1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    [tex]A=\frac{\sigma_R-\sigma_L}{\sigma_R+\sigma_L}\,,[/tex]​

    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

    [tex]A=\frac{6}{5}\left(\frac{\sqrt{2}Gk^2}{e^2}\right)\left(a_1+a_2\frac{1-(1-y)^2}{1+(1-y)^2}\right)\,,[/tex]​

    with

    [tex]a_1=c_A^e(2c_V^u-c_V^d)[/tex]
    [tex]a_2=c_V^e(2c_A^u-c_A^d)\,.[/tex]​

    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

    [tex]\frac{d\sigma}{d\Omega}(\text{e}_R\text{u}_L\rightarrow\text{e}_r\text{u}_L)=\frac{\alpha^2}{4s}(1+\cos\theta)^2|Q_u+rc_R^ec_L^u|^2\,,[/tex]​

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Halzen and Martin Problem 13.12
  1. Lagrangian problem (Replies: 0)

  2. Diffraction problem II (Replies: 0)

  3. Problem is. (Replies: 0)

Loading...