All Questions
22
questions
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
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
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
0
votes
1
answer
185
views
How does the Nambu-Goldstone mode explain the absence of parity doubling?
I've been doing some reading about chiral symmetry breaking since it was not touched in my particle physics course
I found these slides
As explained in the above link, if we take $|\psi \rangle$ as ...
- 3,464
0
votes
0
answers
76
views
Are the arrangements of quarks in hadron ground-state wavefunctions rotationally symmetric?
The Hamiltonian of quantum chromodynamics (like the rest of the Standard Model) is rotationally symmetric. My question is whether these space symmetries are spontaneously broken in the ground state of ...
- 48.4k
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
1
vote
1
answer
327
views
Quark condensate and spontaneous symmetry breaking?
It is known the quark condensate $<\bar{\psi}^{i}_L\psi^j_R>=\sigma \delta^{ij}$($i,j$ are flavour indices ) breaks the symmetry group $SU(N_f)_L\times SU(N_f)_R$. Because it is only invariant ...
- 995
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
3
votes
0
answers
360
views
Pion mass in theta vacuum
Does the mass of the charged pion depend on the QCD vacuum angle? I've seen it said---e.g., in these TASI lectures---that when the quark mass matrix is real and there is a nonzero QCD vacuum angle $\...
- 61
2
votes
1
answer
260
views
Why is the approximate $\rm U(2)\times U(2)$ global symmetry of QCD that has a special importance?
I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $\rm U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this ...
- 26.8k
1
vote
2
answers
379
views
Derivation of Casher-Banks relation
Consider two-point function $\langle \bar{\psi}\psi\rangle$ in a model with massive fermions $\psi$ and gauge field:
$$
\langle \bar{\psi}\psi\rangle =\frac{1}{V}\sum_{n} \frac{1}{\lambda_{n} +im},
$$...
- 8,901
1
vote
0
answers
46
views
Do hierarchical condensates yield instantaneous or sequential symmetry breaking?
I am wondering whether the formation of a hierarchical vacuum condensate yields an instantaneous or sequential symmetry breaking in a cosmological phase transition. Let me illustrate this question ...
- 1,783
2
votes
1
answer
141
views
gauge-invariant 6-quark order parameter
In this Review paper in p.1462, bottom left: Rev.Mod.Phys.80:1455-1515,2008 -- Color superconductivity in dense quark matter
It says that "There is an associated gauge-invariant 6-quark order ...
- 4,336
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