All Questions
Tagged with quantum-chromodynamics symmetry-breaking
43
questions
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180
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Why does isospin symmetry survive chiral symmetry breaking?
In QCD there is a breaking of chiral symmetry such that, for the lightest quarks only, we have
$$\langle \overline{u} u \rangle = \langle \overline{d} d \rangle = \mathrm{const.}$$
where the constant ...
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1
answer
70
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Do we have an analytic calculation to derive $\frac{F^2}{4}\,\text{Tr}\left\{\partial_\mu U\partial^\mu U^{\dagger}\right\}$ from the QCD Lagrangian?
I have studied the quark condensate and chiral perturbation theory. However, I am not sure where the "kinetic term" of the pion
$$\frac{F^2}{4}\operatorname{Tr}\left\{\partial_\mu U\partial^...
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2
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161
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How do we known that $\langle \bar{\psi}_i \psi_j\rangle=(250 MeV)^3\delta_{ij}$?
I have started to read the phenomenology of QCD in low energy regime. I understand that, from the QCD renormalization group equation, the QCD becomes nonperturbative theory when energy scale is below $...
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2
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How is the pion related to spontaneous symmetry breaking in QCD?
In chapter 19 of An Introduction to Quantum Field Theory by Peskin & Schroeder, they discuss spontaneous symmetry breaking (SSB) at low energies in massless (or nearly massless) QCD, given by
$$\...
- 101
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0
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69
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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)
$$
U(2)_L \otimes U(2)_R = SU(2)_L \...
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votes
1
answer
302
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Global symmetries QCD goldstone bosons
Beside the local $SU(3)$-Color-symmetrie The QCD Lagrangian also has global symmetries:
$$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(...
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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
3
votes
0
answers
267
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Why is the chiral condensate a negative quantity?
The chiral condensate serves as an order parameter for the chiral phase transition. Thus, it is a finite quantity in one phase and vanishes in the other phase. It is given as a vacuum expectation ...
- 457
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0
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69
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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
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76
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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
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170
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$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
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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
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1
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181
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Chiral symmetry in massless QCD
The QCD Lagrangian for two flavors is:
$-\frac{1}{4} G\tilde{G}+i\bar{u}\displaystyle{\not} D u+i\bar{d} \displaystyle{\not} D d-m_u\bar{u} u-m_d\bar{d}d$
or alternaively
$-\frac{1}{4} G\tilde{G}+i\...
user255856
2
votes
1
answer
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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
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360
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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 $\...
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2
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240
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Sufficient and Necessary Conditions for Chiral Symmetry Breaking
In their 2005 paper, the authors write (just below eq. 3.19)
we see that a non-zero value of $F_0$ is a necessary and sufficient criterion for spontaneous chiral symmetry breaking. On the other ...
- 2,648
2
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1
answer
260
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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
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1
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Group structure of QCD‘s chiral symmetry (breaking)
With $3$ flavors of massless quarks, the QCD Lagrangian is invariant under flavor transformations$$SU(3)_V\ \otimes\ SU(3)_A\ \otimes\ U(1)_V\ \otimes\ U(1)_A.$$
Now, this is equivalent to $$SU(3)_R\ \...
- 2,648
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vote
2
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379
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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
4
votes
1
answer
248
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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
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0
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86
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No global monopoles in QCD
If a global symmetry gets both spontaneously and explicitly broken, the explicit symmetry breaking pattern is crucial for understanding the formation of topological defects.
For example, in the axion ...
- 1,783
1
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0
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46
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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
1
vote
2
answers
1k
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Breaking of $SU(3)$ symmetry by bi-fundamental representation
Are there any general theorems which fix the possible symmetry breaking patterns of Lie groups (such as $SU(3)$) by vacuum expectation values of fields in specific representations (such as the quark ...
- 1,783
2
votes
1
answer
141
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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
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1
answer
147
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chiral symmetry condensate and 2SC, CFL breaking C, P and T symmetry?
Because we know that chiral symmetry condensate causes the chiral symmetry breaking, and it produces Goldstone modes of pseudo-scalars, so I believe that chiral symmetry breaking also breaks the T ...
- 4,336
8
votes
1
answer
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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
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1
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403
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Scalar pseudo-Goldstones from hypothetical $SU(3)_V$ symmetry breaking in QCD
The eight light pseudoscalar mesons of QCD are the pseudo-Goldstone bosons of the spontaneously broken chiral (axial) $SU(3)_A$ quark flavor symmetry.
If we consider the hypothetical case of also ...
- 1,783
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0
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195
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Why does the $U(2n)$ flavor symmetry break down to a $U(1)$ group and an $SU(2n)$ group?
I am studying quantum field theory using Srednicki's textbook. Problem 83.1 is:
Suppose that the color group is $G_C=SO(3)$ rather than $SU(3)$, and that each quark flavor is represented by a Dirac ...
- 1,653
9
votes
1
answer
739
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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
4
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1
answer
2k
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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
$$
N = \begin{pmatrix} p \\ n\end{pmatrix}, ...
- 8,901
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0
answers
410
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How to find the explicit value of the fermion vacuum expectation value?
In the derivation for Goldstone modes, a pdf I found online (scipp.ucsc.edu/~dine/ph222/goldstone_lecture.pdf) says it's believed the above-mentioned expectation value $\langle \bar{ \psi} \psi \...
- 737
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1
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483
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Relevance of the condensate $\langle 0 | \bar q q | 0 \rangle$ to SSB of chiral QCD symmetry
The QCD lagrangian with two massless flavours of quarks takes the form $$\mathcal L = \sum_{i=u,d} i \bar q_i \gamma_{\mu} D^{\mu} q_i.$$ Defining operators to project out the left and right handed ...
- 3,569
14
votes
1
answer
3k
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Physical meaning of the chiral condensate in QCD
Considering the QCD Lagrangian in the chiral limit, where all the quarks masses are set to zero. Then the Lagrangian has the following chiral symmetry:
$$
SU(L)_{V} \times SU(L)_{A} \times U(1)_{V} \...
- 141
2
votes
1
answer
239
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Chiral current VEV below the QCD scale
Let's have pure QCD. I know that after spontaneous symmetry breaking quark bilinear form are replaced by their averaged values:
$$
\bar{q}_{i}q_{j} \to \langle \bar{q}_{i}q_{j}\rangle \approx \Lambda_{...
- 8,901
9
votes
1
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807
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Spontaneous symmetry breaking of anomalous global abelian symmetries and $U(1)$ of QCD
Let me restate the $U(1)$ problem of QCD:
Let us forget about the $s$ quark, and consider the $u$ and $d$ massless. This is
a good approximation since $m_{u,d} \ll \Lambda_{QCD}$. Then $\mathscr{...
- 498
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votes
1
answer
479
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Massive Gauge Bosons without Higgs fields
In a possible theory like our Standard model but without a Higgs i.e.:
$$ \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
1
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1
answer
149
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Interpretation of vector mesons in QCD
It is well-known that scalar mesons are interpreted as pseudogoldstone bosons which is connected with spontaneous broken $SU(3) \times SU(3)$ symmetry to $SU(3) \times SU(3) / SU(3)_{chiral}$.
Is ...
- 6,564
11
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1
answer
528
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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
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votes
2
answers
1k
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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
3
votes
1
answer
1k
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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
8
votes
1
answer
361
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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
11
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1
answer
470
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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
2
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3
answers
886
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The status of $SU(3)_C$ symmetry in the Standard Model
In the Standard Model of Particle physics the $SU(2)_{EW}$ symmetry and the $SU(2)$ isospin symmetry are broken. What about $SU(3)_C$? Is it broken too?
if YES, what breaks the symmetry?
If NO, what ...
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