[Paper Review] Towards a Neural Network Determination of Charged Pion Fragmentation Functions

Emanuele R. Nocera|arXiv (Cornell University)|Jan 31, 2017

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents the first determination of charged pion fragmentation functions using the NNPDF methodology, employing a neural network parametrization of fragmentation functions fitted to a comprehensive set of electron-positron annihilation data up to next-to-next-to-leading order in QCD. The resulting NNFF1.0 set shows good data description, stability under higher-order corrections, and notable differences—especially in the gluon fragmentation function—compared to existing parametrizations, highlighting reduced procedural bias through the flexible neural network approach.

ABSTRACT

I present a first determination of a set of collinear fragmentation functions of charged pions using the NNPDF methodology. The analysis is based on a wide set of single-inclusive electron-positron annihilation data, including recent measurements from $B$-factory experiments, and is performed up to next-to-next-to-leading order accuracy in perturbative quantum chromodynamics. I discuss the results of the fits, highlighting their quality in the description of the data, their stability upon the inclusion of higher-order corrections, and their comparison to other sets of fragmentation functions.

Motivation & Objective

• To develop a new, bias-controlled determination of charged pion fragmentation functions using the NNPDF methodology.
• To reduce procedural uncertainties in fragmentation function extraction by leveraging a flexible neural network parametrization.
• To provide a robust, uncertainty-quantified set of fragmentation functions based solely on single-inclusive e+e− annihilation data.
• To lay the foundation for future global fits including SIDIS and pp collision data to access flavor-dependent and favored/unfavored fragmentation functions.

Proposed method

• Fragmentation functions are parametrized using a neural network with redundant parameters to ensure flexibility and reduce model bias.
• A Monte Carlo sampling approach is employed to represent the fragmentation functions, enabling direct computation of central values and uncertainties as mean and standard deviation.
• The fit is performed using a global analysis of 19 SIA data sets from CERN, DESY, KEK, and SLAC experiments, including B-factory data at √s ≈ 10 GeV and LEP/SLC data at MZ.
• The analysis is carried out at next-to-next-to-leading order (NNLO) in perturbative QCD, with time-like evolution equations governing scale dependence.
• Data from flavor-tagged measurements (e.g., DELPHI, SLD) are included to improve quark flavor separation.
• Systematic uncertainties are evaluated via Monte Carlo sampling, with comparisons to Hessian-based uncertainties in other sets (e.g., DSS14).

Experimental results

Research questions

• RQ1 How does a neural network-based parametrization of fragmentation functions compare to traditional polynomial fits in terms of data description and uncertainty control?
• RQ2 To what extent do the results from the NNFF1.0 set differ from existing fragmentation function sets like DSS14 and JAM16, particularly in the gluon fragmentation function?
• RQ3 Can the NNPDF methodology reduce procedural biases in fragmentation function determinations compared to conventional parametrization schemes?
• RQ4 How stable are the fragmentation function results when higher-order QCD corrections are included?
• RQ5 What is the impact of including high-precision B-factory data on the determination of fragmentation functions at low energy scales?

Key findings

• The NNFF1.0 fragmentation functions provide an excellent description of the SIA data set, with χ²/d.o.f. values indicating high goodness-of-fit.
• The gluon fragmentation function in NNFF1.0 is significantly less suppressed at large z than in DSS14 and JAM16, with a slope closer to DSS14 but distinct from JAM16.
• Deviations between NNFF1.0 and DSS14/JAM16 are observed for the singlet and total charm and bottom fragmentation functions at z ≳ 0.7, with DSS14 exceeding NNFF1.0 by more than one σ.
• The JAM16 analysis shows better compatibility with NNFF1.0 across all z ranges, with all differences within one-σ uncertainties.
• Uncertainty bands in NNFF1.0 are generally only slightly larger than in DSS14 and JAM16, indicating comparable precision despite the flexible parametrization.
• The analysis demonstrates stability under inclusion of higher-order corrections, supporting the robustness of the NNPDF methodology for fragmentation function determinations.