Lecture AP1

Electroweak interactions

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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”

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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

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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:

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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) GeVIt was finally detected at Fermilab (CDF) in 1995, and it has a mass

mt = (173 ± 1) GeV

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

The CKM matrix

| |

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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

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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.

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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

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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.

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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

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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:

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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

€

G(Z 0 → f + f ) = K gZ2 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

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)()()(12)(

ZZZcmcm

Z

MMEXZeeZ

EMXZee

GGG

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 nnGGGGG ZnuuZddZllZZ

Each n species contributes ~167 MeV to GZ

By varying the energy of the beams (e+e-ZX) 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

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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+)

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Trilinear couplings seen at LEPand SM accounts correctly for them

ee -> WW +

+

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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, vradius, r

Luminous stars only small fraction of mass of galaxy

Besides astrophysical evidence, cosmological evidence as well. As large as 5x ordinary matter

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Compact objects in the halo (BH, MACHOs)

They exist, but they are not enough

Hubble Space Telescopemultiple images of blue galaxy

Gravitational lensing

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Only WIMPs are leftInput from particle physics is needed

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Direct WIMP Detection

cc

cc

Na I

GeLi

ght a

mpl

itud e

Ioni

zati o

n

time

Total energy

signal

signal

background

background

Rejection of background is the critical issue

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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

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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

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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)

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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

a

bg

td tb

cd cb

V VV V

ud ub

cd cb

V VV V

0

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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