All Questions
Tagged with quantum-chromodynamics renormalization
76
questions
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
1
vote
0
answers
33
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, ...
- 1,452
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
$$i\Sigma(p)=i\frac{\alpha_s}{4\pi}C_F/\!\!\!{p}\left[\frac{1}{\varepsilon_{\text{UV}}}-\gamma+\ln(4\pi)+1+\ln(\...
- 172
0
votes
1
answer
81
views
Possible cases of matter fields for $SU(2)$ theory which retains asymptotic freedom?
Let us assume $4$ spacetime dimensions.
QCD, the $SU(3)$ gauge theory with quarks as the matter fields, have the asymptotic freedom property as long as there are 16 quark flavors of mass below the ...
- 1,665
1
vote
0
answers
67
views
Deriving Euler-Lagrange Equations in Light-Front Quantization from the Heisenberg Equation
I'm delving into light-front quantization, with a focus on understanding the roles of good and bad fermions. Using Collins' formulation in Foundations of Perturbative QCD, we define the projectors as:
...
- 11
2
votes
1
answer
252
views
Why does non-perturbative QCD need to be regularized and renormalized?
The $n$-point correlation functions of QCD, which define the theory, are computed by performing functional derivatives on $Z_{QCD}[J]$, the generating functional of QCD,
$$\frac{\delta^nZ_{QCD}[J]}{\...
- 343
3
votes
0
answers
72
views
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
1
vote
1
answer
159
views
Asymptotic Freedom and the Continuum Limit
Suppose I have a family of effective field theories, parametrized by a cut-off $\Lambda$ and a coupling constant $g$ and specified in terms of generating functionals $Z_{\Lambda,g}(J)$. Asymptotic ...
- 156
3
votes
1
answer
120
views
Renormalization of quark bilinears
I'm looking at the one-loop corrections to the amputated quark two-point functions ($\Gamma_i$) with insertions of quark bilinears (indexed by $i\in\{S,P,V,A,T\}$) with off-shell legs in Euclidean QCD....
- 71
0
votes
0
answers
242
views
One-loop renormalization of the gauge coupling
Quoting Yuji Tachikawa, chapter 3 of "${\cal N}=2$ Supersymmetric Dynamics for Pedestrians":
Recall the one-loop renormalization of the gauge coupling in a general Lagrangian field theory $$...
user242231
2
votes
1
answer
84
views
Expansion at first order ${\cal O}(\alpha_s)$ in counterterms for the QCD vertex renormalization at 1-loop
What is the meaning of the expansion at first order ${\cal O}(\alpha_s)$ in $\delta_2$ and $\delta_3$ at the second step in the last line? These quantities are not "small" - on the contrary,...
- 152
1
vote
0
answers
279
views
Tadpole diagram in one-loop QCD gluon self-energy renormalization
I am trying to study QCD renormalization at 1-loop order. So, when I take into account the gluon self-energy corrections, the book I am studying from says that there are three diagrams who contribute ...
- 21
1
vote
1
answer
105
views
Why is there still disagreement over the mass of the bottom (or beauty) quark, but none of the others?
Wikipedia (among other places) lists two values for the alleged mass of the B quark, 4.18 and 4.65 GeV.
Only one of the two possible masses listed has a link to another Wiki page explaining the ...
- 4,515
1
vote
1
answer
253
views
What are all the 1PI gluon 3-point function Feynman diagrams at 1-loop?
As an exercise in renormalization, I want to calculate the divergent part of the gluon 3-point function and gluon 4-point function matrix element. What are all the 1PI one-loop Feynman diagrams?
- 2,599
2
votes
1
answer
276
views
Is there a simple explanation of why coupling constants run with $\log(E)$?
The inverse coupling constants run with $\log(E)$, where $E$ is the energy or four-momentum.
Some coupling constants increase, some decrease with $\log(E)$.
Is there a simple argument that explains ...
user85598