All Questions
Tagged with quantum-chromodynamics quantum-anomalies
17
questions
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
69
views
Restoration of symmetry explicitly broken by anomaly
What is the meaning of the restoration at finite temperature of a symmetry that is "broken" by the presence of an anomaly. If the symmetry is not there why is it restored at finite ...
- 861
3
votes
1
answer
170
views
$U(1)_A$ effects on the baryons?
We know that the axial $U(1)_A$ is anomalous thus not a global symmetry. Therefore there is no direct associated pseudo goldstone boson for $U(1)_A$. This makes the $\eta'$ much more massive than the ...
- 4,336
8
votes
1
answer
476
views
Why do we think that the $U(1)$ problem is solved by instantons?
It is usually thought that the $U(1)$ problem is solved when 't Hooft realized that instantons induce additional symmetry breaking of the $U(1)_A$ symmetry aside from the non-vanishing quark masses. ...
- 3,691
2
votes
1
answer
531
views
Peskin's treatment of Pions as Goldstone Bosons
After restoring the mass terms in the Lagrangian
\begin{align}
\mathcal{L}=\bar{u} i \not D u+\bar{d i} \not D d-m_{u} \bar{u} u-m_{d} \bar{d} d,
\end{align}
one obtains equations of motion for the ...
- 321
0
votes
0
answers
412
views
QCD Trace Anomaly and Mass
In the paper in equations 4 and 5, some of the mass of the nucleons comes from the "trace anomaly" of the QCD energy-momentum tensor (as described in the paragraph following these equations). Is there ...
- 1
1
vote
0
answers
75
views
Showing that $U(1)_R$ charge is non-anomalous in SUSY QCD when $r=\frac{F-N}{F}$
I'm trying to show that the value of the R-charge $r$ for which the R-symmetry is non-anomalous is given by $r=\frac{F-N}{F}$.
To do this we must calculate the triangle diagrams for the quarks $\...
- 4,780
19
votes
1
answer
2k
views
What's the real resolution of the $U(1)_A$ problem?
To recap the problem, consider QCD with three massless quark flavors. There is a symmetry
$$SU(3)_L \times SU(3)_R \times U(1)_L \times U(1)_R$$
corresponding to independent rotations of the left-...
- 103k
4
votes
1
answer
248
views
Simple explanation of the QCD VEV in terms of instantons
I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
- 8,901
2
votes
1
answer
263
views
axial anomaly for adjoint fermion v.s. fundamental fermion
It is known that the axial anomaly (chiral anomaly, the left L- right R) shows that $U(1)_A$-axial symmetry is not a global symmetry at quantum level.
In particular, one can consider the (1) ...
- 4,336
3
votes
1
answer
745
views
Is it the chiral anomaly which is solely responsible for having instanton effects (and therefore, the $\theta-$term) in the QCD action?
$\textbf{Fact 1}$ In principle, the QCD Lagrangian should contain a Lorentz invariant, gauge invariant, dimension-4 term $\sim\theta \text{Tr}[F^{\mu\nu}\tilde{F}_{\mu\nu}]$. This term, however, is ...
- 26.8k
4
votes
1
answer
611
views
Anomalies of QCD
I have come across the following statement:
The anomalies of QCD cannot be reproduced by a collection of free fermions
carrying $U(1)_V$, $SU(N_f)_L$ and $SU(N_f)_R$ quantum numbers. That is why ...
- 699
4
votes
1
answer
927
views
Axial anomaly in QCD VS axial anomaly in current algebra QCD
I would like to understand the distinction between an axial anomaly in QCD (Theta Vacuum: axion -> 2 gluons) and an axial anomaly in QCD of current (Chern–Simons term: pion->two photons, photon->three ...
- 215
3
votes
1
answer
206
views
Counting number of gluon fields in ABJ anomaly of QCD
In QCD, the axial singlet quark current $j_5$ is anomalous, which was found by Adler, Bell, and Jackiw (here is a review):
\begin{equation}
\partial_\mu j_5^\mu=G\tilde{G},
\end{equation}
where $G$ ...
- 1,783