All Questions
Tagged with quantum-chromodynamics quantum-field-theory
399
questions
3
votes
0
answers
103
views
The commutation relations of photon and gluon?
In QED, the photon field has the following commutation relations:
\begin{equation}
[A^{\mu}(t,\vec{x}),A^{\nu}(t,\vec{y})]=0, \tag{1}
\end{equation}
where $A^{\mu}(t,\vec{x})$ is the photon filed. ...
- 85
1
vote
1
answer
74
views
Asymptotic Freedom QCD
I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
- 15
0
votes
0
answers
29
views
QCD parton shower hard scale
Currently I'm studying parton showers from QCD and I'm having trouble with understanding how the hard scale $Q$ is related to the virtuality and energy of the parent parton. The Sudakov factor $\Delta(...
- 291
2
votes
1
answer
36
views
Why does an all connected diagram contribute to two-point function?
I am recently reading E.Witten's review for $1/N$ expansion of QCD. In there, considering the main contribution of quark bilinears like $\bar{q}q$, then He mentions that in free field theory there is ...
- 31
0
votes
1
answer
58
views
Visualization of a gauge field with non-null winding number
In QCD you may add the term $\mathcal{L}_{\theta} = \theta\dfrac{g^2}{16\pi^2} \text{Tr}F\tilde{F}$, which turns out to be a total derivative. Now, it can be proven that the action of this lagrangian ...
- 1,452
3
votes
1
answer
65
views
How is the mass distributed in ordinary matter?
How is the mass distributed in ordinary matter?
In the ordinary things around us, we know that most of the mass is in the cores of the atoms, the electrons around it contributing only a very small ...
- 4,673
4
votes
2
answers
666
views
Ghosts in QCD Lagrangian
The QCD Lagrangian is
$$
\mathcal{L}_{\text{QCD}} = -\dfrac{1}{2} \text{Tr}\, G_{\mu\nu}G^{\mu\nu} + \sum_i^{N_f} \bar{q_i} \left(i \gamma^\mu \mathcal{D}_\mu - m_i\right)\,q_i, \tag{1}
$$
where $\...
- 1,452
1
vote
0
answers
52
views
Colour Factor in QCD Pair Annihilation
My question occurred when I was reading Introduction to Elementary Particles by David J. Griffiths. In chapter 8, part 8.5, he is calculating the colour factor of quark-antiquark annihilation.
My ...
- 81
2
votes
1
answer
104
views
Motivation for the shape of the theta vacua
I understand that the reason why we construct the theta vacua is because instantons allow tunnelling between different vacuum states, $\left|n\right>$. This means that we have to consider a real ...
- 1,452
1
vote
1
answer
56
views
Euclidean LQCD not on a lattice?
How much the idea of calculating Euclidean path integrals in LQCD is fundamentally tied to using formulations based on the discretized spacetime lattice?
In computational approaches to quantum many-...
- 2,921
2
votes
1
answer
105
views
How does the on-shell (OS) scheme work if we assume mass to be zero?
When calculating the self-energy correction of a massless quark up to one loop, I get
$$i\Sigma(p)=i\frac{\alpha_s}{4\pi}C_F/\!\!\!{p}\left[\frac{1}{\varepsilon_{\text{UV}}}-\gamma+\ln(4\pi)+1+\ln(\...
- 172
0
votes
0
answers
45
views
Can $\gamma^5$ matrices be ignored in $q\bar{q}\to ZZ$ processes?
In the $q\bar{q}\to ZZ$ process, the following Feynman diagram in LO appears:
This means for each vertex, the Feynman amplitude contains a term proportional to $(g_V-g_A\gamma^5)$, which makes $D$-...
- 172
1
vote
0
answers
71
views
What is the meaning of twist in OPE?
In Operator Product Expansion (such as explained in Peaking) there appear a quantity for an operator called twist, defined to be $d-s$ where $d$ is the scaling dimension of the operator and $s$ is it'...
- 41
0
votes
0
answers
133
views
Deriving gluon propagator in axial gauge
I am currently checking my work against an answer and I understand most of it except I am having difficulty understanding the signs in a particular part. The question is as follows:
(a) Derive the ...
- 90
1
vote
1
answer
57
views
When can colour charge indices be equated?
I'm currently studying QFT and QCD for the first time and I have a question about the colour charge indices given below. I was asked the following question:
(a) Derive the Feynman rule for the 3-...
- 90