The system ( or together with or ) couples two isospin- doublets

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model

Symmetry and Flavour, Ch Isospin as a group: SU(2), Clebsch-Gordan ratios and G-parity

Problem

The

\bar KN

system (

K^-

\bar K^0

together with

p

n

) couples two isospin-

\tfrac12

doublets, just as the

NN

system does, giving total isospin

I=1

I=0

. Coupling the

\bar K

doublet with the sign appropriate to an antiparticle doublet gives

|K^-p\rangle=\frac{1}{\sqrt2}|1,0\rangle-\frac{1}{\sqrt2}|0,0\rangle,\qquad |\bar K^0n\rangle=\frac{1}{\sqrt2}|1,0\rangle+\frac{1}{\sqrt2}|0,0\rangle,

where

|I,I_3\rangle

labels the total isospin of the

\bar KN

pair. The

\Sigma(1775)

resonance, which lies above the

\bar KN

threshold of

1432\,\mathrm{MeV}

, is a pure isospin-1 state; take the isospin-0 amplitude

M_0

to be negligible at its peak compared with the isospin-1 amplitude

M_1

. Predict the ratio

\sigma(K^-p\to\bar K^0n)/\sigma(K^-p\to K^-p)

at the

\Sigma(1775)

peak.