I offer three questions below, and you are welcome to think any or all of them over today and tomorrow. In two days I will give my answer, explain the underlying physics a bit, and comment your own answers, if you have been capable of typing them despite your skyrocketing glycemic index.

**1.**The charged pion is a particle made by a pair of quarks: for the positive one we have the composition , and for its antiparticle . The charged pion decays in about ten nanoseconds into a muon and its neutrino, as in . In the decay, the quark-antiquark pair "annihilate" into a negative W boson, which then materializes the muon-antineutrino pair. The question is: why does the pion prefer to decay to a muon-antineutrino pair instead than in an electron-antineutrino pair ? Note, weak interactions, which are responsible for the decay, are flavor-democratic: there is a thing called "lepton universality of the weak currents" which demands that the intensity of the couplings to all leptons be the same. Also note, the pion has a mass of 139 MeV, the muon a mass of 105 MeV, the electron a mass of 0.5 MeV, and the neutrino is virtually massless. How come the pion prefers the heavier muon, if there would be more "phase space" to yield an electron instead ?

**helicity is the key. Okay, you don't know what helicity is, so go to wikipedia, damn it.**

Hint:

Hint:

**2.**In the famous 1964 experiment that demonstrated the violation of CP invariance and won Cronin and Fitch their Nobel prize in Physics, the four experimenters (Christenson, Cronin, Fitch, and Turlay) allowed a beam of neutral kaons to decay inside a large bag filled with Helium. The observation of the decay of two charged pions of the neutral kaons constituted indisputable proof of the fact that these particles had violated the combined symmetry of charge-conjugation and parity. In fact, the beam of kaons had been treated in a way that only one of the two possible quantum states had survived.

The question is, why Helium ? What properties has this gas that were suitable for the experiment ? Mind you, this is a tricky one.

**Hint:**the answer has only in part something to do with Physics...

**3.**You have a b-tagging algorithm which is capable of properly identifying jets as being originated from b-quark hadronization. You measure two numbers: the probability P(btag|bjet)=0.5 as the probability of tagging a jet if it was originated by b-quark hadronization; and the probability P(btag|not bjet)=0.01 of incorrectly btagging a non-b-jet. From those, you then get P(no-btag|bjet) = 1-P(btag|bjet), and similarly P(no-btag|no-bjet) = 1-P(btag|no-bjet).

The question is: given a sample of 1000 jets tagged as b-jets by the algorithm, what fraction of them are b-jets ? In other words, what is P(bjet|btag) ?

**Hint:**think Bayesian!

Okay, now get your ass off the armchair and put down the glass of wine. It's time for some homework!

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