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

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.

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.

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.

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)

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.

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 ?

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.

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

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

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

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.)

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

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

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

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.

QED vertices

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

Example: QCD Feynman rules

Example II: QCD Feynman rules

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.