How Do You Calculate Cross Sections in Electron-Neutrino Scattering?

  • #1
unscientific
1,734
13

Homework Statement


[/B]
(a) Find the ratio of cross sections.
(b) Find the cross section for electron-neutrino scattering by first writing down relevant factors.
2011_B4_Q8.png


Homework Equations

The Attempt at a Solution



Part (a)[/B]
These represent the neutral current scattering for the muon-neutrino and neutral/charged scattering for electron-neutrino. Feynman diagrams are given by
2011_B4_Q8_2.png


Given that there are 2 possibilities for the electronic case, I say ##R = 2##?

Part (b)

Propagator factor is given by ##\frac{1}{P \cdot P - m_w^2}## which in the zero-momentum frame is ##\approx \frac{1}{m_w^2}##.
There are two vertices, so another factor of ##g_w^2##.
Thus amplitude is ##\frac{g_w^2}{m_w^2}##.
By fermi's golden rule, ##\Gamma = 2\pi |M_{fi}|^2 \frac{dN}{dE_0}##.
Cross section is ##d\sigma = \frac{\Gamma}{v_e}##.

How do I proceed?
 
Physics news on Phys.org
  • #2
Correct me if I'm wrong but it seems the course asks you to do things you haven't seen in class. If that's the case, these lecture notes might help http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf
It's been a while since I've computed cross-sections. If I see something better I'll let you know.
 
  • #3
thierrykauf said:
Correct me if I'm wrong but it seems the course asks you to do things you haven't seen in class. If that's the case, these lecture notes might help http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf
It's been a while since I've computed cross-sections. If I see something better I'll let you know.
I'm looking for a hand-wavy approach in the sense we avoid explicitly calculating the feynman probabilities.

I think the density of states is something like: ##\frac{dN}{dE_0} = \frac{dN_e}{dp_e} \frac{dp_e}{dE_0} = \frac{1}{(2\pi)^6} p_e^2 dp_e \frac{dp_e}{dE_0} ##. How do I proceed?
 
  • #4
bumpp
 
  • #5
Sorry I've been busy! Didn't find time to reply more. I know better what kind of answer is needed. I'll try to post later today.
 
  • #6
bumpp
 
  • #7
As I remember you integrate over angle but not over momenta at tree level.
 
  • #8
thierrykauf said:
As I remember you integrate over angle but not over momenta at tree level.

So How do I find the cross section at tree level feynman diagrams?
 
  • #9
For each tree diagram you have a coupling constant at each vertex, a delta function that says momentum is conserved so inner momentum, that of the Z or W is fixed, because in and out particles are on-shell. So the integration over d3p, 3d momentum. becomes integral over solid angle omega. Let me know if this helps. http://www.iop.vast.ac.vn/theor/conferences/vsop/18/files/QFT-6.pdf
 
Back
Top