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Re: electron-electron vs electron-positron

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On 10/20/2015 4:12 PM, Daniel S. Riley wrote:
> Odd Bodkin <bodkinodd@gmail.com> writes:
>> In QED, I've always been a little muddled on how to tell the
>> difference between electron-electron and electron-positron
>> scattering. There's an s-channel 1st-order diagram that's present for
>> the latter that's not there for the former.
>
> Moller (electron-electron) scattering also has a u-channel tree-level
> diagram that doesn't appear in Bhabha (electron-positron) scattering.

But I thought crossing symmetry irons that out. Although I do think 
there are those Z-mediated diagrams that provides an asymmetry in Moller 
that isn't in Bhabha, right?

Bhabha has a t-channel and s-channel, Moller has a u-channel and a 
t-channel.

Oh, yes, I see it now.
Bhabha differential cross section is
d(sigma)/d(cos(theta)) = (pi*alpha^2 /s)[(s/t)^2 + (t/u)^2 + (u(1/t + 
1/2))^2.
So to get the Moller you do u<->s.
And then there is the phase space factor of 2 for identical particles in 
Moller.

> In addition (and related), with electron-electron the particles are
> identical so the labels on the final state are ambiguous.
>
>> But if were going to ask what's the scattering cross section at a
>> particular angle with respect to incident angle, I've been under the
>> impression that the two cases are essentially identical, even though
>> the bending of the incident particle is due to repulsion in the first
>> case, and due to attraction in the second case.
>
> AIUI, s vs. u channel does noticeably change the differential cross
> section, particularly at very small and large angle scatters, with
> much more very large angle scatters for electron-electron.

I will have to plot that up to see! I would have thought from a 
Rutherford-style argument that the closer the impact parameter, the more 
large-angle scattering you'd get.

> I think
> this is consistent with your observations about the classical effective
> potential.  I don't think this is directly observable because of the
> labeling ambiguity (can't tell large from small angle scatters), but I'd
> guess it has some observable consequences.

I suppose to do this right, we should do a calculation with one of the 
particles very heavy (probably doing it in a frame where the heavy 
particle is at rest for convenience, though it shouldn't matter). Then 
the identical particle factor of 2 goes away.

>
> dunno if that helps any, been a long time since I did any actual QED.

It does! Thanks so much for your reply. Breath of fresh air around here.

>
> -dan
>


-- 
Odd Bodkin --- maker of fine toys, tools, tables

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Thread

electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-19 10:50 -0500
  Re: electron-electron vs electron-positron "reber g=emc^2" <herbertglazier0@gmail.com> - 2015-10-19 09:51 -0700
  Re: electron-electron vs electron-positron dsr@mail.lns.cornell.edu (Daniel S. Riley) - 2015-10-20 17:12 -0400
    Re: electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-20 17:25 -0500
  Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 01:14 +0000
    Re: electron-electron vs electron-positron Poutnik <poutnik4nntp@gmail.com> - 2015-10-21 07:28 +0200
      Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 05:48 +0000
        Re: electron-electron vs electron-positron Poutnik <Poutnik4NNTP@gmail.com> - 2015-10-21 12:27 +0200
    Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-20 22:32 -0700
      Re: electron-electron vs electron-positron "Raymond Luxury Yacht" <invalid@example.com> - 2015-10-21 22:23 -0700
        Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-22 02:39 -0700
      Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-22 02:57 -0700
        Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-22 23:04 -0700
    Re: electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-21 07:31 -0500
      Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 16:15 +0000
        Re: electron-electron vs electron-positron Poutnik <Poutnik4NNTP@gmail.com> - 2015-10-21 20:04 +0200
          Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 19:50 +0000
            Re: electron-electron vs electron-positron Poutnik <poutnik4nntp@gmail.com> - 2015-10-21 22:02 +0200
            Re: electron-electron vs electron-positron Poutnik <poutnik4nntp@gmail.com> - 2015-10-22 08:01 +0200
              Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-22 14:30 +0000
                Re: electron-electron vs electron-positron Poutnik <Poutnik4NNTP@gmail.com> - 2015-10-22 16:49 +0200
        Re: electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-21 15:59 -0500

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