Massive Lepton Pairs as a Prompt Photon Surrogate

TL;DR

This work analyzes the $Q_T$-dependent cross section for massive lepton-pair production in hadron collisions at NLO, linking it to the prompt-photon program while avoiding photon-isolation issues. It demonstrates that in the region $Q_T>Q/2$, gluon-initiated Compton subprocesses dominate the cross section, enabling direct constraints on the gluon density through $d^2\sigma/dQ\,dQ_T$ across fixed-target and collider energies. The paper provides detailed comparisons with UA1 and E772 data and makes predictions for Tevatron-like and LHC energies, highlighting that the massive-lepton-pair channel is substantially smaller than prompt photons but offers a cleaner gluon-density probe with similar partonic dynamics. The findings suggest exploiting this channel to complement prompt-photon analyses, while acknowledging the role of resummation at small $Q_T$ and the need to select the perturbative regime $Q_T\gtrsim Q/2$ for robust, fixed-order interpretations.

Abstract

We discuss the transverse momentum distribution for the production of massive lepton-pairs in hadron reactions at fixed target and collider energies within the context of next-to-leading order perturbative quantum chromodynamics. For values of the transverse momentum $Q_T$ greater than the pair mass $Q$, $Q_T > Q$, we show that the differential cross section is dominated by subprocesses initiated by incident gluons. Massive lepton-pair differential cross sections are an advantageous source of constraints on the gluon density, free from the experimental and theoretical complications of photon isolation that beset studies of prompt photon production. We compare calculations with data and provide predictions for the differential cross section as a function of $Q_T$ in proton-antiproton reactions at center-of-mass energies of 1.8 TeV, and in proton-nucleon reactions at fixed target and LHC energies.

Figures (12)

• Figure 1: (a)Lowest-order Feynman diagrams for the direct process $q + \bar{q} \rightarrow \gamma + g$. (b) Examples of virtual gluon loop diagrams. (c) Examples of next-to-leading order three-body final-state diagrams.
• Figure 2: As in Fig. 1, but for the subprocesses initiated by the $q + g$ initial state.
• Figure 3: Diagrams that illustrate situations in which the photon becomes collinear to a quark in (a) the initial state and (b) the final state.
• Figure 4: Lowest order ${\cal O}(\alpha_s)$ (dashed lines) and next-to-leading order ${\cal O}(\alpha_s^2)$ (solid lines) perturbative calculations of the invariant inclusive cross section $Ed^3\sigma/dp^3$ as a function of $Q_T$ for $p N \rightarrow \gamma^* X$ at $p_{\rm lab}$ = 800 GeV, in the $\overline{\rm MS}$ scheme. Contributions from the $qg$ and $q \bar{q}$ channels are shown separately. The results are integrated over the scaled longitudinal momentum interval 0.1 $<x_F<$ 0.3 and over the interval 5.0 $<Q<$ 6.0 GeV, and they are divided by the bin width in $x_F$.
• Figure 5: Contributions from the various partonic subprocesses to the invariant inclusive cross section $Ed^3\sigma/dp^3$ as a function of $Q_T$ for $p N \rightarrow \gamma^* X$ at $p_{\rm lab}$ = 800 GeV. The cross section is integrated over the scaled longitudinal momentum interval 0.1 $<x_F<$ 0.3 and over the intervals (a) 5.0 $<Q<$ 6.0 GeV, (b) 11.0 $<Q<$ 12.0 GeV, and (c) 2.0 $<Q<$ 3.0 GeV, and divided by the bin width in $x_F$. The contributions are labeled by $qg$ (solid), $q \bar{q}$ (dashed), $gg$ (dotted), $q \bar{q}_2$ non-factorizable parts (dot-dashed), and $qq$ (wide dots). The $qq$ and $q \bar{q}_2$ results nearly coincide.