All Questions
10
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
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
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
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
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
3
votes
1
answer
430
views
Computation of theta-term from triangle diagram
The chiral $U(1)$ anomaly in QCD can be calculated exactly by one-loop Feynman diagrams, for example by the famous triangle diagram. I am currently performing the computation to get a better ...
- 1,783