Physics › Particles › Decays at quark level

Decays at quark level

You can take any hadron decay apart at quark level by writing out the quarks and finding the one that changes flavour. In the beta-minus decay of a neutron, a down quark becomes an up quark, udd to uud, and a W⁻ boson carries off the charge. A change in strangeness shows that the weak interaction is at work.

Quarks and antiquarks: hadrons and beta decay

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Year 12AQA 3.2.1.6CIE 11.2.4OCR A 6.4.2(i), 6.4.2(k), 6.4.2(l)

Quarks and antiquarks, part 2 of 2. Part 1 is Quarks and the hadrons built from them.

IN THIS TOPIC

  • Describe the decay of the neutron in terms of its quarks.
  • Take any decay apart at quark level, naming the quark that changed flavour and the W boson that carried the charge away.

COMMON MISCONCEPTION

Misconception:

In beta-minus decay a down quark turns into an electron.

The down quark is not destroyed and does not become the electron: it changes flavour to an up quark and emits a W− boson, and it is the W that becomes the electron and the electron antineutrino.

The neutron's decay at quark level

The neutron's three quarks, up down down, become the proton's up up down: one amber-marked down quark turns into an up. Below, the W minus becomes an electron and an electron antineutrino.
FIG. 1Neutron decay at quark level: udd becomes uud as one down quark changes to an up, the W minus delivering the electron and antineutrino.

In beta-minus decay, one down quark changes into an up quark through the weak interaction: udd → uud. This turns a neutron into a proton. A W− boson carries away the difference in charge and then becomes the electron and the electron antineutrino. The other two quarks are unchanged.

Any decay, taken apart the same way

The same method works for any decay, and OCR names the general version as an outcome of its own. Write the quark content under every particle on both sides of the arrow, then look for the single quark that changed flavour. Every other quark is a spectator, and a W boson carries off whatever charge the change released.

Run it on the kaon's decay into pions. A K− is su, and it goes to a π− and a π0. The strange quark becomes an up quark, emitting a W− as the neutron's down quark did. That W− becomes a d with a u, which is the π−, while the kaon's own u spectates throughout and pairs with the new up quark to make the π0.

That accounts for the strangeness rule. All of a kaon's strangeness is carried by its one strange quark, so removing that quark takes S from −1 to 0, and only the weak interaction changes quark flavour. Strong interactions conserve quark flavour and therefore conserve strangeness; weak interactions may change it. That is why the strong interaction can create strange particles only in pairs of opposite strangeness, and cannot decay one on its own.

Any decay taken apart the same way: the lambda's strange quark becomes an up quark
Describe the drawing

The lambda's three quarks on the left, u, d and s, and the proton's u, u and d on the right, with the two spectator quarks drawn plain and the changed one highlighted: the strange quark has become an up quark. Below the proton sits the negative pion, a d with an anti-up, which is what the emitted W minus became. Strangeness runs from minus one to zero, so the interaction is the weak one.

FIG. 2The recipe run on the lambda, which is the example below. Its u and d spectate, its s becomes a u, and the W minus that carried off the charge becomes the d and the anti-up of the pion. Strangeness runs from minus one to zero, a change that marks the interaction as the weak one.

INDEPENDENT PRACTICE

A heavier strange particle

A Λ0 baryon has quark content uds, and it decays to a proton and a π−. Identify the quark that changes flavour, name the interaction, and say what happens to strangeness.

Show the working

Line up the contents. The proton is uud and the π− is du, so the lambda's u and d are spectators and the quark that moved is the s, which became a u. The W− it emitted became the d and the u of the pion.

Strangeness runs −1 → 0, a change of one, so this is the weak interaction and nothing else. The lambda's comparatively long life is consistent with that.

ASSESSMENT FOCUS

  • When a question asks about neutron decay, give it at quark level. One d becomes a u, a W− leaves, and it becomes e− with an electron antineutrino. “n → p” alone leaves out the quark-level detail the question asks for.
  • Check the vertex in thirds. A d at −⅓ becoming a u at +⅔ means the W carried off one whole negative charge, and a vertex that does not balance in thirds has the wrong W on it.
  • OCR alone asks for decays beyond beta at quark level, and the method is always the same: write the quark content under every particle, point at the one that changed flavour, and name the W that carried the charge off. For a kaon that is s becoming u, with the W− turning into a pion and strangeness rising by one.
  • Only the weak interaction changes quark flavour, so a decay in which strangeness changes is weak and nothing else. Say that rather than inferring it from the lifetime alone.

CHECK YOURSELF

A Σ− baryon has quark content dds and decays to a neutron and a π− (du). (a) Identify the quark that changes flavour and what it becomes. (b) Name the interaction and justify it. (c) State what the emitted W boson became.

Show a hint

Write the quark content under both sides and look for the single change.

Show the answer

(a) The neutron is udd, so the sigma's two d quarks spectate and the s becomes a u.

(b) Strangeness runs −1 → 0, and only the weak interaction can change quark flavour and so strangeness. The strong interaction conserves it exactly.

(c) The s at −⅓ became a u at +⅔, so a W− left, and it became the d and the anti-up that make the π−.

It is the lambda's decay again with a different spectator pair.

Write the quark content under both sides and find the one quark that changed flavour.

The neutron's decay is one d becoming a u.

Only the weak interaction changes flavour, so a change of strangeness names the interaction.

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  • Describe the decay of the neutron in terms of its quarks.
  • Take any decay apart at quark level, naming the quark that changed flavour and the W boson that carried the charge away.

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