Measuring the Photon Fragmentation Function at HERA

TL;DR

This paper presents a LO parton-level framework to measure the quark-to-photon fragmentation function in deep inelastic scattering at HERA by studying γ+(0+1)-jet events with democratic clustering. The approach jointly treats direct photon emission and fragmentation, using phase-space slicing and various FF parametrisations to show that the photon-energy fraction z inside the photon jet is highly sensitive to D_{q \to \gamma}(z, \mu_{F,\gamma}). It demonstrates that, unlike inclusive photon observables, the γ+(0+1)-jet cross section at LO directly probes the fragmentation function and can thus determine its non-perturbative input, with implications for cross-compatibility with LEP-based fits (ALEPH, BFG). The work also explores isolated photon observables under different jet algorithms, highlighting how fragmentation, LL radiation, and isolation criteria interplay in DIS and informing future NLO studies.

Abstract

The production of final state photons in deep inelastic scattering originates from photon radiation off leptons or quarks involved in the scattering process. Photon radiation off quarks involves a contribution from the quark-to-photon fragmentation function, corresponding to the non-perturbative transition of a hadronic jet into a single, highly energetic photon accompanied by some limited hadronic activity. Up to now, this fragmentation function was measured only in electron-positron annihilation at LEP. We demonstrate by a dedicated parton-level calculation that a competitive measurement of the quark-to-photon fragmentation function can be obtained in deep inelastic scattering at HERA. Such a measurement can be obtained by studying the photon energy spectra in $γ+ (0+1)$-jet events, where $γ$ denotes a hadronic jet containing a highly energetic photon (the photon jet). Isolated photons are then defined from the photon jet by imposing a minimal photon energy fraction. For this so-called democratic clustering approach, we study the cross sections for isolated $γ+ (0+1)$-jet and $γ+ (1+1)$-jet production as well as for the inclusive isolated photon production in deep inelastic scattering.

Figures (8)

• Figure 1: Leading order Feynman amplitudes for hard photon production in DIS. The $QQ$-contribution is obtained by squaring the sum of the upper two amplitudes, the $LL$-contribution from the square of the lower two amplitudes, and $QL$-contribution from their interference.
• Figure 2: Leading order Feynman amplitude for the quark-to-photon fragmentation process in deep inelastic scattering.
• Figure 3: Photon energy distribution inside the photon jet of $\gamma + (0+1)$-jet events. Jets are defined using the inclusive and exclusive $k_T$-algorithm. In the latter case the jet resolution parmeter $y_{cut}$ is taken equal to 0.1,0.004 and 0.001 respectively
• Figure 4: Rapidity distributions of isolated photons in $\gamma+(0+1)$-jet events, in different bins in $E_{T,\gamma}$. The last plot shows the sum over all bins. Isolated photons are defined here using the exclusive $k_T$-algorithm ($y_{cut} = 0.1$) in the HERA frame, requiring $z>0.9$. $LL$ and $QQ$ subprocess contributions are indicated as dashed and dotted lines.
• Figure 5: Transverse energy distributions of isolated photons in $\gamma+(0+1)$-jet events, in different bins in $\eta_{\gamma}$. The last plot shows the sum over all bins. Isolated photons are defined using the exclusive $k_T$-algorithm ($y_{cut} = 0.1$) in the HERA frame, requiring $z>0.9$. $LL$ and $QQ$ subprocess contributions are indicated as dashed and dotted lines.