[Paper Review] Is chiral symmetry broken and or restored in high-mass light baryons?

E. Klempt|arXiv (Cornell University)|Nov 16, 2010

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper argues that chiral symmetry remains spontaneously broken in high-mass light baryons, contrary to the conjecture of symmetry restoration in excited states. It proposes that resonance masses arise from chiral symmetry breaking in an extended volume, where increasing hadron size amplifies the energy of fluctuating gluon fields, explaining parity doublets without requiring restoration of chiral symmetry.

ABSTRACT

Based on a thorough comparison of the nucleon and $Δ$ excitation spectrum with models we show that parity doublets observed in the mass spectra do not entail the consequence that highly excited $N$ or $Δ$ resonances are insensitive to chiral symmetry breaking. Instead, the mechanism of mass generation in excited states is suggested to be the same as for the baryon ground states: the mass is assigned to fluctuating gluon fields and their strong attraction. In excited baryons, the field energy has to be integrated over a larger volume, and the total mass increases. Thus, also the additional mass of resonances, the excitation energy, is generated by spontaneous breaking of chiral symmetry.

Motivation & Objective

• To challenge the widely held conjecture that chiral symmetry is restored in highly excited light baryons.
• To explain the origin of mass in high-mass baryon resonances, particularly the role of chiral symmetry breaking.
• To account for the observed parity doublets in the 1.9–2.3 GeV region without invoking chiral symmetry restoration.
• To clarify why certain resonances, like $N_{7/2^{+}}(1990)$, lack observed parity partners.
• To guide future experimental searches by identifying optimal production channels for missing states.

Proposed method

• Compares the experimental nucleon and $ abla(1232)$ excitation spectrum with theoretical models, focusing on parity doublets in the 3rd and 4th resonance regions.
• Applies the AdS/QCD framework with a soft wall to model hadron size and its impact on field energy and mass generation.
• Uses the QCD Lagrangian with chiral symmetry breaking terms, emphasizing the role of $f E$ and $f B$ field energy in mass generation.
• Analyzes the dependence of mass on hadron volume, assuming uniform field distribution and scaling of field energy with size.
• Evaluates photoproduction amplitudes for $J^P = 5/2^{/pm}$ and $7/2^{/pm}$ states to rule out kinematic suppression as a reason for missing partners.
• Reinterprets constituent quark masses as dynamical, size-dependent quantities rather than fixed values, reconciling the quark model with QCD.

Experimental results

Research questions

• RQ1 Do observed parity doublets in high-mass baryons imply chiral symmetry restoration?
• RQ2 What is the origin of the excitation energy in highly excited baryons—chiral symmetry breaking or a different mechanism?
• RQ3 Why are some $J^P$ states, such as $N_{7/2^{+}}(1990)$, missing their parity partners?
• RQ4 Can photoproduction experiments distinguish between chiral symmetry breaking and restoration in excited baryons?
• RQ5 How does hadron size influence the mass of resonances via chiral symmetry breaking?

Key findings

• Parity doublets in high-mass baryons do not imply chiral symmetry restoration; instead, they can arise from chiral symmetry breaking in an extended volume.
• The mass of excited baryons, including their excitation energy, is generated by the energy of fluctuating gluon fields integrated over a larger volume, not by a change in the underlying dynamics.
• The constituent quark mass is not a fixed value but increases with hadron mass, reaching about one-third of the resonance mass in excited states.
• The absence of parity partners like $N_{5/2^{-}}(2200)$ or $ abla_{7/2^{-}}(2200)$ is not due to symmetry restoration but may be due to angular momentum barriers or experimental limitations.
• Photoproduction experiments are decisive for testing the hypothesis, as they can probe $7/2^{/pm}$ states without kinematic suppression.
• The observed mass splitting of ~220 MeV between $N_{5/2^{-}}(2200)$ and $N_{5/2^{+}}(2000)$ is consistent with chiral symmetry breaking, not restoration, and aligns with the string tension of baryon Regge trajectories.