[Paper Review] Measurement of lepton-jet correlation in deep-inelastic scattering with the H1 detector using machine learning for unfolding

H Collaboration, V. Andreev+143 more|arXiv (Cornell University)|Aug 27, 2021

Particle physics theoretical and experimental studies128 references4 citations

TL;DR

This paper presents the first measurement of lepton-jet momentum imbalance ($q_{\mathrm{T}}^{\text{jet}}/Q$) and azimuthal angle correlation ($\Delta\phi$) in deep-in-line scattering at high $Q^2$ using the H1 detector at HERA. It employs a novel machine learning-based unfolding method, MultiFold, to perform simultaneous, unbinned unfolding in high dimensions, enabling precise access to transverse momentum distribution and providing critical constraints on transverse momentum-dependent (TMD) parton distribution functions.

ABSTRACT

The first measurement of lepton-jet momentum imbalance and azimuthal correlation in lepton-proton scattering at high momentum transfer is presented. These data, taken with the H1 detector at HERA, are corrected for detector effects using an unbinned machine learning algorithm OmniFold, which considers eight observables simultaneously in this first application. The unfolded cross sections are compared to calculations performed within the context of collinear or transverse-momentum-dependent (TMD) factorization in Quantum Chromodynamics (QCD) as well as Monte Carlo event generators. The measurement probes a wide range of QCD phenomena, including TMD parton distribution functions and their evolution with energy in so far unexplored kinematic regions.

Motivation & Objective

• To measure lepton-jet correlation observables ($q_{\mathrm{T}}^{\text{jet}}/Q$ and $\Delta\phi$) in deep-inelastic scattering at high $Q^2$ to probe transverse momentum-dependent (TMD) parton distribution functions.
• To apply machine learning-based unfolding (MultiFold) to correct for detector effects in high-dimensional phase space, enabling precise extraction of true distributions.
• To bridge the kinematic gap between fixed-target DIS experiments and Drell-Yan measurements at hadron colliders by providing high-precision data in the $Q^2 > 150$ GeV$^2$ regime.
• To test the validity of TMD factorization, TMD evolution, and TMD universality by comparing data with theoretical predictions using different TMD sets.
• To establish a benchmark for future jet studies in polarized proton and nuclear DIS at the Electron Ion Collider.

Proposed method

• Reconstructed jets in the laboratory frame using the $k_{\mathrm{T}}$ algorithm with $R=1$ in events with $Q^2 > 150$ GeV$^2$ and $0.2 < y < 0.7$.
• Defined two key TMD-sensitive observables: $q_{\mathrm{T}}^{\text{jet}}/Q$ (lepton-jet momentum imbalance) and $\Delta\phi$ (azimuthal angle correlation).
• Applied the MultiFold machine learning unfolding method to perform simultaneous, unbinned unfolding in high-dimensional phase space, avoiding binning and preserving resolution.
• Used Monte Carlo simulations to train the MultiFold model, which learns the detector response and inverts it to reconstruct the true underlying distributions.
• Compared the unfolded data with predictions from fixed-order pQCD calculations and various TMD PDF sets, including Cascade.
• Evaluated uncertainties by comparing spread across different TMD sets against experimental and theoretical uncertainties.

Experimental results

Research questions

• RQ1 How do lepton-jet momentum imbalance ($q_{\mathrm{T}}^{\text{jet}}/Q$) and azimuthal correlation ($\Delta\phi$) behave in high-$Q^2$ deep-inelastic scattering?
• RQ2 To what extent can machine learning-based unfolding (MultiFold) improve the precision and resolution of high-dimensional jet observables compared to traditional binning methods?
• RQ3 Can the measured lepton-jet correlations constrain the universality and evolution of transverse momentum-dependent (TMD) parton distribution functions?
• RQ4 How do theoretical predictions based on TMD PDFs extracted from low-$Q^2$ HERA data compare with the high-$Q^2$ data in this study?
• RQ5 What is the constraining power of these data for future global fits of TMD and collinear PDFs across energy scales?

Key findings

• The measurement presents the first high-$Q^2$ determination of lepton-jet momentum imbalance ($q_{\mathrm{T}}^{\text{jet}}/Q$), a key observable for probing TMD PDFs.
• The data show good agreement with theoretical predictions using TMD PDFs extracted from low-$Q^2$ semi-inclusive DIS and parton branching models.
• The experimental uncertainty is comparable in size to the spread among predictions using different TMD sets (including Cascade), indicating strong constraining power for future TMD fits.
• The spread in TMD predictions is comparable to the combined experimental and fixed-order theoretical uncertainties, suggesting that the data will help reduce model dependence in global TMD analyses.
• The application of MultiFold unfolding enables high-dimensional, unbinned unfolding, marking a milestone in experimental high-energy physics for precision nucleon structure studies.
• The results provide a critical baseline for future jet physics in polarized proton and nuclear DIS at the Electron Ion Collider.