SH2203 Experimental Particle Physics
Home assignment 1 (of 3)
Issued: 24th January 2014
Examiner: Jonas Strandberg (jostran@particle.kth.se / 070-3155505).
Deadline: 13:00 on 31
thJanuary 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)
(i) What are the dimensions (i.e. using exponents of Mass, Length and Time) of c ? (0.5 points)
(ii) If c = 197 MeV fm, what value of in units of J s has been assumed?
State any further assumptions you need to make. (0.1 points) (iii) The electromagnetic coupling constant can be written as
c e
0
2
4
.
Using dimensional analysis, obtain an analogous coupling constant for the
gravitational interaction in terms of Newton’s constant, a characteristic
mass, M and c . Compare the values of the coupling constants for two
quarks separated by 1 fm. State any assumptions you make! (1 point)
(b)
Experiments have been performed to search for proton decay using the
hypothesized decay mode: p e
0. A large tank of ultra-pure water is used as a convenient source of protons and the tank is placed deep underground to shield it from cosmic radiation. The aim is to identify proton decays via the
Cherenkov light emitted when electromagnetic showers from the decay products traverse the water.
(i) Make a sketch of the experiment that you would use to detect protons decaying via this mode. Indicate how you would identify a decaying proton.
(0.4 point)
(ii) How big should the tank of water be in order to contain the
electromagnetic showers (you can assume that the shower starts at the centre of the tank)?
(1.5 points)
(iii) The annual permissible body dose for a human is approximately 0.05 Gy (J/kg). If 100 times this dose would lead to the extinction of ‘advanced’
life-forms such as ourselves, what limit does this set on the proton
lifetime? State any simplifying assumptions which you make. (1.5 points)
QUESTION 2 (5 points in total)
(a) Why are the following decays of the
+forbidden? (4 x 0.2 points)
e n iv
p iii
K ii
K p i
) (
) (
) (
) (
0 0
(v) Draw the Feynman diagram for the dominant decay mode of the
+. (0.5 points)
(vi) Briefly (in less than half a page), describe how you could determine
the mass of the
+experimentally. (0.6 points)
(b) Consider each of the following interactions. If the interaction is allowed, draw the appropriate Feynman diagram (at quark level for hadronic interactions). If the interaction is not allowed explain why. (7 x 0.3 points)
e
evii
D B
vi
e e e v
K p iv
iii e e ii
K i
) (
) (
) (
) (
) (
) (
) (
0
0 0 0
0
