Λ Decay In Conceptual Example 26.4, you saw one possible decay of the lambda particle (a baryon): Λ → p^+ + π^-. Describe the quark transformation in this decay and in the one that follows it.

Question

Λ Decay

In Conceptual Example 26.4, you saw one possible decay of the lambda particle (a baryon): [latex]\Lambda \rightarrow p^{+}+\pi^{-}[/latex]. Describe the quark transformation in this decay and in the one that follows it.

Accepted Answer

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 [latex]\bar{u} d [/latex].

TABLE 26.6 Quark Compositions of Selected Mesons and Baryons
Quark composition	Meson Particle	Quark composition	Baryon Particle
[latex]u \bar{d}[/latex]	[latex]\pi^{+}[/latex]	uud	[latex]p^{+}[/latex]
[latex]\bar{u} d[/latex]	[latex]\pi^{-}[/latex]	udd	n
[latex]u \bar{S}[/latex]	[latex]K ^{+}[/latex]	uds	Λ
[latex]d \bar{s}[/latex]	[latex]K ^{0}[/latex]	uus	[latex]\Sigma^{+}[/latex]
[latex]c \bar{d}[/latex]	[latex]D ^{+}[/latex]	uds	[latex]\Sigma^{0}[/latex]
[latex]c \bar{u}[/latex]	[latex]D ^{0}[/latex]	uss	[latex]\Xi^{0}[/latex]
[latex]u \bar{b}[/latex]	[latex]B ^{+}[/latex]	dss	[latex]\Xi^{-}[/latex]
[latex]d \bar{b}[/latex]	[latex]B ^{0}[/latex]	sss	[latex]\Omega^{-}[/latex]
[latex]b \bar{b}[/latex]	ϒ	udc	[latex]\Lambda_{C}^{+}[/latex]
[latex]c \bar{c}[/latex]	[latex]J / \Psi[/latex]	uuu	[latex]\Delta^{++}[/latex]
[latex]s \bar{b}[/latex]	[latex]B _{S}^{0}[/latex]	uud	[latex]\Delta^{+}[/latex]
[latex]c \bar{b}[/latex]	[latex]B _{C}^{0}[/latex]	udd	[latex]\Delta^{0}[/latex]
[latex]S \bar{S}[/latex]	φ	ddd	[latex]\Delta^{-}[/latex]

[latex] ext { Therefore, the underlying transformation in the decay } \Lambda ightarrow p^{+}+\pi^{-} ext {is from } u d s ext { to } u u d ext { and } \bar{u} d [/latex].

You can picture this as a strange quark changing into a down quark, and a pair [latex]u \bar{u}[/latex] 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	[latex]\mu^{+} v_{\mu}[/latex]. [latex]2 \gamma[/latex]	[latex]2.6 imes 10^{-8}[/latex]. [latex]8.4 imes 10^{-17}[/latex]	140 135	[latex]\pi^{+}[/latex]. Self	[latex]\pi^{-}[/latex]. [latex]\pi^{0}[/latex]	Pion
0 0 0	1 1 1	0 0 0	0 0 0	[latex]\mu^{+} u_{\mu}, \pi^{+} \pi^{0}[/latex]. [latex]\pi^{+} \pi^{-}, 2 \pi^{0}[/latex]. [latex]\pi^{\pm} e^{\mp} u_{e}, 3 \pi^{0}[/latex]. [latex]\pi^{\pm} \mu^{\mp} u_{\mu}[/latex][latex]\pi^{+} \pi^{-} \pi^{0}[/latex]	[latex]1.2 imes 10^{-8}[/latex]. [latex]9.0 imes 10^{-11}[/latex]. [latex]5.1 imes 10^{-8}[/latex].	494 498 498	[latex]K ^{-}[/latex] [latex]\overline{ K }_{S}^{0}[/latex]. [latex]\overline{ K }_{L}^{0}[/latex].	[latex]K ^{+}[/latex]. [latex]K _{S}^{0}[/latex]. [latex]K _{L}^{0}[/latex]	Kaon
0	0	0	0	[latex]2 \gamma, 3 \pi^{0}[/latex] [latex]\pi^{+} \pi^{-} \pi^{0}[/latex]	[latex]5 imes 10^{-19}[/latex]	548	Self	[latex]\eta^{0}[/latex]	Eta
1 1 1	0 0 1	0 0 0	0 0 0	[latex]e^{+}, K ^{\pm}, K ^{0}[/latex] [latex]\overline{ K }^{0}+ ext { anything }[/latex]. [latex] ext { Same as } D ^{+}[/latex]. Various	[latex]1.0 imes 10^{-12}[/latex]. [latex]4.1 imes 10^{-13}[/latex]. [latex]5.0 imes 10^{-13}[/latex]	1870 1865 1968	[latex]D ^{-}[/latex]. [latex]\overline{ D }^{0}[/latex]. [latex]\overline{ D }_{S}^{-}[/latex]	[latex]D ^{+}[/latex]. [latex]D ^{0}[/latex]. [latex]D _{S}^{+}[/latex]	Charmed D's
0 0	0 0	0 0	0 0	Various Various	[latex]1.6 imes 10^{-12}[/latex]. [latex]1.5 imes 10^{-12}[/latex].	5280 5280	[latex]B ^{-}[/latex]. [latex]\overline{ B }^{0}[/latex]	[latex]B ^{+}[/latex]. [latex]B ^{0}[/latex].	Bottom B's
0	0	0	0	Various	[latex]10^{-20}[/latex]	3097	Self	[latex]J / \psi[/latex]	J/Psi
0	0	0	0	Various	[latex]10^{-20}[/latex]	9460	Self	[latex]\Upsilon( ext { IS })[/latex]	Upsilon
									Baryons
0	0	1	[latex]\frac{1}{2}[/latex]		Stable (?)	938.3	[latex]\bar{p}[/latex]	p	Proton
0	0	1	[latex]\frac{1}{2}[/latex]	[latex]p e^{-}\bar{ u}_{e}[/latex]	886	939.6	[latex]\bar{n}[/latex]	n	Neutron
0	-1	1	[latex]\frac{1}{2}[/latex]	[latex]p \pi^{-}, n \pi^{0}[/latex]	[latex]2.6 imes 10^{-10}[/latex]	1116	[latex]\bar{\Lambda}[/latex]	Λ	Lambda
0 0 0	-1 -1 -1	1 1 1	[latex]\frac{1}{2}[/latex]. [latex]\frac{1}{2}[/latex]. [latex]\frac{1}{2}[/latex].	[latex]p \pi^{0}, n \pi^{+}[/latex]. [latex]\Lambda \gamma[/latex]. [latex]n \pi^{-}[/latex].	[latex]8.0 imes 10^{-11}[/latex]. [latex]7.4 imes 10^{-20}[/latex]. [latex]1.5 imes 10^{-10}[/latex].	1189 1193 1197	[latex]\bar{\Sigma}^{-}[/latex]. [latex]\bar{\Sigma}^{0}[/latex]. [latex]\bar{\Sigma}^{+}[/latex].	[latex]\Sigma^{+}[/latex]. [latex]\Sigma^{0}[/latex]. [latex]\Sigma^{-}[/latex]	Sigmas
0 0	-2 -2	1 1	[latex]\frac{1}{2}[/latex]. [latex]\frac{1}{2}[/latex]	[latex]\Lambda \pi^{0}[/latex]. [latex]\Lambda \pi^{-}[/latex]	[latex]2.9 imes 10^{-10}[/latex]. [latex]1.6 imes 10^{-10}[/latex]	1315 1321	[latex]\bar{\Xi}^{0}[/latex]. [latex]\Xi^{+}[/latex].	[latex]\Xi^{0}[/latex]. [latex]\Xi^{-}[/latex].	Xi
0	-3	1	[latex]\frac{3}{2}[/latex]	[latex]\Lambda K ^{-}, \Xi^{0} \pi^{-}[/latex]	[latex]0.82 imes 10^{-10}[/latex]	1672	[latex]\Omega^{+}[/latex]	[latex]\Omega^{-}[/latex]	Omega
1	0	1	[latex]\frac{1}{2}[/latex]	Various	[latex]2.0 imes 10^{-13}[/latex]	2286	[latex]\bar{\Lambda}_{C}^{-}[/latex]	[latex]\Lambda_{C}^{-}[/latex]	Charmed lambda

[latex]\pi^{-} ightarrow \mu^{-}+\bar{ u}_{\mu}[/latex].

[latex] ext { This is interesting in that the } \pi^{-} ext {(quark composition } \bar{u} d ext { ) }[/latex] gets replaced by leptons, which contain no quarks. You can think of this as the down quark changing to an up (as in [latex]\beta^{-} ext {decay), }[/latex] followed by annihilation of the resulting [latex]u \bar{u} ext { pair. }[/latex]

REFLECT Note that the annihilation of the pair [latex] ext { и } \bar{u}[/latex]in the last step is just the reverse of this pair's creation in the original lambda decay.

Question 26.7: Λ Decay In Conceptual Example 26.4, you saw one possible dec...

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