Obligatory Exercises I
01.03.2013 to be delivered by 13.03.2014 @ 10:15 Farid Ould-­‐Saada 28/02/14
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1.
2.
In the LHC at CERN, 2 proton beams will head-­‐
on with energies Ep=7TeV. a)
What is the centre of mass (CM) energy? b)
What energy would be needed to produce the same CM energy with a proton beam on a fixed hydrogen target? c)
How does this energy compare with cosmic ray energies? The neutral pion decays to two photons (π0 à γγ) with a branching ratio of 98.8%. a)
What is the maximum opening angle between the photons for a pion with momentum 100 GeV? mπ0=135 MeV. b)
Compare to a Higgs boson of similar momentum and decay Hà γγ. mΗ=125 GeV. 01/03/14
http://arxiv.org/pdf/astro-ph/0607109v2.pdf
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The J/ψ particle, a meson with a mass mJ/ψ =3.096 GeV and made of a charm quark-­‐antiquark pair, was discovered both in proton-­‐proton and in electron-­‐positron collisions. 3.
A proton beam collides on a target of protons at rest; calculate the incident proton beam energy required for the reaction: pp→pp J/ψ b)
In the case of electrons, the particle was discovered in a particle collider in which the e+ and e− beams had the same energy but opposite momenta. Calculate the beam energy necessary for the J/
ψ production: e+e− →J/ψ The J/ψ decays with a very short lifetime, τ ∼ 10−20 s. Comment the 2 figures of the discovery. a)
−
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1.
Evaluate the ratio between the cross-­‐sections of the following reactions at the same energy in terms of the isospin amplitudes M0, M1 and M2 : (1) K − p → π + Σ−
(2) K − p → π 0 Σ0
(3) K − p → π − Σ+
(4) K − p → π 0 Λ 0
2.
Charge conjuga/on a)
What are the charge conjugate reac/ons to reac/ons (1) and (2) below? b)
Can a system be an eigenstate of the charge conjuga/on operator? (1) K − p → K 0 n ;
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(2) pp → π +π −
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1.  Which of the following reactions are allowed and which are forbidden? -­‐ If allowed, draw the Feynman graph and state which interac/on is at work. -­‐ If forbidden, give the reasons. −
+ −
0
+ −
1.
K
p
→
K
Ξ
2.
π
→
γ
e
e
3. ρ 0 → γγ
4. Ω− → Ξ0 π −
5. n → pπ −
6. e+e− → µ +µ −
7. e+e− → ν eν e
8. Σ0 → Λ 0γ
9. ν τ p → τ + n
10. e+ n → pν e
11. µ + → e+ν eν µ e+e−
12. Δ + → nπ +
13. ν ee− → ν ee−
14. e+e− → W +W −
15. ν eν e → ν eν e
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1.
2.
Oscilla/on probability with 2 flavour neutrinos a)
Derive the probability for an electron neutrino to oscillate into a muon neutrino? b)
What about an an/-­‐muon-­‐neutrino to oscillate into an an/-­‐electron-­‐
neutrino? A KamLAND type experiment detects ν e neutrinos at a distance of 300 m from a nuclear reactor and finds that flux is (90±10)% of that expected if there were no oscilla/ons. Assuming a 2-­‐component model with maximal mixing (θ=45o) and a mean neutrino energy of 2.5 MeV, es/mate the squared mass difference of the electron an/neutrino and it oscilla/ng partner. What is the principle of detec/on of ν e ? 01/03/14
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