Electron–positron annihilation

In this leacture we will consider reactions of the type:

Such reactions have been extensively studied in electron–positron colliding-beam experiments, and give clear evidence for the existence of color and existance of gluons. Study of these reactions also involves studies of jets of hadrons, and understanding of jets as a of fragmentation process of quarks and gluons. Two-jet events The dominant process in the e+e- annihilation at high energies 15- 40 Gev, considered here, is the electromagnetic production (through virtual photons) of the charged particles predicted in the SM: a) quark-antiquark pairs (all flavors of quarks, and all colors), followed by the fragmentation of quarks into colorless states, see next slide:

a) Quark pairs are produced along production of charged lepton-antilepton pairs (electron, muon and tau pairs). Heavy charged bosons also are coupled electrically to e+e- pairs, but not produced at these energies, because of the higher mass of bozons. Two-jet events (2) The leading diagram of the e+e- annihilation into quark-antiquark pair, accompanied by fragmentation of quarks into colorless jets is at Fig 7.14 below:

The two jets are emitted in opposite directions (back to back) in the center-of- mass frame in order to conserve momentum: Two-jet events (3)

The number of particles in jets and fluctuates quantum mechanically during fragmentation. Still, the overall jet momentum reflects reasonably well the momentum of fragmented quark: the QCD interaction is weak at very short distances (asymptotic freedom!) and the quark and antiquark do not interact strongly until they are separated by ~ 1 fm, which according to uncertainty relation gives rise to a typical momentum transfer of order 200 MeV/c. Thus momenta fluctuations in fragmentation are small compared with the initial momentum of the quark and anti-quark of many GeV: so the total momenta of the jets points almost exactly in the initial quark and antiquark directions. Two-jet events (4) Look at the the angular distribution of muons and two-jets in e+e- annihilation. The calculated cross section for muons is:

And for quarks with 3 colors and fractional charge ea :

Look at the angular dependence For quarks, where there is a term: Three-jet events

sometimes according to QCD, with a probability ~ 0.1 or so, we might expect a high-momentum gluon to be emitted by the quark or antiquark before fragmentation occurs, leading to the formation of a three-jet event (see figure). This is somewhat analogous to the emission of a photon by charge Particles in QED. Three jet events (2)

Three jet events have been observed experimentally. The angular distribution corresponds to the emission of the spin1 gluon, and contradicts spin 0 gluons: 3-jet events in the JADE experiment (see figure below, for the details see M&S) The total cross-section of e+e- annihilation (the ratio R to annihilation to muons)

Define ratio R for the total cross sections of annihilation, where cross section for muons is calculated to be:

One can easily find for any quark flavor(see M&S):

For all flavors, up to b (u,d,s,c,b),we can calculate: The total cross-section of e+e- annihilation When strong interactions corrections are included (e.g. accounting for the gluon emission corrections), the formula for R on the previous slide is modified to:

Comparing the corrected R calculation with the experiment: Ch 8. Quarks and partons