Obligatory Exercises II
22.04.2013 to be delivered 02.05.2013 @ 14:15 Farid Ould-­‐Saada 4/29/13
1
The top quark decays into a W boson and and a b-­‐quark. 1.
2.
3.
4.
1.
2.
Justify this. (Consider the CKM mass matrix). Feynman graph of decay and interaction at work? Assuming the top width to be ~1.5 GeV Estimate the lifetime of the top quark If QCD color interactions can be characterized by the fly-­‐by time of 2 hadrons (time needed to exchange gluons) 1.
2.
What is the ratio of lifetime to interaction time for top quarks? Compare to the properties of b-­‐quarks and draw conclusions. Top-­‐pair production in hadron colliders proceed through p + p →t + t + X ;
p + p →t + t + X
where X stands for any other hadrons ensuring necessary conservation of various quantum numbers 1.
2.
4/29/13
Draw possible Feynman diagrams €Compare p-­‐p and p-­‐antip and draw conclusions. 2
Because of the rapid fall-­‐off in parton distribution functions f(x) with increasing x, where x is the fraction of the hadron momentum carried by the interacting parton, the peak of the production cross section occurs essentially at threshold 5.
1.
2.
What is the typical momentum of the b-­‐quark? What are the typical x values of the colliding partons that can produce top-­‐
pairs at the Tevatron and at the LHC Tevatron :
s = 2TeV
LHC :
s = 7TeV ; 14TeV
Hint: show that the center of mass energies squared of the hadron-­‐hadron and parton-­‐parton systems are related by €
x=
What could be the signature of top-­‐pair production at the LHC? 6.
7.
sˆ = x1 x 2 s
1.
2.
Comment the ATLAS event display below (think of which particles €
are detected by ATLAS) 1.
2.
How come? Hint: draw the B0-­‐B0bar oscillation diagram p parton
p proton
€
The top quark was found to be heavier than expected when B-­‐Bbar mixing was first observed in the 198os. 4/29/13
3
4/29/13
https://twiki.cern.ch/twiki/bin/view/AtlasPublic/EventDisplayPublicResults#Top_events
4
Calculate the binding energy of the last neutron in 4He and the last proton in 16O. 1.
How do these compare with B/A for these nuclei? What does this tell you about the stability of 4He relative to 3He and of 16O relative to 15N? 1.
2.
Calculate the approximate density of nuclear matter in g/cm3. 2.
What would be the mass of a neutron star that had the diameter of an orange? 1.
Calculate the energy released in the spontaneous fission reaction 235
87
145
U
→
Br+
92
35
57 La + 3n
3.
1.
Explain why fast neutrons are needed to induce fission of 238U, contrary to 235U. €
4/29/13
5