Particle Physics Tutorial 11 - Particle Interactions

Conservation rules in Interactions

All particle interactions must follow certain conservation rules in order to happen.  These are:

 

Question 1

Write down the 5 quantities that must be conserved for a particle interaction to occur

Answer

 

 

If there are strange particles involved and strangeness is conserved, the strong interaction is responsible.  If strangeness is not conserved, the weak interaction mediates the particle interaction.

 

Consider this annihilation process between a proton and an antiproton.

 


In this case, one anti-up and one up quark annihilate to produce a burst of energy.  There are an up and anti-up, and a down and an anti-down left over. (The black cells indicate antiparticles.)  The energy will be lost as photons.

 

Quarks

u d u

+

u  d u

u

d

+

u

d

Charge

+1

+

-1

+1

+

-1

Baryon Number

+1

+

-1

0

+

0

Lepton Number

0

+

0

0

+

0

 

Question 2

Show that this interaction can proceed:

  p+ ® m+ + nm

Answer

 

Particle Decay

Let us look at Kaon decay, using the K+ meson.  Kaons are strange particles because they have a quark (or anti-quark) that belongs to the strange family.

 

K+ →  p+  + p0

 

Analyse the quantum numbers:

 

Q:        +1        →   +1             +          0

B:         0         →     0             +          0

L:         0         →     0             +          0

S:         +1        →     0             +          0

 

The strangeness number of +1 is because it’s an anti-strange quark.  Notice that the strangeness is NOT conserved.  This decay will go ahead, but will do so by the weak interaction.  For the strong interaction to be involved the strangeness must be conserved.

 

Baryons decay in the same way, following the same rules.  Here are some typical decays:

 

 

Most baryons in the particle zoo have strange looking symbols.  They are Greek capital letters.  L = lambda, the letter 'L'; S = sigma, the letter 'S'; W = omega, the letter long O, 'Ō'.

 

Mesons have lower case Greek letters: p = pi, a Greek letter 'p'.

 

The proton is the only stable baryon.  All the others spontaneously decay, although the neutron within a nucleus is stable, apart from beta decay. 

 

Question 3

Show that this decay is possible for the lambda baryon.

               L0 ® p + p-

Answer

 

As in radioactivity, the decay of particles is random.  The values shown are the mean lifetimes, not half-lives.

 

 

Feynman Diagrams

Particle interactions can be quite complex to describe, but they have been represented in quite a simple way by Feynman diagrams.  These were devised by Richard Phillips Feynman (1911 - 1988), an American Physicist.  He introduced them to a conference in 1941 (Physics carried on as usual despite the War) attended by the world's leading physicists.  Neils Bohr (whose model of the atom we still use at this level) was outraged, and only just restrained himself from thumping Feynman.

 

Feynman diagrams have evolved from the simple doodles that they were then, but at this level, we will use them as little more than a doodle.

 

Let us look at a beta minus decay:

 

 

The Feynman diagram is a space against time diagram.  We are interested in the before, during, and after:

 

The Feynman diagram looks like this:

 

 

Often we miss out the space and time axes.  This is shown in the next example:

 

 

A diagram like this will get you the marks in the exam.

 

Question 4

Use the conservation of quantum number to explain why, in beta minus decay, an electron antineutrino is observed instead of an electron neutrino.

Answer

 

 

However, there are some further rules as suggested by the Institute of Physics:

 

So the Feynman diagram for out beta decay becomes:

 

 

 The picture here suggests that the electron antineutrino is coming in to participate in the interaction.  It is the result of the interaction, but, because it's an antiparticle, the arrow points downwards.  If this is confusing, just change the direction of the arrow.  You won't lose any marks.

 

 

There are variations on beta decay that we will sum up, using Feynman diagrams.

 

Beta Plus decay.

 


In beta plus decay, a proton turns into a neutron.  The positive charge is transferred by the W+ boson, which then becomes a positron and an electron neutrino.  Note how the positron arrow points towards the interaction, as the positron is an antiparticle.  Beta decay occurs in proton rich nuclei.

 

Here is an example:

 

 

Beta plus decay is not an anti-particle version of beta minus decay.  The proton is not an anti-neutron for a start!

 

 

 

Electron capture is another way in which a proton can be turned into a neutron:

The electron falls from one of inner shells.  It is attracted by the electromagnetic interaction, but the negative charge is transferred to the proton by the W+ boson.  An electron neutrino is emitted.

 

Here is an example:

 

Note how the nucleon number stays the same, but the proton number decreases by 1.

 

 

Question 5

This image appeared on this website for a number of years. (Tut-tut)  Why is it wrong?

Answer

 

Electron collision is slightly different.  The electron strikes the nucleus from outside:

 

In this case the negative charge is transferred from the electron to the proton using the W- boson.  To ensure that all quantum numbers are balanced, an electron neutrino is emitted.

 

Neutrino capture is the way that physicists can detect neutrinos.  Interactions between neutrinos and nuclei are very rare, despite the fact that the Universe is alive with the little brutes.

 

 

The capture of an electron neutrino leads a neutron to be converted to a proton, with the emission of an electron.  The electron ionises another atom.  This causes photon emission which can be detected using a photo-multiplier tube, which picks up the tiny flash and sends it to a computer.

 

The Feynman diagram shows the capture of an electron anti-neutrino.

 

 

In this case, a positron is emitted, the charge being transferred by the W+ boson.

 

Question 6

Draw a Feynman diagram to show the interaction between two electrons, showing the exchange particle.

Answer