A critical phenomenological study of inclusive photon production in hadronic collisions

TL;DR

This study critically assesses inclusive prompt photon production in hadronic collisions, focusing on how theoretical predictions in NLO QCD depend on structure functions and the unphysical scales $\mu$, $M$, and $M_F$. It finds that no single set of scales and PDFs can fit all fixed-target and ISR data, with E706 data consistently lying above predictions and some ISR data displaying normalization/slopes that diverge from theory. The authors argue that introducing an intrinsic $k_T$ does not universally improve agreement and highlight potential inconsistencies among datasets and systematic uncertainties. The work underscores the need for careful treatment of experimental systematics and suggests that future RHIC measurements could help resolve the observed discrepancies and guide refinements in perturbative approaches, including possible resummation effects.

Abstract

We discuss fixed target and ISR inclusive photon production and attempt a comparison between theory and experiments. The dependence of the theoretical predictions on the structure functions, and on the renormalization and factorization scales is investigated. The main result of this study is that the data cannot be simultaneously fitted with a single set of scales and structure functions. On the other hand, there is no need for an additional intrinsic $k_{_T}$ to force the agreement between QCD predictions and experiments, with the possible exception of one data set. Since the data cover almost overlapping kinematical ranges this raises the question of consistency among data sets. A comparative discussion of some possible sources of experimental uncertainties is sketched.

Figures (10)

• Figure 1: Variation of the inclusive photon production cross section for proton-beryllium at $E_{\hbox{lab}} = 800$ GeV, $p_{_T} = 6.12$ GeV/c, $\eta = 0.$, as a function of the factorization scale and the fragmentation scale; left: the renormalization scale is "optimized" according to eq. (\ref{['eq:opt']}); right: the renormalization scale is set equal to the factorization scale.
• Figure 2: solid line: $z$ dependence of the perturbative component of the photon fragmentation function eq. (\ref{['eq:approx']}); dashed line: $z$ dependence of the compensating term proportional to ${\bf P}^{(0)}_{\gamma q}(z))$. The scale is $M_{_F}=6$ GeV.
• Figure 3: The differential inclusive photon cross sections as a function of transverse momentum. The cross sections are averaged over the $x_{_F}$/rapidity ranges shown in table \ref{['data']}. Data from the NA24 collaboration EXP are averaged in the rapidity range $-.65 < \eta < .52$.
• Figure 4: Comparison of the UA6 $\bar{p} p- p p$ data UA6 with the NLO theory for various sets of structure functions using the common scale $\mu=M=M_{_F}={p_{_T} }/2$. Only statistical errors are shown.
• Figure 5: Comparison of data with theory, normalized to the theoretical results, for the various experiments as a function of $x_{_T}$. The ABFOW structure functions are used and all scales are set equal to ${p_{_T} }/2$. Statistical error bars are shown as full lines while systematic uncertainties are added in quadrature and shown as dotted lines. An extra 5% uncertainty on the energy scale is not plotted for R110; for AFS and E706 data, statistical and systematic errors are shown combined in quadrature only.