[Paper Review] Simplified QCD fit method for BSM analysis of HERA data

O. Turkot, Katarzyna Wichmann+1 more|arXiv (Cornell University)|Jun 21, 2016

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents a simplified QCD fitting method that accelerates Beyond Standard Model (BSM) analysis of HERA ep scattering data by using a first-order Taylor expansion of cross-section predictions in terms of PDF parameters and BSM couplings. The approach reduces computation time by a factor of 50 compared to full QCD fits, enabling efficient limit-setting for BSM models like quark form factors without sacrificing accuracy, as validated against full fits using replica-based frequentist procedures.

ABSTRACT

The high-precision HERA data can be used as an input to a QCD analysis within the DGLAP formalism to obtain the detailed description of the proton structure in terms of the parton distribution functions (PDFs). However, when searching for Beyond Standard Model (BSM) contributions in the data one should take into account the possibility that the PDF set may already have been biased by partially or totally absorbing previously unrecognised new physics contributions. The ZEUS Collaboration has proposed a new approach to the BSM analysis of the inclusive $ep$ data based on the simultaneous QCD fits of parton distribution functions together with contributions of new physics processes. Unfortunately, limit setting procedure in the frequentist approach is very time consuming in this method, as full QCD analysis has to be repeated for numerous data replicas. We describe a simplified approach, based on the Taylor expansion of the cross section predictions in terms of PDF parameters, which allowed us to reduce the calculation time for the BSM limits by almost two orders of magnitude.

Motivation & Objective

• To address the computational bottleneck in frequentist BSM limit-setting for HERA data, where full QCD fits per replica are prohibitively slow.
• To develop a simplified fitting procedure that maintains accuracy while drastically reducing CPU time for simultaneous PDF and BSM coupling fits.
• To enable scalable extension of BSM analyses—such as quark form factor searches—to other models beyond the standard approach.
• To validate that the simplified method reproduces full fit results for key observables like quark radius limits and chi-squared values.

Proposed method

• The method uses a first-order Taylor expansion of the pQCD+BSM cross-section prediction around the nominal PDF set and zero BSM coupling.
• It pre-computes reference cross-section values and their derivatives with respect to PDF parameters and BSM couplings at the nominal point.
• For each replica, the simplified cross-section prediction is constructed as a linear function of PDF deviations and BSM coupling, using stored derivatives and reference values.
• The approach replaces full QCD evolution and PDF fitting per replica with a fast analytical evaluation of the cross-section model.
• The method is validated by comparing results from the simplified fit against full QCD+BSM fits using identical replica sets.
• The procedure is applied to the quark form factor model, with limit-setting performed via the frequentist approach using replica-based probability distributions.

Experimental results

Research questions

• RQ1 Can a simplified QCD fitting approach reproduce the results of full QCD+BSM fits for BSM analysis of HERA data with significantly reduced computation time?
• RQ2 How accurately does the Taylor expansion approximation preserve the statistical properties of the limit-setting procedure, such as the distribution of fitted BSM parameters?
• RQ3 To what extent can the method be extended to other BSM models beyond the quark form factor scenario?
• RQ4 What is the impact of PDF parameter fluctuations on the accuracy of the linear approximation in the replica-based frequentist framework?

Key findings

• The simplified method reduces the average CPU time per fit by a factor of 50 compared to full QCD fits, cutting the total time for 200,000 fits from over 30 years to under a year.
• The fitted quark radius squared values from the simplified method agree almost perfectly with those from the full QCD fit, with differences smaller than the width of the distribution.
• The chi-squared values from the simplified and full fits show excellent agreement, confirming the method maintains fit quality.
• The probability distribution of the fitted $R_q^2$ values and the resulting 95% C.L. limit on $R_q^2$ are indistinguishable from the full fit results, as confirmed by comparison plots.
• The method enables efficient exploration of other BSM models, such as those with new couplings or form factors, that were previously computationally infeasible to study.