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Summary

Summary. Standard Model of Particles (SM ) - particles and interactions - the electro-weak model. The situation in the sixties. Chaotic. similar to chemistry of 1800. The periodic table. Mendeleev (1869) introduced the periodic table. Atomic model explains the Mendeleev table.

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Summary

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  1. Summary Standard Model of Particles (SM) - particles and interactions - the electro-weak model A. Bay Beijing October 2005

  2. The situation in the sixties Chaotic similar to chemistry of 1800 A. Bay Beijing October 2005

  3. The periodic table Mendeleev (1869) introduced the periodic table A. Bay Beijing October 2005

  4. Atomic model explains theMendeleev table Rutherford (1912) showed that atoms contain a central nucleus 10-10m A. Bay Beijing October 2005

  5. The Standard Model of Particles each particle has an associated anti-particle: e- and e+ , u and u , n and n , ... _ _ Matter Interactions (quanta) Electric charge [e] n n n e Weak (W+, W-, Z) m t 0 Electromagetic (photon) - - - e 1 m t - u c t 2/3 Quarks -1/3 d s b Strong (gluons) spin 1/2 spin 1 Gravity is absent: hopefully its effects are too weak... how to distinguish these two ? A. Bay Beijing October 2005

  6. Elementary particles in interaction:e. m. q g e q e Exchange of photons Affects all the electrically charged particles: quarks + e, m, t Feynman graph: A. Bay Beijing October 2005

  7. Elementary particles in interaction:Weak q W n q e Exchange of W and Z Affects the full set of particles Feynman graph: A. Bay Beijing October 2005

  8. Elementary particles in interaction:Strong q g q q q Exchange of gluons Affects only quarks Feynman graph: A. Bay Beijing October 2005

  9. Quark model u u u d PROTON: d NEUTRON: d d u u u PROTON: NEUTRON: d d d Quarks hold together by "strong interaction" to form "hadrons": baryons (half-integer spin): p, n, D, ... mesons (integer spin) : p, r, K, B, ... A few examples: protons and neutrons are made of 3 quarks: Q=+1 Q=0 Charge mirror Q=-1 Q=0 A. Bay Beijing October 2005

  10. Quark model .2 Easier to indicate the quark content of the hadrons with a vector. Proton and neutrons and their antiparticles are: C represents the "charge mirror" More precisely, the "wave function" of a proton must contain the information of the movement of the 3 quarks, of their spin orientation, of the quark "flavour", and of of an entity called the "colour" of the quark: new concept similar to atomic wave functions A. Bay Beijing October 2005

  11. Quark model .3 The mesons are built with one quark and one antiquark. Lightest meson system are the 3 "pions": the 1/sqrt(2) is to "QM average" the 2 possible configurations uubar and ddbar the minus sign is to respect a special condition of symmetry! A. Bay Beijing October 2005

  12. Quark model .4 Theory must calculate the masses, spin, magnetic moments, decay probabilities, ... , of the hadrons. Quite a difficult task: M(proton) ~ 1 GeV (remember: c=1) 3 quarks in the proton: 1 GeV/3~330 MeV/quark M(pion) ~ 140 MeV 2 quarks in the pion: 140 MeV/2 = 70 MeV This shows that the strong interaction dynamics defining the binding energy is very important, very "strong". The theory of strong interactions is the colour theory: "chromodynamics". If one "switch of" strong interactions, the mass of the quarks should be M(u)<M(d)<10 MeV, M(s)~100 MeV, M(c)~ 1.2 GeV, M(b)~4.5 GeV, M(t)~174 GeV A. Bay Beijing October 2005

  13. Hadron decay * p is (seems) stable, lifetime is at least 1029 years * n is unstable, lifetime ~15min * pions are unstable, for instance: this is an e.m. interaction W is the vector of the weak interactions A. Bay Beijing October 2005

  14. The leptons Neutrinos are neutral and have masses ~0. The electron is the lightest (known) charged particle (511 keV). The muon m (106 MeV) and the tau t (1780 MeV) are unstable. time Seen by the theory of weak interactions the process look like this: A. Bay Beijing October 2005

  15. Measurement of masses Mass of a particle of momentum p and energy E: M = sqrt(E2-p2) Example of measurement: p0gg - measure the 2 photons 4-vectors: (E1, p1), (E2, p2) - compute the parent (p0) four-vector: (E, p)=(E1 +E2, p1 +p2) - compute M E1 g1 p0 E2 g2 detector (e.m. calorimeter) M=135 MeV A. Bay Beijing October 2005

  16. The measurement of masses .2 +0.2 -0.3 = 1776.9 ±0.2 MeV Mt The production threshold method was used by BES to measure with very high precision the tau mass Mt : Production rate e+ e- collider with beam energy Ebeam. Minimal E needed to produce 2 taus is Emin = 2 Mt c2 Ebeam Each beam must have at least Ebeam = Mt c2 A. Bay Beijing October 2005

  17. The BES method In order to optimize the search, the energy scan was done by the method of signal appearance / disappearance A. Bay Beijing October 2005

  18. Summary on SM elementary particles The "elementary particles" of the Standard Model there are the quarks and the leptons (spin 1/2, they are "Fermions") Quarks have fractional charge (units of e), and they are the building blocks of hadrons (p, n,..., pions, kaons,...). Lepton have charge 0 or -1 (+1 the anti-leptons). How can we explain this mass spectrum ? A. Bay Beijing October 2005

  19. The interactions interaction gravitation e.m. weak strong manifestation weight light beta decay nuclear forces range weak Coupling w/o dimension lifetime by analogy: A. Bay Beijing October 2005

  20. The interactions .2 Coulomb scattering of an electron by the field of a nucleus Decay of a muon in electron and 2 neutrini A. Bay Beijing October 2005

  21. The interactions .3 annihilation of e+ e- into photon/Z decaying into a pair of particles when the 2 particles are quarks, they "hadronize" (i.e. they become hadrons) producing jets of particles ... we have not seen individual quarks ! A. Bay Beijing October 2005

  22. Open a parenthesis: jets of particle is an evidence of the existence of quarks Jets of hadrons TASSO event at PETRA q 1+cos2q distribution proving that the quark is a 1/2 spin particle A. Bay Beijing October 2005

  23. The interactions .4 We have also events with 3 or more jets quarks and gluons hadronize into one jet each ECAL HCAL A. Bay Beijing October 2005

  24. Phenomenology of hadronization How individual quarks (or gluons) transform into jets of hadrons ? This phenomenon is difficult to treat analytically because the intensity of the force is too strong (cannot do a "perturbative": calculation) Potential model of qq interaction: ~ Coulomb at very short r (< 1fm) E grows fast with r (but not as much as elastic: E = kd2/2) A. Bay Beijing October 2005

  25. Phenomenology of hadronization .2 Field lines at very small r Field lines stay concentrated when you pull the two quarks apart. They form a string. A. Bay Beijing October 2005

  26. Phenomenology of hadronization .3 Energy accumulates in the string when enough energy/fm couples quark-antiquark can be produced mesons fly apart jet 2 jet 1 A. Bay Beijing October 2005

  27. The interactions .5 Quantum mechanics: interactions are mediated by quanta Interaction quanta mass typical range Strong 8 gluons 0 1 fm E.m. photon 0 infinite Weak W, Z ~100 GeV 10-3 fm Gravity graviton 0 infinite later we will try to understand why only Weak forces have quanta which are massive... A. Bay Beijing October 2005

  28. The interactions .5 * A photon travelling from a source to your eye has mass=0. If you measure p and E of this photon, you will find that it has mass=0 : E2-p2 = 0. This is a "real" photon. In a "collision", two charged particles exchange some p and E. QM says that this exchange is mediated by a photon. Ex: electron and muon are charged particles, they can exchange the E and p transported by a photon, the quantum of e.m. interaction g m e A. Bay Beijing October 2005

  29. The interactions .6 with pa = (Ea, pa), etc... the transferred momentum is: q = pa- pc = - (pd- pb) photon charged particles If you try to compute the mass of this photon, you will find a value different from zero: this is a "virtual"photon. This is possible within some restrictions imposed by the Heisenberg uncertainty principle... A. Bay Beijing October 2005

  30. The interactions .7 Heisenberg: measurements of position and momentum can only be done with a finite precision because the microscopic processes are controlled by A virtual photon violating momentum conservation by some Dp, can travel a length Dx ~1/Dp. Real photons do not violate anything and they can travel as much as they want. This photon can travel ~1/mass = 1/|q| A. Bay Beijing October 2005

  31. The interactions .8 We are interested to determine the probability for a particle a to interact with particle b giving momenta pc and pd. Consider a and b like 2 wires carrying electric currents Ia=Qava and Ib=Qbvb. The force acting between the 2 is given by: The QM result is similar: Ia Ib 1/mass of the photon ~ distance A. Bay Beijing October 2005

  32. The interactions .9 The QM theory of e.m. is called Quantum ElectroDynamics (QED) From the idea seen before we can infer a theory to compute the probability that a given process take place. The typical behaviour of a QED process, for instance of e+ e-m+ m- expressed as a function of the total energy E is: Probability of the QED process ~ (aem / E)2 Indeed we have the cross section: which has the nice behaviour s 0 when E  infinity, no "ultraviolet catastrophe". A. Bay Beijing October 2005

  33. The interactions .10 All these calculations are possible at the "perturbative level", which means that the "higher order corrections" must become smaller and smaller (expansion must converge). Diagrammatically something like: contribution from one quantum2 quanta 3 quanta > ... > > Mathematically: Aa < Ba2 < Ca3 < Da4< ..... where A, B, C, D,... come from (often complex) calculations. One sees that the coupling constant has better to be < 1 ! A. Bay Beijing October 2005

  34. The interactions .11 The technique has been generalized to the other interactions. "Currents J" of particles with charges g interact via their specific quanta. g g J1 J2 * e.m.: charge is e (or a fraction of e for the quarks) and the quanta are the photons (or use a= aem  e2) * weak interaction: charge is gW (or simply g), quanta are W and Z * strong interactions: charge is gs (or as  gs2) with 8 gluons While Coulomb needs only 1 kind of charge, + and -, strong interactions have 3 kinds (r,g,b and -r,-g,-b) !!! A. Bay Beijing October 2005

  35. The interactions .12 While Coulomb needs only 1 kind of charge, + and -, strong interactions have 3 kinds (r,g,b and -r,-g,-b) !!! Consider the Coulomb force between 2 particles An electron has charge minus e, its anti-particle has charge plus e. Quarks have electric charge (2/3)e or (-1/3)e , and opposite sign for antiparticles. Consider the strong force now. * The electron does not have strong interaction: its strong charge is 0. * Quarks strongly interacts with a much more complicated algebra. They behaves like if they could be of 3 kind (SU(3) group) For instance, in a proton they must be of the 3 different colours to give a white particle (r+g+b = white). A. Bay Beijing October 2005

  36. The interactions .13 For a quark u, there are 3 possibilities u, u, u, etc. During e.m. interaction, the electric charge stays on the particle, because the photon is neutral. During strong interaction, the charge can be transferred because the gluons carry the colour charge. Example: time red and blue quarks blue-antired gluon exchange blue and red quarks A. Bay Beijing October 2005

  37. The interactions .14 Group theory: SU(3)couleur , basis 3 and 3: Coloured gluons belongs to the 8 of g4 (r,g,b is an arbitrary index !) A. Bay Beijing October 2005

  38. Interactions: some results QED is capable to predict the Landé factor g for electron and muon at the level of 10-9 precision: for the electron with aem= 1/137.0339... from "static" measurement of e QED: (g-2)/2 = ( 1'159'652.2 ± 0.2 ) 10-9 measured: ( 1'159'652.188 ± 0.004 ) 10-9 dipolar magnetic moment of a particle of spin s, charge q, masse m g=2 for the Dirac electron g = Landé factor A. Bay Beijing October 2005

  39. Positronium gives aem at low energy E2 Coulomb potential E1 => A. Bay Beijing October 2005

  40. aem at ~ 100 GeV g jet1 g jet2 jet1 jet2 The relevant parameter is aem giving the interaction strength at 100 GeV aem~1/128 A. Bay Beijing October 2005

  41. Some results .3 jet1 g jet3 jet2 The relevant parameter is as (alpha strong) giving the interaction strength. at 100 GeV as~ 0.11 A. Bay Beijing October 2005

  42. as at low(er) energy Use "quarkonia" bound states of cc () and bb (Y). Potential is now @ ~3 GeV @ ~10 GeV A. Bay Beijing October 2005

  43. Running of the alphas It is found that both the e.m. coupling constant aem and as vary with the energy of the process: running of as At 1 GeV (proton mass) as>1, while at LEP energy (~100 GeV) we have as~ 0.1. The opposite happens for aem. At low energy its value is ~1/137, and ~1/128 at LEP. E of the process GeV A. Bay Beijing October 2005

  44. Running of the alphas Hint of an unification of forces at high E ? a strong e.m. E (GeV) 1 GeV Energy of (Grand) unification ? Nice, but why do we whish some sort of "unification" ? A. Bay Beijing October 2005

  45. Unification of forces a strong e.m. Why we whish some sort of "unification" ? Unification means the reduction the number of entities in the theory => more internal constraints => less free parameters => the theory becomes more "predictive" First example of (successful) unification of forces is the Maxwell theory of electromagnetism. A second example of unification is the electro-weak theory, which is part Standard Model. A. Bay Beijing October 2005

  46. The electro-weak theory Historical background: The e.m. theory was translated into a QM formalism at the beginning of 1900, giving the Quantum Electro Dynamics. We have seen that this theory is very successful. In 1934 E. Fermi wrote a model for the Weak Interactions (WI) inspired to QED. Because he didn't know the existence of the W and Z, he reduced the calculation to a "point-like theory" QED Fermi model A. Bay Beijing October 2005

  47. The electro-weak theory .2 The Fermi model works well at very low energy (beta decay,...), but it cannot work at high energy: cross section Probability of a Fermi weak process: s(E) ~ (GF E)2 This grows to infinity quite fast ! Compare to the nice behaviour of QED: Fermi constant Probability of a QED process: s(E) ~ (aem / E)2 To avoid the ultraviolet catastrophe the simplest solution is to introduce a particle playing a role analogous to the photon in QED. The main difference with QED is that the W must be massive... A. Bay Beijing October 2005

  48. The electro-weak theory .3 The QED term becomes Why do we need a massive W ? The Fermi model is OK at low energy. It starts to be wrong only around 100 GeV. So the virtual particle must become "real" at this energy: This explains why we do not have free W going around like the photon. To produce them you need a lot of energy. q It also explain why the weak interaction is "weak": in reality it is weak only at E<<MW. At high E, it is comparable to e.m. More of this in a moment. A. Bay Beijing October 2005

  49. The electro-weak theory .4 contributions from these processes allow to exactly get rid of the infinities, if ... Why do we need a neutral Z? Because "second order" diagrams diverge, like in the calculation of corrections to e+ e-m+ m- this diagram gives a divergent result A. Bay Beijing October 2005

  50. The electro-weak theory .5 ... if we impose the correct relations to link e.m. and weak sectors. The needed relations between Z, W and photon are incorporated in the Glashow Weinberg Salam electroweak theory: Weinberg angle Here gg is related to the electric charge gg =e/2√2 e=1.60 10-19 C We introduce here two "weak charges" gW (GF~(gW)2) and gZ. gW, and qW are free parameters of the theory (not predicted) A. Bay Beijing October 2005

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