Consider the strong reaction .

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 Isospin: a symmetry used as bookkeeping

Problem

Consider the strong reaction

\pi^-p \to \pi^0 n

. ((a)) Write down the quark content of

\pi^-

p

and

n

; the

\pi^0

has

Q=0

B=0

and

S=0

. Use these to check that charge, baryon number and strangeness are each conserved across the reaction. ((b)) Assign the isospin

I

and its third component

I_3

\pi^-

p

and

n

from their quark content and to

\pi^0

from its place in the pion family, and check that the total

I_3

of the two incoming particles equals the total

I_3

of the two outgoing particles. ((c)) The strong interaction is blind to the difference between

u

and

d

. Using this blindness, explain in one or two sentences why the

pp

pn

and

nn

strong forces are equal (once electric repulsion is removed), and why that same blindness ties the rate of

\pi^-p\to\pi^0n

\sqrt{s}=1232\ \mathrm{MeV}

to the rate of

\pi^-p\to\pi^-p

at the same energy.

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