Quantum Physics

30.9 Conservation Laws 989LeptonsLeptons (from the Greek leptos, meaning “small” or “light”) are a group of particlesthat participate in the weak interaction. All leptons have a spin of 1/2.Included in this group are electrons, muons, and neutrinos, which are less massivethan the lightest hadron. Although hadrons have size and structure, leptonsappear to be truly elementary, with no structure down to the limit of resolution ofexperiment (about 10 19 m).Unlike hadrons, the number of known leptons is small. Currently, scientistsbelieve there are only six leptons (each having an antiparticle): the electron, themuon, the tau, and a neutrino associated with each: e e The tau lepton, discovered in 1975, has a mass about twice that of the proton.Although neutrinos have masses of about zero, there is strong indirect evidencethat the electron neutrino has a nonzero mass of about 3 eV/c 2 , or 1/180 000 ofthe electron mass. A firm knowledge of the neutrino’s mass could have great significancein cosmological models and in our understanding of the future of theUniverse.30.9 CONSERVATION LAWSA number of conservation laws are important in the study of elementary particles.Although the two described here have no theoretical foundation, they are supportedby abundant empirical evidence. Baryon NumberThe law of conservation of baryon number tells us that whenever a baryon is createdin a reaction or decay, an antibaryon is also created. This information can bequantified by assigning a baryon number: B 1 for all baryons, B 1 for allantibaryons, and B 0 for all other particles. Thus, the law of conservation ofbaryon number states that whenever a nuclear reaction or decay occurs, the sumof the baryon numbers before the process equals the sum of the baryon numbersafter the process.Note that if the baryon number is absolutely conserved, the proton must beabsolutely stable: if it were not for the law of conservation of baryon number, theproton could decay into a positron and a neutral pion. However, such a decay hasnever been observed. At present, we can only say that the proton has a half-life ofat least 10 31 years. (The estimated age of the Universe is about 10 10 years.) In onerecent version of a so-called grand unified theory (GUT), physicists have predictedthat the proton is actually unstable. According to this theory, the baryon number(sometimes called the baryonic charge) is not absolutely conserved, whereas electriccharge is always conserved. Conservation of baryon numberEXAMPLE 30.4 Checking Baryon NumbersGoal Use conservation of baryon number to determine whether a given reaction can occur.ProblemDetermine whether the following reaction can occur based on the law of conservation of baryon number.p n: p p n pStrategy Count the baryons on both sides of the reaction, recalling that that B 1 for baryons and B 1 forantibaryons.SolutionCount the baryons on the left: The neutron and proton are both baryons; hence, 1 1 2.