1. Deep Inelastic Scattering ep->eX

2. Structure of Matter  Stuff -> atoms.  Atoms -> nucleons  Nucleons -> ?  This is what deep-inelastic scattering is designed to tell us.

3. The Experiment  Elastic Scattering can give form factor.  Increase momentum of probe to look at hadron constituents.  Break up hadron.

4. Inelastic Scattering  Consider classical inelastic scattering.  Energy loss -> new particles in this case.  Resonant baryon states.

5. Parton Model  Large momentum transfer for high momentum probe.  Scattering happens fast compared to processes inside of the hadron.  Treat the hadron as an assembly of non- interacting partons.  There is a problem with this since QCD is a renormalizable (not super renormalizable) theory. (Time scale of processes). ->OPE.

6. Hadron Tensor  The cross-section for the process depends on the Hadron Tensor, which allows for the possibility of non-conservation of the hadron current (neutrino used as probe).  This can be expanded in terms of structure functions (W 1, …, W 6 )

7.  W 6 =0 due to strong interaction time reversal invariance.  W 3 =W 4 =W 5 =0 for electromagnetic processes.  Define new scaling structure functions: Calculating the Structure Functions

8. More Calculation  Can relate the Hadron Tensor to the time- ordered Green’s function:  This Green’s function can be expanded like the hadron tensor.  We can expand in 1/x and relate to F’s.

9. How does this relate to hadron structure?  Perform OPE to relate T μν to W μν via the scaling structure functions F i.  The moments of the structure functions satisfy:

10.  Calculate lowest order coefficients for the OPE.  Using electromagnetic current:  Expand about 1/x = 0. Scattering on a Quark Target Electromagnetic process.

11. OPE Coefficients  We can then calculate the coefficients by matching.  For an incident neutrino, for example, we would have additional terms for the various other W i ’s.  Could also calculate quark probability distributions.