[Paper Review] Pentaquark in a supersmmetric quark-diquark model

D. B. Lichtenberg|ArXiv.org|Jun 17, 2004

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proposes a supersymmetric quark-diquark model in QCD to estimate the mass of an exotic pentaquark with strangeness +1. By replacing two antiquarks in an antibaryon with diquarks—leveraging approximate dynamical supersymmetry between antiquarks and antitriplet diquarks—it predicts a lower mass limit of 1741 MeV, exceeding the reported Θ⁺ mass by at least 200 MeV and indicating the state would be too broad to observe as a resonance.

ABSTRACT

According to QCD, there exists a broken dynamical supersymmetry between an antiquark and a diquark. This supersymmetry can be used to relate the mass of a pentaquark to the mass of an antibaryon by replacing two antiquarks in an antibaryon by two diquarks to form a pentaquark. Using this technique, we find that the mass of an exotic pentaquark with strangeness plus 1 is greater than 1.74 GeV, or at least 200 MeV larger than that of the reported $Θ^+$ pentaquark. Furthermore, there is no reason for the pentaquark to be narrow; on the contrary, it is expected to be so broad that it will be difficult to observe.

Motivation & Objective

• To assess the viability of the exotic Θ⁺ pentaquark state with strangeness +1 using a QCD-motivated supersymmetric quark-diquark model.
• To determine whether the reported mass of the Θ⁺ baryon (1540 MeV) is consistent with theoretical expectations from dynamical supersymmetry between antiquarks and diquarks.
• To evaluate the decay width of such a pentaquark state, predicting it would be too broad to observe experimentally.
• To establish a lower mass bound for the S = +1 pentaquark using mass replacement rules derived from QCD symmetries.
• To challenge the experimental existence of the Θ⁺ by showing its predicted mass and width are inconsistent with observation.

Proposed method

• Utilizes approximate dynamical supersymmetry between antiquarks (fermions) and antitriplet diquarks (bosons) in QCD, based on shared color antitriplet structure.
• Applies mass replacement: replaces two antiquarks in an anti-Λ baryon with two light ud diquarks to model a pentaquark state.
• Assigns constituent quark mass of 313 MeV based on nucleon mass (939 MeV) divided by three, assuming mass additivity for ground-state hadrons.
• Calculates a lower mass limit for the pentaquark as 1115 MeV (anti-Λ mass) + 2×313 MeV = 1741 MeV.
• Considers spin and symmetry constraints: spin-zero diquarks are lighter than spin-one, and identical bosonic diquarks require antisymmetric spatial wave functions.
• Estimates additional energy cost from orbital angular momentum or spin-one diquarks, suggesting states above 1741 MeV, and argues for broad decay widths via color rearrangement to N + K.

Experimental results

Research questions

• RQ1 Does the reported mass of the Θ⁺ pentaquark (1540 MeV) satisfy the lower mass bound predicted by a QCD-motivated supersymmetric quark-diquark model?
• RQ2 Can the dynamical supersymmetry between antiquarks and diquarks in QCD explain the mass hierarchy between mesons and baryons, and extend to pentaquarks?
• RQ3 What is the expected decay width of a pentaquark state with the quantum numbers of the Θ⁺, and is it consistent with experimental observation?
• RQ4 Why would a pentaquark with S = +1 be expected to be broad rather than narrow, based on the model’s dynamics?
• RQ5 Does the model predict any stable or narrow pentaquark states with the quantum numbers of the Θ⁺, or is such a state fundamentally unstable?

Key findings

• The pentaquark mass is predicted to be at least 1741 MeV, which exceeds the reported Θ⁺ mass of 1540 MeV by at least 200 MeV.
• The model predicts that the pentaquark would have a very broad decay width due to a Q-value exceeding 300 MeV for the decay into nucleon + kaon, making it difficult to observe as a resonance.
• Spin-zero diquarks are lighter than spin-one diquarks, and the inclusion of spin-one diquarks increases the mass by several hundred MeV, further raising the energy above 1740 MeV.
• The spatial wave function of two identical spin-zero diquarks must be antisymmetric, requiring orbital angular momentum one, which adds additional energy cost.
• The model does not support the existence of a narrow, stable pentaquark with the quantum numbers of the Θ⁺, due to both mass and width constraints.
• The conclusion is that the Θ⁺ baryon, as reported, is unlikely to exist in this supersymmetric quark-diquark model, contradicting experimental claims.