Quarks and Gluon Fragmentation Functions into Photons

TL;DR

The paper addresses how quarks and gluons fragment into photons beyond Leading Log accuracy, distinguishing perturbative (anomalous) and non-perturbative components and examining factorization-scheme invariance. It reframes the decomposition so scheme dependence resides in the perturbative part and constrains the non-perturbative input via Vector Dominance Model using vector-meson fragmentation data from LEP. Through numerical studies and fits to LEP data, it provides two new sets of parton-to-photon fragmentation functions and demonstrates reasonable agreement with direct-photon measurements, highlighting the importance of inclusive photon data to robustly test perturbative QCD predictions. The work also clarifies the theoretical handling of heavy quarks, scheme choices (MSbar vs DIS_γ), and the role of small- and large-$z$ behavior in shaping observable photon production.

Abstract

The fragmentation functions of quarks and gluons into photons are studied beyond the Leading Logarithm approximation. We address the nature of the initial conditions of the evolution equation solutions and study problems related to factorization scheme invariance. The possibility of measuring these distributions in LEP experiments is discussed, and a comparison with existing data is made.

Figures (11)

• Figure 1: Anomalous component with $D^{\gamma , AN}(z, M_0^2= 0.5\ GeV^2)= D^{\gamma , \overline{MS}}(z)$
• Figure 2: Anomalous component with $D^{\gamma , AN}(z, M_0^2= 0.5 GeV^2)=0$
• Figure 3: Comparison of the anomalous gluon fragmentation functions with a null input at $Q_0^2 = 0.5\ GeV^2$ and various singularities removed from kernels.
• Figure 4: Comparison between ALEPH data and predictions corresponding to set I and II. Black dots correspond to points used in the fits.
• Figure 5: Comparison between HRS data and predictions corresponding to set I and II. Black dots correspond to points used in the fits.