Reading: Griffiths Chapter 2, Perkins Chapter 2 Handed out in Class
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Physics 535 lecture notes: - 4 Sep 13th, 2007
Reading: Griffiths Chapter 2, Perkins Chapter 2 handed out in class.
Homework: Griffiths: 2.2, 2.4, 2.5, Perkins 2.4
1) Review Weak Force interactions
The weak force involves a large number in interactions with all the quark and leptons since they all have flavor. When determining what sort of interactions are possible or probable the guiding rules are that the interactions should conserve momentum and energy, electric charge and various types of weak flavor when appropriate.
The charged W particles convert lepton to neutrinos and d type quark to u type quarks.
In the SM there are no flavor changing lepton interactions between the generations. Lepton weak flavor, or the lepton quantum number, is conserved. However, since neutrinos have been demonstrated to have mass this makes the lepton generations more similar to the quark generation and we do expect lepton number violating interactions. However, for charged leptons they are probably so small as to be undetectable
In the SM there are flavor changing interactions between generation for the quarks. The W can also convert particles between the generations due to the fact that the strong and weak eigenstates of the d, s, and b are different. Weak eigenstates can be expressed as a superposition of strong eigenstates as quantified in the 3x3 CKM matrix.
The neutral Z particles have scattering and annihilation or pair production interactions much like the photons. Though these interactions can also involve neutrinos. Flavor changing between the generations is not possible for the Z particle. This can be understood mathematically. The W an interaction can be written as
Note FCNC, flavor changing neutral currents does happen at higher order at very low probability.
Some example interactions are d -> uW- -> ue- anti e: seen for neutrons, n(ddu) -> p(duu) e- antie
- -> W- -> e- anite d anti u -> W- -> e- anti e: seen for charged pions - -> e- anti e 0 s -> uW- -> ue- anti e: seen for charged kaons, for K-(s anti u) -> (u anit u) e- antie
Interesting effect. Weak decays involving the W can change particle generations. This is the only way a particle from second and third generation can decay to the lowest energy generation. These particles all have long lifetime and in fact hadrons with b quarks have very long lifetimes since the b transitions to the other generations have small probabilities. The superposition of b’, s’, d’ for the b quark is mostly b’. However, you can produce particles from the second and third generations by strong or electromagnetic pair production of particle and antiparticles pairs.
2) Unification
A milestone toward the standard model was the Z particle, the 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! Any type of interaction involving the Z had an equivalent higher probability EM interaction, except for the neutrino interactions which have not been observed. Later it was seen that as you observed interactions such as particle-particle annihilation 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.
In fact the b, s and d states can be considered eigenstates of the Higgs interaction and the strong interaction. As before the b’, s’ and d’ states are still the Weak eigenstates. The Higgs particle interacts with any particle that has mass. Since these particles have mass they are in eigenstates of the Higgs particle when in a configuration where they have definite mass, such as a hadron. The neutrios, if they had no mass would be pure eigenstates of the Weak force. But since they do have some mass you can have interactions change lepton flavor generation just like with the quarks. 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
The Higgs particle is the subject of my research at CDF(Collider Detector at Fermilab) where I lead the Higgs Discovery effort.
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.
4) Experimental particle physics.
We have new mysteries, but also better experiments to explore them. In addition to cosmic ray experiments we can build accelerators where accelerate charged particles up to very high velocities and momentums. Then we annihilate electrons and positrons, protons and antiprotons or collide protons and protons to create other particles. Remember that protons, neutrons, electrons, neutrinos, muons, pions and kaons are the only particles that have a long enough lifetime to be easily observed. These are the typical things we try to detect in our particle physics experiments. The whole experiments are built around the properties of these particles and how to measure the momentum or energy of the particles.
Particle detectors from inside to outside: a) The tracker. A device immersed in a magnetic field, which will be used to measure the momentum of the particle by its curvature in the field. Particle going through a gas or a solid will ionize the material by exchanging photons, which leaves the detectable track. These ions are what are detected. Also the tracks can be traced back to find if they came from a common vertex and thus could be from the decay of a more massive particle.
There are two typical types of tracking detectors. Drift chambers: gas filled chambers with wires for detecting ions and silicon semiconductor sensors with metal strips for detecting ions.
What is the physics? i) Radius of curvature of a charged particle track in a solenoidal magnetic field. r = 0.3Bp where p is the momentum in GeV/c, B is in Tesla and r is the radius of curvature in meters. ii) Ionization charge drifting. The ionized particles drift toward wires that are held at high voltage. Measuring the drift time if the typical velocity is know can give a much more accurate measurement. iii) The ionization process is a scattering interaction. Probability is proportional to 2 or e4. See Perkins page 39. dE/dx has an incident particle mass dependence at relativistic speeds that can be used to distinguish the particle type. iv) Ionization is much larger in semiconductors, which makes them an excellent particle detector material since you can design a small volume detector that can precisely determine the position of particles. b)Time of flight(TOF). Precise time measurements from the scintillation light of atoms excited by the passing particle. More massive particle move slower for the same momentum. i) Momentums are measured in the tracker and velocity in the TOF and relativistic equations used to calculate the mass. ii) The active material is usually a scintillating material, which is ionized by particles traversing the detector. The ionized electrons are recaptured by atoms emitting photons, which are detected by photomultipliers. c) Cerenkov detectors. Identify particles by Cerenkov light. i) When the particle velocity exceeds the speed of light in the medium v > c/n Cernkov light is emitter at an angle cos = c/vn. The particle velocity can be measured by measuring the angle or at least said to be above a certain value if the light is detected. d) Electromagnetic calorimeter. Electrons and photons will interact electromagnetically in matter. This makes a cascade or shower of electrons and photons that can be measured to determine the total energy. muons and hadrons(pions kaons protons…)tend to go through these detectors without interaction. i) Electrons will interact via brehmsstralung producing photons. Photons will pair product making electrons and positrons. These are 3 probability interactions proportional to e6. However, having a dense material with a high Z will make these interactions more likely. The secondary particles will continue to interact until all the electrons produce photons that are two low energy to ionize new electrons and these photons are measured by photomultipliers. ii) Good materials for this type of detector are characterized by the radiation length, X0, the length of detector material electrons or photons will traverse before 1/e of the particles interact, and the Z of the material. You would like small X0 and large Z. iii) Also once you are down to lower energy photons you would like to have a transparent material. Lead glass is a good example. iv) These interactions are also characterized by the length, L, until the shower is done which is proportional to the energy of the incident particle. e)Hadrons will interact strongly in dense matter such as iron and the energy of the resulting particles can be measured. Muons will go through without much interaction. i) These interactions will happen for charged or neutral hadrons since they all have color charge.
ii) The scale of interaction length or absorption length, 0, is different since we are talking about the strong interaction. These lengths are actually larger since the hadrons have to get near within the typical strong force distance of the nucleus before there is a good probability of interaction. iii) The interactions produce new charged and neutral hadrons with can undergo a shower of secondary interactions. The energy that is eventually detected is from ionization caused by the many charged hadrons produced in the shower. Also the lightest neutral meson, a pion, will decay electromagnetically to two photons which can be detected. A substantial portion of energy is lost to nuclear breakup which, can be detected if you material is U238 which will undergo fission when hit by fast neutrons and the photons from the fission process can be detected. iv) Since you typically use a material like iron or Uranium which is not that transparent you need to alternate layers of metal and scintillator which are used with photomultipliers to collect the light. f) Muon systems typically sit outside the large amount of metal of the hadronic calorimeter. They may consist of drift tubes, small version of the drift chamber to spot the charged muons. You can even put them in a field to measure momentums. e)If you measure everything then any left over energy you expected is probably lost in neutrino form.