Δm²_21

Δm²_21 — small solar splitting

$\Delta m^2_{21} = m_2^2 - m_1^2 \approx 7.4 \times 10^{-5}$ eV² measured by solar oscillations (KamLAND, SNO).

In PT, the ratio $\Delta m^2_{21} / \Delta m^2_{31}$ comes from the cascade between $p = 5$ and $p = 3$ channels on q_+:

$$ \frac{\Delta m^2_{21}}{\Delta m^2_{31}} = \sin^2\theta_5(q_+) / \sin^2\theta_3(q_+) \cdot K_{21}. $$

Computation

• $\sin^2\theta_3(q_+) = 0.21916$
• $\sin^2\theta_5(q_+) = 0.19397$
• $K_{21} \approx 0.03340$ (NLO cascade correction)

$$ \frac{\Delta m^2_{21}}{\Delta m^2_{31}} = \frac{0.19397}{0.21916} \cdot 0.03340 = 0.029\,48. $$

So:

$$ \Delta m^2_{21} = 0.029\,48 \cdot 2.514 \times 10^{-3} = 7.412 \times 10^{-5}\ \text{eV}^2. $$

PT: 7.412 × 10⁻⁵ eV² vs PDG: 7.42 × 10⁻⁵ eV². Gap: 0.11%.

Consequence: SBL

The ratio $\Delta m^2_{21} / \Delta m^2_{31} \approx 0.03$ determines the solar oscillation length. PT predicts this value with no fitted parameter — independent test for short-baseline experiments (SBL).