March 8, 2018

PHY357 Problem Set #4(Due on March 21, 2018)

This problem set consists of five (5) questions all of which are weighted equally. Each problem set is worth 6% of thefinal grade in PHY357. Problem sets turned in late will have 12% of their grade deducted for each day they are late and willbe worth 0 eight days later – when they will be returned in tutorial and the solutions will be posted on the course website.

1) Draw the Feynman (particle flow) diagrams for each of the following decays:

(a) τ− → e− + ν̄e + ντ

(b) K0 → π− + e+ + νe

(c) D+ → K̄0 + µ+ + νµ

(d) τ+ → π+ + ν̄τ

(e) Λ → p+ e− + ν̄e

(f) Ξ− → Σ0 + π−

(g) K+ → π+ + π− + π+

For reactions with hadrons do this at the quark level and indicate clearly which quarks belongs to each hadron.

2) We don’t use bubble chambers any more because their readout is much slower than modern electronic detectors.But they still provide the most iconic images of what is going on in a particle interaction, along with ‘continuous’trajectories of charged particles. Modern detectors tend to sample these trajectories with much higher precision, butmuch more sparsely (fewer, high precision hits) and rely on pattern recognition algorithms to match hits from a singletrack and interpolate the particle trajectory. The picture below is from the Big European Bubble Chamber that Idiscussed in class. It was an enormous device used to investigate neutrino interactions, and early studies of charmparticles. Charm particles are like strange particle, but have a c-quark in them, instead of an s-quark. You can find theirquark content from: http://pdglive.lbl.gov/ParticleGroup.action?node=MXXX035&init=

The above is a picture of a neutrino interaction producing a charm meson. You can follow the complete productionand decay process including the interaction of the secondary K−. In order to understand this interaction, you shouldremember that in addition to the uud valence quarks inside the proton, there is also a sea of ss̄ pairs, that do not givethe proton any net strangeness. In this case the neutrino interacts with this ss̄ sea.

(a) What is the lepton flavour of the incoming neutrino?(b) What is the minimum energy of the neutrino beam necessary for this? You explored the threshold energy

necessary for reactions on the first problem set. This is another application of that result. You do not need tore-derive the equation here. If a question like this were to appear on the final exam you would be given thethreshold energy expression (along with others...) and be expected to find/understand/use it.

(c) Write down what force is involved in producing each interaction and decay vertex in the picture.(d) Draw a quark line diagram for each interaction and decay in this reaction chain.(e) Look at the properties of the D0 at: http://pdglive.lbl.gov/Particle.action?node=S032&

init=0. There are two π+ in this picture, only one of them comes from the decay of the D0. From theproperties of the D0 and the momenta on the picture, calculate (roughly) the angle between the K− and each ofthe π+, each time assuming that the K− and the π+ are the decay products of the D0. Which π+ is the one thatactually came directly from the D0 decay?

(f) How would the following table allow you to identify the correct pion without any calculation?

3) Draw the Feynman (particle flow) diagrams for each of the following reactions:

(a) νe + e− → ve + e−

(b) e− + p→ n+ νe

(c) µ+ + e− → ν̄µ + νe

(d) νµ + p→ µ− + ∆++

For reactions with hadrons do this at the quark level and indicate clearly which quarks belongs to each hadron.

4) (a) Explain with a sketch what is meant by a neutrino being left-handed and an anti-neutrino being right-handed(b) Why does this concept of handed-ness only make sense if the neutrinos and anti-neutrinos are massless?(c) What are the physical consequences of applying the Parity operation to a physical system? Illustrate your answer

with a sketch that demonstrates what happens to the spatial coordinates, the momentum and the spin of a particleunder a Parity transformation.

(d) In which of the following decays is parity conserved? Why?

η → γγ

∆++ → pπ+

Ξ− → Λπ−

Draw a Feynman diagram for each reaction, in which you show the initial and final state quarks, and also thevirtual force carrying particles. In a strong interaction you may assume only one force carrier is dominant anddraw that, even if other reactions are possible. Remember that only the weak interaction can turn one quarkflavour into another.

5) Show that the following decays cannot occur by first order weak interactions:

(a) D0 → K+ + π− + π0 + π0

(b) D− → K0 + π−

(c) D0 → K+ + µ− + ν̄µ

(d) K0 → π+ + e− + ν̄e

For each decay you should draw the second order weak diagram (ie. one that involves to weak bosons to show howthe decay can proceed, albeit at much lower rate.