selected observables; such corrections are insensitive to dependence the parametrization cannot accommodate, and that error is absorbed into the systematic uncertainty. On simulated dijet events, the root mean square across pseudorapidity bins of the post-correction residual slope against the pile-up variables is lower for the network than for the parametric baseline in both the lo- and hi- injection regimes, averaging about 0.11 and 0.14 of the baseline over seven values of the pile-up-variable correlation.
Each network is trained directly against the quantity its stage is meant to remove, not against the particle-level energy. Direct regression on particle-level energy makes the result depend on the spectrum of the training sample, so the pile-up stage instead uses a covariance loss built from the corrected residual and the pile-up variables. That loss penalizes linear, quadratic and joint dependence on the number of reconstructed vertices and the mean interactions per crossing, evaluated separately in bins of pseudorapidity and transverse momentum, with training on Delphes-simulated ATLAS detector response.
Large-radius jet calibration can take sub-jet positions as extra inputs and so separate the two classes of jets that straddle a calorimeter crack. A parametric method returns one correction curve for jets of the same pseudorapidity and energy, and cannot distinguish which side of the crack the sub-jets fall on. On simulated photon plus hadronically decaying W boson events, adding the positions of the two leading soft-drop sub-jets makes the network return different corrections for sub-jet axes along the longitudinal direction and along the azimuth, with the closure improvement concentrated near the step.
Perspective
The demonstrated setting is the Delphes fast simulation of ATLAS detector response, with hand-injected pile-up dependence, absolute energy-scale distortion and data–simulation differences; the large-radius part uses simulated photon plus hadronically decaying W boson events. The authors frame the work as a prototype and name replacing Delphes with a learned simulation such as Parnassus as a next step.
The authors state this is a prototype using fast detector simulation with injected distortions, and that systematic uncertainties of the in-situ methods are not treated; the absolute-scale stage defines closure by the median, and with the peak of the core instead the parametric baseline closes slightly better in the lo- regime; for data–simulation differences the two methods agree within the spread over sample divisions for the undistorted sample and the linear, exponential and step distortions, with the network better only for the quadratic and pile-up-density-dependent distortions.