All Questions
Tagged with quantum-chromodynamics quantum-field-theory
402
questions
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