SH2203 Experimental Particle Physics

SH2203 Experimental Particle Physics

Home assignment 3 (of 3)

Issued: 14

Feb 2014

Examiner: Jonas Strandberg (jostran@kth.se / 070-3155505).

Deadline: 13:00 on 21

of Feb 2014. In fairness to all, late scripts will be penalized – 0.2 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 lose 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) (i) Calculate the following ratio:

) (

) (















 



 e e Rate

hadrons all

e e R Rate

as a function of centre-of-mass collision energy up to 25 GeV. (1 point) You should assume that:

 The u,d and s quarks are massless

 The c quark has a mass of 1.5 GeV

 The b quark has a mass of 5 GeV.

(ii) Comment on the significance of your result and on how it compares to the experimental data presented below. (1 point)

Figure 1: The ratio, R, as a function of the total e

e

centre-of-mass energy, E

(GeV). The data is compiled from many different accelerator experiments. The vertical arrows indicate the location of known resonances.

(b) Explain, in your own words, how the measurement of the Z boson cross

section σ as a function of the collision energy in e

e

collisions can tell us

something about how many neutrinos there are. (1.2 points)

(c) Show that the rotation of a spin-1/2 system through a finite angle θ about the 2-axis corresponds to the unitary transformation:

sin 2 cos 2

2

2/

  



i

e

 

Hint: Start by Taylor-expanding the exponential. (1.8 points)

QUESTION 2 (5 points in total)

This question concerns e

e

collisions produced with the Large Electron Positron (LEP) collider that was operational at CERN until 2001. One of the experiments used to study the e

e

collisions was OPAL (‘Omni Purpose Apparatus for LEP’).

You can learn more about the OPAL experiment at http://opal.web.cern.ch/Opal/.

Some of the data recorded is presented as a series of ‘event displays’ at the following link: http://www.particle.kth.se/SH2203/collision_lab. The reconstructed event properties are also shown. As with any experimental measurement, bear in mind that these properties are subject to uncertainties.

For the first three events, answer the following questions:

(a) Event 1

(i) This event and the following two events involve the production of quarks. Other events at LEP may involve the production of leptons instead. What differences between the behaviour of leptons and quarks gives rise to the very different event structure seen here compared to the very few tracks in lepton events? (0.5 point)

(ii) It is very likely that this event is due to a Z

decaying into a b-quark pair. With reference to the event views, justify this statement.

(0.5 point)

(iii) Briefly explain how you could measure the lifetime of the b hadrons which have been produced. (0.5 point)

(b) Event 2

(i) What has caused the extra `jet' of particles in this event. Can you draw a Feynman diagram to explain this? (0.5 point)

(ii) The theory of Quantumchromodynamics (QCD) describes the interactions of particles which carry colour, such as quarks and gluons. The strength of the chromodynamic force is set by the 'strong coupling constant'. This coupling constant is not actually constant as it decreases as the energy involved in the interaction increases

(corresponding to smaller distances). Particle physicists say that the coupling constants `runs' with energy.

The electromagnetic force also runs with energy. Can you find out a

good explanation for this ? Does it 'run' in the same sense? (0.5 point)

(c) Event 3

(i) This is an impressive event recorded in July 1996. At this time the aim of LEP was no longer to produce Z

bosons. What have the e

e

beams produced upon annihilation now? (0.5 point)

(ii) Draw Feynman diagram to describe this event. (0.7 point)

(iii) Finally, explain how the mass of the objects produced in the e

e

annihilation can be determined experimentally. (0.3 point)

(d) Particle Identification

Explain, in your own words and/or with the help of drawings, how a modern general purpose detector like the OPAL detector or the ATLAS detector can use a combination of sub-detector signals to identify (and distinguish between) the following particles assuming they are created in the collision in the center of the detector:

i. Electrons.

ii. Photons.

iii. Muons.

iv. Quarks and gluons.

v. Neutrinos.

(1.0 point)