Regge theory in hadron physics

TL;DR

This work surveys Regge theory as a nonperturbative framework for hadron scattering, grounded in analyticity in the complex angular momentum plane and crossing symmetry. It details moving Regge poles on the $\ell$-plane via trajectories $\alpha(E)$, discusses the historical development from dual models to QCD-inspired phenomenology, and reviews modern applications that connect high-energy Regge behavior to low-energy amplitudes through dispersive constraints such as FESR and Roy equations. Key contributions include empirical Regge trajectories (e.g., the Pomeron and reggeons), residue factorization, and the interpretation of resonances through complex-$\ell$ trajectories, as well as explicit methods to extract and constrain these trajectories from data. Overall, Regge theory remains a valuable tool for soft QCD phenomenology, guiding the analysis of peripheral processes, hadron spectroscopy, and the search for exotic states within a framework consistent with analyticity, unitarity, and crossing.

Abstract

We provide a pedagogical introduction to Regge theory as it pertains to the study of hadrons and their interactions. We clarify the fundamental concepts of analyticity in the complex angular momentum plane and their implications for scattering amplitudes. We highlight historical developments that significantly shaped our understanding of scattering theory and the strong interaction, both before and following the discovery of QCD. We end with a review of more recent applications of Regge theory in QCD phenomenology, including describing exchange processes, constraining low-energy amplitudes, and analyzing resonances in the complex angular momentum plane.

Figures (14)

• Figure 1: Diagrammatic representation of a diffractive production at high energies from Ref. Nys:2018vck. At small momentum transfers, i.e., $t\sim 0$, the beam particle dissociates and a rapidity gap emerges between the produced particles and the recoiling target.
• Figure 2: Deformation of the integration contour $C\to C^\prime$ from encircling poles at every integer $\ell \geq 0$ to integrating the imaginary axis with fixed $-1 < \text{Re }\ell < 0$. We pick up contributions from any possible poles contained in $f(\ell,E)$ in the right-half $\ell$-plane. Poles in the left-half plane with $\text{Re }\ell < -1$ are "screened" by the background integral.
• Figure 3: Experimental data for charged pion-proton scattering cross section from Ref. ParticleDataGroup:2020ssz. At small energies the total cross section (in red) is dominated by elastic resonances, while the smooth power-law behavior expected of reggeon exchanges dominates asymptotically.
• Figure 4: Early evidence for "Regge dips" in the total (top) and natural parity component (bottom) of the differential cross section for $\pi^0 p \to \rho^0 p$ in Ref. Gordon:1973vc. The dip corresponds to the first wrong-signature point $\alpha_\rho(t) = 0$.
• Figure 5: Original 1962 Chew-Frautschi plot from Ref. Chew:1962eu (left) compared to those from the spectrum of light mesons as of 2018 in Ref. Mathieu:2018mjw (right).