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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 - PowerPoint PPT Presentation


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Lecture AP1Electroweak interactions

Reminder on the weak interactionThe 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) GeVMZ = 91.188(2) GeVwhich would imply, in the Yukawa theory, a rangeR ~ 1/M ~ 0.0002 fm ( the point interaction representation a la Fermi works welland a very weak interaction.The interaction proceeding via W exchange is called charged current; if Z exchange, neutral current

2The leptons3

Neutrinos are peculiar: they feel only the weak force.

Charged current reactions (W-mediated)Leptonic processes, eg

W -> l n kinematically possible; since the lepton weak charges are the same for all families, the only difference can be due to phase spaceSmall difference since MW >> MtExperimentally, G(W -> en) ~ 0.23 GeV

Total width 2.09(4) GeV4

Charged current reactions - IIThis cannot be simply extended to quark doubletsOtherwise 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 = d cosqc + s sinqc and s = -d sinqc + s cosqc (qc Cabibbo angle)The q-lepton symmetry applies to the doublets (u d), (c s)5


W boson decayssince 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:


The 3rd generation of quarksBy 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 bemt = (170 30) GeVIt was finally detected at Fermilab (CDF) in 1995, and it has a massmt = (173 1) GeV7

At the 1st order, b = b, and the b quark is relatively stable.


The CKM matrix

||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


Properties of the top quarkThe 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( 1023 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. 10

Discovery of the topFurthermore, 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 199511

Electroweak unificationGlashow, 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 bosonsAlthough 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.12

Neutral currentsNeutral weak interaction are mediated by the ZLike the W lepton vertices, these conserve the lepton numbers Le , L and L in addition to the electric charge Q


Flavor Changing Neutral Currents?Correspondingly, one has hadronic verticesuuZ, ccZ, ddZ, ssZ

ddZ + ssZ = ddZ + ssZExperimentally: 14

Probability of the couplingsThe coupling is described by a vector term and an axial vector term, with appropriate coefficientsImpressive experimental tests especially at LEP (20 million Z from 1989 to 1999) and SLAC15

1989-2000 LEP Run

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. fe+Z0e- ffe+ge- fAt center of mass energies close to MZ the reactionthrough Z dominates over the reaction through g. e+e- cross section vs CM energyg dominatesE-2Z decays

fZ0fWith 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)fermionpredicted G(MeV)e, m, t 84ne, nm, nt 167u, c 300d ,s ,b 380Z cannot decay into thetop quark since Mt>MZ/2Z decays and the number of light neutrinosM&S 9.1.4

GZ is the total width of the Z

The shape of the curve depends on GZ. GZ depends on the number of neutrino species:

Each n species contributes ~167 MeV to GZBy varying the energy of the beams s(e+e-ZX) can be mapped and GZ determinedExcellent agreement with only 3 (light) neutrino families!

Data from the four LEP experiments.All experiments are measuring the cross sectionfor e+e-hadrons (X) as a function ofcenter of mass energy.Experimentally: total width = 2.495(2) GeV

ExercisesThe 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 rates19

How good is the Standard Model ?The Standard Model is verysuccessful in explaining electro-weakphenomena. Summary of Standard Model measurements compared withPredictions (LEP+)

Trilinear couplings seen at LEPand SM accounts correctly for them21

ee -> WW

++2Limits of the Standard ModelWhats in the SM? QFT based on SU(3)xSU(2)xU(1) symmetry containing:spin point-like objects: quarks and leptonsspin 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.Whats 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, 1996A convitato di pietra: dark matter

Gravity:G M(r) / r2 = v2 / renclosed mass: M(r) = v2 r / Gvelocity, vradius, rLuminous stars only small fraction of mass of galaxyBesides astrophysical evidence, cosmological evidence as well. As large as 5x ordinary matter

23Compact objects in the halo (BH, MACHOs)24They exist, but they are not enough

Hubble Space Telescopemultiple images of blue galaxyGravitational lensing25Only WIMPs are left

Input from particle physics is needed2526Direct WIMP DetectionccccNa IGeLight amplitudeIonizationtimeTotal energysignalsignalbackgroundbackgroundRejection of background is the critical issue26

WIMPs (probably) not found yetVery smart searches (bolometers, )ModulationNeeds large volume, shielding, dE/dX,

New particles needed!Is gravitation universal?MOND, extra dimensions27


CP violation and the excess of matterCP violation was discovered in KL decaysKL decays into either 2 or 3 pions

Couldnt happen if CP was a good symmetry of NatureLaws of physics apply differently to matter & antimatterThis might explain the matter-antimatter asymmetry?They are not T-invariantChristenson et al. (1964)

Final states have different CP eigenvalues28CP violation in the SMUnitarity leaves 4 free parameters, one of which is a complex phaseThe 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 ModelIt could not be done with a 2x2 matrixNeeds phase shifts

29The CKM matrix looks like this Non-diagonal (mixing)Off-diagonal components smallTransition across generations allowed but suppressed

30Precision physics: the unitarity triangleVV = 1 gives us

Experiments measure the angles a, b, g and the sides

This one has the 3 terms in the same order of magnitudeA triangle on the complex plane

30If its not a triangle, new physics beyond the SMCan be exg new quark families, extra CP violation

New frontier: high intensity (B-factories)31

SM, running couplings, unification of forcesOur 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)

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 1015 GeV. At the unification mass, all the processes are characterized by a single grand unified coupling constant gUAt ordinary energies, these processes are suppressed

GUTThis GUT explains why the charges of the proton and of the electron are equal in absolute valueBut it predicts the decay of the proton in 1029-1033 yearsTo detect proton decays with such small lifetimes requires a very