PomeronEdit
The Pomeron is a cornerstone concept in the theory of high-energy hadronic interactions. It encapsulates how hadrons scatter at high energies without exchanging the kind of quantum numbers that would change the identities of the particles involved. In broad terms, the Pomeron describes a colorless, vacuum-like exchange that governs diffractive processes and the slow rise of total cross sections with energy. While it originated in the language of Regge theory, modern understanding treats the Pomeron as a manifestation of gluonic dynamics within quantum chromodynamics (QCD), the theory of the strong interaction.
Across the decades, the Pomeron has served as a bridge between nonperturbative phenomenology and perturbative QCD. In Regge theory, it is associated with a Regge trajectory carrying vacuum quantum numbers, and its intercept dictates how rapidly total cross sections grow with energy. In QCD, the Pomeron is not a single particle but an emergent color-singlet exchange, most naturally described as a gluon ladder that can be dominated by soft, nonperturbative physics at low momentum transfers or by hard, perturbative dynamics at high momentum transfers. This dual character has shaped how experimental results are interpreted, from elastic scattering at small momentum transfer to diffractive deep inelastic scattering and central exclusive production at modern colliders.
History and concept
The name Pomeron commemorates early work on the high-energy behavior of scattering amplitudes and the idea that certain exchanges carry vacuum quantum numbers. In Regge theory, which analyzes how scattering amplitudes depend on energy and momentum transfer, the Pomeron is the leading trajectory with quantum numbers consistent with the vacuum, yielding distinctive diffractive phenomena. A key feature of this framework is that the Pomeron’s intercept, alpha_P(0), controls the energy dependence of total cross sections, often producing a slow but persistent rise with energy, in contrast to trajectories corresponding to known hadrons.
In the traditional Regge description, a rising total cross section is possible if alpha_P(0) is slightly greater than unity. Experimental data from hadron-hadron collisions in the late 20th century supported this behavior, and the Pomeron became the working language for explaining diffractive processes such as elastic scattering and single- or double-diffractive events. Over time, the Pomeron’s interpretation expanded beyond a purely phenomenological Regge trajectory to embrace a dynamical picture within QCD. The modern view treats the Pomeron as a colorless exchange formed by gluons, with different realizations depending on the energy and momentum transfer of the interaction.
Theoretical frameworks
Regge theory perspective
In Regge theory, the Pomeron corresponds to a trajectory alpha_P(t) in the complex angular-momentum plane, where t is the squared momentum transfer. The trajectory’s intercept alpha_P(0) and slope alpha′_P determine how the cross sections and diffraction patterns evolve with energy and angle. A typical soft Pomeron picture assigns alpha_P(0) just above 1 (about 1.08 in classic fits) with a modest slope, accounting for the slowly rising total cross sections and the characteristic diffraction patterns seen in hadronic collisions. This framework provides a coherent, model-independent language for describing diffraction at moderate energies and small momentum transfers.
QCD perspective
Within the framework of Quantum chromodynamics, the Pomeron emerges as a color-singlet exchange of gluons, rather than a single, well-defined particle. In perturbative regimes, the Balitsky–Fadin–Kuraev–Lipatov (BFKL) equation describes the evolution of gluon ladders that can effectively generate a hard Pomeron, with an intercept larger than one and a rise of cross sections at high energies and large momentum transfers. This hard Pomeron is most evident in processes with a hard scale, such as high-Q^2 deep inelastic scattering, and it coexists with the soft, nonperturbative Pomeron that dominates purely hadronic diffraction at low momentum transfer.
In practice, many analyses employ a two-Pomeron or multi-Pomeron approach, combining a soft Pomeron relevant at low Q^2 with a hard Pomeron relevant at high Q^2, to describe a broad range of phenomena. The precise balance between these components varies with energy and process, and it remains a subject of active investigation. The perturbative description also requires unitarization and saturation effects at very high energies, which can temper the growth of cross sections and influence diffractive rates.
Phenomenology and factorization
Experimentally, diffractive processes reveal the Pomeron’s imprint through rapidity gaps and characteristic momentum distributions. In diffractive deep inelastic scattering, a clean factorization of the hard scattering from the diffractive exchange is often observed, enabling parton-level interpretations of the Pomeron’s structure. However, in hadron-hadron collisions, additional soft interactions can fill rapidity gaps, leading to suppression of diffractive events. This phenomenon—gap survival probability—highlights how the Pomeron’s effective behavior depends on the surrounding event environment and the modeling of multi-parton interactions. See Diffractive scattering and BFKL for related theoretical developments.
Phenomenology and experiments
The Pomeron underpins the explanation of several observed features in high-energy collisions. Elastic scattering at small momentum transfer is naturally described by the exchange of a colorless object with vacuum quantum numbers, producing the characteristic diffraction peak in differential cross sections. Total cross sections for proton-proton and proton-antiproton collisions rise slowly with energy in a manner consistent with a Pomeron intercept just above unity. At collider energies, diffractive processes—ranging from single diffraction to central exclusive production—provide a laboratory for probing the Pomeron’s structure and its interplay with QCD dynamics.
Experiments at facilities such as the Tevatron, the Large Hadron Collider (LHC), and electron-proton colliders like HERA have mapped the manifestations of diffractive phenomena across a wide range of energies and momentum transfers. The LHC detectors, for example, have measured total cross sections and diffractive cross sections with increasing precision, offering data that tests soft-Pomeron parameterizations as well as perturbative, hard-Pomeron contributions. The ongoing synthesis of Regge-inspired intuition with perturbative QCD calculations remains essential for a unified understanding of diffraction in the high-energy regime. See TOTEM for total cross-section measurements and Diffractive scattering for a broader discussion of diffraction in collider environments.
Controversies and debates
A central topic in Pomeron physics is whether a single, universal Pomeron suffices to describe all diffractive phenomena or whether multiple components are needed to reconcile soft and hard processes. The conventional view allows for both a soft Pomeron, governing nonperturbative, low-momentum-transfer diffraction, and a hard Pomeron, arising from perturbative QCD dynamics at high scales. Critics of overly simplistic models argue that a complete description requires careful treatment of unitarization, saturation, and multi-Pomeron interactions, particularly at very high energies where parton densities become large. The interpretation of diffractive deep inelastic scattering and the extent to which factorization holds beyond specific processes continues to be a topic of active theoretical and experimental investigation. See Diffractive scattering and BFKL for related debates.
Another point of discussion concerns the nature of the Pomeron in the language of QCD: is it best described as a propagating object with a definite trajectory, or as a resummed class of gluon exchanges that depends sensitively on the scale and environment of the interaction? The answer has implications for how one writes down factorization theorems, predicts rapidity-gap survival probabilities, and interprets the energy evolution of diffractive structure functions. Ongoing comparisons between data and models—ranging from Regge-based fits to perturbative QCD calculations—continue to refine the practical utility of the Pomeron as a predictive tool. See QCD and BFKL for the underpinning theory.