Physics 535 lecture notes: - 3 Sep 11th, 2007
Don’t forget homework due Thursday
Homework: 1.1, 1.2, 1.3, 1.16(compare to particle data book online)
Office hours: Tuesday’s 3PM
1) Forces
Electromagnetic Force
Quantum Field Theory: Quantum Electrodynamics
Field Quanta, force carrier: Photon, m=0
Charge: Electric charge
Couples to: All things with electric charge
Diagrams: three line vertex with electron (positron), electron (positron) and photon
Conserves: Energy and momentum, electric charge, baryone number, lepton number,
quark generations(first, second and third generation), P Parity, C charge congregation, T
time, CP, CPT
Potential: V = -CqQ/r = -/r
Range: infinite
Strength:  = e2/4hbar = 1/137
Cross section: 10-33 m2
Lifetime: 10-20 sec
Charge conjugation: reverse all the charges. This interaction should occur with the same
rate
Parity: reverse all the special coordinates
Time: reverse time to make the backwards reaction
Examples:
Basic vertex, electron absorbing a photon: Photon electron electron vertex Probability .
Not a real process must actually happen in the field of a nucleus where it can absorb an
additional photon to conserve energy.
Each vertex contributes a factor of  to the probability of the interaction.
Electron positron annihilation and creation: Probability 2
Electron (positron) Electron (positron) scattering: Probability 2
Note for an electron and a positron the above two have the same result! To get the total
probability we must sum them
(Rutherford scattering relation)
Brehmstrahlung (must be near nucleus): Probability 3
Pair production (must be near nucleus): Probability 3
These examples drive much of the function of particle detectors
Could include higher order diagrams in the sums but they contribute less due to the extra
factors of  from each vertex.
One more interesting effect: The virtual photons radiating from a charged particle can
split into electrons and positrons and then annihilate back to a photon. These charges will
orient with the positron toward the original charge (if negative) and the electron away
from the charge. This effect, which is like a dielectric medium, tends to screen the
original charge. As a result the effective coupling constant changes, becoming larger
depending on how close you get to the original charge and smaller further away. We
would say the coupling constant runs.
Strong Force
Quantum Field Theory: Quantum Chromo Dynamics
Field Quanta, force carrier: 8 gluons , m=0
Charge: red green and blue color charge, 8 gluons carry different combinations of color
anti-color
Couples to: quarks
Diagrams: three line vertex with qaurk (antiquark), quark (antiquark) and gluon
Conserves: Energy and momentum, electric charge, baryon number, lepton number,
quark generation, color charge, C, P, T, CP, CPT
Potential: V =- s/r + kr
Range 10-15 m – by confinement of color neutral combinations
Strength: s = 1.3
Cross section: 10-30 m2
Lifetime: 10-23 sec
Examples
Strong quark annihilation…
All gluon interactions
Note quark annihilation would also have a contribution from the electromagnetic force
but it is so small compared to the strong contribution that it can usually be ignored.
These interactions explain the behavior of hadrons in dense matter particle detectors.
Interesting effects.
Virtual gluons can split into quarks or gluons and annihilate back to gluons. This effect
tends to anti-screen. A bare quark would radiate a strong color field attracting other
quarks. Until you have 3 (red green blue) or 2 (color anti-color) you don’t have a stable
color neutral system. In fact as small distances inside hadrons the strength of the strong
force is very small. Small enough that perturbation theory works and in fact quark inside
a nucleon are essentially free – asymptotic freedom.
As you get very close to the quark(takes very small wavelengths or high energy) the
coupling constant get very small. Near EM level.
If momentum is transferred to one of the quarks in this system the kr part of the potential
will pull back the quark back. This is due to the strong color field. If the quark has
enough momentum the gluon string between the quarks will build up enough energy to
form two new quarks. The new configuration of two new quark and shorter gluon strings
has a lower potential.
Note: nucleons are held together by the residual color charge just as molecules are held
together by the residual electric charge outside of the otherwise electrically neutral atoms.
Weak Force
Quantum Field Theory: Quantum Flavor dynamics
Field Quanta, force carrier: W+ and W- m=81GeV and Z m=91GeV
Charge: Flavor charge. Lepton number, quark flavor
Couples to: All things with flavor charge (all the quarks and leptons)
Diagrams: W, three line vertex with electron neutrino and W or quark quark and W.
Three line vertex with lepton anti-lepton or quark anti-quark and Z.
Conserves: Energy and momentum, electric charge, baryon number, lepton number, CPT
Violates: quark generation (W only, no Flavor changing neutral current involving the
neutral Z), C, P, CP(at a very small level)
Potential: V = -W/r = -/M(W,Z)2r
Range: 10-18
Strength: W = 10-5
Cross section: 10-44 m2
Lifetime: 10-8 sec or longer
Examples:
Same types of diagrams as for the other two forces but now the W(not the Z) changes
particle types.
Note that the weak boson couple to each other also but the interactions are very low
probability so you don’t see them very often. They don’t lead to interesting new effects
like in QCD.
Interesting effect. Weak decays involving the W can change particle generations.
This is the only way particles from second and third generations can decay to the lowest
energy generation. This is why they all have long lifetimes. However, you can produce
particles from the second and third generations by strong or electromagnetic pair
production of particle and antiparticles pairs.
Flavor changing between the quark generations can be explained by the idea that the
three down type particles d, s, and b and the three up type particles u, c, and t are
eigenstates of the strong force, but that the eigenstates of the weak force are slightly
different for the down type particles d’, s’ and b’ which can be expressed as a linear
combination of the d, s and b strong eigenstates. These coefficients can be summed up in
the 3x3 CKM rotation matrix. The W particle could convert b’ to t’ type
eigenstates(particles) b(-1/3) -> W- t(2/3) – ignoring the mass of the t quark. However,
the b quark was in a meson or baryon coupled to other particles by gluons so it was
definitely in a strong eigenstate. Therefore, it was in some superposition of d’, s’, and b’.
When it interacts with the W+ it might interact as any of the three with a probability
governed by the components of the linier combination is was in(CKM matrix) If it
interacts as a d’ what you will see is
-> W- u or if a s’ what you will see is -> W- c. Therefore there is a finite probability of
decaying to a c or a u quark. T is forbidden by energy conservation. According to the
CKM matrix constants c is much more likely.
Flavor changing neutral current b->Zd are not allowed.(Part of my research is
investigating such interactions)
2)Particles
Leptons: electron, electron neutrino
Charges: q=1,0, weak lepton number = 1
Interacts electromagnetically (electron only) and weakly
Quarks, u and d quarks
Charges: q=2/3,-1/3, weak quark flavor u and d, color red, green and blue
Interacts electromagnetically, strongly and weakly
2 and third generations can only decay via weak quark flavor changing decays involving
the W boson.
Generations: muon and tau leptons and c,s,t and b quarks
3) Unification
A milestone toward the standard model was the Z particle. A third quanta of the weak
force. This particle was neutral and had similar interactions to the electromagnetic force
such as e+e- -> Z -> e+e-. However it took a long time to find this particle since no one
expected it! Later it was seen that as you observed this type of interactions at higher and
higher energies the constants that governed the electromagnetic and weak interactions
changed and eventually unified at a high value. Essentially at energies well above the Z
mass(91 times the proton mass) the mass of the carrier becomes irrelevant to the
interaction. This was the first strong hint that there had to be some unifying theory
behind all the diverse quantum field theories that had existed.
Another way to put this is the both interactions have the same coupling constant and it’s
just the extra factor of the mass of the gauge boson in the denominator that makes that
gives the difference between the strengths of the interaction. Doing that calculation using
the measured strength of the weak and electromagnetic interactions in similar
configurations involving photons and Zs gives mZ=91GeV. Exactly what was later
measured.
Also a milestone for theory since it was predicted before it was found!
In addition the strong force is seen to weaken at higher energies so it may also unify.
One mystery is still present. Why do the W and Z have large mass. To explain this you
need to introduce an additional particle that by coupling with particles can give them
mass. This is the Higgs particle. The Higgs also gives mass to all the other massive
particles. Still unfound. The Higgs particle is the subject of my research at
CDF(Collider Detector at Fermilab) where I lead the Higgs Discovery effort.
These quantum field theories including the unified electroweak theory with the Higgs
particle to explain the mass of the W and Z make up the standard model (SM).
4) New physics
The above set of quantum field theories account for every process we have observed and
measured in collider experiments. So why would be we interested in new theories of
particle physics. The answer is that we have observed a number of phenomena that can’t
be explained by the SM. Also the Higgs piece of the SM is undiscovered
1) Neutrinos have mass
2) Dark matter. Observations of galactic rotation curves, the expansion of the
Universe and gravitational lensing indicate that there is some sort of particle out
there that doesn’t interact via any of the forces except gravity. This matter would
not radiate so we call it dark matter.
3) Dark energy. The universal expansion rate is bigger than expected given the
amount of matter and dark matter. Something is pushing it apart. We call this
dark energy
4) Why is everything in the Universe made of matter? CP violating processes can
result in antimatter decaying slightly more often than matter, but nothing like the
observed rate.(Another part of my research is investigating CP violating and
matter antimatter conversion processes)
There are a number of other problems as well.
1) We would like the forces to unify at high energy. If you try to calculate the
strengths of the interaction at very high energies, like those at the big bang, you
find that they get very close to each other but don’t match up.
2) Some diagrams in the SM have divergent contributions at high energy.
Probabilities greater than 1 or 100%.
3) Why three generations, why all the masses we observe, why the coupling
constants we measure and why so complex?
However, even though we know the SM has to be wrong it’s very important to
understand it in detail so we can understand how our particle detectors work and when
we have seen something new that we need to pursue it to start understanding the new
physics.
Next time: experimental particle physics