Lectures 1-10

Question 1

What are the assumptions made about scattering?

Answer 1

1. Target Particles separated by distances&raquo_space; de Broglie
2. Target low density
3. Collision energy high - negligible binding energy
4. Beam Intensity Low - Non-interacting
5. Single exchange dominates

Question 2

What is the key jargon in deriving the differential cross-section?

Answer 2

No. of states / per particle per unit volume of momentum space. From this - > No. of final states per particle, which is the Lorentz Invariant Phase Space.

Question 3

What are the contributions to M_fi from the possible vertices in Feynmann diagrams?

Answer 3

1. Particle-antiparticle (ie(p1-p2))
2. Particle particle QED Channel (ie(p1+p2))
3. Exchange Photon (-ig_munu)/q^{2}

Question 4

Describe the Theory behind the CKM Matrix?

Answer 4

Quarks taking part in the weak interaction (“weak eigenstates”) are not the same as quarks inside hadrons (“mass eigenstates”).
Weak eigenstates are orthogonal combinations of mass eigenstates -> results in mixing between quark combinations in weak decays. Mixing between d,s quarks can be considered as flavour-axis rotation by angle theta_c ~ 13%.
Can lead to Cabbiba favoured, Cabibbo Supressed and Doubly Cabibbo Supressed decay modes.

Question 5

How are the matrix elements measured?

Answer 5

V_ud - > Nuclear beta decay.
V_us - > Semi-leptonic neutral and charged Kaon decays.
V_cd - > Semi-leptonic D decays & neutrino scattering.
V_cs - > Semi-leptonic D & leptonic D_s decays
V_cb - > Semi-leptonic B decays to charm.
V_ub - > Semi-leptonic charmless B decays.

Question 6

What is the Wolfrenstein Parameterisation?

Answer 6

A 3x3 Unitary matrix can be fully specified by 3 angles and 1 phase. Phase term leads to CP violation in some processes. Bottom row of dagger matrix * first column in triangle. Dividing by 2nd term gives baseline triangle a length of 1. All of O(lambda^3).
This triangle is most accessible to experiment.

Question 7

CP in the Weak Interaction?

Answer 7

W couples preferentially to LH F and RH AF. In Ultra-relativisitc limit, coupling of W to RH F vanishes completely. Most of the Time, CP (transforms LH F - > RH AF) is nearly conserved.

Question 8

How are the Lengths and Angles measured from Wolfrenstein Parameterisation?

Answer 8

Lengths of Upper two:

• B decay rates
• B^{0} mixing

Angles:
- Interference between diagrams, measured from CP violation.

Question 9

How is Kaon Mixing measured

Answer 9

K_0 evolves in time to mixture of K_0 and antiparticle. Subsequently Weak decay, and charge of pion/electron “tags” which Kaon decayed.
Produce pure K_0 beam from pion proton collision, being above threshold.
K_1 (short) decays to pipi (CP Even), K_2 (long) decays to pipipi (CP Odd). K_1 has much shorter lifetime due to greater phase space for 2pi decay.