Electron-muon scattering

The fundamental interaction is the electromagnetic scattering of the electron on a parton qi. The details of how the struck parton recombines with those partons that did not interact, so as to form physical hadrons, is not well understood. Since partons or quarks are assumed not to exist as real physical particles there must be unit probability for them to transmute into physical hadrons. 

In order to understand the parton model properly one clearly requires a good understanding of the basic lepton-quark process 

We thus begin with a pedagogical example. We study the very simple reaction  

In lowest order perturbation theory of QED the reaction is described by the one-photon exchange diagram shown in Fig. 15.1. 

Using the rules given in Appendix 2 the Feynman amplitude can be written down and has the form 

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In the above, the electron and muon are treated as point-like spin Dirac particles and thus possess only the intrinsic magnetic moments of magnitude eft/2meC and ehj2m c respectively. We now generalize to electron-proton scattering where the proton will be allowed an additional, i.e. anomalous, magnetic moment and will not be considered point-like. 

The next term A mij,/me) has contributions from 469 Feynman diagrams containing v-p loops and/or l-l scattering subdiagrams. They falls naturally into four (gauge invariant) groups according to the way closed electron or muon loops appear in them. 

Comparison of this value with the one obtained from electron-helium nucleus elastic scattering experiments [3] can define the limits of a possible muon-hadron anomalous interaction [4,5]. 

The Mott cross-section is just the cross-section for the scattering of a spin 5 particle in the Coulomb field of a massive (spinless) target. The extra factors in (15.1.19) arise (i) because the target has spin 5 and there is a contribution due to the magnetic interaction between electron and muon, and (ii) because the target has finite mass and recoils. 

In Section 15.6 we introduced the formalism necessary for studying deep inelastic scattering using polarized electron or muon beams on polarized nucleon targets. Here we briefly present the parton model predictions for the structure functions Gi,2 and consider what may be learnt from the experiments with polarized beams and targets. 

Here 7, is the total angular moment of the initial target state indices and are the incident and discrete state energies, respectively to the incident and captured muons. Further it is convenient to use the second quantization representation. In particular, the initial state of the system atom plus free muon can be written as a l final state is that of an atom with the discrete state electron, removed electron and captured muon in further 7 > represents one-particle (IQP) state, and F > represents the three-quasiparticle (3QP) state. The imaginary (scattering) part of the energy shift ImAE in the atomic PT second order (fourth order of the QED PT) is as follows [27,31] ... 

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