All Questions
Tagged with quantum-chromodynamics symmetry-breaking
43
questions
14
votes
1
answer
3k
views
Physical meaning of the chiral condensate in QCD
Considering the QCD Lagrangian in the chiral limit, where all the quarks masses are set to zero. Then the Lagrangian has the following chiral symmetry:
$$
SU(L)_{V} \times SU(L)_{A} \times U(1)_{V} \...
- 141
11
votes
1
answer
528
views
From which dimensionful constants does proton mass arise?
It is well known that the most of the proton (or any other hadron with light quarks) mass is not made up from quark masses, but it is dynamically generated by QCD mess inside. I've also heard that, ...
- 305
11
votes
1
answer
470
views
What's the heuristic reasoning for Chiral Symmetry breaking
In Peskin and Schroeder (page 669), and other references, the heuristic reasoning for why one would expect chiral symmetry breaking at low energies is that quark masses are small and hence it's not ...
- 3,492
9
votes
2
answers
796
views
How is the pion related to spontaneous symmetry breaking in QCD?
In chapter 19 of An Introduction to Quantum Field Theory by Peskin & Schroeder, they discuss spontaneous symmetry breaking (SSB) at low energies in massless (or nearly massless) QCD, given by
$$\...
- 101
9
votes
1
answer
739
views
Why do we have a non-zero quark vacuum condensate even though the QCD coupling goes to zero in the deep infrared?
It is well-known that QCD has a Landau pole at $\Lambda_{\rm QCD}\sim 200$ MeV, which means that the perturbative QCD coupling becomes strong at this scale. Conventionally, this is claimed to be the ...
- 1,783
9
votes
1
answer
807
views
Spontaneous symmetry breaking of anomalous global abelian symmetries and $U(1)$ of QCD
Let me restate the $U(1)$ problem of QCD:
Let us forget about the $s$ quark, and consider the $u$ and $d$ massless. This is
a good approximation since $m_{u,d} \ll \Lambda_{QCD}$. Then $\mathscr{...
- 498
8
votes
1
answer
2k
views
Peccei-Quinn-symmetry and effective Lagrangian for the Axion field
To solve the strong CP-problem Peccei and Quinn suggested the use of a new $U(1)$-symmetry called the PQ-symmetry. For this symmetry they constructed an effective Lagrangian involving the Nambu-...
- 1,114
8
votes
1
answer
361
views
Intuitive explanation of how hadron mass emerges from the strong force
I'm not familiar with QCD, but I'm looking for intuitive explanation of this phenomenon (it could be that easy explanation does not exist).
What I've read is that large part of hadron masses arises ...
- 421
7
votes
1
answer
479
views
Massive Gauge Bosons without Higgs fields
In a possible theory like our Standard model but without a Higgs i.e.:
$$ \mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}] $$
where $b,f$ run over the typical ...
- 823
5
votes
2
answers
1k
views
Origin of quark masses
Does all the mass of the quarks in the standard model come from the Higgs sector or is there also a contribution to quark masses due to QCD chiral symmetry breaking?
- 26.8k
4
votes
1
answer
2k
views
Question about the linear sigma-model
Suppose the linear sigma-model lagrangian:
$$
L = \bar{N}(i\gamma_{\mu}\partial^{\mu}-g_A \phi)N + |\partial_{\mu}\phi|^{2} - V(|\phi|) - c\sigma ,
$$
where
$$
N = \begin{pmatrix} p \\ n\end{pmatrix}, ...
- 8,901
4
votes
1
answer
302
views
Global symmetries QCD goldstone bosons
Beside the local $SU(3)$-Color-symmetrie The QCD Lagrangian also has global symmetries:
$$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
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
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
3
votes
1
answer
1k
views
Dilaton field and Scale symmetry breaking
I have read at some places that a dilaton field is associated with the spontaneous breaking of scale symmetry in a theory. (While others would be difficult to trace right now, the most easily ...
- 405