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- Title: Lecture 06
- Type: Notes
- School: SUNY Stony Brook
- Course: PHY 585
- Term: Fall
6 Lecture 35 Oct 30, 2002 5 The Quanta of the Standard Model A long series of experiments and theoretical studies and advances has established the so-called Standard Model of elementary particle physics. This theory encompasses the electromagnetic theory (unified by Maxwell), the weak interaction (responsible for radioactive decays of for instance the neutron and the muon, and for the burning of hydrogen into helium and heavier elements in the Sun), and the strong interaction (which binds protons and neutrons inside the nucleus). The SM is the (incomplete) theory (in the sense of our current best approximation to the truth) of the fundamental matter particles and their interactions. We know that the Standard Model is incomplete: it does not truly unify the electroweak and the strong interaction, just combines them. Further, it does not predict the model's parameters (of which there are 21) and only experimentation lets us determine the values of these. It does not include the much weaker gravitational interaction in the same quantum mechanical framework, because a the quantization of gravity, unlike that for electromagnetism, is very poorly understood. Finally, SM calculations break down i.e. something new must happen at energies of a few TeV, energies that will become accessible by 2006 at the Large Hadron Collider now under construction at CERN near Geneva. However, all present data are in excellent agreement with predictions made within the framework of the Standard Model, and it is the best theory we have at present. Many famous and less famous physicists, both experimenters and theorists, have contributed to the present picture of the elementary particles, which developed from the early 1900s until now. The Standard Model is thus the result of a long and arduous search for the correct description of nature at its most elemental level. In that search, experimental study and theoretical insight always go hand-inhand: theory tends to diverge if not checked by experimental feedback, and experimentation becomes meaningless without theoretical analysis of its findings. We expect that the next generation of experiments, at the Fermilab Tevatron and at the CERN LHC will result in exploration of the physics beyond the Standard Model. The Standard Model divides the world of elementary particles in fermionic matter: leptons (6 electronlike particles, and 6 anti-leptons), and quarks (6 quarks of different flavors, and 6 anti-quarks), see Table 4. The fermions are the sources of a variety of fields: interactions between the leptons and quarks are mediated by Intermediate Vector Bosons, listed in Table 5. Table 4. Elementary matter Fermions. Antiparticles have opposite quantum numbers. Baryon / Spin Matter Fermions Weak ElectricWeak Lepton HyperCharge Isospin number (Mass [MeV]) charge B L Q [e] I3 Y 2(Q-I3) 0 1 0 +1 /2 (eutrino)e (eutrino) (eutrino) (< 1eV) (< 1eV) (< 1eV) -1 0 1 -1 -1/2 e(lectron) (uon) (au) (0.511) (105) (1680) 1 +1/2 +2/3 u(p) u u c(harm) c c t(op) t t /3 0 (3) (3) (1.5 103) (0.3 103) (174 103) (5 103) d(own) d d s(trange) s s b(ottom) b b 1 /3 0 -1 /3 -1/2 +1 /3 Lecture 6 36 Oct 30, 2002 Leptons have no strong interaction. The neutral leptonic fermions (electron, muon, and tau neutrino types) have only the weak interaction; the charged leptons have both the weak and the electromagnetic interaction. All quarks have the EM and weak interaction, and, in addition, carry a so-called color charge, a whimsical name for a strong charge that comes in three varieties: red (R), green (G), and blue (B). Each color can have two values: e.g. red and anti-red, or +blue and -blue, etc., see Table 5. Table 5. Quanta of the fundamental forces Force Electroweak Carriers (Mass) JPC 1-1 1 1- (0 eV) (photon) (0 eV) W (80.4 GeV) 0 Z (91.2 GeV) g(luon)i i=1..8 G(raviton) Color 2 The color charge is mediated between quarks by glu- Gravity ons, which themselves are colored. There exist 8 different gluons, which all have zero mass. Note, that the electromagnetic force carrier, the photon, is also massless, but is itself electrically neutral. The weak force is carried by the (three) weak vector bosons, which are very massive (thereby explaining the weakness and short range of the weak force compared to electromagnetism). The flavor of quarks is a quantum number: e.g. up-flavor (U), charm (C), strangeness (S), top-flavor (T), which is conserved by the electromagnetic and the strong interactions, but not by the weak interaction. Name Statistics Examples Forces Leptons Hadrons Mesons qCqC' Fermions e, e, , , , Bosons ,,,',,K*,,,J/,',D,,B, ... EM Weak EM Weak Strong1) Baryons qRqG'qB" Fermions n,p,,,,,,, c,c,b, ... The known strongly interacting particles: protons, neutrons, pions, Kaons, and hundreds more, are thought to consist of colorless combinations of quarks (called hadrons): so is the proton a uRuGdB combination (or uRdGuB, etc.); the RGB combination is colorless (like white light). Similarly, auRuR combination, is which colored red plus anti-red, is colorless! Only colorless combinations of quarks can exist; the colorless three-quark states are called baryons (half-integer spin fermions, which are proton and neutron-like), and the quark-antiquark colorless combinations are called mesons (integer spin bosons; examples are the pion, Kaon, , ', , etc.). The color charge can be depicted as a vector in two dimensional space: green red would be a unit vector along the +ve x-axis, green a unit vector at 120 120 , and blue a vector at 240 . For the three colors these unit vectors green red would point outwards, whereas the anticolors (the colors of antiquarks: 120 red antired, antigreen, antiblue) would point inwards. Thus green + antiQ(e+) green would give zero, etc.; also, the vector sum red + green + blue blue would give zero! Clearly, these are the only two possibilities that yield blue Q(e-) "colorless" combinations. Note, that this is a straightforward generalization of electric charge (see the figure): there the electron charge Mesons and baryons are quark states bound by the color force (by gluons). The interactions between individual, colorless, hadrons are much less strong (although far from weak), and are like di-pole color interactions... 1 Lecture 6 37 Oct 30, 2002 (black arrow) is a unit vector along the +ve x-axis; the positron has the corresponding anticharge, positive, represented by an antiparallel unit vector. It is only because naked color does not appear in nature, unlike electric charge, that causes the color charge to seem so weird! The fact that the gluons are themselves massless and bi-colored (red/anti-blue, green/anti-green, etc.), makes for the peculiar character of the color interaction: the color force grows (approximately linearly) with distance of separation, much like a spring force. If one tries to work two colored quarks apart, the color field stretches and intensifies, like the growing tension in a spring that is stretched: the field's energy density grows until it becomes energetically advantageous to create a pair of quarks, thereby breaking the "color spring". e-, p1 q, p3 Thus, trying to pry open a hadron just creates more hadrons ine Qqe stead of liberating a quark! x The existence of three types of charges, or three "colors" is well q p2+p1=s t established experimentally. The total cross section for the process + q, p4 e+e- + - is calculable to a high degree of precision in Quan- e , p2 tum Electro-Dynamics (QED): d (e + e - + -) 2 e2 1 = (1 + cos2 ), with ; d 4s 4 0 c 137 (I.92) 4 2 4 2 = thus: (e + e - + - ) = ( c )2 = 86.8 nb/GeV / s 3s 3s and where s is the total cms energy squared, and where the masses of the particles were neglected (masses << s). The above formula resembles the Rutherford scattering formula, but is different because for e+e- scattering the target particle is not infinitely massive! Moreover, unlike for Rutherford scattering, we have included spin effects. For the production of a quark-antiquark pair, e+e- qq, the calculation is the same except for the fractional quark charge. In principle, any type of quark pair can be created, compatible with the available energy in the center of mass system: e.g. for s < 40 GeV the possibilities are q = u,d,s,c, or b quark but not q = top. In addition, if quarks come in Nc different colors, then each a quark pair of a given flavor (u,d,s, etc.) can be produced in Nc different colors as well. The strongly interacting quarkantiquark pairs will create a series of quark-antiquark pairs (i.e. mesons) when they separate from one another. Thus, because the coupling of the quark or muon pair is proportional to its charge, the ratio of the cross section for hadron production over the cross section for muon-pair production is: 2 2 2 (e + e- q q) 1 11 2 = N cQi = N c 2 + 3 = N c R (I.93) 3 9 3 (e+ e- + - ) i =u ,d ,s ,c ,b Experimentally, see Figure 8, the ratio is R4, which shows that in equation (I.93) the number of colors Nc=3. Figure 8. The ratio R of hadron production over the production of muon pairs in e+e- collisions between 10 and 60 GeV center of mass energy. Ref: Particle Data Group, http://pdg.lbl.gov/2000/contents_plots.html Lecture 6 38 Oct 30, 2002 The Fermionic character of leptons and quarks is essential in the building of atoms and of hadrons: the Pauli exclusion principle forbids identical fermions to co-exist. The Pauli exclusion principle follows from the fact that a wave function describing a system of fermions must be fully anti-symmetric under interchange of the coordinates of any pair of fermions. Thus, if two fermions are in the same state and therefore are indistinguishable, then under interchange the wave function stays the same, while it must also equal its opposite (be anti-symmetric); therefore it must vanish. For bosons the situation is completely different: the wave function of a system of bosons is symmetric under coordinate interchange, and thus many bosons can occupy the same quantum state.
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