All Questions
12
questions
1
vote
0
answers
76
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
2
votes
0
answers
50
views
When to consider and when not to consider the loop contributions from light quarks?
Consider the following Lagrangian:
$$
\tag 1 \mathcal{L} = \frac{\partial_{\mu}a(x)}{f}\sum_{q}\bar{q}\gamma^{\mu}\gamma_{5}q
$$
This is a Lagrangian of the axion-like particles (ALPs) $a$ interacting ...
- 8,901
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
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
0
votes
0
answers
42
views
How to expand the QCD loops in terms of infrared scale for matching with heavy quark effective field theory
According to Manohar:"argument applies almost without change to a practical example,the derivation of the HQET Lagrangian to one-loop."
on page 37 of the following paper on effective field ...
- 1,268
1
vote
0
answers
307
views
Calculating the pion decay constant in Chiral Perturbation Theory
I am trying to calculate the pion decay constant by following this paper [arXiv].
Since the decay constant is defined via
$$ \langle 0| A_\mu (0) | \phi(p)\rangle = \text{i} p_\mu F_0 \tag{3.19}$$
...
- 2,648
2
votes
1
answer
292
views
How is the chiral condensate estimated from the pion decay constant?
In low-energy QCD, there are several dimensionful quantities that come up. Writing the chiral condensate as
$$\langle \Omega | \bar{q}_{Ri} q_{Lj} | \Omega \rangle = - v^3 \exp \left(\frac{2 i \pi^a(...
- 103k
2
votes
1
answer
76
views
Renormalising $\Delta$ baryon mass in chiral effective field theory
I have essentially no experience of quantum field theory, other than a superficial knowledge of some basic ideas - my apologies if I've phrased anything unusually or made any mistakes in my question ...
- 613
0
votes
1
answer
147
views
Properties of the nucleons and the nucleus from the interactions between quarks and gluons
Is it possible to deduce the properties of the nucleus or that of the nucleons from the QCD interactions between the constituent quarks and gluons?
- 26.8k
2
votes
1
answer
505
views
NRQCD: Why are quarks and anti-quarks treated independently?
I am studying these lectures on effective field theories and I am having some problems to understand how the Non-Relativistic QCD (NRQCD) Lagrangian is constructed.
This theory is often used to ...
- 1,109
9
votes
2
answers
2k
views
What are threshold corrections?
As the title goes, what are threshold corrections in quantum field theory?
In particular, I would be glad if a good reference is provided. Standard QFT books such as Peskin, Weinberg, etc seem to ...
user5800
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