1. Nuclear Physics: The Liquid Drop Model Bohr +Wheeler
Semi-empirical mass formula from the liquid drop model.
Volume term
Surface term
Coulomb term
Asymmetry term
(Pauli exclusion)
Pairing term

2. Today’s plan Collect homework More on QCD: nucleon substructure
structure functions,
neutrino-nucleon scattering
QCD Feynman rules
Hope to reach Feynman rules for QCD today or Monday.

3. Differential cross-section for deep inelastic scattering
Rutherford scattering: Chapter 1
Spin flip term
Bjorken scaling means: dependence on x-only
F1,2(x, Q2)≈F1,2(x) (Q2>>M2)
Mott Scattering (spin ½ particles)
Chapter 1 of Bettini
Sometimes called the Callan-Gross relation; experimentally verified.

4. Scaling data Bjorken scaling is working well in this region.
Adapted from Chekanov, S. et al. (2001); Eur. Phys. J. C21 443
Bjorken scaling is working well in this region.

5. Breakdown of scaling in deep inelastic scattering
Question: Why does Bjorken scaling break down at low x and high Q2
Ans: Gluon bremstrahlung and q qbar pair production occur. The resolving power improves a) vs b) at high Q2
Gluon emission moves the quarks to lower x, hence the structure fcn increases at large Q2
Can be used to measure αS(Q2)

6. Why ? How can the LHC get away without using anti-protons ?
Question: At the Fermilab Tevatron (center of mass energy 2 TeV) used proton-antiproton collisions to make new particles such as top-anti top pairs or Higgs bosons. However, the LHC (center of mass energy 14 TeV) uses proton-proton collisions.
Why ? How can the LHC get away without using anti-protons ?
Typical x –value is a factor of 7 smaller at the LHC. Gluons are prolific. So g g scattering replaces q qbar.

9. Parton Distribution Functions (PDF)
We define f(x) as the distribution function for the momentum fraction of quark of type f.
Then f(x) dx is the probability that a quark of type f carries momentum fraction between x and x+dx
The quantity x f(x) dx is the total momentum fraction.
Isospin invariance (symmetry between p and n, rotate ud) gives the following useful relationships
Question: How are the PDFs of the “sea” distributions of the s and sbar quarks related for the proton and neutron ?

10. Parton Distribution Functions and ep scattering
Electrons “see” or interact with the EM quark charges inside the proton.
N.B. that u(x) contains all u quarks (valence and sea). The same for d(x).
Question: Can you write a similar function for the neutron ? (hint use isospin symmetry)
Note that F2(x) for ep scattering is only sensitive to charges squared and hence cannot distinguish between quark and antiquark.

11. Question: Is neutrino-nucleon scattering a strong, weak or EM process ?
Is it sensitive to the u(x) and anti-quark distributions function separately ? (Can you draw a typical Feynman diagram ?) - +
Which if these reactions are possible ? Draw the Feynman diagrams

12. Question: Which if these anti nuetrino reactions are possible
Question: Which if these anti nuetrino reactions are possible ? Draw the Feynman diagrams
Recapitulation

13. All the possibilities (only 4) and their cross-sections and angular dependences.
M.A. Thomson

14. We can obtain these results (factor of 2 related to helicity c. f
We can obtain these results (factor of 2 related to helicity c.f. Chap 7.)

15. Not easy to stop a neutrino and measure a cross section (WA1 experiment at CERN)

16. Ratio of 0.45; valence quarks are fractionally charged with some sea contribution

17. For an isoscalar target
Evidence that the valence quarks in the proton are fractionally charged

18. Question: What is this stuff ?
Obtained by integrating F2(νN) or F2(ep) over all x
This means that 50% of the proton momentum is carried by entities that have no electromagnetic or weak interactions !!
Question: What is this stuff ?
Ans: the gluons in the nucleon.

19. QED vertices

20. QCD Feynman rules Gluons carry color –anti color combinations
The singlet is symmetric and color less and does not mix
In SU(3)QCD combine a color triplet (R,G,B) and an anti-triplet
There are 8 gluons

21. Example: QCD Feynman rules

22. Example II: QCD Feynman rules

23. Very important: QCD three gluon vertex
4 gluon scattering
Question: How do QCD couplings depend on
quark flavor
Electric charge
The strong coupling is independent of quark flavor and electric charge.