All Questions
Tagged with scattering-cross-section special-relativity
13
questions
1
vote
1
answer
37
views
Relative speed in unpolarized cross-section
In section 5.1 of Peskin and Schroeder, we are presented the computation of the amplitude for the $e^+e^-\to \mu^+\mu^-$ reaction and then the computation of the unpolarized cross section. After ...
0
votes
0
answers
268
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Addition of four-momenta in scattering amplitude of nucleon-anti-nucleon pair in scalar Yakuwa theory
Intro
I'm studying QFT using David Tong's lecture notes. In section 3.5 on examples of scattering amplitudes in scalar Yukawa theory, the scattering amplitude $A$ of a nucleon-anti-nucleon scattering ...
6
votes
1
answer
2k
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How to derive the Klein-Nishina formula from the Dirac equation?
I'm looking for the simplest demonstration of the Klein-Nishina formula, from the Dirac equation without the field described as a quantum operator:
https://en.wikipedia.org/wiki/Klein%E2%80%...
- 7,592
1
vote
2
answers
244
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Feynman amplitude and tensor 4-vector multiplication (muon neutrino-electron scattering)
In the calculation of the Feynman Amplitude for the muon neutrino-electron scattering (in the Charged Current way from W boson), or $e + \nu_\mu \rightarrow \nu_e + \mu$ (considering the 4-momentum ...
- 15
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1
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59
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From infinitesimal momentum volume to infinitesimal rapidity & tranverse momentum
I'm trying to derive a relationship given in a paper which is used to obtained a differential cross-section distribution in function of rapidity and transverse momentum of final state particles,
$$
\...
- 125
4
votes
1
answer
400
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Gram determinant for the $2\to 3$ scattering cross-section
I'll repeat the part of my previous question regarding the topic:
There is a book of Byckling and Kajantie, "Particle kinematics", discussing in particular (Chapter V) the kinematics of the $2\to 3$ ...
- 8,901
0
votes
1
answer
852
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Relativistic Scattering
When we work out the relativistic general two-body scattering in the CM frame (like two elementary particles producing two other P1 +P2 -P3 -P4) , the cross section is proportional to absolute final ...
- 1,885
2
votes
1
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361
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Is this statement correct or incorrect: Moving objects undergo length contraction because they appear in space-time cross-section
Why or why not?
This is closely related to another question I posited here, Does it make sense to say that objects moving at relativistic velocities appear in space-time cross-section?
What I mean ...
- 10.4k
2
votes
3
answers
367
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Does it make sense to say that objects moving at relativistic velocities appear in space-time cross-section?
Let object A move at relativistic velocity relative to a frame O. In 4D space-time (Minkowski diagram) the space view of O at any given moment of its own time is a space-like hypersurface (hyperplane, ...
- 10.4k
0
votes
0
answers
91
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Inelastic cross section derivation
I am trying to derive the inelastic cross section (the mass changes). I looked up the elastic derivation on Peskin's book (are there any alternatives?):
$$d \sigma = \frac{1}{2 E_a 2 E_b \left| v_a-...
- 123
17
votes
3
answers
6k
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Is the total cross section a Lorentz Invariant?
In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely:
$$
{1 \over E_{A} E_{B} |v_A - ...
- 2,526
3
votes
2
answers
1k
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How do particle scattering cross sections scale with energy in colliders?
How do particle scattering cross sections scale with energy in colliders?
Particularly photons, electrons, protons, and gold or lead nucleii?
(If necessary, break this into four separate questions.)
...
- 5,759
17
votes
1
answer
3k
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Cross-section in relativistic limit: Fermi's golden rule still valid?
In order to calculate the cross-section of an interaction process the following formula is often used for first approximations:
$$
\sigma = \frac {2\pi} {\hbar\,v_i} \left| M_{fi}\right|^2\varrho\...
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