[Paper Review] The exact quantization of the CLEO and BELLE data for $D$ mass differences by the harmonic quarks and oscillators

Oleg A. Teplov|ArXiv.org|Apr 27, 2006

Quantum and Classical Electrodynamics6 references3 citations

TL;DR

This paper proposes that mass differences in charmed mesons (D and Ds) are exactly quantized by the rest masses of harmonic quarks and their complete oscillators. Using precise CLEO and BELLE data, it shows that transitions like D*(2007)⁰ → D⁰ are explained by the annihilation of a d-oscillator and u⁰-quark with rest energy 142.124 MeV, achieving full agreement with experiment within 4σ, establishing a novel quantization mechanism via quark rest masses.

ABSTRACT

The harmonic quarks and their complete oscillators are successfully used for the exact quantitative results and an explanation of the $D$ meson mass differences. For the first time it is shown that the mass differences of the charmed mesons with the same flavors are strictly quantized by the rest masses of harmonic quarks in both "free" state and complete oscillator state. The $D^*(2007)^0$ $ o$ $D^0$ transition has the following neutral quark group: $d$-oscillator + $u^0$-quark with rest energy 142.124 MeV. It is argued that it is the unique model solution within the 4$σ$ experimental interval. The $D_s^{*+}$ - $D_s^+$ mass difference is quantized by the simplest quark reaction with the difference energy 143.756 MeV. The energy of the $D_{sJ}$(2460)$^+$ $ o$ $D_s^+$ transition explains by the decay of the one complete $s$-oscillator with the energy 491.33 MeV. The full agreement with experimental data of CLEO and BELLE is obtained. The problems of a quark shells and the quantization by quark rest masses are discussed.

Motivation & Objective

• To explain the observed mass differences in charmed mesons using a novel quantization framework based on harmonic quarks and oscillators.
• To test whether mass differences in D and Ds mesons are strictly determined by the rest masses of harmonic quarks and their bound oscillator states.
• To identify unique quark group configurations responsible for specific transitions, particularly those involving electromagnetic decays.
• To reduce experimental mass uncertainties in excited Ds states by applying the quantized energy model.
• To explore the implications of quark shell structures and the role of rest masses in hadron spectroscopy.

Proposed method

• The model uses rest masses of harmonic quarks (d, u, s, c) and their complete oscillators (e.g., ŝ, ū) as fundamental building blocks for hadron mass differences.
• Transitions are interpreted as quark annihilation processes: e.g., d-oscillator + u⁰-quark → γ or π⁰, with energy equal to the rest mass of the annihilating group.
• Theoretical energy differences are calculated from combinations of harmonic quark and oscillator masses, as listed in Table 1.
• Experimental data from CLEO and BELLE on D meson transitions are used as constraints to validate the model.
• The model assumes no electromagnetic splitting in the spectrum, focusing only on mass differences from quark rest masses.
• Masses of excited Ds states are recalculated using the precise energy of the basic transition DsJ(2460)+ → Ds+ = 491.33 MeV, reducing uncertainty to ±0.5 MeV.

Experimental results

Research questions

• RQ1 Can the mass differences between D mesons be exactly quantized by the rest masses of harmonic quarks and their oscillators?
• RQ2 Is there a unique quark group configuration that explains the D*(2007)⁰ → D⁰ transition within experimental uncertainty?
• RQ3 Do transitions in strange charmed mesons (Ds*) follow the same quantization rule as non-strange D mesons?
• RQ4 Can the model reduce the experimental uncertainty in masses of excited Ds states by using precise quantized energy values?
• RQ5 What is the physical interpretation of a quark group annihilating as a whole, with no internal motion, via γ or π⁰ emission?

Key findings

• The D*(2007)⁰ → D⁰ transition is explained by the annihilation of a d-oscillator and u⁰-quark with rest energy 142.124 MeV, matching the experimental value of 142.12 ± 0.05 MeV within 4σ.
• The Ds*(2112)+ → Ds+ transition is quantized by the reaction 1/2(ŝ + ū) → ū + d̄, yielding a difference energy of 141.86 MeV, consistent with experimental data.
• The DsJ(2460)+ → Ds+ transition is explained by the decay of a single complete s-oscillator with energy 491.33 MeV, matching the experimental value of 491.4 ± 0.9 MeV.
• The model reduces the mass uncertainty of excited Ds states to ±0.5 MeV, with recalculated masses for Ds*(2112)+, DsJ*(2317)+, and DsJ(2460)+ in excellent agreement with experiment.
• The D*(2010)+ → D+ transition energy of 140.64 MeV is consistent with the model’s prediction of 143.756 MeV, though not exact, suggesting it may not be a basic transition.
• The model identifies the DsJ(2460)+ → Ds+ transition as the primary basic transition, with the DsJ(2460)+ → DsJ(2317)+ transition possibly being secondary, based on energy hierarchy.