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  • Print publication year: 2020
  • Online publication date: May 2020

Chapter 9 - Neutrino and Electron Scattering from Point Particles

Summary

Introduction

We have seen in Chapter 8, that the standard model for the leptons developed by Salam [37] and Weinberg [157], which was later extended to the quark sector by Glashow [64], unifies weak and electromagnetic interactions. It predicts, in a unique way, the interaction Lagrangian for charge changing (CC) weak interactions of leptons and neutrinos of all flavors with charged gauge vector bosons, W± and the electromagnetic interactions of charged leptons with photons. It also predicts the existence of neutral current(NC) weak interactions of charged leptons and neutrinos of all flavors with the neutral gauge boson, Z0. The strength of the interaction of the charged, neutral, and electromagnetic currents with the W±, Z0, and A gauge bosons are described in terms of the weak coupling constants g, electromagnetic coupling constant e, and a free parameter θW called the weak mixing angle. Specifically, the interaction Lagrangian discussed in Chapter 8 is written here again as:

where Zμ, and Aμ are the charged, neutral and electromagnetic gauge fields and

with is the fine structure constant. In the following sections, we use the interaction Lagrangian in Eq. (9.1) to calculate the cross sections for some weak and electromagnetic processes using point particles, that is, charged leptons and neutrinos.

Scattering

This scattering process can take place through an electromagnetic process mediated by a virtual photon as well as by the weak neutral current mediated by a Z0 boson in the standard model [400].

When an electron interacts with a photon field (Figure 9.1(a)), the interaction Lagrangian is given by:

and when it interacts with the Z0 boson field (Figure 9.2(a)), the Lagrangian is given by:

Using the aforementioned Lagrangians corresponding to Figure and following the Feynman rules the transition amplitude for the process

mediated through virtual photon exchange of momentum in the lowest order, may be written as:

and for the process mediated through the virtual Z0 exchange, shown by the Feynman diagram in Figure 9.2(b) as:

where. The process proceeding through Z0 is highly suppressed as compared to the photon exchange therefore, in the present case, we present the cross section for the process given in Eq. (9.7) mediating through -exchange.