All Questions
Tagged with scattering kinematics
20
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Relation bitween Mandelstam Variables in three-body final state
What is the relation between Mandelstam variables in the three body final state?
There are 5 independent Mandelstam variables. What is the relationship between them?
- 11
0
votes
1
answer
63
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How to Express the Cross Section of a Three-Body Final State Scattering in Terms of Invariant Masses $s_{ij}$?
I'm working on calculating the cross section for a scattering process that results in three bodies in the final state. My goal is to express the cross section in terms of the invariant masses $s_{ij}$...
- 11
1
vote
1
answer
72
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Inconsistency in the $2\to 2$ kinematics
I must be confusing something horribly, because this should be very simple, but I am keep getting inconsistent results in the basic 2->2 scattering kinematics.
Let the process be $$a(p_1) + b(p_2) \...
- 857
4
votes
1
answer
142
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How many relativistically invariant degrees of freedom in $n$-particle scattering?
Suppose we have a scattering process with $n$ external legs with four-momenta $p_1, \cdots, p_n$. Naively there are $4n$ degrees of freedom, however most of these putative degrees of freedom are not ...
- 858
1
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Discontinuities in the $u$ channel
if we consider a 2-to-2 scattering, we have normally an $s$ channel a $t$ channel and $u$ channel. In CMS frame $s$ is positive and $t$ and $u$ negative, by crossing symmetry there are kinematics ...
- 41
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93
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While defining the Mandelstam variables, we take only certain 3 combinations of the momentum vectors. Why not other combintions?
While defining the Mandelstam variables for a process, we only take these three combinations of the momentum vectors:
\begin{equation}
(p_1 + p_2)^2, (p_1 - p_3)^2, (p_1 - p_4)^2
\end{equation}
My ...
- 392
0
votes
1
answer
69
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Denominator scattering amplitude
I try to calculate the scattering amplitude of a process $A + A \rightarrow B + B $ in lowest order contribution.
For one part of the amplitude $M$ i got: $$M=\frac{g^2}{(p_4-p_2)^2-m_C^2}$$
We are ...
- 3
1
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1
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167
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On relativistic kinematics of particle accelerators
While reading these lectures I came across the following
Putting together the first two formulae one reads $M=E_{cm}$, or equivalently, the centre of mass is always at rest. But is it true? It might ...
- 1,644
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0
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145
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Running of the fine structure constant
In Measurement of the Running of the Fine-Structure Constant, the L3 collaboration reports their fine structure constant data for various values of momentum transfer which they call $Q^2$. This is ...
- 713
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109
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In a $2 \rightarrow 2$ scattering, is the matrix element always momentum-independent?
I have the same problem as in this question.
Basically the problem is that it looks like the scattering amplitude is being pulled out of the momentum-integrals even though it might not be momentum-...
1
vote
1
answer
177
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Why Mandelstam variables in Minkowski do not cover the whole allowed space?
It was mentioned by N.Arkani-Hamed https://www.youtube.com/watch?v=uPrlD0vorzk that Mandelstam variables in Minkowski signature $(+---)$ do not cover that whole allowed space of $s$, $t$, whereas in ...
- 4,883
0
votes
2
answers
1k
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Calculating the charge density from a form factor
For an atomic form factor $F(\textbf q)$, the corresponding charge density distribution is given by
$$ \rho(\textbf r) = \frac{1}{(2\pi)^3}\int\text{d}^3 \textbf q \,F(\textbf q)\,\text{e}^{-\text{i}\...
- 2,648
2
votes
1
answer
2k
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Equivalence between $t$ and $u$ channels
Reading about QFT diagrams, I've seen examples like Bhabha scattering where the channel $u$ wasn't necessary due to the final states are distinguisable for being made of the different particles and ...
- 1,597
2
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1
answer
158
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How does one prove the channel independent inequality satisfied by the product of the three Mandelstam variables?
How does one prove the following equation (67.5) from the BLP Quantum Electrodynamics book? The q's are the 4 momenta, and h is the sum of all four masses. Two q's written after one another in the ...
- 21
-1
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1
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75
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Compton Scattering Assumption: $p^2=m^2$ for electron and $k^2=0$ for photon?
In section 5.5 of Peskin, the book assumes that $p^2=m^2$ for electron and $k^2=0$ for photon. Why can we assume this?
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