The and quarks form an isospin doublet with , , ; the strange quark carries

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

Problem

The

u

and

d

quarks form an isospin doublet with

I=\tfrac12

I_3(u)=+\tfrac12

I_3(d)=-\tfrac12

; the strange quark carries

I=0

. The physical kaons are

K^+=u\bar s

K^0=d\bar s

(an isospin doublet,

I=\tfrac12

) and their antiparticles

K^-=\bar u s

\bar K^0=\bar d s

. ((a)) State the

I_3

K^-

and of

\bar K^0

, using the

I_3

\bar u

and

\bar d

. ((b)) The naive antiquark doublet

(\bar d,\bar u)

must be corrected by a sign to transform correctly, giving

(-\bar d,\bar u)

. Give the

I_3

values, in the order (top, bottom), of the correspondingly signed doublet built from

(\bar K^0,K^-)

, i.e. of

(-\bar K^0, K^-)

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