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Halzen and Martin Problem 13.12

  1. May 1, 2007 #1
    Hi. We just finished the chapter on electroweak interactions. So it turns out that QED processes gets altered by the weak neutral current (exchange of Z boson) which introduces a tiny parity-violating asymmetry.

    There is an experiment which measures the minute parity-violating asymmetry in the inelastic scattering of longitudinally polarized electrons off nuclear targets. The asymmetry is defined by


    where [itex]\sigma_R[/itex] is the cross section [itex]d\Omega/dy[/itex] for [itex]\text{e}_R\text{N}\rightarrow \text{e}_R\text{X}[/itex]; [itex]\text{e}_R[/itex] denotes a right-handed electron.

    For the deep inelastic scattering process [itex]\text{eN}\rightarrow\text{eX}[/itex], we can use the parton model to predict the asymmetry.

    I need help on the following problem.
    Taking [itex]\text{N}[/itex] to be an isoscalar target, show




    Here, [itex]y=(E-E')/E[/itex] is the fractional energy loss of the electron in the lab frame. Constants [itex]c_V[/itex] and [itex]c_A[/itex] are the vector and axial coupling constants of the Z bosons.

    I may assume [itex]k^2\ll M_Z^2[/itex] and the target contains equal numbers of up and down quarks since it is an isoscalar target (and neglect antiquarks).

    Here's what I've done.
    I know the idea is to consider is helicity case separately and combine the everything at the end. But, I'm a little shaky on the Parton model to do this. For example, the cross section of electron-quark scattering is


    where [itex]r=-\sqrt{2} Gk^2/e^2[/itex].

    If anybody can help me with this, that woud be great!
    Last edited: May 1, 2007
  2. jcsd
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