Regge trajectories

Regge trajectories
Name	Regge trajectories
Field	Theoretical physics
Discoverer	Tullio Regge
Year	1959

Regge trajectories Regge trajectories are functions used in high-energy theoretical physics to relate the angular momentum and mass squared of hadronic resonances within scattering theory and particle spectroscopy. They bridge concepts from Tullio Regge's analytic S-matrix program to modern frameworks involving the S-matrix, Quantum Chromodynamics, and string-inspired models such as the Veneziano amplitude and AdS/CFT correspondence. These trajectories inform analyses in experiments at facilities like CERN, Fermilab, and SLAC, and they influenced theoretical developments at institutions including Princeton University and the Institute for Advanced Study.

Introduction

Regge trajectories organize families of hadrons by plotting complex angular momentum against squared mass, a perspective that emerged in the context of the S-matrix and analytic continuation techniques pioneered by Tullio Regge and contemporaries at places such as Cambridge University and Scuola Normale Superiore. The approach connects to the Veneziano amplitude developed at CERN and to ideas in dual resonance models that later inspired string theory and work by researchers at Harvard University, University of Chicago, and California Institute of Technology. Regge trajectories provide phenomenological fits used by collaborations like Particle Data Group to classify resonances observed in detectors at LEP, Tevatron, and Belle.

Origin and theoretical background

The concept originated with Tullio Regge's analytic continuation of angular momentum in nonrelativistic potential scattering, an innovation influenced by earlier analytic S-matrix research at institutions such as Institute for Advanced Study and CERN. The idea was built upon methods from Scattering theory developed by physicists including Lev Landau, Eugene Wigner, and John von Neumann and was incorporated into particle physics programs at Brookhaven National Laboratory and DESY. Regge's work catalyzed dual resonance models by theorists like Gabriele Veneziano, Murray Gell-Mann, and Gabriele Veneziano's collaborators, later shaping string-theoretic frameworks explored at Princeton University and Stanford University.

Mathematical formulation

Mathematically, a trajectory α(t) relates complex angular momentum to the Mandelstam variable t, leveraging analytic continuation of partial-wave amplitudes introduced in formalisms by Tullio Regge and analyzed with tools from Complex analysis and integral equations studied by researchers at University of Cambridge and École Normale Supérieure. The pole structure of the partial-wave S-matrix in the complex l-plane gives rise to poles α(t) whose linear approximations α(t) ≈ α0 + α' t are parameterized similarly to fits used by the Particle Data Group. Techniques to extract α(t) use dispersion relations associated with concepts explored by G. F. Chew and by groups at Imperial College London, employing methods later adapted in perturbative studies by teams at CERN and Brookhaven National Laboratory.

Applications in hadron spectroscopy

In hadron spectroscopy, trajectories classify mesons and baryons into nearly linear families where J ≈ α(M^2), a pattern evident in data compiled by the Particle Data Group and in analyses from experiments at CERN, SLAC, and Jefferson Lab. Phenomenological fits separate trajectories for light mesons (e.g., families studied by Gell-Mann and Yuval Ne'eman) and heavy-quark states examined in programs at Fermilab and Belle II. The linear Regge behavior supports models developed by theorists at SISSA, CEA Saclay, and Max Planck Institute for Physics that connect to bag models, potential models by groups at Yale University, and string-inspired pictures explored at Princeton University.

Role in Regge theory and scattering amplitudes

Within Regge theory, trajectories dictate the high-energy behavior of scattering amplitudes and total cross sections via Regge pole exchanges such as the Pomeron and various meson trajectories named after families cataloged by the Particle Data Group. These ideas were central to the analytic S-matrix program involving figures like Geoffrey Chew, Stanley Mandelstam, and institutions including CERN and Brookhaven National Laboratory. Reggeon exchange models were implemented in Monte Carlo event generators used at CERN and DESY and interfaced with perturbative approaches developed by groups at SLAC and Brookhaven National Laboratory.

Experimental evidence and phenomenology

Experimental support arises from spectroscopy patterns observed in experiments at CERN experiments such as COMPASS, at SLAC, and at KEK facilities including Belle, where resonance masses and spins align on near-linear trajectories compiled by the Particle Data Group. Phenomenological success is seen in fits to scattering data from ISR, Tevatron, and LHC measurements interpreted by collaborations like ATLAS and CMS, and in exclusive processes measured at Jefferson Lab. Discrepancies and refinements involve analysis groups at DESY, Fermilab, and theoretical input from Institute for Advanced Study and Perimeter Institute for Theoretical Physics.

Extensions and modern developments

Modern developments integrate Regge behavior with perturbative approaches such as the Balitsky–Fadin–Kuraev–Lipatov (BFKL) framework developed by researchers including Lipatov and groups at CERN and Steklov Institute of Mathematics, and with holographic models stemming from the AdS/CFT correspondence pioneered by Juan Maldacena and explored at Princeton University and Harvard University. Contemporary work at CERN, SLAC, DESY, and Perimeter Institute for Theoretical Physics explores nonlinear trajectories, multi-Regge kinematics studied by teams at Brookhaven National Laboratory, and dualities connecting trajectories to string states analyzed at Caltech and Rutgers University. Applications extend to modeling in heavy-ion programs at RHIC and to amplitude program efforts by groups at Institute for Advanced Study and Stanford Institute for Theoretical Physics.

Category:Particle physics