[E12-15-001] transformation from invariant frame to lab coordinate

[Marie Boer]

  Dear all, 

I calculated the Jacobian of the transformation from invariant frame to lab frame, which I need if I would like to cross check cross sections. 
I assumed cross sections are differential in solid angle and energy of scattered electron, in theta_CM of the photons and in phi(lepton vs photon plane). i.e. the phase space: dE'dΩ'dcos(Θ)dφ. Please correct me if this is wrong.
My code is using cross sections differential in x_b, Q², t and phi, i.e. phase-space: dxdQ²dtdφ.

I attached my calculations. 

Could someone please redo these calculation to check if I am correct? I have not done such calculation in a while and I would like to make sure of my result.

Thank you very much, 

Marie
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