The two-body hyperfine model predicts that the spin-weighted average of a vector ( )…

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Symmetry and Flavour, Ch The constituent quark model: wave functions, magnetic moments and hyperfine masses

Problem

The two-body hyperfine model predicts that the spin-weighted average

\dfrac{3M_V + M_P}{4}

of a vector (

1^-

) and pseudoscalar (

0^-

) meson of the same quark content equals the sum of the constituent quark masses,

m_1 + m_2

, since the hyperfine term averages to zero over the four spin states. Use the isospin-averaged masses

M_{K^*} = 893.6\,\mathrm{MeV}

and

M_K = 495.6\,\mathrm{MeV}

, and constituent masses

m_u = 336\,\mathrm{MeV}

m_s = 510\,\mathrm{MeV}

. ((a)) Compute

\dfrac{3M_{K^*} + M_K}{4}

. ((b)) Compare it with

m_u + m_s

and comment on the size of the discrepancy.

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