Physics 0081 Fall 1999 (00-1) Handout #16 Conservation, Reaction, Decays and All That

Physics 0081 Fall 1999 (00-1) Handout #16 Conservation, Reaction, Decays and all That

Baryon and Lepton Conservation (then and now): Recall that baryons are particles that are involved with strong interaction and are like the neutron and proton. Letpons are the particles that participate in weak (and electromagnetic) interactions, namely the electron, muon and tau. Experiments revealed that there is lepton and baryon conservation; for example, the usual nuclear reactions (e.g., radioactive decay) display baryon conservation. The subtlety for leptons is that the lepton number for each family should be conserved. Here is an example.

¹+ e+ + º + º ! e ¹ The ¹+ is an antiparticle of the muon and has lepton number L = 1: The positron is an ¹ ¡ antiparticle in the electron family and has muon lepton number L¹ = 0; as does the electron type neutrino. The muon type anitneutrino has lepton number -1 because it is antiparticle. Hence the sum of the muon lepton number on the left (-1) equals the sum on the right. Likewise the ¹+ has electron lepton number equal to zero. So you can see that the electron lepton number is conserved since 0 = -1 +1 +0, recalling that the positron has electron lepton number, Le = 1: This may sound confusing, so let's look at one more example, the decay of a pion ¡

¼¡ ¹¡ + º ! ¹ The pion is a meson (strong interactions, made of quark antiquark pair) so has lepton number (of all families) = 0. On the right there is a muon with lepton number +1 and a mu type antineutrino with lepton number -1. That's how lepton conservation works; you need only a table to do the \lepton accounting," but you must remember that there is conservation for the three families. Now baryon conservation. This is the conservation of the \mass number" that you do in nuclear reactions. Consider the decay of the proton into pions

p ¼0 + ¼+ ! This conserves charge, but there are no baryons on the right side, but baryon number =1 (for the proton) on the left side. This isn't observed, although energetically it could happen.Another example is the start of the proton-proton cycle in stars, where d is used for 2 a deuterium nucleus (1H )

p + p d + e+ + º ! e This is very instructive, both for the conservation laws and for understanding processes in the sun. Charge is conserved as it must be always (as far as anyone knows). On the left is baryon number =2, for the two protons. The deuterium nucleus has one neutron and one proton, so it has baryon number =2. The positron and neutrino have zero for baryon

1 number (they aren't baryons, they are leptons). So baryon number is conserved. Can you verify that lepton number is conserved? For your reference, the main proton interactions in stars looks like (the net e®ect of several reactions)

4 4p + 2e¡ He + 2º + 6° ! where the ° are high energy photons. Finally, note: an antiparticle has the negative of the baryon number of the respective particle Now: The above story is ¯ne for most purposes, but, if some form of GUT (grand uni¯ed theory) is correct, it is not quite right. That is a big \IF," since GUT theories are attractive, but not yet fully accepted. GUT theories propose transformations between leptons and quarks, that is, yielding baryon (and lepton) nonconservation. Finally, for the scenario for the \origin of matter" to hold up (as discussed in the text), there must be some asymmetry between particles and antiparticles. We already have some documented examples of that (e.g., connected with parity nonconservation experiments). Exercises:

+ + + + 0 0 + 1. Complete the reaction K ¼ + ¼ +?. (a)¼ (b) ¼¡ (c)¼ (d)K (e) K¹ !

2. A muon has lepton number L¹ = 1. What is the lepton number and charge of an antimuon?

3. The lepton number for a ¼+ is (a) +1 (b) -1 (c) 0 (d) +2

+ 4. Is lepton number conserved in each of the following? (a) n p + e¡ + ºe (b) ¼ ¹+ + º (c) ¼+ e+ + º ! ! ¹ ! e + 5. The annihilation of a pion and antipion according to ¼¡ + ¼ ° , where ° rep- resents a photon, is forbidden because of the violation of (a) cha!rge conservation (b) energy conservation (c) momentum conservation (d) lepton conservation (d) baryon conservation.

6. A very energetic gamma ray photon, passing by a nucleus, can create a proton an- tiproton pair. If the mass of a proton is about 938 MeV, what is the minimum energy the photon must have? (a) 938 MeV (b) 1876 MeV (c) 2814 MeV (d) 0 MeV (e) any energy will do.

7. With modern detectors it is possible to study the iteraction of neutrinos with matter, for example º + n p + e¡. Why isn't the reaction º + n p + e¡ seen to occur? e e ! (a) It violates charg!e conservation. (b) It violates baryon conservation. (c) It violates lepton conservation. (d) It violates photon conservation.

8. Consider the decay of the ¥¡ particle according to ¥¡ p + 2(e¡+ º ) + 2(º + º ): ! e ¹ ¹

(a) Is the ¥¡ particle a meson, or baryon? (b) Is the decay an example of lepton nonconservation?