1 Introduction

In high-energy particle collisions, direct photons are those photons which are directly produced in elementary processes, and as such are not products from hadronic decays. In proton-proton and nuclear collisions, direct photons are colourless probes of QCD processes. Photons originating from hard scatterings of partons from the incoming hadrons are called prompt photons. They provide a handle for testing perturbative QCD (pQCD) predictions, and they are probes of the initial state of protons or nuclei. At the lowest order (LO) in pQCD, prompt photons are produced via two processes: (i) quark-gluon Compton scattering, \(q g \rightarrow q \gamma \), (ii) quark-antiquark annihilation, \(q \bar{q} \rightarrow g \gamma \), and, with a much smaller contribution, \(q \bar{q} \rightarrow \gamma \gamma \). In addition, prompt photons are produced by higher-order processes, like fragmentation or bremsstrahlung [1]. The collinear part of such processes has been shown to contribute effectively also at LO.

A discussion of early prompt photon measurements can be found in [2], and measurements are also available from experiments at the SPS collider [3], the Tevatron [4, 5] and RHIC [6]. Recently, measurements have been performed at the LHC by the ATLAS and CMS collaborations in pp collisions at various energies [7,8,9,10,11,12,13,14,15].

These measurements allow one to study a wide range of transverse momentum (\(p_\mathrm {T}\)) of prompt photon production from 15 to 1000 \(\mathrm {GeV}/c\), the lowest limit being partially defined by the use of a high-energy photon trigger. A more fundamental limitation for direct photon measurements is imposed by the general experimental conditions. In particular, photon conversions in detector material imply a worsening of momentum resolution and signal reduction that is especially important at low momentum. For converted photons, the original energy may even be recovered for very high momentum, but a strong bias will be introduced at low transverse momentum. The low material budget in the ALICE experiment (\(X/X_0=0.7-0.9\) in front of the photon detector) makes photon measurements at low \(p_\mathrm {T}\) more reliable and allows one to move the \(p_\mathrm {T}^{\gamma }\) reach to a lower value.

In some of the above-mentioned references, the term “direct prompt photons” is introduced to denote photons from the \(2 \rightarrow 2\) processes and is contrasted in particular with fragmentation or bremsstrahlung photons emitted directly from partons. We follow a nomenclature that was adopted in a CERN Yellow Report [16] where direct photons referred to all photons that do not originate from hadronic decays and prompt photons to all photons that are directly emerging from a hard process or produced by bremsstrahlung, in any order of perturbative QCD. When needed, we speak explicitly of “photons from \(2 \rightarrow 2\) processes” in this paper.

Photons from \(2 \rightarrow 2\) processes provide clear constraints of the underlying parton kinematics, but making a clean separation between the different types of prompt photons is difficult.

In a consistent theoretical description, the separate treatment of certain diagrams is somewhat arbitrary and only justified quantitatively to reach a desired accuracy in a given calculation. A physical definition of a subset of photons has to be related to measurable criteria. This has led to the prescription of so-called “isolated photons”. An isolation criterion is applied on photon candidates, where one requires the sum of the transverse energies (or transverse momenta) of produced particles in a cone around the photon direction to be smaller than a given threshold value – this can be done both in the experiment and in theoretical calculations. Fragmentation and bremsstrahlung photons are expected to be accompanied by fragments of the parton that has been close in phase space, while photons from \(2 \rightarrow 2\) processes should be free of such associated fragments. Thus, an isolation cut should significantly suppress fragmentation and bremsstrahlung, while it should affect the \(2 \rightarrow 2\) processes only marginally [17]. A strong additional motivation of an isolation cut is to reduce the background of decay photons in the measured signal. This can be achieved, because hadrons at reasonably high \(p_\mathrm {T}\) would in general be produced in jet fragmentation and would thus be accompanied in their vicinity by other jet fragments.

Measurements of prompt and in particular isolated photons provide constraints on the proton [17] and nuclear [18] Parton Distribution Functions (PDFs). At the LHC, because of the high centre-of-momentum energy (\(\sqrt{s}\)), such PDF studies are potentially sensitive to very small values of the longitudinal momentum fraction x of the initial-state parton. For a \(2 \rightarrow 2\) process with the two particles (3 and 4) in the final state being emitted at similar rapidities \(y_3\approx y_4 \approx y\), which is the dominant contribution to the inclusive single particle cross section, the x values in the initial state can to a good approximation be calculated as:

$$\begin{aligned} x_{1,2} \approx \frac{2 p_\mathrm {T}}{\sqrt{s}} \exp (\pm y) \equiv x_{\mathrm {T}} \exp (\pm y), \end{aligned}$$

where \(p_\mathrm {T}\) is the transverse momentum and y the rapidity of the final state particles. The variable \(x_{\mathrm {T}}\) defined here is often used to compare transverse momentum distributions for different beam energies. For photons measured at mid-rapidity (\(y \approx 0\)), it is closely related to the Bjorken x-values: \(x_{\mathrm {T}} \approx x_1 \approx x_2 \equiv x\). At the LHC, the most important contribution to photon production, the quark-gluon Compton diagram, where the above relation can be applied, has the additional advantage to be directly sensitive to the gluon density, which has the largest uncertainty among the PDFs. These \(2 \rightarrow 2\) processes, which should be enriched in the measurement via the isolation cut, should therefore probe the low-x gluon content of one of the incoming hadrons. Any higher order effects will weaken the kinematic constraints, and in particular, fragmentation photons will be sensitive to much larger values of x. Also, when measuring only one of the final-state particles, the uncertainty on the rapidity of the other particles will lead to a broadening of the distribution of x values probed.

To get a better understanding of the ranges of kinematic parameters of the partonic processes that are explored in prompt photon measurements, we have performed a study of photon production with the PYTHIA 8 generator (version 8.235 [19] with Monash 2013 Tune [20]), where we extract the values of factorisation scale Q and parton momentum fractions \(x_1\) and \(x_2\) directly as specified in the PYTHIA event record. PYTHIA does not contain all effects of h