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TriTertButoxy
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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
with
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!
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]
[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!
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