[Paper Review] The long road from Regge poles to the LHC

Vittorio Del Duca, Lorenzo Magnea|arXiv (Cornell University)|Dec 14, 2018

Particle physics theoretical and experimental studies44 references4 citations

TL;DR

This paper traces the evolution of Regge theory from its origins in complex angular momentum analysis to its modern applications in high-energy physics, particularly in perturbative non-abelian gauge theories and LHC phenomenology. It demonstrates how Regge trajectories and high-energy scattering amplitudes underpin key predictions for total cross sections and multi-jet production, with successful fits to LHC data using resummed high-energy logarithms.

ABSTRACT

The Regge limit of gauge-theory amplitudes and cross sections is a powerful theory tool for the study of fundamental interactions. It is a vast field of research, encompassing perturbative and non-perturbative dynamics, and ranging from purely theoretical developments to detailed phenomenological applications. It traces its origins to the proposal of Tullio Regge, almost sixty years ago, to study scattering phenomena in the complex angular momentum plane. In this very brief contribution, we look back to the early days of Regge theory, and follow a few of the many strands of its development, reaching to present day applications to scattering amplitudes in non-abelian gauge theories.

Motivation & Objective

• To trace the historical development of Regge theory from its inception in quantum mechanical potential scattering to its modern applications in quantum field theory.
• To illustrate how Regge theory provides a unifying framework for understanding both non-perturbative hadron spectroscopy and perturbative scattering amplitudes in non-Abelian gauge theories.
• To demonstrate the phenomenological relevance of Regge theory in describing total hadronic cross sections and multi-jet production at the LHC.
• To highlight the role of Regge theory in enabling all-order resummation of rapidity logarithms in high-energy QCD processes.
• To show that Regge-inspired models, including effective string theories and AdS/QCD, remain relevant for non-perturbative strong interaction dynamics.

Proposed method

• Uses Regge trajectory analysis to connect bound states in quantum mechanics to scattering amplitudes in complex angular momentum planes.
• Applies Gribov-Regge theory to relativistic quantum field theory, leveraging crossing symmetry and Lorentz invariance to constrain high-energy amplitudes.
• Employs the Lipatov approach to derive perturbative high-energy behavior in non-Abelian gauge theories, particularly in $N=4$ SYM and QCD.
• Utilizes effective Reggeon exchange models to parametrize total hadronic cross sections via power-law forms $\sigma^{\rm tot}_{ab} = X_{ab} s^{\alpha} + Y_{ab} s^{\beta}$.
• Applies the High Energy Jet (HEJ) framework to resum leading logarithms in rapidity, enabling accurate predictions for multi-jet cross sections at high di-jet invariant masses.
• Compares theoretical predictions with LHC data, including ATLAS measurements of $W$+jets production, to validate Regge-based resummation techniques.

Experimental results

Research questions

• RQ1 How do Regge trajectories emerge from the analytic structure of scattering amplitudes in quantum mechanics and field theory?
• RQ2 In what way does Gribov-Regge theory unify non-perturbative hadron spectroscopy with perturbative high-energy scattering in gauge theories?
• RQ3 How do Regge-inspired models describe the energy dependence of total hadronic cross sections across multiple orders of magnitude in energy?
• RQ4 To what extent can Regge theory provide all-order resummation of rapidity logarithms in multi-jet production at the LHC?
• RQ5 What is the role of Regge theory in connecting string theory, effective field theories, and modern LHC phenomenology?

Key findings

• Linearly rising Regge trajectories provide excellent fits to meson and baryon resonance spectra, as shown in fits to $\rho$ mesons and $\Delta^*$ baryons using both data and AdS/QCD-based models.
• The Donnachie-Landshoff parametrization of total cross sections using $\sigma^{\rm tot}_{ab} = X_{ab} s^{\alpha} + Y_{ab} s^{\beta}$ with $\alpha \simeq 0.08$ and $\beta \simeq -0.45$ successfully describes proton-proton and proton-antiproton data, including early LHC measurements.
• The High Energy Jet (HEJ) framework, incorporating Regge contributions at leading logarithmic accuracy, accurately predicts the $W$+jets cross section at high di-jet invariant masses, matching ATLAS data in the high-mass region.
• Regge theory enables all-order resummation of rapidity logarithms in multi-jet production, a crucial ingredient for precision LHC phenomenology as statistical uncertainties shrink with increased luminosity.
• The same effective Regge trajectory parameters ($\alpha \simeq 0.08$, $\beta \simeq -0.45$) describe diverse processes, indicating that the exchange particle properties—not the initial hadrons—dominate the energy dependence.
• Regge theory remains a central theoretical tool in modern high-energy physics, with deep roots in string theory and ongoing relevance for both non-perturbative and perturbative QCD.