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19 -- Part 2: .1 Show that

- Both W+ and W- exist because of charg e-raising and charge-lowerin g currents.

- We are going to follow a more scenic route for the time being and accept that we have ordinary 'unsophisticated' massive particles, charged and un charged.

- The IVB model relates to the current-current one.

- I re 21.

- The equation (22.29) of chapter 22 shows that this is a fundamental relation.

- Out of all the apparent differences between the two, W is so larg e.

- We investig ate wh e th er th e I VB m o d e l can d o any b.
- We will take you at issu e a g in sectio.

- The section heading indicates that matters will be fundamentally no better in the IVB model, but the demonstration demonstrates that.

- As will be explained in sectio n 22.1.2, th e factors o f two have been chosen to be those that would actually appear in the unitary gauge.

- The photon propagator was responsible for the fall with the QED cross-sectio n 21.12 and at least for the process.

- The answer is no.

- To calculate the total cross-section, we must combine the three states of polarization for each of the W's.

- It is worth taking a closer look at this term.

- Oth e r U n itar ity - v io latin g p r o cesses can easily b e inve n ted, a n d we h ave to conclude that the IVB model is no more fit to be called a model.
- It was not a good enough cure that F was not dimensionless.

- I re 21.

- We turn in our distress to the QED.
- The fact that there are two r ather than one is significant.

- We need to sum over the photon polarization states in the cross-section.

- This is not a trivial point.

- Since the longitudinal W's caused the 'bad' high-energy behavior of the IVB model, the 'good' high-energy behavior of QED might have its origin in the absence of such states.

- It requires the gauge field quanta to be massless.
- If the local sy mmetry is broken, this peculiarity can arise.
- Before we implement th at id, we need to be aware of the unitarity one.

- There is an objection to the argument about unitarity violations.
- The argument is conducted completely with the perturbatio n theory.
- It's simply that p ertu rbatio n theory is so me.

- F o r d e r p er tu r b atio n th e o r y a r e ir r e leva.
- Another way of stating the results of the previous two sections is to say the current one is weak.

- Chapters 1 0 and 11 of vo lu me 1 were given an elementary in troductio n. In particular, we d iscussed in some d etail, in sectio n 11.8, th e d ifficu lties th a t a r ise wh en o n e tr ies to d o h ig h e r- o F, also h a d d e n sio n ( m a ss)-2 The 'non-renormalizable' p roblem was essentially th at, as one approached the dangerous scale and needed to supply the values from the experiment.

- I re 21.

- I re 21.

- Th is ex actly th e c o m p a r iso n we wer e m ak in g in the previous section, but now we have arrived at it from considerations.

- The blame once again lies with the longitudinal p o lar izatio n states.
- This problem can be avoided if L et U see h ow QED--a r en o r m alizab le theo r y.
- Replacing the 1 T h e r eader would give us the leading high-energy behavior.

- I re 21.
- Four- poi nt e+ e- ve r t ex.

- I re 21.

- There is a question of renormalizing figure 21.7.
- The particles in this process are virtual and not real.
- 3 f o r so m e th in g sim ilar in the case of one-loop diagrams.

- W+W is translated into a figure of 21.8--and the r e is n o'c r o ssed'.
- The introduction of a new vertex, figure 21.10, is not present in the original IVB theory.

- If we include it, the theory is non-renormalizable, as in the current-current case.

- The search for such mechanisms can be pushed to a su ccessf.

- We have a more powerful principle.

- The'spontaneously broken' gauge theory concept was developed in chapter 19.

- This strongly suggests that these theories are renormalizable.
- It was clear that it would be possible to make h igher- if Hooft's p roof th at th ey were to explode.

- We now have all the pieces in place, and can introduce the G SW theory based on the local gauge symmetry of SU(2) x U(1).

- In sectio n 2 0, 5 were recorded.

- In the limit in which all the people are neglected.

- When the photon inands are replaced by the photon momentum, the two amplitudes disappear.

- It is now well established that the one originally proposed by Glashow, which was subsequently treated as a spontaneously broken gauge symmetry by Weinberg and Salam, produces a theory which is in.
- We will not give a critical review of all the ex p erimen tal ev id en ce bu t.

- Considering the transitions caused by these interactions is what gives an im p o r tant.
- This is similar to discovering the m ultiplet structure of atomic levels and hence the representations of the rotation group, a prominent symmetry of the Sch r "odinger equation.
- Between th e'weak m U ltip lets' we sh all b e consid ering and those asso ciated with symmetries which are not spontaneously.
- In chapter 12 we saw how an unsymmetrical non-Abelian symmetry leads to a state of mind.
- The result only holds if the vacuum is left invariant.
- This is the situation in the theory.

- The consequences of the weak symmetry group are accessible to experiment.
- In section 20.10 we saw how weak transitions invo lv in g charg ed quarks suggested a doublet structure.
- The simplest way to think about it is that there is a 'weak SU(2) g roup' involved.
- We emphasize once more the weakness of iso sp in is d istin ct f r o m th e h a d r o n ic iso sp in o f ch ap ter 1 2

- The left-handed components of the field enter as a consequence of the V - A structure.

- No te at, as anticip involve ated for a spontaneously broken sy mmetry, th ese doublets all pairs of particles which are not mass degenerate.
- This is a g e n e r a lizatio n to 3x 3 m ix in g o f th e 2x 2 GIM mixing introduced in section 20.10, and it will be discussed further in section 22.7.1.
- For the time being, we ignore the mixing in the neutrino sectors, but return to it in section 22.7.

- The two gauge fields associated with transitions between doublet members will have charge +-1 because the members of a weak isodoublet differ by one unit of charge.
- The photon is massless and the W's must somehow acquire mass.
- Schwinger arranged the th e th e th e th e th e th e th e th e th e th e th e th e th e th e th e th e th e th e No prediction of the W mass could be made.
- The breakdown of a non-Abelian gauge must be the cause of the W mass, as we saw in sectio n 1 9.

- There is an obvious suggestion to have the neutral member W0 of the SU2L act as a conduit for these currents.
- The plan was to put the W mass in 'by hand'.
- The attractive f eature o f including the photon has been lost.

- A key contribu tio n was made by Glashow in 1961.
- The structure is g roup.

- The piece of mathematics we went through in section 19.6 is an important part of the Standard Model.

- The main results of section 19.6 are reproduced here.

- Weak Is ospi n and hyper charge.

- The rules for the propagators can be read off from 22.8 and are in appendix Q.

- There is no weak in ter actio n s co and a b asic assu mp.
- We all see 5 terms.
- We arrive at our assignments in table 22.1.

- The table has 'R' components in it.
- The original Standard Model took the neutrinos to be massless with no mixing.

- We proceed in the massless n eutr inos approximation.

- The raising and lowering operators are used for doublets.

- I re 22.

- The form we used in the current-current theory may be compared with W.

- This is an important equation that gives a precise version of the qualitative relation.

- There is no theory that can predict the value of the scale of symmetry breaking.

- I n g en er al, th e ch arg e- ch an g in g p ar t o f.

- Her m itian c o n ju g a te.

- The phenomenological currents of the earlier model are exactly what L gauge th eory are.
- The rules can be read off from 22.33

- I re 22.

- Z 0 is not a pure 'V - A'.
- A n d h e n c e ex h ib it.

- There are two more rules contained in (22.37) and (22.38).

- W (22.46) is already suggested in chapter 19.
- 5 cancel from 21:45.

- The matrix is the Cabibbo-Kobayashi-Maskawa matrix.
- We are all in the same sectio n 2 2.

- The sum will be over all the quark flavours.

- The expressions are the same as given.

- We note one important feature of the Standard Model currents.
- In sectio n 1 8 an o m alies wer e d iscu ssed.
- There is no explanation provided by the Standard Model.

- We n o ted in sectio.

- The predictions of the theory show the power of the underlying symmetry to tie together many unrelated quantitities, which are all determined in terms of only a few basic parameters.

- Neutrino-electron graphs are related to Z0 exchange.

- The width of the quark channels would be the same, apart from a factor of three for the different colour channels.

- We neglected all fermion mass in making these estimates.

- The GIM mechanism ensures that all flavourchanging terms are canceled.
- The hadronization of the q-q channels has a branching ratio of 69.3%.

- I re 22.

- There was a scattering in sectio n 20.11.

- Wherever possible, the lepton mass has been neglected.

- I re 22.

- The experimental fits to these predictions are reviewed by Commins and Bucksbaum.

- The Standard Model parameters can be determined at the e+e- colliders.
- 30 years ago, the cross-section calculations were made.

- The flu x o f scattered electrons were inelastically scattered.
- A c lear sig n a l f o r p a r ity v io latio n and an asy mmetry b etween th e results.

- The W+- and Z0 1983 are some of the main experimental evidence.

- The sea quarks will be expected to contribute.

- It is required that the QCD corrections to (22.81) be included.

- The order is 1.5-2 at these energies.

- I re 22.
- On model a mpl I tude f or W+- or Z 0 pr oduct.

- I re 22.

- The total cross-section for p-p is about 70 MB at these energies, and hence (22.84) is 10 times smaller.

- The rates could go up if the q-q modes of W and Z0 were used.
- W and Z 0 would appear as slight shoulders on the edge of a very steep hill.
- Ite th e u n favo, th e lep to n ic m o d e s prov id.

- The signature for (22.87) is an isolated and back to back, e+ e- pair with an invariant mass of around 90 GeV.
- The e+ e- pairs required come from the decay of a m assive slowly moving Z 0 The mass resolution was folded in.

- The uncertainty in the absolute calibration of the calorimeter energy scale is reflected in the systematic error.
- The agreement with (22.57) is good, but there is a suggestion that the tree-level prediction is on the low side.

- I re 22.

- I re 22.

- The dotted, full and dashed lines are predictions of the Standard Model.

- It is possible to use (22.90) as an important measure of such neutrinos.

- It is possible to determine Z accurately.
- The mass resolution of the -pp experiments was of the same order as the total expected Z0 width, so that (22.90) could not be used directly.

- The W+- is where we turn now.
- As in the case of Z0 - e+e- decay, slow moving massive W's will emit isolated electrons with high energy.

- calorimetry can be used to balance the energy of the electrons.

- The following argument shows W. Consider the decay of a W at rest.

- A maximum likelihood fit was used to find the most probable value.

- I re 22.

- The agreement b etween the experiments is good and the predictions are on the low side.

- One renormalization sch e m e is one of the Radiative corrections that can be applied.

- I re 22.
- I'm on the beam and he's on the posi t r on.

- We may say that the early discovery experiments were remarkably convective in their confirmation.

- We are going to further aspects o f the th eory.

- It is not invariant if L is su bject to a tr a n sf o r m atio n o f th e form.
- The same is true for Majorana fermions.

- This kind of explicit breaking of the gauge symmetry cannot be condoned.

- 0 is lo n g itu d in a l. We studied the unitarity violations in the lowest-order theory for the IVB model.

- The cancellation feature is one aspect of the renormalizability of the theory.
- We will eventually have a 'nonrenormalizable' problem on our hands, all over again, because the cancellation no longer occurs.

- I re 22.

- Even though the breakdown occurs at energies beyond those currently reachable, it would constitute a serious flaw in the theory.

- There is a way to give fermion mass without introducing an explicit mass term in the Lagrangian.
- The model shows how a fermion with a Yukawa-type coupling will generate a fermion mass.

- In each term, the two doublets aredotted together so as to form an SU(2)L scalar.
- The symmetry is preserved at the Lagrangian level if (22.104) is SU(2)L-invariant.

- I re 22.
- I am on a ph.

- The reader will not be surprised to hear that this graph is what is required to cancel the 'bad' high-energy behavior found in (22.10).

- The upper component of (22.11) has a p p ear.

- It is possible to arrange for all the fermions, quarks and leptons to get the same'mechanism'.
- The quarks will be looked at more closely in the next section.

- It appears that we are dealing with a 'phenomenological model' once more.

- h oweve r, th er e is a n o th e r p o ssib ility.
- It is possible to make a Dirac-type mass term of the form.

- The anti-Hermitian 2 x 2 matrix would disappear for classical fields.

- Majorana neutrinos do not have a number.

- The (1,1) operator cannot combine with the (1,01) operator to form a singlet.

- We can't make a tree-level Majorana mass by the mechanism of Yukawacoupling to the Higgs field.

- We could generate effective operators via loop corrections, similar to how we generated an effective operator in QED.
- The operator would have to violate the standard model interactions if it is true.
- It was not possible to generate an effective operator in the theory.
- It could arise as a low-energy limit of a theory defined at a higher mass scale, as the current- current model is the low energy limit of the G SW one.

- appendix P, sectio n P.2 contains further discussion of the neutrino mass.

- We will not pursue these considerations beyond the Standard Model.
- We need to generalize the discussion to the three- family case.

- We have to consider what is the most general interaction between the Higgs field and the various fields.
- If we abandon renormalizability, we might as well abandon the whole motivation for the 'gauge' concept.
- The 2 appearing are non-normalizable and have a coupling with dimensions.

- We can still manage with only one field.

- Consider the gauge-invariant interaction part of the Lagrangian.

- The CKM matrix is well known.

- The CKM matrix has many independent parameters.
- A matrix has 2x32 real parameters.

- R has to change in the same way as mass terms.

- This leads to a parametrizatio.

- I re 22.
- T he uni t a r i t y t r i a ngl e' r e pr esent

- This is a triangle.

- The original Cabibbo-GIM type is considered in section 20.10 to be a fundamental difference.

- Thematrix must be real.

- 13 was stressed by Kobayashi and Maskawa.

- The construction of B factories is influenced by the effects of the B0 system.

- The fit is consistent with (22.153).

- A similar analysis can be done in the leptonic sector.

- See also Pontecorvo 1967.

- These are the states that we would identify with the physical neutrino states.
- It is clear that the mixing of flavours does take p lace, indicating that there are differences in the mass of the particles.

- It is an open question if the particles are Dirac or Majo rana.

- Global phase transformations can't be made on Majorana fields as they don't carry a number.

- The phases were violated.

- Because the mass differences of the neutrinos are so small, they can be observed to occur over distances.
- Section 20.6 has a description of decay.

- The reason why we need a renormalizable electroweak theory is because of such remarkable precision.

- One can be around in more ways than one.
- The unconstrained b y theory is a p arameter.
- The presence of 'new physics' may be indicated by the analysis of small discrepancies between data and predictions.

- The introduction to one-loop calculations in QED at the end of volume 1 may have given the reader a right to expect an exposition of loop corrections.
- We want to talk about a few of the simpler and more important aspects of one-loop corrections.

- Cut-off independent results from loop corrections in a renormalizable theory can be obtained by taking the values of certain parameters from the original experiment, according to a welldefined procedure.

- 2 bu t these relations are changed.

- In practice, the renormalizatio n scheme is to be sp ecified at any finite order.
- 1989 Hollik; 1990 for reviews.

- The scheme is defined by (22.170).

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