All Questions
Tagged with quantum-chromodynamics quantum-field-theory
402
questions
0
votes
0
answers
55
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A list of failed attempts towards a proof of confinement [closed]
Can one give a list of failed or open attempts (not necessarily Supersymmetric) towards a proof of confinement in 4d regarding YM or QCD?
- 1,268
6
votes
1
answer
130
views
How to avoid the ordinary Coulomb solution in QCD?
To see where QCD starts to differ from the behavior of EM fields, we might begin by looking at the classical field. A search brings up
[question 339978] and [question 360061] but no answer is found ...
- 4,912
5
votes
1
answer
74
views
$ \pi^0\to \gamma\gamma$ parity conservation
Let's consider the decay process $\pi^0\to \gamma \gamma$. After we spontaneously broke the chiral symmetry of QCD coupled to an abelian gauge field $A^\mu$, we end up with the Goldstone boson ...
- 357
3
votes
0
answers
106
views
The commutation relations of photon and gluon?
In QED, the photon field has the following commutation relations:
\begin{equation}
[A^{\mu}(t,\vec{x}),A^{\nu}(t,\vec{y})]=0, \tag{1}
\end{equation}
where $A^{\mu}(t,\vec{x})$ is the photon filed. ...
- 85
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
0
votes
0
answers
31
views
QCD parton shower hard scale
Currently I'm studying parton showers from QCD and I'm having trouble with understanding how the hard scale $Q$ is related to the virtuality and energy of the parent parton. The Sudakov factor $\Delta(...
- 291
2
votes
1
answer
37
views
Why does an all connected diagram contribute to two-point function?
I am recently reading E.Witten's review for $1/N$ expansion of QCD. In there, considering the main contribution of quark bilinears like $\bar{q}q$, then He mentions that in free field theory there is ...
- 31
0
votes
1
answer
59
views
Visualization of a gauge field with non-null winding number
In QCD you may add the term $\mathcal{L}_{\theta} = \theta\dfrac{g^2}{16\pi^2} \text{Tr}F\tilde{F}$, which turns out to be a total derivative. Now, it can be proven that the action of this lagrangian ...
- 1,611
3
votes
1
answer
66
views
How is the mass distributed in ordinary matter?
How is the mass distributed in ordinary matter?
In the ordinary things around us, we know that most of the mass is in the cores of the atoms, the electrons around it contributing only a very small ...
- 4,912
4
votes
2
answers
672
views
Ghosts in QCD Lagrangian
The QCD Lagrangian is
$$
\mathcal{L}_{\text{QCD}} = -\dfrac{1}{2} \text{Tr}\, G_{\mu\nu}G^{\mu\nu} + \sum_i^{N_f} \bar{q_i} \left(i \gamma^\mu \mathcal{D}_\mu - m_i\right)\,q_i, \tag{1}
$$
where $\...
- 1,611
1
vote
0
answers
52
views
Colour Factor in QCD Pair Annihilation
My question occurred when I was reading Introduction to Elementary Particles by David J. Griffiths. In chapter 8, part 8.5, he is calculating the colour factor of quark-antiquark annihilation.
My ...
- 81
2
votes
1
answer
107
views
Motivation for the shape of the theta vacua
I understand that the reason why we construct the theta vacua is because instantons allow tunnelling between different vacuum states, $\left|n\right>$. This means that we have to consider a real ...
- 1,611
1
vote
1
answer
57
views
Euclidean LQCD not on a lattice?
How much the idea of calculating Euclidean path integrals in LQCD is fundamentally tied to using formulations based on the discretized spacetime lattice?
In computational approaches to quantum many-...
- 2,921
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
0
answers
46
views
Can $\gamma^5$ matrices be ignored in $q\bar{q}\to ZZ$ processes?
In the $q\bar{q}\to ZZ$ process, the following Feynman diagram in LO appears:
This means for each vertex, the Feynman amplitude contains a term proportional to $(g_V-g_A\gamma^5)$, which makes $D$-...
- 172
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
0
votes
0
answers
141
views
Deriving gluon propagator in axial gauge
I am currently checking my work against an answer and I understand most of it except I am having difficulty understanding the signs in a particular part. The question is as follows:
(a) Derive the ...
- 90
1
vote
1
answer
57
views
When can colour charge indices be equated?
I'm currently studying QFT and QCD for the first time and I have a question about the colour charge indices given below. I was asked the following question:
(a) Derive the Feynman rule for the 3-...
- 90
1
vote
0
answers
32
views
Subleading correction to the gluon propagator in large $N$ expansion
I was reading Callan, Coote and Gross' paper on 2-dimensional QCD, where they show that the model that 't Hooft proposes in his work indeed produces quark confinement. In section VIII, they analyze ...
- 370
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
0
votes
1
answer
41
views
Parton distribution functions and virtual particles
Parton distribution functions are distributions of quarks and gluons inside the nucleon, but besides the three valence quarks, they are virtual particles right? So if virtual particles are just a ...
- 13
0
votes
0
answers
52
views
Using Compton scattering to derive the deep inelastic cross-section for the parton model
In the second volume of The Quantum theory of Fields, Weinberg provides the inelastic cross-section for the scattering of an electron from a nucleon with four momentum $p$ based on the parton model:
$$...
- 163
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
0
votes
0
answers
106
views
Schwinger proper-time representation of Feynman propagator in Coordinate space
I'm working on a QCDSR paper which calculates mass of $B$ meson in the present of external magnetic field.
the author works with Schwinger proper-time representation of Feynman propagator in momentum ...
1
vote
0
answers
137
views
Has the mass of a proton been calculated from current quarks, through the renormalization process?
That's basically my question. Has the mass of the proton been calculated using QCD and the interactions between the current quarks? Perturbative methods obviously can't be used as they deal with ...
- 450
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
votes
2
answers
206
views
How exactly does a proton form from quarks? What is the exact sequence and mechanism?
What are the steps that lead to the bonding of two up quarks and one down quark into a proton? For instance, does an up quark "bind" with a down quark in quark-gluon plasma, which then binds ...
- 29
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,
$$\frac{\delta^nZ_{QCD}[J]}{\...
- 343
5
votes
1
answer
268
views
Why is there only one coupling constant in Yang-Mills theory? Why are gluon self-coupling and gluon-matter coupling constants the same?
Is it non-trivial that the coupling constant $g$ in gluon self-interaction terms is the same as the coupling constant $g$ in gluon-fermion interaction term in Yang-Mills theory?
Pure Yang-Mills theory ...
- 192
3
votes
2
answers
161
views
How do we known that $\langle \bar{\psi}_i \psi_j\rangle=(250 MeV)^3\delta_{ij}$?
I have started to read the phenomenology of QCD in low energy regime. I understand that, from the QCD renormalization group equation, the QCD becomes nonperturbative theory when energy scale is below $...
- 31
0
votes
0
answers
140
views
Integral of the square of the spectral density in a quantum field theory
The quantity of interest is
$$
\int_0^\infty dE \, \rho(E)^2
$$
where $\rho(E)$ is the spectral density in a Quantum Field Theory. I am wondering whether
it has any physical meaning, and
it can be ...
- 1
0
votes
1
answer
81
views
Theta vacua eigenstates
I have been trying to prove the very simple result that the eigenstates of an operator with matrix elements
$$
\langle n^\prime | H | n \rangle \sim g(|n^\prime-n|),
$$
in a basis $\{|n\rangle\}^{+\...
- 1,742
9
votes
2
answers
796
views
How is the pion related to spontaneous symmetry breaking in QCD?
In chapter 19 of An Introduction to Quantum Field Theory by Peskin & Schroeder, they discuss spontaneous symmetry breaking (SSB) at low energies in massless (or nearly massless) QCD, given by
$$\...
- 101
2
votes
0
answers
69
views
Goldstone bosons in 2 and 3 quark flavor symmetries [closed]
In my (undergraduate) advanced elementary particles class last semester, we learnt that for a 2 quark (u/d) model the symmetry of the Lagrangian is (and breaks as)
$$
U(2)_L \otimes U(2)_R = SU(2)_L \...
- 23
3
votes
0
answers
72
views
Renormalizability of massless Gross-Neveu theory
We have the following Lagrangian density:
$$ \mathcal{L} = \bar{\psi}_i i \gamma^\mu \partial_\mu \psi_i
+ \frac{g^2}{2} \left( \bar{\psi}_i \psi_i \right)^2 $$
which corresponds to the two-...
- 1,124
2
votes
1
answer
174
views
1-loop Feynman diagrams of $g \to gg$ in pure QCD
I'm very new to QFT, and I'm drawing one-loop Feynman diagrams of the process $g \to gg$ in pure QCD. I use MadGraph to generate all the diagrams by
...
- 21
1
vote
1
answer
106
views
Generalities about propagators and its application to scalar chromodynamics
In an exercise for a course on quantum field theory, I am given the following Lagrangian:
$$
\mathcal{L} = -\frac{1}{2} G_{\mu\nu}^a G^{a\mu\nu} + 2 (D_\mu \phi^\dagger)^a(D^\mu \phi)^a - 2 m^2\phi^{\...
- 307
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
233
views
Why Lambda Baryon and Sigma Baryon unequal sum isospin with "really" isospin?
For information isospin for $u$-quark = 1/2, isospin for $d$-quark = -1/2 and isospin for $s$-quark = 0.
Lambda Baryon consists $uds$ quarks,therefore sum isospin 1/2-1/2+0=0, It true.
But sum isospin ...
- 23
1
vote
1
answer
265
views
Why there is only $t$-channel for $u+\bar d\rightarrow u+\bar d$ scattering?
I am reading Griffith's textbook on particle physics about the $u+\bar d\rightarrow u+\bar d$ scattering for QCD. On page 285, it says there is only one possible channel ($t$-channel):
Why there are ...
- 1,783
3
votes
1
answer
111
views
Structure functions for mesons
I was researching about structure functions and understand how it's a probability density function that describes the distribution of quarks inside hadrons. However, since mesons also have quark gluon ...
- 625
0
votes
1
answer
136
views
Are all mass eigenstates also spin eigenstates?
Is there a rigorous way to show that a mass eigenstate of a particle must also be an eigenstate of the total spin operator? If this wasn't true, you could imagine that a composite particle in a mass ...
- 867
1
vote
0
answers
75
views
How do we measure the gluon scattering?
In QFT, we often calculate the 'Feynman amplitude' for gluon scattering. As we know, Gluon is gauge boson mediating the strong force between quarks. By color confinement, Quarks are never seen in our ...
- 108
0
votes
0
answers
61
views
Calculating Diagrams with Wilson Lines to One Loop
I have a question concerning the calculation of amplitudes containing Wilson lines.
I want to calculate the jet function defined by equation (3.3) from this paper.
$$\mathcal{J}(\text{arguments})u_s(p)...
- 2,983
4
votes
1
answer
302
views
Global symmetries QCD goldstone bosons
Beside the local $SU(3)$-Color-symmetrie The QCD Lagrangian also has global symmetries:
$$L_{QCD}=\sum_{f,c}\bar{q_{fc}}(i\gamma^\mu D_\mu - m ) q_{fc} - \frac{1}{4}F^a_{\mu \nu} F^{a \mu \nu} $$
$SU(...
- 63
1
vote
3
answers
166
views
Which configurations are important in lattice QCD?
The failure of perturbation theory in describing strongly-coupled QCD is because it can't account for field configurations that are 'large'.
My questions is: from experience in lattice QCD, what kind ...
- 742
3
votes
0
answers
47
views
Topology active subgroup for the QCD vacuum
I've been reading about the nontrivial topological structure of the QCD vacuum and, when studying the different equivalence classes created by the pure gauge fields, all papers say that it is possible ...
- 96
3
votes
1
answer
213
views
What gives rise to mass gap for gluons, even if they are massless?
It is known that QED does not have a mass gap.
On the other hand, at the heuristic level, QCD has a mass gap.
But photons and gluons are both "massless". Could anyone explain (at least at ...
- 1,669
4
votes
1
answer
214
views
How does AdS/CFT help us understand non-perturbative aspects of QCD?
I've heard AdS/CFT has found applications in many areas of physics where nonperturbative aspects leave us crippled in making any simple calculations.
Among these applications, I also have heard that ...
- 1,268
1
vote
1
answer
81
views
How can I show the following contraction of the electromagnetic field strength and its dual? [closed]
Given the electromagnetic field strength $F^{\mu\nu}$, and its dual $$\tilde{F}^{\mu\nu} =\dfrac{1}{2}\varepsilon^{\mu\nu\alpha\beta}F_{\alpha\beta},$$
how can I show that
$$\tilde{F}^{\mu\nu}F_{\nu\...
