Particle Physics Tutorial 12 - Exchange Particles

 

All interactions are mediated by exchange particles.  That means that interactions don't just happen, but a particle of some kind is involved.  The particles will transfer force, and charge where charged particles are involved.

 

The larger the exchange particle, the shorter the range of the force.  Since gravitons and photons have no mass, their range is infinite.

 

Exchange particles are referred to as gauge bosons.  They were first identified by Satyendra Nath Bose (1894 - 1974), an Indian mathematician and theoretical physicist.  The gauge bosons are:

Virtual particles exist for a limited time in time and space.  That means that energy and matter are borrowed for a short time to transfer the force.  Then they are paid back to the matter (without interest).  However the particle from which the matter was borrowed might not get it back.  An example of this would be the W- boson that owes its brief existence to the down quark from which it has borrowed energy and mass.  Enough energy is given to the quark to make it an up-quark.  The rest of the energy and mass are returned to matter in the form of an electron and an electron antineutrino.  The "ripped-off" down quark is now an up quark.

 

 

This kind of borrowing and payment back is going on all the time between nucleons.

 

We can model this as a bank.  Banks lend money to other organisations.  Most of the time they get the money back (with interest).  Occasionally an organisation defaults and does not pay the money back.  The money has not disappeared; it has gone into the accounts of the organisation and from there into other organisations (and the directors?).  Recently we have seen banks producing ever more strange "products" (scams) which we as tax-payers have had to pay for, while a few very rich individuals and organisations have pocketed it all.  Some parallels between the sub-atomic world and the world of high finance? 

 

One thing is for sure.  Physicists and bankers both don't fully understand their respective worlds.  However, physicists will say, "We're note sure what is going on here.  We don't think our data are correct."  Bankers will say, "We have some wonderful packages of derivatives, which you can buy and use for leverage."

 

Question 1 How can a particle be made from nothing?

Answer

 

 

Graviton

This boson has not been found, but is thought to be mass-less.  Since there are so many big objects pulling on each other due to gravity, presumably the Universe is crawling with the little brutes.

 

Gravity is a very weak force.  It is so small that it is ignored in particle interactions.  It is a significant force between stars and planets, both of which have huge masses.  It is only attractive; it is never repulsive.  Gravity is the force that shapes the Universe over thousands of millions of years.

 

Feynman diagrams are irrelevant in gravity.

 

 

 

Photons

The forces between electrically charged particles are thought to be transmitted by photons, which are emitted and absorbed by the particles.  We normally associate photons with the particle properties of electromagnetic waves.  Since the photons are involved transmitting the force, they have never been seen.  If one were captured, it would have been taken “off task”.  This is why you don’t get flashes of light when you pull or push something.  So we describe them as ghost photons or virtual photons.  Photons mediate both pulls and pushes.  The quantum mechanism is very complex.

 

In a Feynman diagram, photons are represented by a wavy line:

The Feynman diagram shows an interaction mediated by a photon:

 

 
Question 2 Use your knowledge of fundamental forces and exchange particles to explain how you are supported when you sit on a chair.  Why is your sitting down not accompanied by flashes of light?

Answer

 

Gluons

Remember that the nucleus is very tiny compared to the size of an atom; its diameter is about 10-14 m as opposed to 10-10 m for an atom.  If the atom were the size of the school canteen, the nucleus would be the the size of a pea (or sweet-corn) dropped in the middle.

 

In this tiny space there are lots of protons, all positively charged.  Why does the nucleus not fly apart?  The answer is provided by the strong nuclear force which holds the nucleons together.  Its attractive force balances the repulsive forces of the protons.

 

At very short ranges, below 0.5 femtometres (0.5 × 10-15 m) the strong nuclear force is repulsive.  It is attractive up to its maximum range of 3 fm (3 × 10-15 m).  If we plot a graph of force against distance, we would see:

 

 

The repulsive force between the two protons is in the order of 200 N (yes, 200 N).  So it is a very strong force.

 

The strong force is mediated by gluons.  In Feynman diagrams, they are shown as a spiral line:

 

 

Gluons were first proposed by the American Physicist Murray Gell-Mann (1929 - ) in 1962.  Gluons have a rest energy between 0 (in theory) and 20 MeV (experimental limit), making them up to 40 times as massive as an electron.  Their range is about 3 fm (3 × 10-15 m).

 

As separate particles, gluons have never been directly identified. They are however the mediators of the strong nuclear force and there is compelling indirect evidence for them. They are thought to be fundamental particles. There are eight gluons that have been identified theoretically from quantum chromodynamics, each having a different “colour”, although all have zero rest mass and zero charge. Gluons act on quarks, changing the colour charge of each quark.  The mechanism is complex, and way beyond what we need to know here.

 

The simple Feynman diagram represents the action of a gluon binding a proton and a neutron.

 

 

We can represent the action of gluons as bonds between quarks:

 

 

Some theoretical physicists have suggested that swarms of gluons can exist in glue-balls.  This is possible because of the colour charge and the strong force.  Identification of glue-balls has proved extremely difficult.

 

 

 

Weak force

These are thought to mediate the weak forceW+ mediates beta plus decay, W- beta minus.  Both have a mass of 80 GeV/c2.  The weak force is not well understood.  Since the bosons are very massive, the force is very short range, about 10-18 m.

 

 

The W- boson is formed from a neutron as it decays into a proton and an electron antineutrino.

 

In beta minus decay down quark gains enough energy (and mass) to form a W- boson, which then turns into an up quark, and the remaining mass being ejected as an electron and an electron anti-neutrino.   The W- boson transfers the force and the charge.  Therefore the electron gains a negative charge of -1e, and the force accelerates both the electron and the anti-neutrino.  The electron travels at about 1/3 the speed of light (i.e. 1 × 108 m s-1).  The anti-neutrino travels even faster.  Momentum is conserved.

 

However it is also possible for an electron antineutrino to interact with a neutron.  The W- boson mediates the interaction and is turned into an electron.  The neutron turns into a proton.  The interaction is shown here:

 

 

The Z boson is so called because it has zero charge.  It has a mass of 90 GeV/c2.  The role of the Z boson is complex.

 

The masses of the W and Z boson are 4 times the mass of a gluon.

 

 

In nuclear fusion in stars nuclei are squashed together really hard.  The repulsive electromagnetic force is overcome, so that the nuclei are close enough together for the strong force to bind them.

 

In the first picture, two hydrogen nuclei (protons) are close, but are repelling.

 

 

Squash them even harder, and they go together, so that the strong force binds them.

 

 

So we have two protons bound together.  This will lead to beta plus decay, where the one of the protons turns into a neutron, emitting a positron and an electron neutrino.  The charge and force is transferred by the W+ boson.

 

 

Thus we have a deuterium nucleus formed.  Further fusion reactions occur to form helium (and then other materials) in stars.  You will see this more in A2.