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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.
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 space– Small difference since MW >> Mt
• Experimentally, G(W -> en) ~ 0.23 GeV
• Total width 2.09(4) GeV
4
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’ = 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’)
~1/20
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:
6
7
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 be
mt = (170 ± 30) GeV
It was finally detected at Fermilab (CDF) in 1995, and it has a mass
mt = (173 ± 1) GeV
8
• At the 1st order, b’ = b, and the b quark is relatively stable.
The CKM matrix
| |
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 + ssZExperimentally:
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
Properties of the ZffZee 0
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.
f
e+
Z0
e-
ff
e+
g
e-
f
At center of mass energies close to MZ the reactionthrough Z dominates over the reaction through g.
e+e- cross section vs CM energy
g dominates
E-2
Z decays
€
Γ(Z 0 → f + f ) = KgZ
2 MZ
48π[| cV
f |2 + | cAf |2] f
Z0
f
With K=1 for leptons and K=3 (color factor) for quarks.cV
f and cAf are the vertex factors.
Predicted Standard Model Z decay Widths (first order)fermion predicted G(MeV)e, m, t 84ne, nm, nt 167u, c 300d ,s ,b 380
Z cannot decay into thetop quark since Mt>MZ/2
Z decays and the number of light neutrinos
M&S 9.1.422222
00
2
20
)(
)()(12)(
ZZZcmcm
Z
MME
XZeeZ
E
MXZee
ΓΓΓ
GZ is the total width of the Z
The shape of the curve depends on GZ. GZ depends on the number of neutrino species:
)()(2)(3)(3 0000 ΓΓΓΓΓ ZnuuZddZllZZ
Each n species contributes ~167 MeV to GZ
By varying the energy of the beams s(e+e-®Z®X) can be mapped and GZ determined
Excellent 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
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
How good is the Standard Model ?
The Standard Model is verysuccessful in explaining electro-weakphenomena.
Summary of Standard Model measurements compared withPredictions (LEP+)
21
Trilinear couplings seen at LEPand SM accounts correctly for them
ee -> WW +
+
2
Limits of the Standard Model
What’s in the SM? QFT based on SU(3)xSU(2)xU(1) symmetry containing:a) spin ½ point-like objects: quarks and leptonsb) spin 1 objects: force carriers (W, Z, g, gluons)c) 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
A “convitato di pietra”: dark matter
Gravity:G M(r) / r2 = v2 / renclosed mass: M(r) = v2 r / G
velocity, v
radius, r
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)
They exist, but they are not enough
Hubble Space Telescope
multiple images of blue galaxy
Gravitational lensing
25
Only WIMPs are leftInput from particle physics is needed
26
Direct WIMP Detection
cc
cc
Na I
GeL i
ght a
mp l
it ude
Ion i
zati o
n
time
Total energy
signal
signal
background
background
Rejection of background is the critical issue
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 NatureLaws of physics apply differently to matter & antimatter
This might explain the matter-antimatter asymmetry?They are not T-invariant
Christenson et al. (1964)
(33%)LK
(0.3%)LK 1CP
1CP
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
€
T x' x' = T(Vx1ei(kx−ωt ) + Vx2e
i(kx−ωt ))2
= (Re(Vx1)e-i(kx−ωt ) + Re(Vx2)e
-i(kx−ωt ))2
= x x if phase(Vx1) = phase(Vx2)
T x' x' = T(Vx1ei(kx−ωt ) + Vx2e
i(kx−ωt ))2
= (Re(Vx1)e-i(kx−ωt ) + Re(Vx2)e
iδ e -i(kx−ωt ))2
≠ x x if phase(Vx1) ≠ phase(Vx2)
30
Precision physics: the unitarity triangle
V†V = 1 gives us
– Experiments measure the angles a, b, g and the sides
* * *
* * *
* * *
0
0
0
ud us cd cs td ts
ud ub cd cb td tb
us ub cs cb ts tb
V V V V V V
V V V V V V
V V V V V V
This one has the 3 terms in the same order of magnitude
A triangle on the complex plane
1
td tb
cd cb
V V
V V
ud ub
cd cb
V V
V V
0
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)
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)
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’ gU
– At ordinary energies, these processes are suppressed
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
SUSY
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
SUSY Algebra
• Supersymmetry is a symmetry that relates boson to fermion degrees of freedom.
• The generators of supersymmetry are two component anticommuting spinors, satisfying:
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?
• The lightest neutralino is 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