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Announcements

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Announcements Today: 9.6, 9.8 Friday: 10A 10E Monday: 10F 10H 9.6 Only do differential cross-section See problem 7.7 to do most of the work for us – PowerPoint PPT presentation

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Title: Announcements


1
Announcements
  • Today 9.6, 9.8
  • Friday 10A 10E
  • Monday 10F 10H

9.6 Only do differential cross-section See
problem 7.7 to do most of the work for us
11/14
2
Weak Interactions
Neutrinos
  • First discovered in ?-decay
  • Energy spectrum of electron
  • Must be some particle carrying off the rest of
    the energy
  • We now know it is neutron decay
  • Probably an invisible, neutral particle
  • Must be a fermion to conserve angular momentum
  • Must be neutral
  • Must be very light (lt 1 eV or so)

3
Other Neutrino Interactions
  • Muon like a heavy electron, but unstable
  • Decay requires two invisible particles
  • Pion strongly interacting particle
  • Easily produced in proton-nucleus collisions
  • Decays to muon plus neutrino
  • Neutrinos can be converted back to the
    corresponding charged particles
  • Electron neutrinos make electrons, muon neutrinos
    make muons

4
The Leptons
  • We have already discussed the quarks there are
    six of them
  • They each come in three colors, and have strong
    interactions
  • There are six other spin ½ fermions in the
    standard model, called leptons
  • There are anti-particles for each of these as
    well
  • Neutrino physics is currently evolving better
    names are ?1 ?2 ?3
  • When weak interactions were first researched,
    quarks werent known
  • We will focus on leptons first

5
Fermi Theory of Muon Decay
  • First attempt Fermi Theory assumed this was a
    basic matrix element
  • Original guess was something like this
  • New fundamental constant
  • This is not the only form that respects Lorentz
    invariance
  • These five combinations (and linear combinations)
    are only objects that respect Lorentz invariance
    including P, T, and PT
  • No combination fit all the available date

6
V A Theory of Muon Decay
  • In 1956, it was proposed that parity might be
    violated in weakinteractions
  • In early 1957, this was quickly experimentally
    verified
  • Suddenly there were other possibilities
  • A ?? coupling is called a vector coupling, and a
    ???5 is called axial vector
  • We will call this the V A theory of weak
    interactions
  • Only left-handed fields participate in these
    interactions

7
Muon decay rate calculation
  • Treat electron as massless
  • The ? terms are anti-symmetric under ????, the
    other terms are symmetric
  • The cross terms will automatically vanish

8
Muon decay rate calculation (2)
  • This amplitude squared was solved in problem 4.11
  • Note decay rate rises rapidly as mass increases
  • Weak interactions get stronger as you go up in
    energy
  • Eventually, get probabilities gt1 ? no good

9
Announcements
  • Today 10A 10E
  • Monday 10F 10H
  • Monday

11/16
10
The W - particle
  • This interaction is not renormalizable, since GF
    GeV-2
  • Maybe this is not really what is going on?
  • To get this to work, we need W coupling something
    like
  • The factor of 2?2 is for convenience later
  • The index ? implies the W particle must
    havepolarization vector, like a photon
  • Spin 1, like a photon
  • The W must be charged, unlike a photon
  • The W must be massive, or it would have already
    been discovered

11
Dealing With Spin-1 Massive Particles
  • Polarization vector satisfies same equations as
    before
  • But this time there are three such polarizations
  • For example, if
  • Then the three polarizations are
  • We need to find
  • For propagator
  • For summing over initial/final states
  • The propagator

12
Questions from the Reading Quiz
I have no idea what's going on with the groups
and the electroweak coupling/interaction. I
understand that the SU(2) and U(1) aren't really
independent. But it's all confusing and it's
making my head hurt.
  • Spin 1 particles run into trouble with
    renormalization unless they are gauge-type
    couplings
  • What we think is going on so far is

13
A Toy Model The Two Photon Model
  • Surprisingly, it is sometimes ambiguous which are
    the actual particles
  • Consider the following toy model The Carlson
    two-photon model
  • Classically, if you shake a particle with both
    types of charge, you would make both types of
    fields
  • Quantum mechanically, you would create states
    that are superpositions of each type of field
  • Unless there is something logically picking out
    particular directions in A1A2-space, it is not
    obvious which ones you want to think of as the
    real fields.

14
Rotating Fields Arbitrarily
  • We can change the fields in any arbitrary way,
    for example
  • We can just as easily work with these fields

15
Announcements
  • Today 10F 10H
  • Monday 10.1, 10.3
  • Wednesday 10.4, 10.5, 10.8

11/16
16
Weak Interactions with One Lepton Pair
  • Naively, there is one charged lepton field and
    one neutrino,
  • The left- and right-handed pieces of the massive
    electron have different weak interactions, and
    should be divided
  • Without mass, only the left-handed neutrino has
    weak interactions
  • There is no reason to even believe there is a
    right-handed neutrino
  • Weak interactions connect the left-handed
    neutrino and electron
  • Masses connect the left- and right-handed
    electrons

17
Mass and Couplings with One Lepton
  • The Feynman rule for W-coupling for one lepton
  • There is no reason, in principle, that the mass
    cant be apparently complex
  • This can easily be fixed, for example, by
    redefining the field eR by a phase
  • Hence the phase is irrelevant
  • We work with eL and eR, and drop the primes

18
Weak Interactions with Multiple Leptons
  • Naively, there are three charged lepton fields
    and neutrinos,
  • The left- and right-handed pieces of the massive
    electron have different weak interactions, and
    should be divided
  • Without mass, only the left-handed neutrino has
    weak interactions
  • There is no reason to even believe there is a
    right-handed neutrino
  • Weak interactions connect the left-handed
    neutrino and lepton
  • Masses connect the left- and right-handed leptons

19
The Weak coupling with Many leptons
  • The Feynman rule for W-coupling for many leptons

20
Complicated mass?
  • There is no reason, in principle, that the mass
    cant be apparently complicated
  • This matrix is completely arbitrary
  • We can nonetheless always change basis to
    straighten it out
  • For example, suppose the mass matrix looked like
    this
  • Define new states
  • The new mass matrix is then

21
Complicated Couplings?
  • We originally had
  • But we now defined new states
  • This makes our W-couplings complicated
  • In the leptons, this can be fixed simply by
    similarly redefining the neutrinos
  • Drop the irrelevant primes

22
Weak Interactions with One Quark Pair
  • Naively, there is one up quark and one down quark
  • The left- and right-handed pieces of the massive
    quarks have different weak interactions, and
    should be divided
  • All four of these exist in the Standard Model
  • Weak interactions connect the up and down quarks
  • Masses connect the left- and right-handed quarks

23
The Weak coupling with many quarks
  • The Feynman rule for W-coupling for many quarks
  • Warning This is actually incorrect!
  • This is different from the leptons
  • As I will explain soon (I hope)

24
Complicated mass?
  • There is no reason, in principle, that the masses
    cant be apparently complicated
  • These matrices are completely arbitrary
  • We can nonetheless always change basis to
    straighten them out
  • For example, suppose the mass matrices looked
    like this
  • Define new states
  • The new mass matrix is then

25
Complicated Couplings?
  • We originally had
  • But we now defined new states
  • This makes our W-couplings complicated
  • In the quarkss, can this can fixed simply by
    similarly redefining the up quarks?
  • No! This messes up the mass matrix M
  • The couplings really are complicated in the quark
    sector

26
The Weak coupling with many quarks
  • By appropriate redefinition of the various
    fields, the mass matrices for the up- and
    down-type quarks can always be made diagonal and
    real
  • Such a redefinition will, however, introduce a
    unitary matrix V into the charged current
    interactions
  • This matrix is called the Cabibbo-Kobayashi-Maskaw
    a matrix, or CKM matrix
  • Some, but not all, of the parameters of V can be
    eliminated by appropriate redefinition of the
    corresponding fields.
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