[Paper Review] A heretical view on linear Regge trajectories

Dmitri Diakonov, V. Petrov|ArXiv.org|Dec 10, 2003

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper proposes that linear Regge trajectories in hadrons arise not from gluonic flux tubes, but from rotating chiral solitons made of pion fields. Using the Skyrme model framework, it shows that rotating pion configurations minimize energy at high spin, yielding linear trajectories with a slope determined by the pion decay constant, α′ ≈ 1.45 GeV⁻², close to the phenomenological value when quantum corrections are included.

ABSTRACT

We discuss a possibility that linear Regge trajectories originate not from gluonic strings connecting quarks, as it is usually assumed, but from pion excitations of light hadrons. From this point of view, at large angular momenta both baryons and mesons lying on linear Regge trajectories are slowly rotating thick strings of pion field, giving rise to a universal slope computable from the pion decay constant. The finite resonance widths are mainly due to the semiclassical radiation of pion fields by the rotating elongated chiral solitons. Quantum fluctuations about the soliton determine a string theory which, being quantized, gives the quantum numbers for Regge trajectories.

Motivation & Objective

• To challenge the conventional gluonic string model of Regge trajectories by proposing an alternative origin in pion field excitations.
• To explain the universal slope of linear Regge trajectories using the pion decay constant Fπ ≈ 93 MeV.
• To show that high-spin hadrons are rotating chiral solitons where pion fields form thick, slowly varying strings.
• To demonstrate that meson and baryon trajectories share the same slope due to identical underlying dynamics in the chiral soliton picture.
• To provide a mechanism for resonance widths via semiclassical pion radiation from rotating solitons.

Proposed method

• Model hadrons as rotating chiral solitons in the effective chiral Lagrangian, using the Skyrme model with the kinetic term S_kin = (F²π/4)∫d⁴x√−g g^{μν} Tr(LμLν).
• Use the energy functional E ∼ F²π r₀ + J²/(F²π r³₀) to minimize total energy for fixed angular momentum J, yielding r₀ ∼ √J / Fπ.
• Derive the Regge slope as α′ ∼ 1/(8π²F²π) ≈ 1.45 GeV⁻², showing universality from pion dynamics.
• Account for quantum corrections via zero-mode quantization of oscillations about the classical soliton solution.
• Distinguish mesons and baryons via the filling of Dirac levels in the transverse pion field background: mesons fill negative-energy states, baryons occupy the zero-mode bound state.
• Justify the classical solution by minimizing radiation width, favoring configurations with minimal energy loss.

Experimental results

Research questions

• RQ1 Why do linear Regge trajectories have a nearly universal slope α′ ≈ 0.8–0.9 GeV⁻² across mesons and baryons?
• RQ2 How can the chiral symmetry breaking in QCD, particularly the light pion mass, be consistently incorporated into a Regge trajectory model?
• RQ3 Why do baryon and meson trajectories have the same slope despite different quark content?
• RQ4 What is the origin of resonance widths in high-spin hadrons within a soliton-based framework?
• RQ5 Can rotating chiral solitons with large spin reproduce the observed linear dependence J ∝ M²?

Key findings

• The Regge slope is predicted as α′ ≈ 1.45 GeV⁻² from the pion decay constant Fπ ≈ 93 MeV, matching the phenomenological value within a factor of 1.5.
• The slope is universal for both mesons and baryons because both arise from the same underlying chiral soliton dynamics.
• The nucleon ground state and its excited states on the Regge trajectory are naturally described as a static and rotating chiral soliton, respectively.
• Finite resonance widths arise primarily from semiclassical radiation of pion fields by the rotating soliton.
• Quantum corrections to the classical soliton energy may resolve the discrepancy between the theoretical α′ and the phenomenological value.
• The model explains parity and signature degeneracy as consequences of the chiral structure of the soliton solution.