[Paper Review] Heavy quark symmetry in strong decays of P-wave heavy-light mesons

Bing Chen, Ling Yuan+1 more|arXiv (Cornell University)|Oct 23, 2012

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper derives the phenomenological transition strengths 𝒫^{j_q,j'_q}_{j_h,l}(0) for P-wave heavy-light mesons within the ³P₀ model, showing strong consistency with experimentally fitted values from the EHQ method. It confirms that heavy quark symmetry is well-preserved in strong decays of these states, with predicted branching ratios and decay widths matching experimental data when β ≈ 0.38 GeV is used.

ABSTRACT

Heavy quark symmetry and its breaking in strong decays of P-wave heavy-light mesons are examined within the EHQ's method. The consistence of theory with experiments indicates that the breaking of heavy quark symmetry in the two-body strong decays of these mesons is not large. The relation between the EHQ's method and the $^3P_0$ model is investigated, and the phenomenological transition strengths $\mathcal {F}^{j_q,j'_q}_{j_h,l}(0)$ of the P-wave heavy-light mesons within the EHQ method are analytically derived within the $^3P_0$ model.

Motivation & Objective

• To examine the validity of heavy quark symmetry in strong decays of P-wave heavy-light mesons.
• To derive the phenomenological transition strengths 𝒫^{j_q,j'_q}_{j_h,l}(0) analytically within the ³P₀ model.
• To compare theoretical predictions with experimentally fitted values from the EHQ method.
• To assess the consistency of the ³P₀ model with experimental data on decay widths and branching ratios.
• To provide a theoretical foundation for the transition strengths used in the EHQ formalism.

Proposed method

• Uses the EHQ formalism to express two-body strong decay widths via a 6-j symbol and a phenomenological transition strength 𝒫^{j_q,j'_q}_{j_h,l}(0).
• Applies the ³P₀ model to derive analytical expressions for 𝒫^{j_q,j'_q}_{j_h,l}(0) in terms of the quark model parameter β.
• Computes decay amplitudes for S-, P-, and D-wave transitions using the ³P₀ model's wavefunction ansatz.
• Relates the ³P₀ model parameters to the EHQ phenomenological transition strength through a normalization and momentum-space overlap calculation.
• Fixes β at 0.38 GeV, consistent with light meson data, and compares predicted transition strength ratios with experimental fits.
• Uses the resulting expressions to compute decay widths and branching ratios for P-wave heavy-light mesons.

Experimental results

Research questions

• RQ1 To what extent is heavy quark symmetry preserved in the strong decays of P-wave heavy-light mesons?
• RQ2 How do the transition strengths 𝒫^{j_q,j'_q}_{j_h,l}(0) derived in the ³P₀ model compare with those experimentally fitted in the EHQ method?
• RQ3 What is the analytical form of the transition strength 𝒫^{j_q,j'_q}_{j_h,l}(0) for P-wave heavy-light mesons within the ³P₀ model?
• RQ4 Do the predicted ratios of transition strengths in the ³P₀ model agree with experimental data within uncertainties?
• RQ5 Can the ³P₀ model provide a consistent theoretical basis for the phenomenological parameters used in the EHQ formalism?

Key findings

• The transition strength 𝒫^{1/2,1/2}_{0,0}(0) depends on both momentum p and the parameter β, while 𝒫^{1/2,1/2}_{1,1}(0) and 𝒫^{3/2,1/2}_{2,2}(0) depend only on β.
• With β = 0.38 GeV, the predicted ratio 𝒫^{1/2,1/2}_{0,0}(0)/𝒫^{3/2,1/2}_{2,2}(0) is 0.33 in the ³P₀ model, close to the experimental value of 0.30.
• The predicted ratio 𝒫^{1/2,1/2}_{1,1}(0)/𝒫^{3/2,1/2}_{2,2}(0) is 1.95 in the ³P₀ model, compared to the experimental fit of 1.64.
• Theoretical predictions for decay widths and branching ratios are consistent with experimental data when β ≈ 0.38 GeV is used.
• The axial vector mesons D_{s1}(2460) and D_{s1}(2536) are found to be mixtures of A′₁ and A₁ states with a mixing angle φ ≈ -5.2° to -1.4°.
• The ³P₀ model provides a consistent and analytically derived foundation for the phenomenological transition strengths used in the EHQ formalism.