All Questions
Tagged with quantum-chromodynamics renormalization
33
questions with no upvoted or accepted answers
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
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
4
votes
0
answers
512
views
Beta function for non-Abelian gauge theory with both fermionic and bosonic matter fields
Consider a non-Abelian gauge theory with both fermionic $\psi$ and bosonic $\phi$ matter fields in 4D, which may be called a QCD-Higgs model,
$$L=-\frac{1}{4 g^2}F_{\mu\nu}F^{\mu\nu}+\bar{\psi}i\gamma^...
- 11.9k
4
votes
0
answers
322
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Why is QCD hard to solve if I know the beta functions?
Why is it still hard to solve QCD if we know the beta functions of the coupling? Aren't only the loops causing problems? And am I not able to write every possible interaction exact at tree-level with ...
- 2,147
4
votes
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104
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Does the number of left handed chiral quark superfields always equal half the number of quark flavours?
In Weinberg's "The Quantum Theory of Fields Vol III" page 267 we're told that $n_f = 2N_f$. Where $n_f$ are the number of flavours and $N_f$ is the number of left chiral quark superfields (...
- 1,978
3
votes
0
answers
72
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Renormalizability of massless Gross-Neveu theory
We have the following Lagrangian density:
$$ \mathcal{L} = \bar{\psi}_i i \gamma^\mu \partial_\mu \psi_i
+ \frac{g^2}{2} \left( \bar{\psi}_i \psi_i \right)^2 $$
which corresponds to the two-...
- 1,124
3
votes
0
answers
124
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The 1-loop anomalous dimension of massless quark field for $SU(N)$ gauge theory with $n_f$ quark flavours
Considering $SU(N)$ gauge theory with $n_f$ massless quarks
I want to find the anomalous dimension to order of 1-loop of the massless quark field, that defined by: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
3
votes
0
answers
86
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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
3
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0
answers
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
3
votes
0
answers
415
views
Effective Field Theories of QCD
Recently, I am studying the online course Effective Field Theory provided by MIT OCW. Prof. Stewart gives a nice picture to summarize the effective theories:
As a newbie in this field (I only have a ...
- 1,701
2
votes
0
answers
106
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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
2
votes
2
answers
77
views
Error estimation of $\alpha_s$
I have calculated the strong coupling constant $\alpha_s$ using and approximate solution of the Renormalization Group Equation
$$\mu_R^2\frac{d\alpha_s}{d\mu_R^2}=-(b_0 \alpha_s^2 + b_1\alpha_s^3 + ...
- 21
2
votes
0
answers
504
views
Mass and wave function renormalization In chiral perturbation theory
Before I put forward my actual question, I think it will be useful to set the context in a clear way and that involves my understanding of a few very basic things of Chiral Perturbation Theory.
...
- 407
1
vote
0
answers
35
views
Evidence of more generations in the QCD beta function
We know that the beta function for QCD is
$$
\beta = -\left(11 - \dfrac{2N_f}{3}\right),
$$
where $N_f$ is the number of fermions in the theory. We have $\beta_{\text{SM}} = -7$.
Now, my question is, ...
- 1,611
1
vote
0
answers
67
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Deriving Euler-Lagrange Equations in Light-Front Quantization from the Heisenberg Equation
I'm delving into light-front quantization, with a focus on understanding the roles of good and bad fermions. Using Collins' formulation in Foundations of Perturbative QCD, we define the projectors as:
...
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