Not surprisingly, this admission exam generated outrage among the several hundred post-docs to which it is addressed, because it completely avoids attacking the real problem of recruitment in particle physics research in Italy: the lack of resources and of positions. Instead, it offers aspiring researchers -most of them already engaged with important tasks within their experiments, but all of them unsure about their near future employment- nothing but a certification -one which was not needed until today. As if a Ph.D. in particle physics plus years of research at physics laboratories was not enough.
Elsewhere I discussed the reasons for boycotting the exam and the reasons for attending it. Here, I just wish to remind those who will choose to attend the exam the kind of test they will be facing, and provide the rest of you with a flavor of the competences which will be tested. The 42 questions listed below were given in 2005 in the only comparable exam given by INFN in the past. Two hours were given to answer these questions -a really short time, which forced candidates to make tough choices on which questions to address first. Note that the total score of each of the four batches of questions is given, in order to provide guidance on which questions to try and answer first -or to just freak out the candidates further.
In a few days I will provide my own answers to the questions. For now, here is the list:
1. Questions on detector physics
(maximum 15 points in total):
Cathode readout may be used in wire detectors such as multi-wire chambers, TPC, LST, and even in RPC. What is it ? What are its advantages ?
One wants to distinguish pions and kaons of p=2 GeV/c momentum by determining the time of flight, on a L=2m basis. If the instrumenta has a time resolution of 0.2ns, it is asked whether
a) it is possible to identify each detected particle;
b) it is possible to measure the fraction of pions and kaons.
A particle at ionization minimum generates on average n electron-positron pairs per cm in a gaseous detector at atmospheric pressure. What is n if the gas is a argon-isobutane mixture (60-40)? Which additional factors besides the statistics of produced electrons determine the standard deviation of the signal ?
The drift velocity of electrons in a given gaseous mixture is v=5cm/us. Which consequences does this value cause in a multi-wire chamber with pitch s=2mm ? And in a drift chamber with TDC having a clock cycle of 500 MHz ?
An electron with medium-high energy releases in a BGO block energy which generates a signal of about 10^6 electrons per GeV, and in a block of lead glass of the same dimensions a signal of about 10^3 electrons per GeV. What is the reason for this difference ?
In a given e.m. calorimeter the statistical contribution to resolution is 0.07/sqrt(E). Can one infer that energy resolution for an electron of 50 GeV energy is 1% ?
Order by decreasing dead-time the following detectors: silicon, plastic scintillator, drift chamber. Which one do you choose for a time measurement with a precision of a few hundred picoseconds ?
A cube of NaI(TI) scintillator read out by a photomultiplier tube measures the line of cesium; estimate the resolution in energy, listing the factors that contribute.
In a measurement where a threshold Vth=0.4V is applied to signals which have a rise time roughly constant and equal to Ts=10ns, but a variation in amplitude between Vmin=0.5V and Vmax=1V, estimate the limit to time resolution due to the variability of height. Is there a technique to reduce this effect ?
A relativistic electron loses energy for ionization and for radiation when it traverses a medium.
a) How do ionization losses and radiation losses depend on the composition of the traversed medium ?
b) How do they depend on the electron energy ?
c) Knowing that the critical energy is defined as the one for which the two losses are equal, would this be smaller for an electron or for a muon ?
In what energy interval does Compton scattering dominates among the processes of interaction betweeh photons and matter ? What prevails at lower and higher energies ? How does all this depend on the absorbing material ?
A completely depleted silicon microstrip detector has a strip pitch of 50 um and woks without charge sharing. What is its spatial resolution ?
2. Questions on apparata and accelerators
(maximum 18 points in total):
Compute the average number of interactions per bunch crossing for a luminosity L=2.5E31 cm-2 s-1, if the total cross section is sigma=20mb and bunch crossings occur every T=4 us. What is the probability of having zero interactions in a bunch crossing ?
Justify the luminosity L=10^34 cm-2 s-1 of LHC starting from a accumulated current I=0.5A per beam and assuming that there are B=3000 bunches. How many are the protons per bunch, Np ? What is the cross section of the beam in the interaction region ? (Electron charge is e=1.6E-19C).
A beam of protons of energy E1=20 GeV is made to collide head-on with a beam of protons of energy E2=5 GeV. Determine:
a) the CM energy;
b) the boost of the CM in the laboratory;
c) the angle in the laboratory of a ultra-relativistic particle produced at 90 degrees in the CM
d) the energy a beam of protons must have to generate the same CM energy in a fixed target collision.
What is the ratio between the radiated power of a proton at LHC and an electron at LEP I ? And between an electron at LEP I and one in Daphne ?
An experiment with continuous beam is endowed with a trigger with efficiency eff=20%. The natural frequency of events to be selected by the trigger is f=5 kHz. The acquisition system generates a dead time T=1 ms per every collected event; during dead time the trigger and detector are ineffective. Determine the average frequency of data collection.
5 kHz of events are analyzed to decide whether the event must be collected or not. The decision takes Tt=20 us and the digitization Td=1 ms. What rate of accepted events can be sustained if the dead time must be kept below D=20% ?
To monitor the luminosity of a collider two scintillation counters A and B are used, which are located before and after the interaction region. The packets cross every T=10 us and for every crossing the two counters detect via digital signals A, B whether there has been at least an event; a logical AND called C signals the coincidence, in the same packet collision, of the A and B signals. Background events of various nature, produced for example by particles belonging to the beam halo or by collisions with residual gas molecules within the vacuum tube, overlap to useful events generating casual coincidences. One measures the following average frequencies for the three signals A,B,C: f_A=7.53E4 Hz, f_B=6.67E4 Hz, f_C=5.43E4 Hz. Compute the average number of collisions per crossing.
How does dP/P depend on the momentum of charged particles tracked in a magnetic field in air ? And in iron ?
A spectrometer for particles with unit charge and momentum of few GeV/c is made by three parallel planes of position detectors with a resolution dx=100 um, distanced a=20 cm and immersed in a uniform magnetic field B=1 T, parallel to the detector planes and orthogonal to the measured coordinate. Particles incide almost perpendicularly to the detector planes. Estimate the transverse momentum resolution at p=2 GeV/c.
3. Questions on probability and statistics
(maximum 5 points in total):
An experiment selects signal events with a frequency f and events of background with a frequency b. Calculate the data taking time necessary to observe the signal with a statistical significance of n sigma.
Given events with four b-quarks, knowing that BR(b->xlv)=20%, where l=e or mu, what is the probability to have at least one lepton ?
If a particle with average lifetime tau has not decayed after a time t, what is the probability that it decays in the subsequent interval delta t ?
After collecting an integrated luminosity L=10/fb the analysis of events B->J/psi K_s (J/Psi->ll, Ks->pi pi) selects N=100 candidates. Using N_sim=1000 events it is found that the detection efficiency is eff=37%. What is the measured BR, what is the statistical error and what is the systematical uncertainty due to the fact of having simulated too few events ? (sigma=1 nb).
4. Questions on subnuclear physics
(at most 22 points in total):
List synthetically the contributions that K physics has brought to the understanding of subnuclear physics in general.
What is K0s regeneration ? How is it explained ?
Can a neutral pion decay into three gamma ? Can a rho decay into two pizeros ? If not, explain why.
How is it explained, at least qualitatively, that phi decays into three pions about 15% of the time while the remaining BR is basically into KK ?
Weak interactions are responsible besides other things of the decay of muons (tau=10^-6 s), of B mesons (tau=10^-12 s), and neutrons (tau=10^3 s). Say what are the dominant factors which create these differences.
Consider the decays D0->antiK0 pi0 and D0->K0 pi0. Draw the Feynman diagrams of the two decays and estimate the relative size of the two decay amplitudes.
What makes it harder to observe D0-antiD0 oscillations than to B0-anti B0 ones ?
What is the value to first order of the ratio R=sigma(had)/sigma(mumu) in a e+e- machine with 6 GeV in the CM ? What is, still to first order, the BR of a W in a lepton-neutrino pair ?
The CM energy, equal to 270+270 GeV, obtained at the antiproton-proton collider at CERN has certainly been sufficient for the production of W and Z0 bosons, but with a rather small margin. Why ?
Draw qualitatively the structure functions xF3(x), F2(x), G(x) at q^2=10 GeV^2. How do structure functions evolve qualitatively as a function of q^2 of the interaction ?
How do coupling constant alpha_em and alpha_strong change as a function of q^2 ?
Order by decreasing cross-section:
a) at a hadron collider the processes of production of Z, top, H (150 GeV mass), b, and elastic scattering;
b) at LHC the following Higgs production processes, for Higgs mass of 150 GeV: qq, gg->Htt, qq->HZ, qq->HW, gg->H, qq->Hqq, qq,gg->Hgg.
What is the ratio between BR(H->bbbar) and BR(H->tau tau), for a Higgs mass of about 120 GeV ?
What is the main background to H->gamma gamma, for a Higgs mass of 120 GeV ?
The decay mu->e gamma and the decay tau-> mu gamma violate the conservation of lepton number.
a) Draw at least one diagram for such decays
b) Describe what are the irreducible backgrounds.
A beam of neutrinos of average energy E=20 GeV is created by the decay of pions alone. Estimate:
a) the energy of the pion beam which generated them;
b) the divergence of the neutrino beam;
c) the order of magnitude of the cross section on nucleon;
d) the mean free path of neutrinos in a detector of density equal to that of water;
e) the ratio between the cross section on proton and on electron.
A photon may convert into an electron-positron pair next to an electron rather than next to a nucleus. In such case, what is the threshold energy ?