Final state photon production at LEP

TL;DR

The paper investigates photon production in e+e- collisions at LEP by contrasting fixed-order and conventional resummation treatments of the quark-to-photon fragmentation function D_{q→γ}(x,μF). It systematically compares four cross-section formulations—combining resummed or expanded D_{q→γ} with fixed-order or conventional direct-term counting—and evaluates GRV and BFG fragmentation parameterizations against ALEPH and OPAL data. Key findings show that ALEPH data favors the resummed BFG parameterization at large x, while OPAL inclusive data is broadly compatible with multiple approaches, highlighting fragmentation-function universality. The work emphasizes the importance of large-x behavior, scheme choices (MS-bar vs DIS_γ), and the practical viability of using fragmentation functions fitted from one observable to predict others, with implications for photon-involved processes at colliders.

Abstract

We present a detailed study of photon production in hadronic events in electron-positron annihilation at LEP energies. We show that estimates of the inclusive photon spectrum using the quark-to-photon fragmentation function determined using the ALEPH `photon' +~1 jet data agree well with the observations of the OPAL collaboration. This agreement shows that the photon fragmentation function determined in this way can be used for inclusive observables. We also compare next-to-leading order and beyond leading logarithm predictions obtained using the numerically resummed solutions of the fragmentation function evolution equation of Bourhis, Fontannaz and Guillet and Glück, Reya and Vogt with the data. Moreover, in order to check the general behaviour of the fragmentation function, we consider an analytic series expansion in the strong coupling. We find that the parameterizations are inaccurate at large $x$ values. While the OPAL data is in broad agreement with estimates based on any of these approaches, the ALEPH data prefers the resummed BFG parameterization. Finally, there is some ambiguity as to whether the fragmentation function is treated as ${\cal O}(α)$ or ${\cal O}(α/α_s)$. We show that at present this ambiguity affects mainly the prediction for the `photon' +~1 jet rate at large $z$.

Figures (15)

• Figure 1: Parton level subprocesses contributing to single photon production at ${\cal O}(\alpha\alpha_s)$.
• Figure 2: The inclusive photon energy distribution normalized to the hadronic cross section as measured by the OPAL collaboration compared with the LO (${\cal O}(\alpha)$) and NLO (${\cal O}(\alpha \alpha_s)$) calculations including the quark-to-photon fragmentation function determined at the appropriate order from the ALEPH 'photon' + 1 jet data.
• Figure 3: The ${\cal O}(\alpha)$ inclusive photon energy spectrum (solid) broken down into photon + $1$ jet (dashed) and photon + $2$ jet (short-dashed) contributions for $z>0.2$ and for $y_{\rm cut}=0.06$.
• Figure 4: The ${\cal O}(\alpha)$ inclusive photon energy spectrum calculated using the range of uncertainty on $\mu_0$ obtained from the ALEPH fit to the 'photon' + 1 jet data at ${\cal O}(\alpha)$.
• Figure 5: The pointlike quark-to-photon fragmentation function for the up-quark evaluated at $\mu_F = M_Z$ at (a) LL and (b) BLL. In each case, we show the numerical resummed prediction as well as the difference with the corresponding fixed order expansions given in eqs. (\ref{['eq:llexp']}) and (\ref{['eq:bllexp']}). The hadronic scale is (a) $\mu_0 = 0.50$ GeV for LL GRV and (b) $\mu_0 = 0.55$ GeV for BLL GRV and $\mu_0 = 0.71$ GeV for BLL BFG. In (a) the difference between the LL GRV result and the leading term in the perturbative expansion eq. (\ref{['eq:alpha']}) is shown short-dashed.