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A constituent quark mass is an effective mass parameter in a low-energy constituent-quark model. It accounts approximately for strong-interaction dressing and some spin-independent bound-state dynamics; it is not identical to a renormalized quark mass in the Standard Model Lagrangian.

The constituent-quark model describes a low-energy hadron using effective massive quarks and phenomenological interactions. Its constituent quark masses include strong-interaction dressing and differ from short-distance running quark masses.

The baryon hyperfine mass formula is a phenomenological constituent-quark model. The three constituent quark masses include effects of strong-interaction dressing and an approximate spin-independent confinement energy; they are not the small running quark masses in a short-distance Quantum chromodynamics calculation.

The residual correction has the form of a colour-magnetic spin-spin interaction. A nonrelativistic reduction of one-gluon exchange produces a contact contribution proportional toAfter taking its expectation in the common spatial wavefunction and the colour singlet, the colour factor, coupling, and contact density are absorbed into $A^{\prime }$. Summing the three quark pairs gives the supplied formula. Positive $A^{\prime }$ raises aligned-spin configurations relative to lower-spin configurations. In natural units, the spin angular momentum operators are dimensionless, so $A^{\prime }$ has units of energy cubed, as in the given $\mathrm{Ge}{\mathrm{V}}^3$.

Use GeV consistently with the supplied $A^{\prime }$:The spin-independent sum is $m_u+2m_s=1.436\mathrm{GeV}$. The spin-spin interaction corrections areThusThe displayed decimal places document the calculation, rather than asserting that this simple constituent-quark model has sub-MeV predictive precision.

The predicted-minus-measured differences areRelative to the measured masses, these are $+0.755\%$ and $-0.416\%$. The predicted spin-spin interaction splitting is $200.62\mathrm{MeV}$, compared with the measured $216.93\mathrm{MeV}$, a discrepancy of about $7.5\%$ in the splitting.

This is an effective constituent-quark model, with a common spatial contact factor and a nonrelativistic spin-dependent interaction applied to light quarks. Relativistic motion, different spatial wavefunctions, and omitted strong-interaction corrections prevent an expectation of accuracy at the experimental $0.2$--$0.3\mathrm{MeV}$ scale. Agreement at the level of several percent in absolute baryon masses would already be useful for such a simple formula; the sub-percent absolute-mass agreement here is better than that rough expectation.

No theoretical uncertainty or fitting prescription is supplied, so there is no unique numerical “expected error” or justified statistical significance to attach to the deviations. Small relative errors in the large spin-independent mass sum also need not imply equally small relative errors in the much smaller spin-spin interaction splitting.