The light vector meson has mass and the strange vector meson has mass

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

Particle Physics, Ch SU(3) flavour and the hadron multiplets

Problem

The light vector meson

\rho

has mass

775.3\,\mathrm{MeV}/c^2

and the strange vector meson

K^{*}

has mass

891.7\,\mathrm{MeV}/c^2

. The charged and neutral pions have masses

139.57\,\mathrm{MeV}/c^2

and

134.98\,\mathrm{MeV}/c^2

. ((a)) Estimate, from the

\rho

K^{*}

mass difference, the cost in

\mathrm{MeV}/c^2

of replacing one light quark by a strange quark in this pair of mesons. ((b)) Estimate, from the pion masses, the isospin-breaking mass difference within a single multiplet. ((c)) Take the ratio of the two estimates and state which symmetry, isospin or three-flavour SU(3), is broken more strongly, and by roughly what factor.

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