All Questions
43
questions
1
vote
1
answer
83
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
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
$$i\Sigma(p)=i\frac{\alpha_s}{4\pi}C_F/\!\!\!{p}\left[\frac{1}{\varepsilon_{\text{UV}}}-\gamma+\ln(4\pi)+1+\ln(\...
- 172
0
votes
1
answer
81
views
Possible cases of matter fields for $SU(2)$ theory which retains asymptotic freedom?
Let us assume $4$ spacetime dimensions.
QCD, the $SU(3)$ gauge theory with quarks as the matter fields, have the asymptotic freedom property as long as there are 16 quark flavors of mass below the ...
- 1,669
1
vote
0
answers
67
views
Deriving Euler-Lagrange Equations in Light-Front Quantization from the Heisenberg Equation
I'm delving into light-front quantization, with a focus on understanding the roles of good and bad fermions. Using Collins' formulation in Foundations of Perturbative QCD, we define the projectors as:
...
- 11
2
votes
1
answer
256
views
Why does non-perturbative QCD need to be regularized and renormalized?
The $n$-point correlation functions of QCD, which define the theory, are computed by performing functional derivatives on $Z_{QCD}[J]$, the generating functional of QCD,
$$\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
163
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 ...
- 155
1
vote
1
answer
255
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
3
votes
1
answer
304
views
Renormalization group applied to a simple QCD problem
Consider page 551 of Peskin & Schroeder's book on QFT, where he is treating the process $e^{+}e^{-} \to \text{Hadrons}$. I have 3 misunderstandings regarding some lines of thought effected there:
...
- 1,742
2
votes
1
answer
576
views
Dependence by the renormalization scheme in the beta function coefficents in QCD
Given the coupling costant $\alpha_s$ of QCD and it's RGE equation $\frac{d\ln \alpha_s(\mu^2)}{d\ln\mu^2}=\beta(\alpha_s)$, with $\beta(\alpha_s)=-\beta_0\alpha_s-\beta_1\alpha_s^2 -\beta_2\alpha_s^3+...
- 823
3
votes
0
answers
124
views
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: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
0
votes
0
answers
71
views
5d nonabelian gauge theory or 5d QCD explicit $\beta$-function
Question: Are there some derived $\beta$-function formula
$$
\beta(g) = \frac{\partial g}{\partial \log(\mu)}
$$ for nonabelian gauge theory in the 5-dimensional spacetime at some energy scale $\mu$ ...
- 7,848
1
vote
0
answers
59
views
What is mass factorisation?
I know that for some observables in QCD, e.g. inclusive DIS cross sections, one can use factorisation by writing said observable as a convolution of hard scattering coefficients with PDFs. But what is ...
- 1,187
0
votes
0
answers
121
views
Negative running coupling constant in QCD?
Considering the one-loop running coupling constant in QCD:
$$\alpha_s(\mu) = \frac{a_s(\mu_0)}{1 + \frac{33-2f}{6 \pi}ln\left( \frac{\mu}{\mu_0}\right)}$$
where f is the number of quarks flavours with ...
- 585
0
votes
0
answers
179
views
QCD quark self-energy, is the propagator momentum in the right direction?
For the quark self-energy diagram the amplitude is giving by:
The fermion propagator is given by $\frac{i}{\not p + l}$ in the lecture. It is not supposed to be $\frac{i}{\not p - l}$? It's seems ...
