Leptons and strange particles

​​​​In a nutshell

Leptons are elementary particles which are not affected by the strong nuclear force, but are influenced by the weak nuclear force. Strange particles are defined as having a strangeness quantum number that does not equal zero. This lesson will discuss what the leptons are and what the lepton quantum number is. It will also discuss what the strangeness quantum number is and how strange particles are produced and decay.

Definitions

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Leptons

Unlike the hadron, leptons are fundamental particles that do not interact by the strong nuclear force, but rather by the weak nuclear force. There are six types of lepton, each with their own antiparticle variant.

Note: An antiparticle has the same mass as its particle equivalent, but with opposite physical charges such as electric charge.

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Lepton quantum number

All leptons are given a lepton quantum number of $$1$$​, while their antiparticles have a lepton number of $$-1$$​. Every other particle that does not fall into these categories has a lepton number of zero. 

Much like the baryon quantum number, the lepton quantum number is always conserved in interactions.

Example

Show that lepton quantum number is conserved during $$\beta^-$$ decay.

​$$\beta^-$$ decay is given by the following interaction:

​$$n \to p+e^-+\overline{\nu}_e$$​​

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where $$n$$ denotes a neutron, $$p$$ denotes a proton, $$e^-$$ denotes an electron and $$\overline{\nu}_e$$ denotes an electron antineutrino. To validate that lepton quantum number is conserved, check both sides and see if the resulting lepton numbers are the same.

$$0\to1+0-1$$​​

Both sides have a total lepton number of zero. The neutron is not a lepton and the lepton numbers of the electron and electron antineutrino cancel each other out.

Therefore, the lepton number is conserved.

Muon decay

The muon has a mass of $$200m_e$$, where $$m_e$$​ is the mass of an electron. The muon also has a lifetime of $$2.2\,\mu s$$. After that, they decay into three particles consisting of an electron or positron and two neutrinos, depending on whether the muon is a particle or antiparticle.

​$$\mu^- \to e^- + \overline{\nu}_e + \nu_\mu$$​​

​$$\mu^+ \to e^+ + \nu_e + \overline{\nu}_\mu$$​​

Strange particles

Strange particles are particles that have a non-zero value of strangeness quantum number. This non-zero value arises when a particle is made with a strange quark or strange antiquark. The strange quark is one of the six types of quark that make up some particles.

Strange particles are always produced in pairs by the strong nuclear force, but decay through the weak nuclear force. Furthermore, strangeness is conserved during the production of these strange particle pairs (pair production) but not during their individual decays.

Example

The kaon is a strange particle that can be produced from four different quark configurations. Two of these types are produced through proton-proton collision. Show that during production, strangeness is conserved.

Kaon production is given by the following interaction:

$$p+p \to p + p + K^+ +K^-$$​​

where $$p$$ denotes a proton and $$K$$ denotes a kaon. To validate that strangeness is conserved, check both sides and see if the resulting strangeness values are the same.

$$0+0 \to 0 + 0 + 1 - 1$$​​

The kaons are the only particles with strangeness. $$K^+$$has a strangeness of $$+1$$​, while $$K^-$$has a strangeness of $$-1$$. The two cancel each other out and strangeness is conserved.

Strangeness is not conserved during decay. A kaon can decay into a muon through the following interaction.

​$$K^- \to \mu^- + \overline{\nu}_\mu$$​​

The left side of this interaction has a strangeness of $$-1$$ due to the kaon, but the products contain no strange quarks and thus has a strangeness of zero, showing that strangeness is not conserved.