[Paper Review] HYTREES: Combining Matrix Elements and Parton Shower for Hypothesis Testing

Stefan Prestel, Michael Spannowsky|arXiv (Cornell University)|Jan 30, 2019

Particle physics theoretical and experimental studies86 references29 citations

TL;DR

HYTREES introduces a perturbative classifier that combines leading-order matrix elements with parton shower evolution to improve hypothesis testing in high-energy physics. By constructing a 'history tree' of possible partonic evolution paths—including hard scattering and successive radiation—it enables optimal discrimination between signal (Higgs boson production in association with jets) and background processes, achieving high sensitivity in kinematic regions identified via matrix-element-weighted event histories.

ABSTRACT

We present a new way of performing hypothesis tests on scattering data, by means of a perturbatively calculable classifier. This classifier exploits the "history tree" of how the measured data point might have evolved out of any simpler (reconstructed) points along classical paths, while explicitly keeping quantum-mechanical interference effects by copiously employing complete leading-order matrix elements. This approach extends the standard Matrix Element Method to an arbitrary number of final state objects and to exclusive final states where reconstructed objects can be collinear or soft. We have implemented this method into the standalone package HYTREES and have applied it to Higgs boson production in association with two jets, with subsequent decay into photons. HYTREES allows to construct an optimal classifier to discriminate this process from large Standard Model backgrounds. It further allows to find the most sensitive kinematic regions that contribute to the classification.

Motivation & Objective

• To develop a perturbative classifier that improves signal-background discrimination in jet-rich final states at the LHC.
• To address the limitations of fixed-order matrix elements in collinear and soft regions by incorporating parton shower dynamics.
• To extend the Matrix Element Method to exclusive, multi-object final states with arbitrary jet multiplicities and reconstructed objects.
• To identify the most sensitive kinematic regions contributing to classification by leveraging full event history reconstruction.
• To implement a framework that avoids double-counting between matrix elements and parton showers while preserving quantum interference effects.

Proposed method

• Constructs a 'history tree' of all possible partonic evolution paths from the hard scattering to the final reconstructed objects, including all flavor and color configurations.
• Uses the Dire parton shower to compute perturbative weights for each event history, ensuring consistent evolution from parton-level to reconstructed object-level final states.
• Incorporates matrix-element corrections for all relevant splittings (e.g., g→gH, H→γγ) to maintain accuracy in radiation patterns and avoid large weight fluctuations.
• Fixes coupling constants (e.g., α(S(p)i, t(p)i) = ΓH→gg(mH)) to ensure proper probability assignment at production and decay vertices.
• Maps reconstructed jets and photons back to on-shell parton momenta using momentum conservation and beam constraints.
• Applies exclusive kinematic cuts (e.g., pT ≥35 GeV, |y| < 2.5, R = 0.4 anti-kT jets) to simplify the final state and reduce non-perturbative contamination.

Experimental results

Research questions

• RQ1 Can a hybrid method combining matrix elements and parton showers improve hypothesis testing in exclusive, multi-jet final states?
• RQ2 How does including full event history reconstruction via a 'history tree' enhance the sensitivity of classification compared to standard MEM?
• RQ3 To what extent can matrix-element-corrected parton showers reduce weight fluctuations and improve stability in high-multiplicity final states?
• RQ4 Which kinematic regions contribute most significantly to the classifier's ability to distinguish Higgs production from QCD and QED backgrounds?
• RQ5 Can the method be generalized to arbitrary numbers of reconstructed leptons, photons, and jets while preserving perturbative accuracy?

Key findings

• The hytrees package successfully implements a perturbative classifier that combines matrix elements and parton showers for hypothesis testing in Higgs boson production with two jets.
• The method identifies specific kinematic regions—particularly those with collinear or soft jet emissions—as most sensitive to the Higgs signal, improving discrimination power.
• By including matrix-element corrections for Higgs production (g→gH) and decay (H→γγ), the classifier maintains accurate radiation patterns even in phase-space regions where fixed-order matrix elements diverge.
• The use of matrix-element-corrected splitting kernels ensures stable and positive weights, avoiding large fluctuations common in standard parton shower approaches.
• The classifier achieves optimal performance by evaluating all possible partonic histories, including all flavor and color configurations, leading to a more robust and physically consistent classification.
• The framework is generalizable to arbitrary final states with reconstructed objects, demonstrating applicability beyond the Higgs→γγ+jets case studied.