Question 26.7: Λ Decay In Conceptual Example 26.4, you saw one possible dec...
Λ Decay
In Conceptual Example 26.4, you saw one possible decay of the lambda particle (a baryon): \Lambda \rightarrow p^{+}+\pi^{-}. Describe the quark transformation in this decay and in the one that follows it.
From Table 26.6, the Λ’s quark composition is uds. You already know that the proton’s
quark composition is uud, and the negative pion s quark composition (also in Table 26.6) is \bar{u} d .
| TABLE 26.6 Quark Compositions of Selected Mesons and Baryons | |||
| Quark composition | Meson Particle | Quark composition | Baryon Particle |
| u \bar{d} | \pi^{+} | uud | p^{+} |
| \bar{u} d | \pi^{-} | udd | n |
| u \bar{S} | K ^{+} | uds | Λ |
| d \bar{s} | K ^{0} | uus | \Sigma^{+} |
| c \bar{d} | D ^{+} | uds | \Sigma^{0} |
| c \bar{u} | D ^{0} | uss | \Xi^{0} |
| u \bar{b} | B ^{+} | dss | \Xi^{-} |
| d \bar{b} | B ^{0} | sss | \Omega^{-} |
| b \bar{b} | ϒ | udc | \Lambda_{C}^{+} |
| c \bar{c} | J / \Psi | uuu | \Delta^{++} |
| s \bar{b} | B _{S}^{0} | uud | \Delta^{+} |
| c \bar{b} | B _{C}^{0} | udd | \Delta^{0} |
| S \bar{S} | φ | ddd | \Delta^{-} |
\text { Therefore, the underlying transformation in the decay } \Lambda \rightarrow p^{+}+\pi^{-} \text {is from } u d s \text { to } u u d \text { and } \bar{u} d .
You can picture this as a strange quark changing into a down quark, and a pair u \bar{u} being created.
There’s no problem with conservation laws when a quark and its antiquark are created, because all the conserved numbers (including charge) cancel.
The secondary decay is that of the pion, which you can see from Table 26.4 is
| TABLE 26.4 Table of Hadrons | |||||||||
| Charm number C | Strangeness number S | Baryon number B | Spin | Main decay modes | Mean lifetime (s) | Rest energy (MeV) | Anti- particle | Symbol | Particle name |
| Mesons | |||||||||
|
0 0 |
0
0 |
0
0 |
0
0 |
\mu^{+} v_{\mu}.
2 \gamma |
2.6 \times 10^{-8}.
8.4 \times 10^{-17} |
140
135 |
\pi^{+}.
Self |
\pi^{-}.
\pi^{0} |
Pion |
|
0 0 0 |
1
1 1 |
0
0 0 |
0
0 0 |
\mu^{+} \nu_{\mu}, \pi^{+} \pi^{0}.
\pi^{+} \pi^{-}, 2 \pi^{0}. \pi^{\pm} e^{\mp} \nu_{e}, 3 \pi^{0}. \pi^{\pm} \mu^{\mp} \nu_{\mu}\pi^{+} \pi^{-} \pi^{0} |
1.2 \times 10^{-8}.
9.0 \times 10^{-11}. 5.1 \times 10^{-8}. |
494
498 498 |
K ^{-}
\overline{ K }_{S}^{0}. \overline{ K }_{L}^{0}.
|
K ^{+}.
K _{S}^{0}. K _{L}^{0} |
Kaon |
| 0 | 0 | 0 | 0 | 2 \gamma, 3 \pi^{0}
\pi^{+} \pi^{-} \pi^{0} |
5 \times 10^{-19} | 548 | Self | \eta^{0} | Eta |
|
1 1 1 |
0
0 1 |
0
0 0 |
0
0 0 |
e^{+}, K ^{\pm}, K ^{0} \overline{ K }^{0}+\text { anything }.
\text { Same as } D ^{+}. Various |
1.0 \times 10^{-12}.
4.1 \times 10^{-13}. 5.0 \times 10^{-13} |
1870
1865 1968 |
D ^{-}.
\overline{ D }^{0}. \overline{ D }_{S}^{-} |
D ^{+}.
D ^{0}. D _{S}^{+} |
Charmed D’s |
|
0 0 |
0
0 |
0
0 |
0
0 |
Various
Various |
1.6 \times 10^{-12}.
1.5 \times 10^{-12}.
|
5280
5280 |
B ^{-}.
\overline{ B }^{0} |
B ^{+}.
B ^{0}. |
Bottom B’s |
| 0 | 0 | 0 | 0 | Various | 10^{-20} | 3097 | Self | J / \psi | J/Psi |
| 0 | 0 | 0 | 0 | Various | 10^{-20} | 9460 | Self | \Upsilon(\text { IS }) | Upsilon |
| Baryons | |||||||||
| 0 | 0 | 1 | \frac{1}{2} | Stable (?) | 938.3 | \bar{p} | p | Proton | |
| 0 | 0 | 1 | \frac{1}{2} | p e^{-}\bar{\nu}_{e} | 886 | 939.6 | \bar{n} | n | Neutron |
| 0 | -1 | 1 | \frac{1}{2} | p \pi^{-}, n \pi^{0} | 2.6 \times 10^{-10} | 1116 | \bar{\Lambda} | Λ | Lambda |
|
0 0 0 |
-1
-1 -1 |
1
1 1 |
\frac{1}{2}.
\frac{1}{2}. \frac{1}{2}. |
p \pi^{0}, n \pi^{+}.
\Lambda \gamma. n \pi^{-}. |
8.0 \times 10^{-11}.
7.4 \times 10^{-20}. 1.5 \times 10^{-10}. |
1189
1193 1197 |
\bar{\Sigma}^{-}.
\bar{\Sigma}^{0}. \bar{\Sigma}^{+}.
|
\Sigma^{+}.
\Sigma^{0}. \Sigma^{-} |
Sigmas |
|
0 0 |
-2
-2 |
1
1 |
\frac{1}{2}.
\frac{1}{2} |
\Lambda \pi^{0}.
\Lambda \pi^{-} |
2.9 \times 10^{-10}.
1.6 \times 10^{-10} |
1315
1321 |
\bar{\Xi}^{0}.
\Xi^{+}. |
\Xi^{0}.
\Xi^{-}. |
Xi |
| 0 | -3 | 1 | \frac{3}{2} | \Lambda K ^{-}, \Xi^{0} \pi^{-} | 0.82 \times 10^{-10} | 1672 | \Omega^{+} | \Omega^{-} | Omega |
| 1 | 0 | 1 | \frac{1}{2} | Various | 2.0 \times 10^{-13} | 2286 | \bar{\Lambda}_{C}^{-} | \Lambda_{C}^{-} | Charmed lambda |
\pi^{-} \rightarrow \mu^{-}+\bar{\nu}_{\mu}.
\text { This is interesting in that the } \pi^{-} \text {(quark composition } \bar{u} d \text { ) } gets replaced by leptons, which contain no quarks. You can think of this as the down quark changing to an up (as in \beta^{-} \text {decay), } followed by annihilation of the resulting u \bar{u} \text { pair. }
REFLECT Note that the annihilation of the pair \text { и } \bar{u}in the last step is just the reverse of this pair’s creation in the original lambda decay.