Hadrons may be either :
The muon is like a heavy electron (rest mass 106 MeV) so it is a lepton. The muons decay to form electrons and positrons:
m+ --> e+ + ne + nm
m- --> e- + nm + ne
Notice that these decay chains all end up as electrons and neutrinos which are stable leptons. Remember though, that leptons are NOT subject to the strong force.
Q1) If Lepton number +1 is assigned to e- , m- , ne and nmand Lepton number -1 assigned to their respective anti-particles, verify that lepton numbers are conserved in the above decays.
Heavier than the Pion is the Kaon, whose charged version K+ and K- have mass 494 MeV and neutral version Ko hass mass 498 MeV. They have very short lifetimes, decaying in 1.2 x 10 -8 s by the weak interaction.The difference between the pion and the kaon is explained in terms of their quark structure - the Kaon containing a 'strange' quark as well as the more familiar 'up' or 'down'.
Q2) Which of these decays for the Kaon cannot occur ? Explain your reasoning.
K+ --> m+ +
nm
.
K+ --> p+ + 2po
.
K+ --> po +
m-
+ nm
Q3) Write a decay equation for beta decay and show that charge, baryon number and lepton number are all conserved.
Baryons heavier than the neutron are termed 'Hyperons' and are all very unstable. The longest lived classes are the L , S , X and W families. The W- (Omega Minus Hyperon - groovy particle name !) is stable for 1.3 x 10 -10 seconds and has the colossal rest mass of 1672 MeV. This was predicted in 1961 as having to exist if the whole theory of Hadrons was to be accepted.
Q4) If all the kinetic energy of a high speed proton was used to provide the rest energy for the W-particle, at what speed would it have to enter a collision ? What fraction of light speed is this ? You will need the formula :
The end result of hyperon decays is always a proton or a neutron. Here is a creation and decay event for the Omega Minus Hyperon :
Q5) Explain the shape of the tracks in the bubble chamber picture. Comment on conservation of charge,baryon number and lepton number in these events.
Even with baryon number B ,lepton number L and electric charge Q , certain elementary particle events could not be esplained fully. This led to the concept of 'Strangeness'.
The strangeness quantum number S is conserved in all strong interactions but may change in a weak interaction.
A quantity called Hypercharge Y has also been found useful in characterising elementary particles.It is conserved in the strong interaction.
Y = S + B
Q6) Look up the B,Q,L,S quantum numbers of the following particles:
p+, p-, po ,K+ ,K -,Ko ,e- ,e+ ,Lo ,X-,p, n
Q7) Is the following a strong or
a weak interaction ? Explain your answer.
p + p ----> Lo + Ko + p + p+
Q8) Is the following scheme a strong
or weak interaction ? Explain.
X- ---> Lo + p- then Lo ---> n + po
It thus appears that S can change in events
governed by the weak interaction but it appears strangeness may only change
by +/- 1 in weak decays.
The Eightfold Way is a classification scheme for Hadrons which collects them into special groups termed 'Multiplets' and 'Supermultiplets'. the members of each supermultiplet would be the same in the absence of any interactions. The strong interaction splits the baryon supermultiplet into the four components X, S, L, andN . The electromagnetic interaction splits these further into charge multiplets.The followingdiagrams show the relationships between one baryon supermultiplet .The left hand diagram shows the size of mass splitting (Symmetry Breaking) due to the two interactions. The right hand diagram shows permissible decays under the weak interaction.
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