Bettini Homework Problem 6.9 (QCD Chapter) “Collisions take place between 28 GeV electrons circulating in one direction and 820 Gev protons circulating in the other. The cms energy squared is 4E1E2 ~ 90,000 GeV2. To achieve a similar energy in a fixed target experiment would require a ~50 TeV lepton beam incident on a stationary proton target. The results from HERA show a enormous increase of the quark density at very small values of x…..Feynman alluded to this as ‘the secrets of wee x’ “ Donald Perkins, 5th edition. Inside the HERA tunnel, proton ring to the far right (superconducting), electron ring below.

EIC = Electron Ion Collider US Nuclear Physicists: “A new electron-ion collider (EIC) could rise to the challenge, bending time and launching light-speed probes to unravel the mysteries of the glue.” Two possible sites for such a facility “At Brookhaven (BNL) on Long Island, NY or Newport News, VA (JLAB). Highest future priority of US nuclear physics (NSAC 2015). Cost 1-1.5 billion dollars. Also being discussed in Europe.

Today’s plan Collect homework Weak interactions (Chapter 7 continued): The τ-θ (tau-theta) puzzle The Co60 experiment of Madame Wu Helicity and Chirality Parity violation FCNC, GIM mechanism Friday: Quiz on QCD

The τ-θ puzzle From emulsion experiments. There are two particles called the τ and θ, which have the same mass and lifetime. (Examples on the right). Question: What are the possible spin-parities of the θ and the τ particles ? (Note that studies of the τ Dalitz plot show that it is flat and the pions are in a s-wave. The decay of the θ is also uniform) Ans: The θ could be a 0+ and the τ would be 0-. Still pretty odd. Hint: The pion is a pseudoscalar particle

Reminder: From Bettini Chapter 4 Folded Dalitz plot for Orear, J. et al., (1956); Phys. Rev. 102 1676

The τ-θ puzzle Marty Block and Dick Feynman were roommates at the 1956 Rochester conference on high energy physics. Brainstorming on the first evening of the conference, Marty suggested that the τ and θ could be the same particle if parity were violated in the weak interaction. Marty thought this was too crazy to bring up at the meeting. Feynman asked C.N. Yang a question that Marty had brought up: “Is it possible that parity is not conserved ?” On the train back to NYC after the meeting, Lee and Yang wrote their seminal paper based on this idea. “To decide unequivocally whether parity is conserved in weak interactions, one must perform an experiment to determine whether weak interactions differentiate the right from the left.” T.D. Lee and C.N. Yang (1956)

Madame Wu’s experiment To detect photons Came to Berkeley from Shanghai in 1936 To detect electrons To detect photons Need cryogenic temperatures (millikelvin) to line up nuclear spins. Spins must be in a vacuum (no leaks).

Cobalt 60 decay scheme Question: How do PNPe and JNPe behave when r-r ? Ans: PNPe is unchanged but JNPe is parity violating. Need all the spins lined up and cryogenic operation.

Data from Madame Wu’s experiment Adapted from Wu, C. S. et al. (1957); Phys. Rev. 105 1413 and ibid. 106 (1957) 1361 Experiment performed during Christmas break 1956 at the NBS (National Bureau of Standards) in Washington, D.C. C.S. Wu cancelled her vacation. Turn on the B field to polarize the spins. Then turn it off and observe the result.

Find α≈1 or pure V-A for the weak interaction. Notice the directions of the electron and neutrino spins relative to their direction of motion.

Reaction from Wolfgang Pauli “That’s total nonsense. God is not a weak left-hander” Pauli assumed the result of C.S. Wu’s experiment was wrong. However, the result was confirmed by many other groups. Maximal parity violation is a characteristic of the weak interaction. Later Pauli reluctantly agreed that the result is correct. “Maybe God is a little left-handed.” Madame Wu was not included in the Nobel Prize for parity violation, which went to the theorists T.D. Lee and C.N. Yang.

One spinor is a particle; the other is an anti-particle. where Let’s apply the spin projection operator to two Dirac spinors Question: What do we obtain ? Ans: +1/2 and -1/2, respectively

Helicity The helicity operator is Two notes: Helicity eigenstates are two component spinors Question: What are the helicity eigenvalues ? Ans: +1/2, -1/2 Two notes: Helicity is not Lorentz invariant. If the particle is not massless, can boost to another frame in which the particle is moving in the opposite direction. Helicity is not the same as chirality.

Chirality If ψ is a solution to the Dirac equation The charge conjugated states are p.78-79 of Bettini Question: Verify that the operators ½ (1-γ5) ½(1+γ5) are projectors i.e. applying twice gives the same result as applying once and applying both gives a null state. Hint: What is γ52

Helicity of the neutrino Photo of L. Grodznis Experiment done by Goldhaber, Grodznis and Sunyar in 1958.

1) Need recoil-less emission and absorption of a photon 2) Need β decay (K-capture) and transfer of neutrino helicity (hν) to a gamma/photon and measurement of the helicity of the latter. Sm* axis is opposite to neutrino direction Question: Doesn’t nuclear recoil make resonant absorption impossible ? In the Samarium slab in a B field, nuclei are aligned and can absorb only one photon helicity. Ans: No, use Sm* photons in the forward direction which are blue shifted.

Perkins:

Helicity of electrons versus speed Adapted from Koks, F. & van Klinken, J. (1976); Nucl. Phys A272 61

1957 CN Yang TD Lee P is violated maximally in the weak interactions, C(charge conjugation) is also violated maximally but CP should be invariant (also postulated by the Russian theorists Okun and Landau)

CP ok LH ν RH ν Charge Inversion Particle-antiparticle mirror P C Parity Inversion Spatial mirror RH anti-ν LH anti-ν

Needed a powerful apparatus to find weak neutral currents (neutrino beam from the SPS and the Gargamelle bubble chamber) Can also have a hadronic vertex.

One of the first weak neutral current events A neutral current event in Gargamelle. © CERN Gargamelle – a large bubble chamber with 15 tons of liquid Freon (Andre Lagarrigue et al)

Five of the collaboration members would not sign this paper because of worries about neutron background.

Question: Which of these weak interaction couplings are allowed and exist ? ✔ Question: What does FCNC mean ? Ans: Flavor Changing Neutral Currents. (very important) Usually suppressed or forbidden. ✔