Nuclear Physics The Liquid Drop Model Semiempirical mass

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

Today’s plan Collect homework More on QCD: 1) nucleon substructure 2) structure functions, 3) neutrino-nucleon scattering 4) 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 Mott Scattering (spin ½ particles) Chapter 1 of Bettini Sometimes called the Callan-Gross relation; experimentally verified. F 1, 2(x, Q 2)≈F 1, 2(x) (Q 2>>M 2)

Scaling data Adapted from Chekanov, S. et al. (2001); Eur. Phys. J. C 21 443 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 Q 2 Ans: Gluon bremstrahlung and q qbar pair production occur. The resolving power improves a) vs b) at high Q 2 Gluon emission moves the quarks to lower x, hence the structure fcn increases at large Q 2 Can be used to measure αS(Q 2)

Question: At the Fermilab Tevatron (center of mass energy 2 Te. V) 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 Te. V) 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 F 2(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 ? Draw the Feynman diagrams Recapitulation

All the possibilities (only 4) and their crosssections and angular dependences. M. A. Thomson

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 (WA 1 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

Obtained by integrating F 2(νN) or F 2(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 In SU(3)QCD combine a color triplet (R, G, B) and an anti-triplet The singlet is symmetric and color less and does not mix 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 1) quark flavor 2) Electric charge The strong coupling is independent of quark flavor and electric charge.