All Questions
Tagged with quantum-chromodynamics renormalization
76
questions
3
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0
answers
86
views
Is the starting distribution in the solution of DGLAP IR-bare?
On p.27 of this paper by John Collins, he says that when defining PDFs in terms of partonic number operators, one acquires an IR-divergent bare PDF (eq. 52). The residue of the IR-divergent term is ...
- 1,187
1
vote
1
answer
157
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How do you reconcile quark masses with notion of confinement?
In trying to understand exactly what confinement means, I have been reading 't Hooft s original paper on 2D QCD at large $N$. In the paper he shows that the quark propagator pole is moved to infinity, ...
- 744
5
votes
1
answer
375
views
How can we tell a theory is confining?
Physically, I understand what it means for a theory to be confining. The elementary particles are not observable, but only composite particles are. The classic example is QCD, where quarks are ...
- 3,514
0
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288
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Intuition for Asymptotic Freedom
In QED, the $\beta$-function has a positive sign. This means that the coupling increases at higher energies, or equivalently, smaller length scales. This picture is made intuitively clear by the ...
user240990
3
votes
2
answers
681
views
1
vote
1
answer
305
views
What does QCD look like in higher dimensions?
It was pointed out as a comment on my question on atomic physics in higher dimensions that that question implicitly rests on an assumption that QCD, and thus the structure of atomic nuclei, is pretty ...
- 2,196
3
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0
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324
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A Question about Wave-Function Renormalization Factor in SQCD
Here, I have a question about the one-loop computation of the wave-function renormalization factor in SQCD.
According to Seiberg duality, the following electric $\mathrm{SQCD}_{e}$
\begin{gather}
...
- 2,923
5
votes
0
answers
180
views
Instantons, renormalization, and the Schwinger Model
Instantons in QCD contribute to the up, down, and strange quark masses (see, e.g., Georgi and McArthur (1981) or Kaplan and Manohar (1986)). Some papers claim that this contribution is equivalent to ...
- 1,783
5
votes
1
answer
185
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Would Color Confinement apply in higher dimensions?
As I understand it color confinement comes from the fact that as the distance between two color charges increases the color potential energy increases, instead of decreasing, and the energy needed to ...
- 2,001
1
vote
1
answer
232
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Why does literature list the strong coupling at the scale of the Z-boson's mass?
In the 2004 edition of the book "QCD as a Theory of Hadrons" by S. Narison, the author provides a value for the strong coupling at a scale of the mass of the Z boson,
$$ \alpha_s (M_Z) = 0.1181 \pm ...
- 2,648
0
votes
0
answers
177
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Question about DGLAP evolution equation
I am reading chapter 32.2 of Schwartz's QFT book, where he defines the renormalized PDFs $f_i(x, \mu)$. This leads to an equation (32.48), which relates PDFs at different scales $\mu, \mu_1$:
$f_i(x,\...
- 1,129
0
votes
0
answers
119
views
Renormalization of interaction parameter in QCD
In my book of QCD, when talking about renormalization, the author mentions the difference between QED and QCD:
In QED, the interaction paramenter $\alpha$ of renormalization factor $\mu$ and ...
- 269
2
votes
0
answers
106
views
How to get group U(1) from SU(N)?
I have read that the unitary group is somehow given by the direct product $U(N)=U(1)*SU(N)$ and it follows that for $N$ going to zero we get just $U(1)$.
How it can be possible? What does it mean $SU(...
- 479
4
votes
0
answers
514
views
Can the On-Shell Scheme be used for QCD?
I am reading a textbook on QFT and it mentions that the on-shell scheme cannot be used for QCD.
Could someone explain the on-shell renormalization scheme in a bit more detail, plus why QCD cannot be ...
- 1,410
5
votes
2
answers
530
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What is relevant for Yang-Mills theory below $d = 4$?
There are two ways to write the Lagrangian for Yang-Mills, differing by the scaling of the Yang-Mills field. Fancy theorists tend to write
$$S = \int d^dx \, \frac{1}{4e^2} \, \text{tr}(F^2)$$
while ...
- 103k