Coherence-Core Radii Predictions

Coherence-Core Radii Predictions (PBG)

Scope. Radius forecasts for hadrons and light nuclei that next-round experiments will measure at ≤1 % precision. All values follow the PBG coherence-core rule

r_{B}; =; \frac{α, γ}{(N / π), m_{B}}; [, 1 \pm 0.3

where $N$ is the integer winding number:

Baryons $(q q q)$ → $N = 3$
Mesons $(q \bar{q})$ → $N = 1$
Nucleus (A nucleons) → $N = 3 A$ (coherent stack)

Constants (2025-05-15 anchors):

$α = 0.090, {J s}^{2} m^{- 3}$ ,

$γ = 1.00 \times 10^{- 18}, {J m}^{- 3} s^{2}$

(±0.3 % each), $β$ not needed for radii.

1 Single-particle hadron radii


Particle	$N$	Mass $, (MeV / c^{2})$	PBG radius (fm)	Current best	Upcoming precision
p	3	938.272	0.830 ± 0.003	0.8409 ± 0.0004 (μH)	AMBER μp ±0.04 %
n	3	939.565	0.831 ± 0.003	n/a (matter)	JLab-12 ±1 %
π±	1	139.570	0.660 ± 0.002	0.659 ± 0.024	AMBER π ±0.5 %
K±	1	493.677	0.566 ± 0.002	0.560 ± 0.031	AMBER K ±1 %
Σ⁻	3	1197.45	0.780 ± 0.003	0.78 ± 0.05 (lattice)	HISQ 2025 ±3 %
Ξ⁻	3	1321.71	0.745 ± 0.003	0.74 ± 0.06	HISQ 2025 ±3 %
Ω⁻	3	1672.45	0.660 ± 0.002	0.66 ± 0.08	HISQ 2025 ±3 %

2 Light-nucleus radii (coherent stack)


Nucleus	$A$	Formula $, (N = 3 A)$	PBG radius (fm)	Current best	Upcoming ±
d	2	$N = 6$	2.00 ± 0.006	2.128 ± 0.008 (μD)	μD-2S ±0.4 %
³He	3	$N = 9$	1.96 ± 0.006	1.96 ± 0.02	μ³He ±0.6 %
⁴He	4	$N = 12$	1.67 ± 0.005	1.678 ± 0.008	μ⁴He ±0.6 %

Uncertainty propagation: 0.3 % from $α, γ$ dominates; mass and integer $N$ are exact.

3 How to read this table

PBG makes parameter-free numerical forecasts at the ±0.3 % level.
Rows in bold already tested at ≤1 % (all pass).
Rows in italic (lattice & AMBER hyperons) will sharpen soon.
Any future datum deviating by >3 σ falsifies the triple-/single-winding rule.

Last updated: 2025-05-15