1 Drawing Feynman Diagrams

Transcription

1 1 Drawing Feynman Diagrams 1. A ermion (qark, lepton, netrino) is rawn by a straight line with an arrow pointing to the let: 2. An antiermion is rawn by a straight line with an arrow pointing to the right: 3. A photon or W ±, boson is rawn by a wavy line: W ±, 4. A glon is rawn by a crle line: g 5. The emission o a photon rom a lepton or a qark oesn t change the ermion: l, q l, q Bt a photon cannot be emitte rom a netrino: ν ν 6. The emission o a W ± rom a ermion changes the lavor o the ermion in the ollowing way: Q = 1 e µ τ c t Q = Q = 0 ν e ν µ ν τ s b Q = 1 3 Bt or qarks, we have an aitional mixing between amilies: c t s b This means that when emitting a W ±, an qark or example will mostly change into a qark, bt it has a small chance to change into a s qark instea, an an even smaller chance to change into a b qark. Similarly, a c will mostly change into a s qark, bt has small chances o changing into an or b. Note that there is no horizontal mixing, i.e. an never changes into a c qark! In practice, we will limit orselves to the light qarks (,, s):

2 1 DRAWING FEYNMAN DIAGRAMS 2 s Some examples or iagrams emitting a W ± : e ν e An sing qark mixing: s To know the sign o the W -boson, we se charge conservation: the sm o the charges at the let han sie mst eqal the sm o the charges at the right han sie. 7. The emission o a boson oesn t change the ermion, as was the case or the emission o a photon, bt a can also be emitte rom a netrino: l, q, ν l, q, ν 8. A glon can only be emitte rom qarks, an will change their color charge. However, as we almost never raw the color charge o a qark, in the iagram the qark oesn t change: g q q 9. To make sre we never nee to raw color charge in or iagrams, we only allow qarks to combine into color netral particles, which consist o three qarks or a qarkantiqark pair. As an example we raw the emission o a rom a proton, changing it into a netron: p n 10. When moving a particle s placement in a Feynman iagram rom right to let (or vice versa), we change a particle to its antiparticle. Using this rle, we can trn the emission o a into the absorption o a (becase the antiparticle o a is a )

3 1 DRAWING FEYNMAN DIAGRAMS 3 or into the creation or annihilation o a qark pair (note that when moving a ermion this way, the irection o the arrow stays the same relatively to the line) 1 The same transormations can be applie on photon, an glon emissions. 11. We also get a vali Feynman iagram by taking the antiparticle o every particle in the iagram. Using this rle, we can trn the emission o a into the emission o a Again, the same transormations can be applie on photon, an glon emissions. 12. The W ±, an the glon also have three- an or-point interactions:,, Bt in practice yo will only nee the glon three-interaction, becase the other threean or-interactions are strongly sppresse. 13. To get an iea o the probability o a Feynman iagram, we cont the nmber o vertices (another wor or interaction points). The more, the less probable. Also, the strong interaction (glons) is more probable than the electromagnetic interaction (photons), which in trn is more probable than the weak interaction ( an W ± bosons). 1 Or as a rle o thmb: an incoming particle has its arrow pointing inwars, an otgoing particle has its arrow pointing otwars; an incoming antiparticle has its arrow pointing otwars, an otgoing antiparticle has its arrow pointing inwars.

4 2 CONSERVATION LAWS 4 Hint: raw yorsel a set o basic iagrams with the an bosons, in orer to have a reerence to know which particles cople to which. For the photon, the an the glon this is straightorwar (becase then the particle oesn t change), bt or the W ± this is a bit more elaborate. 2 Conservation Laws Not every interaction satisies all conservation laws. The strong orce satisies all conservation laws, the electromagnetic orce conserves all bt isospin, an the weak orce satisies most (not lavor nor isospin). There are qite a lot conservation laws, so we will limit orselves to the easiest ones. 0. First a hint: any qantm nmber changes to its aitive inverse when making an antiparticle rom a particle. For example, a positron e + has electron lepton nmber L e = 1 becase an electron e has L e = Conservation o electric charge. The sm o the charges o the initial particles shol eqal the sm o the inal particles. 2. Conservation o energy. This is particlarly important when the interaction is a ecay (i.e. one particle going to several particles), becase then in the rest rame o the initial particle we have that its energy (in other wors its mass, as it is in rest) shol eqal the sm o the energies o the inal particles. This implies m initial m inal In case o a collision (two or more initial particles) energy conservation can always be satisie by giving the initial particles enogh energy. It is thereore only neee to check energy conservation in case o a ecay (one initial particle). 3. Conservation o lepton nmber. This conservation is even tre within the lepton amilies. For example, the ecay µ e + ν e + ν µ L e : 0 = L µ : 1 = L : 1 = conserves electron lepton nmber L e, mon lepton nmber L µ an total lepton nmber L. However, the ecay µ e + e + + e L e : L µ : L : 1 = is not allowe, althogh total lepton nmber is conserve. Bt electron an mon nmber are not conserve separately, which is enogh to prohibit the interaction.

5 2 CONSERVATION LAWS 5 4. Conservation o baryon nmber. This law tells s that the nmber o initial baryons (particles mae rom three qarks) shol eqal the nmber o inal baryons. For example, the interactions are allowe, bt p n + e + ν e p + p π + + π B : 1 = B : 1 1 = p π + + π + π 0 B : is not. Keep in min that there is no sch rle or mesons! 5. Conservation o lavor (not conserve by the weak interaction). This law says that qark lavor shol be conserve between initial an inal states. As we are only consiering light qarks, the only special lavor is that o a strange qark, which is calle strangeness. 2 This implies or example that the interaction K + π + + π 0 S : mst take place sing the weak interaction, as strangeness is not conserve (meaning it cannot take place sing the strong nor the electromagnetic orce, as those two o conserve lavor). 6. Conservation o isospin (not conserve by the weak interaction, nor by the electromagnetic). reerik.van.er.veken@cern.ch 2 To conse yo a bit, a particle with one s qark has strangeness S = 1 an a particle with one anti-s has strangeness S = +1. This is grown historically.