[Paper Review] From pions to pentaquarks

Dmitri Diakonov|ArXiv.org|Jun 4, 2004

Quantum Chromodynamics and Particle Interactions7 citations

TL;DR

This paper proposes that the narrow exotic baryon $Θ^+$ arises as a collective excitation of the chiral field in baryons, driven by spontaneous chiral symmetry breaking via instantons. It explains the $Θ^+$'s extremely narrow width as a consequence of suppressed coupling to the nucleon due to its small 5-quark component, which suppresses decay amplitudes and explains its absence in high-energy experiments.

ABSTRACT

I overview the physical picture of QCD at low energies that has led to the prediction of a narrow exotic baryon Theta^+ which cannot be made of three quarks. The very narrow width of the Theta^+ and a possible reason why it is seen in low- but not in high-energy experiments are briefly discussed.

Motivation & Objective

• To resolve the long-standing problems in constituent quark models, such as the spin crisis and the nucleon sigma term paradox.
• To explain the origin of 93% of the nucleon mass, which cannot be accounted for by current quark masses alone.
• To provide a theoretical framework for the existence of exotic baryons like $Θ^+$, which cannot be described as three-quark states.
• To explain why $Θ^+$ is observed in low-energy but not high-energy experiments, despite its narrow width.

Proposed method

• Uses the instanton liquid model to describe spontaneous chiral symmetry breaking in QCD, generating dynamical quark masses.
• Applies the chiral quark soliton model (CQSM) to describe baryons as solitonic excitations of the chiral field, with collective quantization.
• Derives the $Θ^+$ state as a collective excitation in the baryon soliton, with quantum numbers $J^P = \frac{1}{2}^+$ and quark content $uudd\bar{s}$.
• Calculates the decay width of $Θ^+ \to nK^+$ using the overlap between the $Θ^+$ and the neutron’s 5-quark component, suppressed by $({\cal N}_n^{(5)} / {\cal N}_n^{(3)})^{1/2}$.
• Analyzes transition amplitudes in the infinite momentum frame, showing suppression of axial, pseudoscalar, and vector couplings.
• Argues that high-energy experiments fail to detect $Θ^+$ due to dominance of the gluonic pomeron, which suppresses coupling to 3-quark states.

Experimental results

Research questions

• RQ1 Why is the nucleon sigma term much larger than predicted by the constituent quark model, and what does this imply about the origin of nucleon mass?
• RQ2 How can exotic baryons like $Θ^+$ exist if they cannot be described as three-quark states?
• RQ3 What explains the extremely narrow width of the $Θ^+$ baryon, and why is it observed only in low-energy experiments?
• RQ4 Why is $Θ^+$ not seen in high-energy experiments, despite its predicted production cross-section?
• RQ5 How does the chiral quark soliton model account for the binding of quarks in baryons beyond the non-relativistic quark model?

Key findings

• The nucleon mass is primarily generated via spontaneous chiral symmetry breaking driven by instantons, explaining 93% of its mass.
• The $Θ^+$ baryon is predicted as a collective excitation of the chiral field, not a bound state of five quarks, with a narrow width of approximately 0.7 MeV.
• The suppression of the $Θ^+ \to nK^+$ decay width arises from the small admixture of the 5-quark component in the neutron, estimated to be $\mathcal{N}_n^{(5)} \ll \mathcal{N}_n^{(3)}$.
• All transition couplings (axial, pseudoscalar, vector) of the $Θ^+$ are suppressed due to the same small overlap, explaining its narrow width.
• High-energy experiments fail to detect $Θ^+$ because only the gluonic pomeron survives at high momentum transfer, which couples weakly to the exotic 5-quark state.
• The model suggests that exciting a 5-quark nucleon resonance may be a more promising route to producing $Θ^+$, as in the CLAS experiment proposal.