SH2203 Experimental Particle Physics
Home assignment 2 (of 3)
Issued: 5th February 2014
Examiner: Jonas Strandberg (strandbe@particle.kth.se / 070-3155505).
Deadline: 13:00 on 12th Feb 2014. In fairness to all, late scripts will be penalized – 0.3 points will be deducted from your total score for every day after the deadline.
Grading: Each question is worth 5 points – the point breakdown is indicated for each question.
Pay attention to the grading philosophy described in the ‘kurs-PM’ – e.g.: you will loose marks if you simply provide a numerical answer with no comments.
Special note: You are encouraged to discuss the problems in groups. However, the final presentation of solutions must be your own work. Identical scripts will be treated as cheating and the appropriate disciplinary measures taken.
Good luck!
QUESTION 1 (5 points in total)
(a) Draw the lowest order Feynman diagrams for the decays and
K . From the principle of the decays estimate the ratio
) (
Rate
) (
Rate
K
R
The experimental value is about 1.3. Comment on the difference compared to your estimate (try to use your intuition and best guesses). (1.5 points)
(b) Explain in your own words why the ratio
) (
) (
e e
is as small as 1.2x10-4 (1.5 points)
(c) In an experiment where a low energy anti-proton beam hit a target, among others occasionally a charged and a neutral Kaon were produced.
i) At some distance from the target, the neutral Kaon decayed to ee and ee with almost equal probability independently of if the charged Kaon was K+ or K-. Explain. (1 point)
ii) In an another experiment where a neutral Kaon beam was created, decays at short distances was dominated by two pion decays, while at long distances the pion, lepton and neutrino decays dominated.
Nevertheless at very long distances from the target decays into two pions where found. Explain why and the significance of this. (1 point)
QUESTION 2 (5 points in total)
(a) Explain with the aid of Feynman diagrams why the process (i) below provides unique evidence for neutral current interactions, whereas process (ii) does not. (0.5 points)
e
e
e e
ii
e e
i
) (
) (
(b) At the LHC collider, which is operating since 2010, two beams of counter-rotating protons each of energy 7 TeV will be collided (the beam energy up to now has been 4 TeV, but this will be increased to the nominal 7 TeV in 2015). The LHC accelerator sits in the existing LEP accelerator tunnel which has a circumference of 27 km.
(i) Estimate the average magnetic field needed to keep one of these proton beams in orbit around the tunnel? (0.5 points)
(i) In practice, this will be achieved with 1296 superconducting dipole magnets of length 13.5m. What magnetic field is required in each dipole? (0.5 points)
(ii) Estimate the energy loss per turn per proton for the LHC beams (1.0 points) (c) Tau leptons can be produced in both electron-positron collisions at LEP and in proton-antiproton collisions at the Tevatron.
(i) With the aid of Feynman diagrams, show that this is a correct statement. (0.5 points)
The tau lepton was discovered by Martin Perl in 1975. He was awarded the Nobel Prize in Physics in 1995 for his discovery (for the record, he shared the Prize with Frederick Reines, who discovered the electron neutrino). Perl used the SPEAR electron-positron
collider at SLAC to produce the tau leptons. Read his recollections of this discovery in the attached article (from Scientific American, March 1978) and answer the following three questions:
(i) Perl claimed discovery of the tau lepton by observing an electron and a muon in his detector system. Explain his reasoning (0.5 points).
(ii) It appears that momentum is not conserved since the electron and muon are not produced ‘back-to-back’ in the detector. How do you explain this? (0.5 points)
(iii) During the lectures we have discussed the concepts of ‘signal’ and
‘background’, where ‘background’ are processes giving the same final state but through a different mechanism than the signal. Perl’s signal signature was the observation of an electron and muon in the detector system. Identify two sources of background which could give rise to the same signature in the detector, but have nothing to do with the production of tau leptons. In both cases, explain in detail how Perl was able to distinguish between the signal and background. (1.0 points)
