Resolved Photon Processes: A Tribute to Rohini Godbole

Abstract: Hadrons are particles composed of elementary quarks and gluons, which have strong interactions described by Quantum Chromodynamics (QCD); examples are protons and neutrons, which bind to form atomic nuclei. In contrast, photons are usually thought of as the elementary force carriers of quantum electrodynamics (QED). However, at the quantum level a photon can fluctuate into a quark antiquark pair. At sufficiently high energies these virtual quarks can become real, physical particles by interacting with other particles, in particular with other hadrons. In this way photons with energies exceeding a few GeV acquire properties of a hadron. Resolved photon processes are reactions that probe these hadronic properties. These processes often dominate the production of hadronic final states, including jets (sprays of collimated hadrons), at electron--proton and electron--positron colliders. Implications of this for backgrounds at future high--energy lepton colliders remain poorly understood.

• The paper explains that photon parton distributions scale as O(αem/αS), making resolved and direct processes the same perturbative order and often making resolved channels dominant.
• The paper reviews predictions confirmed at HERA and TRISTAN, including resolved contributions dominating ep dijets below about 30 GeV and accounting for roughly 70% of ZEUS events above 14 GeV.
• The paper shows that beamstrahlung-generated γγ collisions can create significant hadronic backgrounds, whose effects on FCC-ee W-mass measurements and future muon colliders remain insufficiently quantified.

Overview

"Resolved Photon Processes: A Tribute to Rohini Godbole" (2608.17864) is Manuel Drees's memorial essay reviewing the physics of resolved photons, framed around the collaborative work he carried out with Rohini M. Godbole. The article serves simultaneously as a pedagogical introduction to the hadronic structure of the photon and a historical account of the predictions that shaped the jet-physics programs at HERA and TRISTAN/LEP. Its central thesis is that at sufficiently high energies a photon behaves as a hadron, and that reactions initiated by the partonic constituents of the photon — "resolved photon processes" — frequently dominate hard hadronic final states at lepton colliders, a fact whose implications for backgrounds at future colliders remain, in the author's assessment, poorly understood.

The hadronic structure of the photon

The essay opens by situating resolved photons within QCD. Because of asymptotic freedom and collinear splitting, the content of a proton probed at momentum transfer $Q \gtrsim 1$ GeV is a flux of quarks, antiquarks and gluons described by parton distribution functions (PDFs) whose $Q$-evolution is governed by the DGLAP equations. The photon case is analogous but distinct: since the photon carries no color, any parton content must originate from a $\gamma \to q\bar{q}$ splitting, which involves the electromagnetic coupling. Naively this makes photonic PDFs $\mathcal{O}(\alpha_{\rm em})$ quantities, suggesting they could be treated as higher-order corrections.

The crucial observation, traceable to Witten's 1977 analysis, is that the DGLAP evolution drives all photonic PDFs to grow logarithmically with $Q$ — unlike proton PDFs, whose basic normalization moments stay fixed. Photonic PDFs are therefore properly counted as $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$ quantities, placing them at the same perturbative order as direct processes rather than as suppressed corrections. This is the conceptual pivot of the whole field.

The paper is also careful about what cannot be computed. Although the "asymptotic" perturbative prediction exists, at NLO it yields negative PDFs at small $x$ when applied at finite $Q$; moreover, in the strict asymptotic limit all proton PDFs collapse to $\delta$-functions at $x = 0$, far from reality even at LHC scales. The correct procedure, following Rossi and Glück–Grassie–Reya, is to fit input distributions at low $Q$0 and evolve them with modified DGLAP equations. A non-perturbative component is also physically unavoidable: the photon can fluctuate into a virtual vector meson ($Q$1, $Q$2, $Q$3) via vector meson dominance, and the PDFs inside such mesons are as non-perturbative as those in the proton. The author notes the related modern development that PDF fits of the proton now include a photon constituent, itself an $Q$4 quantity.

Photoproduction at $Q$5 colliders

At an $Q$6 collider, quasi-real photons emitted by the electron (Weizsäcker–Williams flux $Q$7) scatter off the proton. Drees and Godbole predicted, in work predating HERA's operation, that dijet photoproduction receives both "direct" contributions ($Q$8, with the full photon energy entering the hard scattering) and "resolved" contributions, where a parton from the photon initiates the scattering. The key point — stated by the author as not having been appreciated previously — is that resolved contributions are also $Q$9, because the hard partonic cross section is $\gamma \to q\bar{q}$0 but the photonic PDF carries $\gamma \to q\bar{q}$1.

The resolved channel benefits from $\gamma \to q\bar{q}$2-channel gluon exchange and color factors unavailable to the direct process, so it dominates at moderate transverse momentum; the paper reports the prediction that resolved processes dominate for $\gamma \to q\bar{q}$3 GeV at HERA kinematics ($\gamma \to q\bar{q}$4 GeV). Experiment confirmed this: the ZEUS measurement found that roughly 70% of dijet events persisted as resolved-photon events even after a cut of $\gamma \to q\bar{q}$5 GeV — a strikingly large resolved fraction. A qualitative signature distinguishing the two classes is the photon remnant: resolved events contain additional low-energy hadrons near the electron direction, which also implies that direct and resolved contributions must be added incoherently.

Regarding future facilities, the author notes that the Electron–Ion Collider at Brookhaven ($\gamma \to q\bar{q}$6 GeV, possibly 140 GeV) could probe resolved photons, though this has so far been studied only in conference proceedings, while the planned Chinese EIC at $\gamma \to q\bar{q}$7 GeV is probably too low to reach the perturbative regime.

Two-photon physics at $\gamma \to q\bar{q}$8 colliders

Each beam lepton carries its own photon flux, so an $\gamma \to q\bar{q}$9 collider is automatically also an $\mathcal{O}(\alpha_{\rm em})$0 and $\mathcal{O}(\alpha_{\rm em})$1 collider. Although two-photon cross sections carry four powers of $\mathcal{O}(\alpha_{\rm em})$2 versus two for annihilation, the flux factors contribute $\mathcal{O}(\alpha_{\rm em})$3, and — decisively — the annihilation cross section falls as $\mathcal{O}(\alpha_{\rm em})$4 while fixed-hardness $\mathcal{O}(\alpha_{\rm em})$5 cross sections do not. The paper states the strong quantitative consequence that already at $\mathcal{O}(\alpha_{\rm em})$6 GeV, $\mathcal{O}(\alpha_{\rm em})$7 collisions, not $\mathcal{O}(\alpha_{\rm em})$8 annihilation, are the main source of $\mathcal{O}(\alpha_{\rm em})$9 pairs, and that above a few tens of GeV the same holds for dijet production.

Three classes of contributions exist in $Q$0 scattering: direct, single-resolved and double-resolved, all at $Q$1 in the $Q$2 subsystem. Drees and Godbole predicted that resolved contributions dominate dijet production at TRISTAN ($Q$3 GeV) for $Q$4 GeV. The author identifies the quantitative description of these "minijets" at TRISTAN — which required resolved photons — as possibly the main physics achievement of that program, and links the rising minijet cross section to the growth of total inelastic cross sections in $Q$5, $Q$6, $Q$7 and $Q$8 scattering. Notably, the paper concedes a gap in the experimental record: no $Q$9 dijet analysis was ever published using the high-luminosity LEP data at $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$0 GeV, which could have extended coverage to $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$1 GeV.

Beamstrahlung and backgrounds at future colliders

The most forward-looking section concerns the cleanliness of future lepton colliders. To maintain annihilation event rates at high energy, luminosity must scale as $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$2, achieved by strong final focusing — which enhances beamstrahlung, the radiation emitted by beam particles in the intense electromagnetic field of the opposing bunch. Drees and Godbole showed that some early designs for a 500 GeV linear $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$3 collider would have produced more than one hadronic $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$4 collision per bunch crossing. While this pile-up is far milder than the $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$5 $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$6 overlaps expected at the high-luminosity LHC, it undermines the categorical claim that $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$7 colliders always offer a very clean environment.

The paper makes this concrete with the FCC-ee proposal: the recommended method for measuring the $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$8 mass via the $\mathcal{O}(\alpha_{\rm em}/\alpha_S)$9 threshold cross section at $x$0 and 162.5 GeV requires controlling point-to-point acceptance variations at the few-$x$1 level, yet the multi-hadron $x$2 background cross section itself varies by several percent between these two energies, with an uncertain magnitude. The impact of this background on the proposed $x$3 mass measurement is stated to be currently unclear. For a future multi-TeV $x$4 collider, the $x$5 flux scaling reduces two-photon rates by only about a factor of 2 relative to an $x$6 machine at $x$7 TeV, and the implications of the hadronic content of muon beams for backgrounds remain unexplored.

Limitations and open questions

The essay is candid about the boundaries of the field. The photon remnant structure cannot be predicted from first principles in perturbative QCD; photonic PDFs require non-perturbative input fitted to data, and the exact magnitude of the $x$8 multi-hadron background variation near the $x$9 threshold is uncertain. Several questions are explicitly left open: whether resolved photon processes at the EIC will be studied in the literature beyond conference proceedings; what effect the $Q$0 hadronic background has on precision $Q$1 mass measurements at circular colliders; and how the hadronic nature of high-energy muon beams affects backgrounds at a muon collider.

Conclusion

The paper is both a technical review and a tribute. Its core results — the $Q$2 counting of photonic PDFs, the dominance of resolved contributions in $Q$3 dijet production up to $Q$4 GeV, the dominance of $Q$5 processes in muon-pair and dijet production at $Q$6 colliders, and the beamstrahlung-driven hadronic pile-up at linear colliders — were confirmed by ZEUS, TRISTAN and early LEP measurements. The unifying message is that the hadronic structure of the photon is not a higher-order curiosity but a leading effect, and that its consequences for precision physics at future lepton colliders remain insufficiently quantified.