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No. of Pages: 4 No. of Questions: 73648MIDSUMMER EXAMINATIONS 2012 Blackboard version with numerical answersSubject PHYSICS, PHYSICS WITH ASTROPHYSICS PHYSICS WITH NANOSCIENCE AND TECHNOLOGY PHYSICS WITH PLANETARY SCIENCE PHYSICS WITH SPACE SCIENCE AND TECHNOLOGYTitle of paper COURSE 3648 – ELEMENTA...

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No. of Pages: No. of Questions:

4 7

3648

MIDSUMMER EXAMINATIONS 2012

Blackboard version with numerical answers

Subject

PHYSICS, PHYSICS WITH ASTROPHYSICS PHYSICS WITH NANOSCIENCE AND TECHNOLOGY PHYSICS WITH PLANETARY SCIENCE PHYSICS WITH SPACE SCIENCE AND TECHNOLOGY

Title of paper

COURSE 3648 – ELEMENTARY PARTICLES

Time allowed

Seventy-five Minutes

Instructions to candidates

Candidates should answer all questions in Section A and ONE from Section B. Each question in Section A is worth 10 marks. The marking scheme for each question in Section B is indicated by the numbers in square brackets on the right-hand side of the question.

NO PAPERS MAY BE REMOVED FROM THE EXAMINATION ROOM.

CANDIDATES MUST NOT OPEN EXAMINATION PAPERS OR BEGIN WRITING UNTIL INSTRUCTED TO DO SO.

Continued . . .

2.

3648

SECTION A

A1. Describe the concept of isospin in terms of the quark model A2. What is the charge conjugation transformation, C, of the process µ+ → e+ + ν¯µ + νe and why is it not observed? A3. Estimate the value of the cross-section ratio R = σ(e+ e− → hadrons)/σ (e+ e− → µ+ µ− ) at centre-of-mass energies, above the J/ψ resonance (quark content c¯ c). A4. A Λ0 (rest mass 1.116 GeV/c2 ) has a kinetic energy of 4.70 GeV. On average what distance will it travel before decaying? (The mean lifetime of the Λ0 is 2.63 × 10−10 s at rest.)

SECTION B

B1. (a) Explain qualitatively the differences between the Schr¨odinger, Klein-Gordon and Dirac equations. Explain why the Klein-Gordon equation is useful for understanding the long-range interactions of nucleons.

[10]

(b) There is a peak in the proton-neutron differential cross-section at very large (as well as very small) angles. Explain with the aid of a diagram why this should be the case.

[10]

(c) Draw a Feynman diagram for the short range strong interaction of two up quarks, giving an example of possible colour charges on all particles.

[10]

(d) Explain the concepts of quark confinement and asymptotic freedom with reference to the energy dependence of the relevant coupling constant.

[10]

Continued . . .

3.

3648

B2. (a) Draw the fundamental vertices for charged current and neutral current weak interactions of quarks.

[10]

(b) Use one of these vertices to construct a lowest-order Feynman diagram for elastic quark-quark scattering. Explain why the contribution of this process to the quark-quark scattering amplitude can almost always be neglected.

[10]

(c) The Ξ0 baryon (strangeness |S| = 2) decays in 99.5% of cases to a Λ0 baryon and a π 0 . Draw a quark-level Feynman diagram for this decay.

[10]

(d) The occurance of this interaction is deduced from the appearance of three distinct pairs of tracks in a bubble chamber. Identify the 6 particles which produce the tracks, and their origin.

[10]

B3. The overburden (X, the integral of the density from a height h above sea level to infinity) of the Earth’s atmosphere can be approximated as X ≈ XA exp(−h/hA ), where XA ≈ 104 kg m−2 is the overburden at sea level and hA ≈ 8 km. The radiation length (Bremsstrahlung mean free path) in the atmosphere is ≈ 400 kg m−2 . (a) Estimate the mean height above sea level of the first interaction of gamma-rays entering vertically into the atmosphere.

[10]

(b) The critical energy in air is ≈80 MeV. Estimate the mean height above sea level at which the electromagnetic cascades initiated by 1 TeV photons will reach their maximum particle number.

[16]

(c) The refractive index of air n as function of height above sea level can be approximated as n(h) − 1 ≈ 3 × 10−4 exp(−h/hA ). Estimate the angle at which Cherenkov light is emitted by an ultra-relativistic electron at the height of the shower maximum calculated above.

[8]

(d) Use this result to estimate the effective collection area for TeV gamma-rays of a single air-Cherenkov detector at sea level.

[6]

Continued . . .

4. SECTION A NUMERICAL ANSWERS

A1. None. A2. None. A3. 10/3. A4. 40.3 cm.

SECTION B NUMERICAL ANSWERS

B1. None. B2. None. B3. 23.7 km, 4.86 km, 1.04◦ , 2.44 × 104 m2 .

3648

No. of Pages: No. of Questions:

5 7

3648

MIDSUMMER EXAMINATIONS 2013

Blackboard version with numerical answers

Subject

PHYSICS, PHYSICS WITH ASTROPHYSICS PHYSICS WITH NANOSCIENCE AND TECHNOLOGY PHYSICS WITH PLANETARY SCIENCE PHYSICS WITH SPACE SCIENCE AND TECHNOLOGY

Title of paper

COURSE 3648 – ELEMENTARY PARTICLES

Time allowed

Seventy-five Minutes

Instructions to candidates

Candidates should answer all questions in Section A and ONE from Section B. There are 40 marks each for Sections A and B. The marking scheme for each question in Section B is indicated by the numbers in square brackets on the right-hand side of the question.

NO PAPERS MAY BE REMOVED FROM THE EXAMINATION ROOM.

CANDIDATES MUST NOT OPEN EXAMINATION PAPERS OR BEGIN WRITING UNTIL INSTRUCTED TO DO SO.

Continued . . .

2.

3648

PARTICLE MASSES AND CONSTANTS Particle e+/− µ+/− π0 π +/− K +/− p +/− τ Υ W +/− Z0 H0

Mass (GeV/c2 ) 5.11×10−4 0.106 0.135 0.140 0.494 0.938 1.78 9.46 80.4 91.2 126

h ¯ = 6.58 × 10−25 GeV s h ¯ c = 1.97 × 10−16 GeV m

SECTION A

A1. Write down an expression for the range of an exchange particle as a function of its rest mass. Use this expression to derive the approximate ranges of the strong nuclear and electromagnetic forces. A2. What is the charge conjugation (C) transformation of the process π − → µ− + ν¯µ ? Why is this new process not observed in nature? A3. Draw the fundamental vertex for the electromagnetic interaction and use it to construct a Feynman diagram for electron Bremsstrahlung. A4. A K + has a momentum of 830 MeV/c. On average what distance will it travel before decaying? (The mean lifetime of the K + is 1.24 × 10−8 s at rest.)

Continued . . .

3.

3648

SECTION B

B1. (a) Draw a Feynman diagram for the process e+ e− → µ+ µ−

[8]

u (where u is (b) Give two reasons why the cross-section for the process e+ e− → u¯ the up quark) is different from that for the process given above.

[8]

(c) Explain why this process (and similar processes involving different quark flavours) always lead to the appearance of hadrons rather than free quarks, illustrating your answer with a quark-flow diagram and with reference to the form of the strong potential at large (> 10−15 m) distances.

[12]

(d) Derive an estimate for the value of the cross-section ratio R = σ(e+ e− → hadrons)/σ (e+ e− → µ+ µ− ) at centre-of-mass energies above the Υ resonance which has quark content b¯b.

[12]

B2. (a) Draw a Feynman diagram for a neutral current contribution to the process e− + νe → e− + νe

[8]

(b) Why is the cross-section for the above process (usually) much lower than that for electron-electron scattering (e− + e− → e− + e− ), despite the fact that the intrinsic coupling constants of the electromagnetic and weak forces are comparable? Under what circumstances will electron/electron and electron/neutrino scattering occur with comparable cross-sections?

[8]

(c) Evidence has recently been found by the ATLAS and CMS collaborations for the process H 0 → e− + e+ + µ− + µ+ where H 0 is the Higgs Boson. Draw a Feynman diagram which represents a significant contribution to this process. Explain why this contribution is significant, with reference to the strength of the Higgs coupling to the other particles involved.

[12]

(d) The process H 0 → γγ is also expected to occur. Explain, with the aid of a (Feynman) diagram, why this is so, despite the fact that the Higgs is not expected to couple directly to photons.

[12]

Continued . . .

4.

3648

B3. The Superkamiokande (Super-K) detector employs a vessel containing 5 × 107 kg of water as a target for neutrino interactions. For the following questions the total neutrino-nucleon interaction cross-section at MeV energies can be taken as 10−46 m2 and the refractive index of water as 1.33. (a) Explain the detection principle of Super-K, and how interactions between electron-neutrinos and muon-neutrinos can be differentiated in this detector.

[8]

(b) A muon with total energy 225 MeV is produced in the interaction of an atmospheric ν¯µ with a proton, 5 m from the wall of the tank. i. Draw a Feynman diagram for this process

[8]

ii. What is the radius of the ring of light incident on the wall?

[8]

(c) Estimate the number of neutrinos interacting inside Super-K from a supernova explosion at a distance of 3 × 104 light-years which emits 1046 J of energy in the form of ∼ 10 MeV neutrinos.

[9]

(d) Which neutrino flavours are expected to arrive at the Earth from such an explosion? Which of them are potentially detectable with an instrument such as Super-K? Explain your answer.

[7]

Continued . . .

5. SECTION A NUMERICAL ANSWERS

A1. 1.4 × 10−15 m. A2. None. A3. None. A4. 6.3 m.

SECTION B NUMERICAL ANSWERS

B1. d) 33/9. B2. None. B3. b) ii) 3.07 m, c) 1.8 × 104 interactions.

3648

3648 All candidates MIDSUMMER EXAMINATIONS 2014

Blackboard version with numerical answers

DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR

Department

PHYSICS AND ASTRONOMY

Module Code

3648

Module Title

COURSE 3648 – ELEMENTARY PARTICLES

Exam Duration

Seventy-five Minutes

CHECK YOU HAVE THE CORRECT QUESTION PAPER

Number of Pages

5

Number of Questions

7

Instructions to Candidates Candidates should answer all questions in Section A and ONE from Section B. There are 40 marks each for Sections A and B. The marking scheme for each question in Section B is indicated by the numbers in square brackets on the right-hand side of the question. NO PAPERS MAY BE REMOVED FROM THE EXAMINATION ROOM.

For this exam you are allowed to use the following Calculators

Casio FX83GTPLUS or Casio FX85GTPLUS

Books/Statutes

Physical Constant and Mathematical Formula sheets

Additional Stationery

NOT APPLICABLE

Page 1 of 5

3648 All candidates

PARTICLE MASSES AND CONSTANTS Particle π0 π +/− K +/− p Σ+ ∆+ D +/−

Mass (GeV/c2 ) 0.135 0.140 0.494 0.938 1.189 1.235 1.870

SECTION A

A1. Draw a Feynman diagram for the elastic scattering of a muon anti-neutrino, ν¯µ with an electron. Which force is responsible for this interaction? A2. Give the charge conjugation (C) and charge/parity (CP) transformations of the process K − → π + + π − + e− + ν¯e ? Why is only the CP-transformed process observed in nature? A3. A D− with a kinetic energy of 34.0 GeV is produced on axis in a collider. Is it more likely to reach the innermost tracker at a distance of 5 mm, or to decay before reaching the tracker (show your workings)? Note: The mean lifetime of the D− is 1.04 × 10−12 s at rest. A4. The expected timescale for the decay of bounds states is ∼ g −4 r/c, where g is a dimensionless coupling constant associated with the fundamental forces responsible for the decay, r is the size of the system, and c is the speed of light. Use this expression to estimate the decay timescales of the ∆+ and π 0 hadrons, which decay via the strong and electromagnetic forces, respectively.

Page 2 of 5

3648 All candidates

SECTION B

B1. (a) The strength of the coupling associated with the strong force decreases with increasing energy. Describe two important consequences of this for the interactions of colour-charged particles, and calculations of such interactions.

[12]

(b) Draw a Feynman/quark-flow diagram for the interaction p + π + → Σ+ + K + .

[12]

(c) Calculate I3 for each of the particles involved in the above interaction, based on their quark content, and show that Isospin is conserved.

[8]

(d) If the colliding p and π + have (oppositely directed) momenta of 0.6 GeV/c in the centre of mass frame, is the above interaction possible (show your working)? [8] B2. (a) Explain why the existence of the strangeness |S| = 3 Ω− baryon provides evidence for the existence of colour.

[10]

(b) Draw a Feynman diagram for the decay of an Ω− to an |S| = 1 Λ0 baryon and an |S| = 1 K − meson.

[12]

(c) The above process is the most common decay mode of the Ω− . Comment on why the process Ω− → Λ0 π − is not seen.

[8]

(d) Describe briefly the detection systems that would be required to measure the charge, mass and momentum of the Ω− and its decay products.

[10]

Page 3 of 5

3648 All candidates B3. The Pierre Auger Observatory (PAO) is an 3000 km2 detector of ultra-high energy (UHE, E > 1018 eV) cosmic rays. (a) The energy flux of UHE cosmic rays is ∼ 10−13 W m−2 sr−1 . Estimate the detection rate, in events/year, of such cosmic rays with the PAO.

[8]

(b) The flux of cosmic rays is expected to be suppressed above an energy EGZK by the excitation of the ∆+ resonance in interactions of UHE protons with cosmic microwave background (CMB) photons. Given that the temperature of the CMB is 2.7 K, estimate EGZK .

[8]

(c) If the typical fraction of the energy lost in one interaction is 0.2, estimate the distance, in light-years, that a particle with E ∼ EGZ K can propagate through the universe. Note: The density of the CMB is ∼ 400 cm−3 and the pγ cross-section around the ∆+ resonance is ∼0.5 mb = 5 × 10−32 m2 .

[8]

(d) Draw a Feynman/quark-flow diagram for the decay ∆+ → p + π 0 .

[10]

(e) What is the quark content of a π 0 ?

[6]

END OF PAPER

Page 4 of 5

3648 All candidates

SECTION A NUMERICAL ANSWERS

A1. None A2. None A3. None A4. 1.2 × 10−15 s, 3 × 10−24

SECTION B NUMERICAL ANSWERS

B1. None B2. None B3. a) 1.8×105 events/year, b) of order 1020 eV, c) 3 × 107 light years

Page 5 of 5

3648 All candidates MIDSUMMER EXAMINATIONS 2015

Blackboard version with numerical answers

DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR

Department

PHYSICS AND ASTRONOMY

Module Code

3648

Module Title

COURSE 3648 – ELEMENTARY PARTICLES

Exam Duration

Seventy-five Minutes

CHECK YOU HAVE THE CORRECT QUESTION PAPER

Number of Pages

9

Number of Questions

7

Instructions to Candidates Candidates should answer all questions in Section A and ONE from Section B. Each question in Sections A carries 10 marks. In Section B each question carries 40 marks and the marking scheme is indicated by the numbers in square brackets on the right-hand side of the question. NO PAPERS MAY BE REMOVED FROM THE EXAMINATION ROOM.

For this exam you are allowed to use the following Calculators

Casio FX83GTPLUS or Casio FX85GTPLUS

Books/Statutes

Physical Constant and Mathematical Formula sheets

Additional Stationery

NOT APPLICABLE

Page 1 of 9

3648 All candidates

PARTICLE MASSES AND CONSTANTS Particle e+/− π0 π +/− K +/− p n Σ− ∆++/+/−

Mass (GeV/c2 ) 5.11 × 10−4 0.135 0.140 0.494 0.938 0.940 1.197 1.232

h ¯ = 6.58 × 10−25 GeV s h ¯ c = 1.97 × 10−16 GeV m

Page 2 of 9

3648 All candidates

SECTION A

A1. Give the charge conjugation (C) and charge/parity (CP) transformations of the process μ− → e− + νµ + ν¯e . Which of these two processes is observed in nature, and why?

A2. A particle passes through a detection system consisting of a tracker, a water (n = 1.33) Cherenkov detector and finally a calorimeter. In the tracker it leaves a curved track with an ionisation level consistent with a single elementary charge and a momentum of 2.9 GeV/c (assuming q = e). The signal produced in the calorimeter is consistent with a total energy 3.14 GeV. Estimate: (a) the particle rest mass energy in GeV, (b) the expected Cherenkov angle in the water in degrees.

A3. Draw a quark-level Feynman diagram for a contribution to the process π + + n → π 0 + p. Which forces contribute to the total amplitude of this process?

A4. The idea of particle exchange is central to our understanding of fundamental forces. Identify the exchanged particles in the Yukawa model of nuclear interactions and in electromagnetism. Describe how the mass of these particles is related to the range of the forces.

Page 3 of 9

3648 All candidates

SECTION B

B1. (a) Draw the fundamental vertex of the electromagnetic interaction and use this to construct lowest order Feynman diagrams for i) Inverse Compton scattering and, ii) electron/positron pair production in the field of a nucleus.

[14]

(b) Draw two distinct higher order diagrams for either of these processes, and explain why their contributions are suppressed.

[10]

(c) Describe briefly how an electromagnetic calorimeter works and derive an expression for the required depth of a calorimeter as a function of the maximum particle energy to be measured.

[16]

B2. The most common decay mode of the strange (|S| = 1) Σ− baryon is the process: Σ− → nπ − (a) Draw a Feynman diagram for a leading order contribution to this process.

[13]

(b) Explain why the process Σ− → nπ − γ is much rarer and estimate the relative branching ratios of the two processes.

[8]

(c) For each of the processes below, explain why they are not observed: i. Σ− → n + p¯ ii. Σ− → n + e− + νe iii. Σ− → ∆− + π 0

[12]

(d) Explain briefly why the strangeness quantum number is apparently conserved in the production, but not the decay, of strange hadrons.

[7]

Page 4 of 9

3648 All candidates B3. (a) Explain why the existence of the ∆++ baryon provides evidence for the existence of colour.

[6]

(b) Calculate the value of I3 for the ∆++ and the value of I for the ∆ family.

[7]

(c) Draw a Feynman diagram for the short range strong interaction of an anti-up ¯ quark, giving an example of possible colour (¯ u) quark and an anti-down (d) charges on all particles.

[13]

(d) Sketch the effective energy dependence of the strong coupling constant and use this to briefly explain the concepts of quark confinement and asymptotic freedom.

[14]

END OF PAP...