Correction: Roman, H.E. Embedding Vacuum Fluctuations in the Dirac Equation: On the Neutrino Electric Millicharge and Magnetic Moment. Axioms 2025, 14, 779

Roman, Hector Eduardo

doi:10.3390/axioms15100723

Errors in Table 1

In the original publication [1], there were mistakes in Table 1 as published. The values for the creation times were off by a missing factor of 1/2π. The corrected Table 1 appears below.

Table 1. Unstable particle (1st column) and its creation time [s] (2nd column). The 3rd column reports the unstable particle lifetime T_p [s], and the 4th column the main decay channel. The 5th column reports the ’creation’ times for each daughter particle (p). The creation time, t_c, is assumed to be given by t_c = ℏ/2m_pc² (see text). For neutrinos we have taken the mass value 0.4 eV for illustration. We have included the neutral Higgs boson for comparison.

Unstable Particle	Creation Time [s]	Lifetime [s]	Decay Channel	Daughter Particle Creation Times [s]
neutron	3.5 × 10⁻²⁵	≃611	p⁺ + e⁻ + ${\bar{ν}}_{e}$	3.5 × 10⁻²⁵, 6.5 × 10⁻²², 8.3 × 10⁻¹⁶
μ⁻	3.2 × 10⁻²⁴	2.2 × 10⁻⁶	e⁻ + ${\bar{ν}}_{e}$ + ν_μ	6.5 × 10⁻²², 8.3 × 10⁻¹⁶, 8.3 × 10⁻¹⁶
τ⁻	1.9 × 10⁻²⁵	2.9 × 10⁻¹³	e⁻ + ${\bar{ν}}_{e}$ + ν_τ	6.5 × 10⁻²², 8.3 × 10⁻¹⁶, 8.3 × 10⁻¹⁶
Higgs boson	2.7 × 10⁻²⁷	1.6 × 10⁻²²	$\bar{b} + b$	7.8 × 10⁻²⁶, 7.8 × 10⁻²⁶
top quark	1.9 × 10⁻²⁷	5 × 10⁻²⁵	W⁺+b	4.1 × 10⁻²⁷, 7.8 × 10⁻²⁶

Text Corrections

There were additional errors in the original publication, also related to the same mistake reported in Table 1. The main one occurred in the last equation of the paper, which was written as

m_{q} c^{2} > \frac{ℏ}{2 T_{τ}} ≃ 0.007 eV .

The corrected equation now reads,

m_{q} c^{2} > \frac{ℏ}{2 T_{τ}} ≃ 0.001 eV .

A second mistake occurred below Equation (67), where it was wrongly reported,

“Later, we suggest a lower bound for the mass, yielding m_𝔮c² > 7 meV.”,

that must be replaced by the correct one,

“Later, we suggest a lower bound for the mass, yielding m_𝔮c² > 1 meV.”.

A similar related mistake occurred below Equation (72),

“The lowest mass value 7 meV will be justified in Section 5.2.”,

which must read,

“The lowest mass value m_𝔮c² > 1 meV will be justified in Section 5.2.”,

Finally, in Section 6 Concluding Remarks, the following sentence contains an error:

“From this relation, confirmed in the cases considered, we derive a lower bound for the effective neutrino mass, where T_τ ≃ 2.9 · 10⁻¹³ s is the τ lepton lifetime, namely m_𝔮c² > ℏ/(2T_τ)≃7 meV, a prediction which may be tested in future experiments.” It must now read,

“From this relation, confirmed in the cases considered, we derive a lower bound for the effective neutrino mass, where T_τ ≃ 2.9 · 10⁻¹³ s is the τ lepton lifetime, namely m_𝔮c² > ℏ/(2T_τ)≃1 meV, a prediction which may be tested in future experiments.”.

The author states that the scientific conclusions are unaffected. These corrections were approved by the Academic Editor. The original publication has also been updated.

Reference

Roman, H.E. Embedding Vacuum Fluctuations in the Dirac Equation: On the Neutrino Electric Millicharge and Magnetic Moment. Axioms 2025, 14, 779. [Google Scholar] [CrossRef] [Scilit]

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