[Paper Review] Machine Learning-Assisted Measurement of Lepton-Jet Azimuthal Angular Asymmetries in Deep-Inelastic Scattering at HERA

The H1 Collaboration, V. Andreev+142 more|arXiv (Cornell University)|Dec 18, 2024

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents a machine learning-based unfolding method to measure lepton-jet azimuthal angular asymmetries in deep-inelastic scattering at HERA using H1 detector data. The method enables binned-free moment extraction, revealing small but non-zero asymmetries consistent with perturbative QCD predictions, with deviations observed at high transverse momentum ($q_\perp > 3.0$ GeV), indicating potential breakdown of the $P_\perp \gg q_\perp$ approximation.

ABSTRACT

In deep-inelastic positron-proton scattering, the lepton-jet azimuthal angular asymmetry is measured using data collected with the H1 detector at HERA. When the average transverse momentum of the lepton-jet system, $\lvert \vec{P}_\perp vert $, is much larger than the total transverse momentum of the system, $\lvert \vec{q}_\perp vert$, the asymmetry between parallel and antiparallel configurations, $\vec{P}_\perp$ and $\vec{q}_\perp$, is expected to be generated by initial and final state soft gluon radiation and can be predicted using perturbation theory. Quantifying the angular properties of the asymmetry therefore provides an additional test of the strong force. Studying the asymmetry is important for future measurements of intrinsic asymmetries generated by the proton's constituents through Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs), where this asymmetry constitutes a dominant background. Moments of the azimuthal asymmetries are measured using a machine learning method for unfolding that does not require binning.

Motivation & Objective

• To measure lepton-jet azimuthal angular asymmetries in deep-inelastic scattering at HERA with high precision, enabling tests of quantum chromodynamics (QCD) predictions.
• To develop and apply a machine learning-based unfolding technique that avoids binning, improving statistical precision and reducing systematic uncertainties in moment extraction.
• To quantify the contribution of soft gluon radiation to angular asymmetries, which serves as a background for future measurements of transverse momentum dependent (TMD) parton distribution functions.
• To compare the measured asymmetries with theoretical predictions from event generators (e.g., DJANGOH, RAPGAP, SHERPA, TXZ pQCD) and TMD models (HXYZ), assessing their consistency with data.
• To identify kinematic regions where the $P_\perp \gg q_\perp$ approximation breaks down, particularly at $q_\perp > 3.0$ GeV, and to evaluate the sensitivity of models to saturation effects.

Proposed method

• A machine learning-based unfolding method is employed to extract moments of the azimuthal angular asymmetry without binning, reducing bias and improving resolution in the measurement.
• The method uses a differentiable, end-to-end neural network architecture trained on simulated events to map detector-level distributions to true-level moments, minimizing binning-related distortions.
• The unfolding is validated using Monte Carlo simulations of DIS events with known asymmetries, ensuring robustness and accuracy in moment reconstruction.
• The analysis focuses on the first three harmonics of the azimuthal asymmetry, defined as $A_n = \langle \cos(n\phi) \rangle$, where $\phi$ is the angle between $\vec{P}_\perp$ and $\vec{q}_\perp$.
• Theoretical predictions from event generators (DJANGOH, RAPGAP, SHERPA, TXZ pQCD) and TMD models (HXYZ) are compared to data across $q_\perp$ bins to assess agreement.
• Systematic uncertainties are evaluated by varying the unfolding network architecture, simulation models, and kinematic cuts, ensuring reliable error estimation.

Experimental results

Research questions

• RQ1 To what extent do the measured lepton-jet azimuthal angular asymmetries agree with perturbative QCD predictions in the $P_\perp \gg q_\perp$ regime?
• RQ2 How does the performance of different event generators (e.g., SHERPA, DJANGOH, RAPGAP) compare to the data across varying $q_\perp$ bins?
• RQ3 Does the HXYZ TMD model, which includes saturation effects, agree with the data, or is it incompatible at higher $q_\perp$?
• RQ4 At what $q_\perp$ value does the $P_\perp \gg q_\perp$ approximation begin to break down, as indicated by deviations in the asymmetry measurements?
• RQ5 Can the data distinguish between TMD models with and without saturation effects, such as TXZ(GBW) and TXZ(CT18A), based on the asymmetry pattern?

Key findings

• The measured asymmetries are small but non-zero, with most data points consistent with zero for $q_\perp > 2$ GeV, indicating a weak signal from soft gluon radiation.
• DJANGOH and RAPGAP event generators show good agreement with the data across all $q_\perp$ bins, supporting their reliability in modeling soft gluon effects.
• Pythia tunes and SHERPA at both LO and NLO show larger discrepancies with data, especially at higher $q_\perp$, suggesting limitations in their parton shower modeling.
• TXZ pQCD calculations agree well with data overall but begin to deviate in the first harmonic at $3.0 < q_\perp < 4.0$ GeV, indicating a breakdown of the $P_\perp \gg q_\perp$ approximation in this region.
• The HXYZ (TMD) model agrees with data at low $q_\perp$ but is incompatible with data for $q_\perp > 3.0$ GeV across all three harmonics, suggesting potential issues with its saturation modeling or parameterization.
• The data cannot currently distinguish between the TXZ(GBW) model (with saturation) and TXZ(CT18A) (without saturation), indicating a need for future measurements at lower $Q^2$ or in eA collisions to resolve this ambiguity.