[Paper Review] Comment on the Theta+ width and mass

Dmitri Diakonov, V. Petrov+1 more|ArXiv.org|Apr 23, 2004

Cosmology and Gravitation Theories3 citations

TL;DR

This paper reaffirms the prediction of a narrow, light exotic baryon Θ⁺ with mass ≈1530 MeV and width ≤15 MeV, based on the chiral quark soliton model. It counters Jaffe's claim of an arithmetic error by showing that the narrow width arises from a strong cancellation among symmetry constants G₀, G₁, and G₂, particularly when G₁/G₀ ≈ 0.4–0.6, leading to Γ ≈ 3.6–11.2 MeV.

ABSTRACT

We discuss the relatively low mass and narrow width prediction for the exotic baryon Theta+, and comment on recent statements by R.L. Jaffe on the subject. We reaffirm that a narrow width of 3.6-11.2 MeV follows from the equations of our 1997 paper.

Motivation & Objective

• To respond to R. L. Jaffe's claim that an arithmetic error in the 1997 paper would increase the Θ⁺ width to 30 MeV.
• To reaffirm the original prediction of a narrow Θ⁺ width (≤15 MeV) based on the chiral quark soliton model.
• To clarify that the narrow width arises from a dynamical cancellation between G₀, G₁, and G₂ symmetry constants.
• To demonstrate the consistency of the width prediction with phenomenological constraints on G₀, G₁, and G₂.
• To emphasize that the low mass and narrow width of the Θ⁺ are robust predictions from the model, despite model uncertainties.

Proposed method

• Uses the width formula from DPP1997 (Eq. 1): Γ_Θ = (3G̅₁₀² / 2π(m_N + m_Θ)²) * (m_N / m_Θ) * (1/5) * |p|³, where |p| is the kaon momentum in the decay Θ⁺ → NK.
• Expresses the antidecuplet-octet transition constant as G̅₁₀ = G₀ - G₁ - (1/2)G₂, using symmetry constants from the chiral quark soliton model.
• Applies phenomenological constraints: g_πNN ≈ 13.3 from Eq. (4), and g_A^(0) ≈ 0.3–0.1 from Eq. (3), to estimate G₀ and G₁.
• Uses the ratio ρ = G₁/G₀ ∈ [0.4, 0.6] as a theoretical input to fix G̅₁₀, based on chiral quark soliton model estimates.
• Computes the kaon three-momentum |p| using relativistic phase space (Eq. 7), yielding |p| ≈ 254 MeV for m_Θ = 1530 MeV.
• Evaluates the width numerically for different ρ values, confirming the narrow width range.

Experimental results

Research questions

• RQ1 Does the original prediction of a narrow Θ⁺ width (≤15 MeV) in DPP1997 remain valid despite Jaffe's claim of an arithmetic error?
• RQ2 What is the origin of the narrow width in the Θ⁺ baryon within the chiral quark soliton model?
• RQ3 How do the symmetry constants G₀, G₁, and G₂ contribute to the width, and what role does their cancellation play?
• RQ4 Can the Θ⁺ width prediction be consistently derived from phenomenological constraints on g_πNN and g_A^(0)?
• RQ5 Why does the Skyrme model fail to predict the narrow width, and how does the chiral quark soliton model overcome this?

Key findings

• The width of the Θ⁺ baryon is predicted to be 3.6 MeV for ρ = G₁/G₀ = 0.6, 6.7 MeV for ρ = 0.5, and 11.2 MeV for ρ = 0.4.
• The narrow width arises from a strong cancellation between the G₀, G₁, and G₂ contributions in the transition constant G̅₁₀.
• The prediction of a width ≤15 MeV is robust and consistent with the original 1997 analysis, even after accounting for small corrections.
• The model predicts a Θ⁺ mass of approximately 1530 MeV, consistent with experimental observations.
• The Skyrme model cannot produce a narrow width because it sets G₁ and G₂ to zero, eliminating the cancellation mechanism.
• The prediction of a narrow Θ⁺ width is not an artifact of model assumptions but a consequence of the dynamical interplay of symmetry constants in the chiral quark soliton model.