OverviewThe Structure of the Proton Lecture 1- Chs1/2Quark-Parton Model Lecture-1 Chs1/2QCD and the QCD improved parton model Lectures 2/3 Chs 3/4 DGLAP resumming LL NLL in ln(Q2) Lecture 3 Ch 4Parton Distribution Functions and their Uncertainties Lectures 4/5/6 Ch 6,7,8QCD at low-x, low-Q2 Lecture 6/7/8 Ch 9Importance for LHC physics Lecture 9/10 Ch 10 but not always in a book!Devenish and Cooper-SarkarDeep Inelastic Scattering OUP 2004

Scattering: elastic, inelastic,deep-inelastic

For a charge g from a potential charge Zg through the mediation of a quantum of mass . Assume free waves for r>>1/

where

The Matrix Element has the form of a coupling constant squared times a propagator

Then using the Golden Rule

Which can describe Rutherford Scattering as 0,

What happens if the scattering centre has finite size?

The form factor for a proton is ~

Such a form is NOT point-like.

Now consider Inelastic scattering

q=k-k, p2=mN2, PX2=MX2

k+p=k+pX , pX2 = p2 +q2 +2p.q, soQ2 =-q2= 2p.q + mN2 mX2 defines the positive momentum transfer squared.

If the target is at rest and the incident and scattered energy of the lepton probe is E and E respectively thenIf the final state hadronic mass is known- as for elastic scattering OR the production of specific hadron resonances like N* and - then E and are not independent

But if we integrate over final states inclusive cross-sections- then they are and we usually use the two variables Q2 and x=Q2/2p.q to describe the process. (For elastic scattering x=1).We will then need form factors or structure functions which depend on x and Q2The figures show inclusive spectra for E at low and slightly higher energies.The peaks correspond to the nucleon resonances. One can see the importance of these decreasing as the energy increases- we are moving into the deep-inelastic region. What is the origin of region B? Could it be scattering from constituents of the proton? Wouldnt this lead to more peaks?Not if these constituents have momentum~200MeV

-due to their confinement

d ~2L WEeEEpq = k k, Q2 = -q2s= (p + k)2x = Q2 / (2p.q) y = (p.q)/(p.k)Q2 = s x ys = 4 Ee EpQ2 = 4 Ee E sin2e/2y = (1 E/Ee cos2e/2)x = Q2/syThe kinematic variables are measurableLeptonic tensor - calculableHadronic tensor- constrained by Lorentz invariancePDFs were first investigated in deep inelastic lepton-nucleon scatterning -DISThis is the scale of the vector boson probeThese are 4-vector invariants

d2(eN) = [ Y+ F2(x,Q2) - y2 FL(x,Q2) Y_xF3(x,Q2)], Y = 1 (1-y)2dxdyF2, FL and xF3 are structure functions which express the dependence of the cross-section on the structure of the nucleon (hadron)

The Quark-Parton Model interprets these structure functions as related to the momentum distributions of point-like quarks or partons within the nucleon AND the measurable kinematic variable x = Q2/(2p.q) is interpreted as the FRACTIONAL momentum of the incoming nucleon taken by the struck quark

We can extract all three structure functions experimentally by looking at the x, y, Q2 dependence of the double differential cross-section- thus we can check out the parton model predictions(xP+q)2=x2p2+q2+2xp.q ~ 0for massless quarks and p2~0 so x = Q2/(2p.q)The FRACTIONAL momentum of the incoming nucleon taken by the struck quark is the MEASURABLE quantity xWithout assumptions as to what goes on in the hadron the double differential cross-section for e N scattering can be written as Leptonic part hadronic part

Now consider neutrino scatteringLets see the early data on Bjorken scalingAnd on FL=0

There is clearly a need for the qbar termThis leads to the idea of 3-valence quarks PLUS a q-qbar Sea

Where does the Sea come from?qq g gq-qbar

So hopefully you now believe that the Quark Parton Model has some basis in fact

End lecture-1