Griffiths Introduction to Elementary Particles · Problem 4.38

Bound States — David J. Griffiths

Physics — QFT · particle-mixing-neutral-mesons

Problem

For two particles to interconvert,

A \rightleftharpoons B

, it is necessary that they have the same mass (which in practice means that they must be antiparticles of one another), the same charge, the same baryon and lepton numbers. In the Standard Model, with the usual three generations, show that

A

and

B

would have to be neutral mesons, and identify their possible quark contents. Which of these particles have been found, so far? Why doesn't the neutron mix with the antineutron, in the same way as the

K^0

and

\bar{K}^0

mix to produce

K_1

and

K_2

? Why don't we see mixing of the neutral strange vector mesons

K^{0*}

and

\bar{K}^{0*}

Intuitive explanation

Particle mixing requires identical quantum numbers across all conserved charges and flavor labels—mass equality forces antiparticle pairs. The Standard Model's three generations and strict conservation laws (baryon number, lepton number, strangeness in weak interactions) severely restrict which neutral particles can actually interconvert. The key insight is that mixing occurs only when particles are indistinguishable under the theory's symmetries yet separated by weak interactions; most candidates are ruled out by unbroken conservation laws or kinematic constraints. You'll need to systematically check which neutral mesons satisfy all requirements, then consider why some observed particles mix while others don't—the answer lies in lifetime, decay modes, and whether the weak interaction can actually connect them.

Intuitive explanation

Related theory

Particle On A Chain Particle In A Box

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