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Lecture AP1

Lecture AP1. Electroweak interactions. Reminder on the weak interaction. The weak interaction is mediated by the charged W and the neutral Z bosons. Their masses are measured with extremely high accuracy: M W = 80.40(2) GeV M Z = 91.188(2) GeV

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Lecture AP1

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  1. Lecture AP1 Electroweak interactions

  2. Reminder on the weak interaction • The weak interaction is mediated by the charged W and the neutral Z bosons. Their masses are measured with extremely high accuracy: MW = 80.40(2) GeV MZ = 91.188(2) GeV which would imply, in the Yukawa theory, a range R ~ 1/M ~ 0.0002 fm (<< the proton radius) => the point interaction representation “a la Fermi” works well …and a very weak interaction. • The interaction proceeding via W exchange is called “charged current”; if Z exchange, “neutral current”

  3. The leptons Neutrinos are peculiar: they feel only the weak force.

  4. Charged current reactions (W-mediated) • Leptonic processes, eg • W -> lnkinematically possible; since the lepton weak charges are the same for all families, the only difference can be due to phase space • Small difference since MW >> Mt • Experimentally, G(W -> en) ~ 0.23 GeV • Total width 2.09(4) GeV

  5. Charged current reactions - II • This cannot be simply extended to quark doublets • Otherwise this process, experimentally observed, would be forbidden • The idea is that the d and s quarks participate in the weak interaction via the linear combinations d’ = dcosqc + ssinqcand s’ = -dsinqc + scosqc (qcCabibbo angle) • The q-lepton symmetry applies to the doublets (ud’), (cs’) ~1/20

  6. W boson decays since the mechanisms of these reactions are identical, but q pairs can be produced in 3 colors, while universality gives • Since these are the only first-order weak decays possible and there are two quark combinations contributing to the hadron decays:

  7. The 3rd generation of quarks By 1977 five known quarks (with mb ~ 4.5 GeV) and an extra quark of charge 2/3 was needed to restore lepton-quark symmetry. The mass of this quark was predicted (from loop diagrams) to be mt = (170 ± 30) GeV It was finally detected at Fermilab (CDF) in 1995, and it has a mass mt = (173 ± 1) GeV

  8. The CKM matrix • At the 1st order, b’ = b, and the b quark is relatively stable. | |

  9. Exercise: if tt ~ 3 10-13 s, what to expect for tb? • By dimensionality arguments, phase space propto m5 • It is instead ~ 1ps => |Vbx|2 ~ 0.001

  10. Properties of the top quark The lifetime comes out to be ~10-25 s. A hadron state of diameter d≈ 1 fm cannot form in a time less than t ≈ d/c = O( 10−23 s) . The other five quarks have lifetimes of order 0.1 ps or more, and there is time for them to form hadrons, which can be observed in the laboratory. In contrast, when top quarks are created they decay too rapidly to form observable hadrons.

  11. Discovery of the top • Furthermore, the quarks released in these decays are not seen directly, but ‘fragment’ into jets of hadrons. • This explains why the top was discovered only in 1995

  12. Electroweak unification • Glashow, Salam, Weinberg formulated in the ‘60s the Electroweak Model (Nobel prize in 1979), which is of the cornerstones of what we call today the “Standard Model” of particle physics (the others being QCD and the set of fundamental particles: 6 quarks and 6 leptons) • Electroweak theory relates the strengths of the em and weak interactions of the fundamental particles through the weak mixing angle, qw, and through the masses of the gauge bosons • Although these two forces appear very different at everyday energies (3K ~ 0.3 meV), the theory models them as two different aspects of the same force which undergoes a breaking below ~100 GeV • The proof relies on the gauge invariance of the theory.

  13. Neutral currents • Neutral weak interaction are mediated by the Z • Like the W lepton vertices, these conserve the lepton numbers Le , Lμ and Lτ in addition to the electric charge Q

  14. Flavor Changing Neutral Currents? • Correspondingly, one has hadronic vertices uuZ, ccZ, d’d’Z, s’s’Z • d’d’Z + s’s’Z = ddZ + ssZ Experimentally:

  15. Probability of the couplings • The coupling is described by a vector term and an axial vector term, with appropriate coefficients • Impressive experimental tests especially at LEP (20 million Z from 1989 to 1999) – and SLAC 1989-2000 LEP Run

  16. Properties of the Z The fermions could be charged leptons, neutrinos, quarks. The mass the fermion has to be < MZ/2. (MZ~91 GeV). Both accelerators collided e+e- beams with energy »MZ/2. g dominates f f f f Z0 g E-2 e+ e- e+ e- e+e- cross section vs CM energy At center of mass energies close to MZ the reaction through Z dominates over the reaction through g.

  17. Z decays f f Z0 With K=1 for leptons and K=3 (color factor) for quarks. cVf and cAf are the vertex factors. Predicted Standard Model Z decay Widths (first order) fermion predicted G(MeV) e, m, t 84 ne, nm, nt 167 u, c 300 d ,s ,b 380 Z cannot decay into the top quark since Mt>MZ/2

  18. Z decays and the number of light neutrinos M&S 9.1.4 GZis the total width of the Z The shape of the curve depends on GZ. GZ depends on the number of neutrino species: Each nspecies contributes ~167 MeV to GZ By varying the energy of the beams s(e+e-®Z®X) can be mapped and GZdetermined Data from the four LEP experiments. All experiments are measuring the cross section for e+e-®hadrons (“X”) as a function of center of mass energy. Experimentally: total width = 2.495(2) GeV • Excellent agreement with only 3 (light) neutrino families!

  19. Exercises The reaction drawn below is forbidden to occur via lowest-order weak interactions. However, it can proceed by higher-order diagrams involving the exchange of two or more bosons. Draw examples of such diagrams. Make a simple dimensional estimate of the ratio of decay rates

  20. How good is theStandard Model ? Summary of Standard Model measurements compared with Predictions (LEP+) The Standard Model is very successful in explaining electro-weak phenomena.

  21. Trilinear couplings seen at LEPand SM accounts correctly for them 2 ee -> WW + +

  22. Limits of the Standard Model • What’s in the SM? QFT based on SU(3)xSU(2)xU(1) symmetry containing: • spin ½ point-like objects: quarks and leptons • spin 1 objects: force carriers (W, Z, g, gluons) • spin 0 (scalar) object(s): Higgs Boson(s) • The minimal SM has been very successful in describing known phenomena and predicting new physics. • The minimal SM has a), b), massless neutrinos, and one massive neutral Higgs. What’s wrong with the SM? There are (at least) 25 parameters that must be put into the SM “by hand”: masses of quarks (6) masses of leptons (6) CKM matrix (4); neutrino matrix (4) coupling constants, aEM, astrong, aweak (3) Fermi constant (GF) or vacuum expectation value of Higgs field (1) mass of Higgs (or masses if more than one Higgs boson) (1+?) based on point particles (idea breaks down at very very high energies, Planck scale). “The 18 arbitrary parameters of the standard model in your life”, R. Cahn, RMP V68, No. 3, 1996

  23. A “convitatodipietra”: dark matter velocity, v radius, r Gravity: G M(r) / r2 = v2 / r enclosed mass: M(r) = v2r / G Luminous stars only small fraction of mass of galaxy Besides astrophysical evidence, cosmological evidence as well. As large as 5x ordinary matter

  24. Compact objects in the halo (BH, MACHOs) Hubble Space Telescope multiple images of blue galaxy Gravitational lensing • They exist, but they are not enough

  25. Only WIMPsare left Input from particle physics is needed

  26. Direct WIMP Detection c c c c Rejection of background is the critical issue signal Light amplitude Na I background time background Ionization Ge signal Total energy

  27. WIMPs (probably) not found yet… • Very smart searches (bolometers, …) • Modulation • Needs large volume, shielding, dE/dX, … • New particles needed! • Is gravitation universal? • MOND, extra dimensions

  28. CP violation and the excess of matter • CP violation was discovered in KL decays • KL decays into either 2 or 3 pions • Couldn’t happen if CP was a good symmetry of Nature • Laws of physics apply differently to matter & antimatter • This might explain the matter-antimatter asymmetry? • They are not T-invariant Christenson et al. (1964) Final states have different CP eigenvalues

  29. CP violation in the SM • Unitarity leaves 4 free parameters, one of which is a complex phase • The complex phase in the CKM matrix explains CP violation (Kobayashi and Maskawa 1973; Nobel in 2008) • It is the only (?) source of CP violation in the Standard Model • It could not be done with a 2x2 matrix • Needs phase shifts • The CKM matrix looks like this  • Non-diagonal (mixing) • Off-diagonal components small • Transition across generations allowed but suppressed

  30. Precision physics: the unitaritytriangle V†V = 1 gives us • Experiments measure the angles a, b, g and the sides This one has the 3 terms in the same order of magnitude A triangle on the complex plane

  31. If it’s not a triangle, new physics beyond the SM… • Can be exg new quark families, extra CP violation • New frontier: high intensity (B-factories)

  32. SM, running couplings, unification of forces • Our dream has to be compared to the extrapolation from the best of our knowledge: • If we believe in unification, we must go beyond the Standard Model • (which in addition besides its success, is somehow unsatisfactory)

  33. Scenarios beyond the Standard Model? • In the Grand Unification Theory (GUT) by Georgi & Glashow (1974) quarks of different colors, and leptons, can convert into each other by the exchange of two new gauge bosons X and Y with electric charges −4/3 and −1/3, respectively, and masses ~ MX ≈ 1015GeV. • At the unification mass, all the processes are characterized by a single ‘grand unified coupling constant’ gU • At ordinary energies, these processes are suppressed

  34. GUT • This GUT explains why the charges of the proton and of the electron are equal in absolute value • But it predicts the decay of the proton in 1029-1033 years • To detect proton decays with such small lifetimes requires a very large mass of detector material • For example, 300 tons of iron would only yield about 1 proton decay per year if the lifetime were of order 1032 years. • Several large detectors of various types have been built, but no clear example of a proton decay event has been observed: Another scenario under exploration is SUperSYmmetry

  35. SUSY

  36. Some other features of SUSY Soft symmetry breaking SUSY is broken in nature, this is why we don’t observe it everyday This gives SUSY particles different masses Minimal Supersymmetic Model Electroweak symmetry breaking emerges naturally Unification R-Parity

  37. SUSY Algebra • Supersymmetry is a symmetry that relates boson to fermion degrees of freedom. • The generators of supersymmetry are two component anticommuting spinors, satisfying:

  38. The lightestneutralinois a very well motivated dark matter candidate: it is a WIMP and could be observed in direct detection experiments • And it is a Majorana particle Direct detection through the elastic scattering of a WIMP with nuclei inside a detector. Many experiments around the world are currently looking for this signal with increasing sensitivities How large can the neutralino detection cross section be?

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