4.3
Lepton conservation
Before
After
Interaction 1
p + π–
S
0+0=0
→
1 + (−1) = 0
Interaction 2
p + π–
→
K– + Σ+
S
0+0=0
→
(−1) + (−1) = −2
→
K0 + Λ0 Allowed Not allowed
Table 7 Particle interactions and conservation of strangeness, S
In ‘production’ reactions, where two or more particles combine, strangeness is always conserved. Table 7 shows two examples of such interactions, one allowed by strangeness conservation, the other not allowed. However, when strange particles decay via the weak interaction, their strangeness can change by ±1. This helps to explain the relatively long decay times for some mesons.
For example, Λ0 → p + π– is a decay that is allowed, since charge and baryon number are conserved (Λ0 is a baryon, B = 1). Similar decays that take place by the strong interaction lead to typical particle lifetimes of the order of 10–23 s. But the Λ0 has a lifetime of around 10–10 s. This is because Λ0 is a strange particle, and the decay products, p and π, are not. The decay must therefore take place via the weak interaction, which leads to a much longer lifetime.
QUESTIONS 3. Which of these interactions is forbidden because it contravenes the conservation of strangeness? a. p +
π– → K– + Σ+
b. π– + p → K+ + Σ– c. K+ + p → π+ + Σ+ d. Φ → K+ + K– e. Φ → π+ + K– 4. The positive kaon decays to two pions with a mean lifetime of about 1.28 × 10–8 s. The decay is written K+ → π+ + π0. A similar decay, ρ0 → π+ + π–, has a mean lifetime of 4 × 10–24 s. What difference in the decay mechanism might explain the huge difference in lifetime? (Hint: the ρ0 is a meson with zero strangeness.) 5. For a reaction to take place it must satisfy conservation of charge, baryon number and strangeness. Which of these reactions are forbidden? Give the reason for each of your answers. (You will need to refer to Table 2.) a. π+ + n → π+ + Λ b. n → π+ + e– c. K+ + K– → π0 d. π+ + p → Σ+ + K+ e. p + π– → K+ + K– f. p + π– → K0
KEY IDEAS
›› Hadrons each have a fixed value for charge, Q, baryon number, B, and strangeness, S. Strong interactions involving hadrons can only take place if the interaction conserves charge, Q, baryon number, B, and strangeness, S.
›› All interactions must also conserve mass–energy and momentum.
›› Decays of strange particles that take place by
the weak interaction may result in a change of strangeness of ±1.
4.3 LEPTON CONSERVATION Particle interactions obey a number of other conservation laws. One of these applies to lepton number, L. In any particle interaction, the number of leptons is always conserved. So the total number of leptons after any interaction must be the same as the number of leptons before the reaction. In fact, the conservation law is even more constraining. Each generation of the lepton family, for example the electron and the muon, have their own lepton number, Le and Lμ (see Table 8), which must be conserved separately. Notice that the quantum numbers in Table 8 for an antiparticle have the opposite sign to those of the corresponding particle.
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