LHCC

1
Weak Interactions

• Take place between all the quarks and leptons
• (each of them has a weak charge)
• Usually swamped by the much stronger em and
  strong interactions
• Observable weak interactions either involve
• 1) n (which do not undergo
  em and strong interaction)
• 2) quarks with a flavor change
• Like in QED and QCD, the force carriers are
  spin-1 bosons that
• couple to quarks and leptons

Neutron b-decay Antineutrino absorption Hadronic
S decay
2

• Force carriers of weak interactions are three
  intermediate vector
• bosons W and W- (mass 80.4 GeV), and Z0 (91.2
  GeV)
• The three bosons are very massive particles ?
  weak interactions
• are very short ( 2x10-3 fm)
• Before the Electroweak theory was developed all
  observed weak
• processes were charged current reactions (e.g.
  B-decay) mediated
• by W and W- bosons
• Electroweak theory predicts a neutral current
  caused by Z0 boson
• Predicted neutral current reaction
• no muon in final state

3
First dedicated experiment to study vectorbosons
SPS proton- antiproton collider at CERN
(detectors UA1 and UA2)
Mechanism of W/Z production in pp annihilation
4
From the quark point of view, processes are
quark-antiquark annihilations To obtain
sufficient cms energies, proton and antiproton
beams at SPS had energy of 270 GeV each

W boson, UA1 detector in 1982
5
Signature of a W boson

• A lepton with large momentum (gt 10 GeV/c) emitted
  at a wide angle
• to the beam (gt 5O )
• Large missing transverse momentum carried out by
  neutrino
• If pt(W)0 ? missing pT pT(l)
• From 43 events observed by UA1, the mass of W
  was defined as
• MW 80.33 ? 0.15 GeV/c2
• And the decay width as GW 2.07 ? 0.06 GeV
• Which corresponds to a lifetime of 3.2x10-25 s
• Branching ratios of leptonic decay modes of W are
  about 11 for
• each lepton generation

6
W bosons can be pair-produced in ee-
annihilation, and the up-to-date world average
for the W-mass is
7
Signature of a Z boson

• Pair of leptons (ee-) with very large momenta
• Mass of the Z0 is then invariant mass of leptons.
  
• Knowing Mw, Mz was predicted to be 90 GeV/c2
• -

UA1


8
Dilepton mass spectra near the Z0 peak (CDF
Collaboration) More precise methods give
world average values of MZ 91.187?0.007
GeV/c2 GZ 2.490 ?0.007 GeV/c2 corresponding
to a lifetime of 2.6x10-25 s Branching ratios of
leptonic decay modes of Z0 are around 3.4 for
each lepton generation
9
Carlo Rubbia (1934) Simon van der Meer (1925)

• Nobel Prize 1984
• for their decisive contributions to the large
• project, which led to the discovery of the field
• particles W and Z, communicators of weak
• interaction

10

• W? exchange results in change of charge of the
  lepton and hadron
• taking part. It is called charged-current
• Purely leptonic processes
• 2) Purely hadronic processes
• 3) Semileptonic reactions
• RECALL leptonic weak interaction processes can
  be built from a
• certain number of reactions corresponding to
  basic vertices

?e
u
W-
W
e-
11

• W? exchange results in change of charge of the
  lepton and hadron
• taking part. It is called charged-current
• Zo-exchange does not and is called a neutral
  current reaction
• The small value of the aw constant can be put in
  relation with the
• high mass of the bosons

?e
u
Z0
Z0
?e
u
12

• If we simplify (using same coupling g to quarks
  and leptons for W
• and Z)

To be compared with for the em scattering

• If , the amplitude is independent
  of q2 in this case we
• say that the interaction is pointlike
• Fermi postulated such an interaction (1935), of
  strenght G,
• between 4-fermions to describe b-decay
• As q2 ? 0
• (from measured decay rates)

13
Given the two basic vertices, one can derive 8
basic reactions
These processes are virtual 2 or more have to be
combined to conserve energy
14

• Weak interactions always conserve lepton quantum
  numbers
• It is not possible
• Leptonic vertices are characterized by the
  corresponding strength
• parameter aW independently on the lepton type
  involved.
• -Knowing the decay rate of W?en one can estimate
  aW to the first
• order G(W?en) 0.2 GeV
• Since the process involves only one vertex and
  lepton masses 0 ?
• G(W?en) aWMW80aWGeV
• which gives aW 1/400 O(a) similar to the
  electromagnetic one

15
Analogues of electron-electron scattering by
photon exchange Time ordering implies
changing the sign of the current! A conventional
muon decay looks like
Including higher order diagrams
16

• Since W bosons are very heavy, interaction can be
  approximated by
• a zero-range interaction
• Taking into account spin effects, the relation
  between aW and GF in
• zero-range approximation is
• where gW is the coupling constant in W-vertices
  aWg2W/4p by
• definition. This gives the estimate of aW
  4.2x10-30.58a
• Weak interactions of hadrons quarks emit/absorb
  W bosons
• Lepton-quark symmetry corresponding generations
  of quarks/
• leptons have identical weak interactions

17
The corresponding coupling constants do not
change upon exchange of quarks/leptons gud
gsc gW
For example, allowed reaction is
18
Weak interactions violate isospin conservation.
However there appears to be a selection rule in
non-leptonic decays DI 1/2 Generally
obeyed in the decay of the strange
particles. Example Since IL 0 this rules
states that the nucleon and the pion must be in
a I 1/2 state. Looking at the Clebsh-Gordan
coefficients As confirmed by experiments
19
For leptonic decays of strange particles, the
isospin cannot be Specified. Empirically saw
that the rule is valid DQ DS From the
relation Q I3 1/2(BS) it follows that
DI31/2 if DQ DS1 Example If one
considers the hyperon leptonic decay modes The
rates are roughly 20 times smaller than those
expected if the couplings were the same as for
the S-conserving decay.
20
Gell-Mann and Levy (1960) and Cabibbo (1963)
proposed a way out The baryon state of
spin-parity ½ form an octet as we saw.
However, this symmetry is broken in nature, and
the baryon get all different masses. In the
splitting, there is no a priori way to
determine how the weak coupling is
divided. Cabibbo postulated that, for DS0
decays, weak coupling Gcosq DS1 decays, weak
coupling Gsinq Consequences The DS1
baryonic decays are suppressed relative to the
DS0 ones. The coupling constant for Fermi
transitions in b-decay becomes Gcosq rather than
G.
21
In more detail the quark mixing hypothesis
was introduced by Cabibbo d- and s-quarks
participate the weak interaction via the linear
combinations Parameter qc is the Cabibbo
angle, and hence the quark-lepton symmetry
applies to doublets like
22
1967-68 Electroweak Theory of Glashow, Salam and
Weinberg
Proposes that the coupling g of W and Z to
leptons and quarks is the same as that of the
photon g e The weak and em
interactions are unified From the measured value
of G, it was expected that
23
(No Transcript)
24
Sheldon Lee Glashow (1932) Abdus Salam (1926
1996)Steven Weinberg (1933)

• Nobel Prize 1979
• for their contributions to the theory of the
• unified weak and electromagnetic interaction
• between elementary particles, including, the
• prediction of the weak neutral current

25

• Self-coupling W-Z

• Couplings with photons

26
Summary of interactions
27
Decay time of ?0??? is about 10-16 sec (em
interaction) For S0?L?, time is about 10-19 sec
(em interaction) For D?pp, time is about 10-23
sec (strong interaction) The neutron decay
via n ?pen takes 15 minutes! (weak
interaction) A new weak coupling constant
has to be introduced
28
u d
?,Z,g
W
W-
?,Z,g
?e e-
Z
W
W-
?,Z