[Paper Review] Masses of Heavy Hadrons

Harpreet Kaur, M. P. Khanna|ArXiv.org|May 9, 2000

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper improves nonrelativistic quark model predictions for heavy hadron masses by incorporating flavor-dependent variations in the wavefunction at the origin, |ψ(0)|², and the strong coupling constant αₛ. By allowing the hyperfine interaction parameter bᵢⱼ to vary with quark flavor, the model achieves better agreement with experimental masses of charmed and bottom baryons, particularly predicting Ξ′꜀ at 2580 MeV, consistent with observation and theoretical expectations.

ABSTRACT

An estimate has been made of the masses of heavy hadrons in nonrelativistic quark model, which includes spin and flavor-dependent hyperfine splitting for two quarks. The effect of variation of the wavefunction value at origin and the strong coupling constant, with flavor, has also been included in calculating the mass values.

Motivation & Objective

• To improve theoretical predictions of heavy baryon and meson masses by accounting for flavor-dependent variations in |ψ(0)|² and αₛ.
• To address the limitation of previous nonrelativistic quark models that assumed constant b parameters across quark flavors.
• To provide more accurate mass estimates for unobserved heavy baryons, such as Ω꜀* and Ξ′꜀, to guide experimental searches.
• To test the consistency of the model with known mass relations and experimental hyperfine splittings.

Proposed method

• The nonrelativistic quark model is extended by replacing the constant hyperfine parameter b with flavor-dependent bᵢⱼ, which scales with |ψᵢⱼ(0)|² and αₛ(μ).
• The parameter bᵢⱼ is related to the wavefunction at the origin and the running strong coupling constant via bᵢⱼ ∝ |ψᵢⱼ(0)|² αₛ(μ).
• Experimental hyperfine splittings are used to estimate |ψ(0)|² values for c- and b-quark systems, informed by data from charmed and strange baryons.
• The model uses ratios of bᵢⱼ parameters to infer relative |ψ(0)|² values across quark sectors, such as |ψ_cu|²/|ψ_su|² = 3.3 and |ψ_bu|²/|ψ_su|² = 11.3.
• Mass predictions are derived from modified mass formulae (eqs. 3 and 4) that include flavor-dependent bᵢⱼ terms.
• The model preserves known mass relations such as ΔN/(ρ−π) = 1/2 and Σ*−Σ = 1/2(D*−D), validating its consistency with established spectroscopic patterns.

Experimental results

Research questions

• RQ1 How does including flavor-dependent |ψ(0)|² and αₛ improve nonrelativistic quark model predictions for heavy hadron masses?
• RQ2 What are the inferred values of |ψ(0)|² for c- and b-quark systems relative to strange quarks, and how do they compare to lattice and other estimates?
• RQ3 Does the model reproduce known mass splitting patterns such as (Σ*−Σ)/(ρ−π) = 1/2 and (Σ*−Σ) = 1/2(D*−D)?
• RQ4 How well does the model predict the mass of the Ξ′꜀ baryon, which has experimental observation?
• RQ5 What is the predicted mass of the Ω꜀* baryon, and how does it compare to existing theoretical estimates?

Key findings

• The model predicts Ξ′꜀ at 2580 MeV, in excellent agreement with the experimental value of 2575±5 MeV.
• The predicted mass difference Ξ′꜀ − Ξ꜀ = 107 MeV matches the experimental value closely.
• The model predicts Ω꜀* at 2766 MeV, consistent with other theoretical estimates around 2770 MeV.
• The ratio |ψ_cu|²/|ψ_su|² is estimated at 3.3, and |ψ_bu|²/|ψ_su|² at 11.3, indicating significant flavor dependence in the wavefunction at origin.
• The model successfully reproduces known mass relations such as (Σ*−Σ)/(ρ−π) = 1/2 and (Σ*−Σ) = 1/2(D*−D), confirming internal consistency.
• Predicted mass differences in the b-sector, such as Ω*ᵦ − Λᵦ = 469 MeV, are consistent with expectations and provide benchmarks for future experiments.