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Solution for (a)

Before the decay, the Ξ has strangeness S = 2 size 12{S= - 2} {} . After the decay, the total strangeness is –1 for the Λ 0 size 12{Λ rSup { size 8{0} } } {} , plus 0 for the π . Thus, total strangeness has gone from –2 to –1 or a change of +1. Baryon number for the Ξ is B = + 1 before the decay, and after the decay the Λ 0 has B = + 1 and the π has B = 0 size 12{B=0} {} so that the total baryon number remains +1. Charge is –1 before the decay, and the total charge after is also 0 1 = 1 size 12{0 - 1= - 1} {} . Lepton numbers for all the particles are zero, and so lepton numbers are conserved.

Discussion for (a)

The Ξ size 12{Ξ rSup { size 8{ - {}} } } {} decay is caused by the weak interaction, since strangeness changes, and it is consistent with the relatively long 1 . 64 × 10 10 -s size 12{1 "." "64" times "10" rSup { size 8{ - "10"} } "-s"} {} lifetime of the Ξ size 12{Ξ rSup { size 8{ - {}} } } {} .

Solution for (b)

The decay K + μ + + ν μ size 12{K rSup { size 8{+{}} } rightarrow μ rSup { size 8{+{}} } +ν rSub { size 8{μ} } } {} is allowed if charge, baryon number, mass-energy, and lepton numbers are conserved. Strangeness can change due to the weak interaction. Charge is conserved as s d size 12{s rightarrow d} {} . Baryon number is conserved, since all particles have B = 0 size 12{B=0} {} . Mass-energy is conserved in the sense that the K + size 12{K rSup { size 8{+{}} } } {} has a greater mass than the products, so that the decay can be spontaneous. Lepton family numbers are conserved at 0 for the electron and tau family for all particles. The muon family number is L μ = 0 size 12{L rSub { size 8{μ} } =0} {} before and L μ = 1 + 1 = 0 size 12{L rSub { size 8{μ} } = - 1+1=0} {} after. Strangeness changes from +1 before to 0 + 0 after, for an allowed change of 1. The decay is allowed by all these measures.

Discussion for (b)

This decay is not only allowed by our reckoning, it is, in fact, the primary decay mode of the K + size 12{K rSup { size 8{+{}} } } {} meson and is caused by the weak force, consistent with the long 1 . 24 × 10 8 -s size 12{1 "." "24" times "10" rSup { size 8{ - 8} } "-s"} {} lifetime.

There are hundreds of particles, all hadrons, not listed in [link] , most of which have shorter lifetimes. The systematics of those particle lifetimes, their production probabilities, and decay products are completely consistent with the conservation laws noted for lepton families, baryon number, and strangeness, but they also imply other quantum numbers and conservation laws. There are a finite, and in fact relatively small, number of these conserved quantities, however, implying a finite set of substructures. Additionally, some of these short-lived particles resemble the excited states of other particles, implying an internal structure. All of this jigsaw puzzle can be tied together and explained relatively simply by the existence of fundamental substructures. Leptons seem to be fundamental structures. Hadrons seem to have a substructure called quarks. Quarks: Is That All There Is? explores the basics of the underlying quark building blocks.

The image shows a picture of physicist Murray Gell Mann, who looks like a pleasant white-haired gentleman.
Murray Gell-Mann (b. 1929) proposed quarks as a substructure of hadrons in 1963 and was already known for his work on the concept of strangeness. Although quarks have never been directly observed, several predictions of the quark model were quickly confirmed, and their properties explain all known hadron characteristics. Gell-Mann was awarded the Nobel Prize in 1969. (credit: Luboš Motl)

Summary

  • All particles of matter have an antimatter counterpart that has the opposite charge and certain other quantum numbers as seen in [link] . These matter-antimatter pairs are otherwise very similar but will annihilate when brought together. Known particles can be divided into three major groups—leptons, hadrons, and carrier particles (gauge bosons).
  • Leptons do not feel the strong nuclear force and are further divided into three groups—electron family designated by electron family number L e size 12{L rSub { size 8{e} } } {} ; muon family designated by muon family number L μ size 12{L rSub { size 8{μ} } } {} ; and tau family designated by tau family number L τ size 12{L rSub { size 8{τ} } } {} . The family numbers are not universally conserved due to neutrino oscillations.
  • Hadrons are particles that feel the strong nuclear force and are divided into baryons, with the baryon family number B size 12{B} {} being conserved, and mesons.

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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