34
votes
Accepted
How do photons affect each other gravitationally?
One can quantize linearized spacetime perturbations in General Relativity and compute the effect of photons scattering elastically by exchanging virtual gravitons. This theory isn’t consistent at ...
- 52.2k
15
votes
Accepted
Why does Gadolinium have the highest neutron cross section?
Welcome to the world of nuclear physics, where the answer is "It's a little more complicated than that."
Density of the solid
You can rule this out: cross sections are tabulated per target ...
rob♦
- 94.2k
13
votes
How do photons affect each other gravitationally?
Yes. It is possible to treat linearized gravity like a QFT, write the graviton propagator and study the scattering of two photon thought a graviton exchange.
The amplitude, given the momentum of the ...
- 1,094
12
votes
Accepted
What is cross section?
"Who cares"? You care. You are shooting at a swarm of bees of known number density n and depth d (the foil thickness) trying to infer the size (surface area) of each combined with your ...
- 66.3k
10
votes
Why is the laboratory frame energy always greater than the center of mass frame energy?
We need to be precise: the total energy of the system is always greater in the lab frame than the center of momentum frame (unless the lab frame is the same as the center of momentum frame).
If you ...
- 7,331
10
votes
If the probability of a point (photon) hitting another point (electron) is zero why do they interact?
In popular presentations of particle physics you often find the statement that photons and electrons are "point particles", while protons and other composite entities are not. However to ...
- 61.8k
9
votes
Differential Cross Section
Differential cross section is defined to be:
$$ \dfrac{d\sigma}{d\Omega} $$
In plain words, this expression gives the probability that a particle passing through an area of $d\sigma$ before ...
- 313
8
votes
What is cross section?
"Cross section" simply means that the barn is a measure of area; $1$ barn is equal to $10^{-28}$ square metres. It measures the size of the "target" that a neutron (or any other ...
- 60.5k
6
votes
Is the total cross section a Lorentz Invariant?
I present a deviation of the differential cross section, that (at least i hope so) makes things clearer. We rely on the following definition:
$$
\mathrm d P = \mathrm d \sigma \times F.
$$
Here $\...
- 103
6
votes
Accepted
What is the cross-section size of a photon?
How "wide" is a photon,
The photon is a point particle in the standard model of particle physics. It has no extent to be described with "wide". Interactions of photons with charges or magnets can ...
- 235k
6
votes
How to determine the sign of coupling constant in quantum field theory?
By properly redefining the gauge field
$$
eA_\mu \rightarrow A_\mu,
$$
one can reduce the coupling constant to the YM term only,
$$
\sim \frac{1}{4e^2} F^{\mu\nu}F_{\mu\nu}.
$$
Therefore, the absolute ...
- 4,833
6
votes
Why do we refer the cross section ratios to muons?
Muons are easy to measure. They're extremely long-lived relative to most other particles, and they're pretty massive compared to electrons, which means they have substantial penetrating power that is ...
- 35.8k
6
votes
Accepted
Why amplitudes are rational functions?
After the OP explained in the comments what exactly they're looking for, I will attempt an answer. There are a few separate facts that need explanation:
Tree amplitudes are rational functions of ...
- 754
6
votes
Accepted
In particle physics what is the derivation of the mean free path length: $\ell=\frac{1}{n \sigma}$?
As it moves along covering some total travel distance $L$, the particle's motion carves out a tube of length $L$ and cross sectional area $\sigma$, making a volume $L \sigma$. If $n$ is the number ...
- 61.8k
6
votes
Accepted
Trouble deriving expression for differential scattering cross section from $S$-matrix
I did this calculation some time ago myself. Since I am not sure what is your problem precisely I just give you my old notes. As far as I remember they should be fairly detailed and approximately ...
- 1,209
6
votes
Accepted
On the range of validity of General Relativity and Quantum Field Theory in terms of energy and impact parameter (from Rovelli & Vidotto's book)
Yes, OP is right:
From the HUP the region below the hyperbola $$E b \lesssim \hbar c$$
in the $(b,E)$-diagram is in the quantum regime.
For constant COM energy $E$ and growing impact parameter $b$, ...
- 213k
6
votes
What exactly does the quantity $\sigma(\theta)$ represent in scattering problems? What is the interpretation of the differential cross section?
There's a lot of different terminology and notation surrounding cross sections, which can make it difficult to learn the subject. However, fundamentally what is going on is not difficult -- we are ...
- 55.4k
6
votes
Total cross-section for Bhabha scattering
However, the total cross section, obtained by integration over all angels diverges. Why is this so?
The total cross section is infinite because the interaction has infinite range and does not fall ...
- 23.3k
5
votes
Cross Section Peskin vs Srednicki
The formula given by Srednicki
$$d \sigma_{\textrm{CM}} = \frac{1}{64 \pi^2 s } \frac{|\bf{p}'|}{|\bf{p}|}|\mathcal{M}|^2 d \Omega_{\textrm{CM}}$$
is the general result for the CM $2 \to 2$ ...
- 276
5
votes
Accepted
Why does $2\to 2$ scattering cross-section have $E_{CM}^2$ in denominator?
Can we make the general statement that total cross section increases
as $E_{CM}$ decreases for scattering processes?
If the considered QFT is unitary (at least perturbatively), there is a ...
- 8,971
5
votes
Accepted
At what stage is it necessary to introduce a field theory in the regeon-pomeron-odderon model of hadron interactions?
OK, now I have found a partial answer to my own question. I will post it here just in case someone is interested in this topic:
If you are only interested in elastic scattering you do not need any ...
- 457
5
votes
Why is the laboratory frame energy always greater than the center of mass frame energy?
I should say, in this answer I've set $c=1$.
In the centre of mass frame, the total energy is just the rest mass energy of all your particles. If you think about the system collectively (e.g. as a "...
- 2,456
5
votes
Accepted
Mass dimension of an $n$-particle scattering amplitude in 4D
The claimed result $[A_n]=4-n$ is correct, and so is the reasoning of Helvang and Huang in the quoted text in the OP. Notice that $n$ is the total number of particles involved in the process, the in+...
- 5,192
5
votes
Expected number of events at a neutrino telescope
The paper does not say that this is the number of detected events, it says that the "number of events scales as". Whether it is exact depends on how you specify the flux and the cross-section.
If the ...
- 137k
5
votes
Accepted
Conservation of angular momentum in pair annihilation in scalar QED
Given the infinitesimal version of rotation:
\begin{equation}
\frac{\partial \phi}{\partial \theta}
= \left({\cal{J}}_z\right)^\mu_{\; \nu} x^\nu \left( \partial_\mu \phi \right)
= x \partial_y \phi - ...
- 1,450
5
votes
Accepted
Why does the term $i\epsilon^{\alpha\mu\beta\nu}p_{\alpha}q_{\beta}$ vanish in the squared amplitude of the top decay?
In your expression, you have a term of the form
$$I = \epsilon^{\alpha \mu \beta \nu} S_{\mu\nu}$$
where $S_{\mu\nu} = - g_{\mu\nu} + k_\mu k_\nu / m_W^2$ is a symmetric tensor. The contraction of an ...
- 105k
5
votes
Accepted
Why do we refer the cross section ratios to muons?
To first order, muon pair production:
$$ e^+ + e^- \rightarrow \mu^+ + \mu^- $$
only proceeds via the $s$-channel. That is, the electron position pair annihilate into a virtual photon or Z-boson, ...
- 39.6k
5
votes
Accepted
Unitarity and amplitudes
Unitarity ($SS^\dagger = 1$) dictates that
\begin{equation}\label{key}
T-T^\dagger = iTT^\dagger
\end{equation}
For tree-level $2\rightarrow 2$ scattering, we have then that
$$
\langle p_1,p_2|T|p_3,...
- 2,494
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