Questions tagged [quantum-chromodynamics]
Quantum-ChromoDynamics (QCD) is the quantum field theory believed to describe the strong nuclear force.
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Yang-Mills mass gap caused by gluonballs or because dark matter WIMPs?
Yang-Mills quantum field theory predicts the existence of the lightest massive Bosonic (i.e. integer spin) particle.
This massive Boson will be much lighter than the $W$ and $Z$ Boson and therefore ...
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How can I calculate action of $\mathfrak{su}(3)$ or other simple algebra ladder operators on "states" from the algebra commutators?
I wanted a way to "derive" Gell-Mann matrices for $\mathfrak{su}(3)$ and generalise this to other semi-simple algebras $\mathfrak{g}$. The way I wanted to approach this is start from the ...
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Ghosts in QCD Lagrangian
The QCD Lagrangian is
$$
\mathcal{L}_{\text{QCD}} = -\dfrac{1}{2} \text{Tr}\, G_{\mu\nu}G^{\mu\nu} + \sum_i^{N_f} \bar{q_i} \left(i \gamma^\mu \mathcal{D}_\mu - m_i\right)\,q_i, \tag{1}
$$
where $\...
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Colour Factor in QCD Pair Annihilation
My question occurred when I was reading Introduction to Elementary Particles by David J. Griffiths. In chapter 8, part 8.5, he is calculating the colour factor of quark-antiquark annihilation.
My ...
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Quark condensate and VEV of $\pi^0$
In David Tong's lectures on the Standard Model I saw that there is a quark condensate, which is just a Vacuum Expectation Value (VEV) of the $\bar{q}_{Li}\, q_{Ri}$ operator,
$$
\left< \bar{q}_{Li}...
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How to derive the gauge invariance of Yang-Mills action with external source?
In the Faddeev-Popov procedure of path integral of
$$
Z[J] = \int [DA] e^{iS(A,J)},
\quad S(A,J)= \int d^4x [-\frac{1}{4}F^{a\mu\nu}F_{a\mu\nu} + J^{a\mu}A_{a\mu} ]
$$
we have used that $S(A,J)$ is ...
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Motivation for the shape of the theta vacua
I understand that the reason why we construct the theta vacua is because instantons allow tunnelling between different vacuum states, $\left|n\right>$. This means that we have to consider a real ...
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Isospin doublet and quark content from contraction of quarks
Let's introduce a quark $SU(2)$ doublet. We are in the $m_u \approx m_d$ limit. So we have
$$
q = \begin{pmatrix}
u\\
d
\end{pmatrix}.
$$
Then we can construct the Nucleonic field
$$
N := q q q = \...
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Quark-Gluon vertex 1-loop correction in QCD
I'm trying to calculate the one loop correction to the quark-gluon vertex of QCD using euclidean formalism ($x^0 \rightarrow -ix^4$) and I'm having trouble to compute the integral in the picture below....
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What is the meaning of dynamically generated states in particle physics?
In hadron spectroscopy, a structure may be interpreted as various "configurations", such as conventional quark-antiquark states, tetraquarks, hybrid states, dynamically generated states or ...
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Do all antiquarks carry and anti-color charge, or can they carry RGB color charges as well?
I know there are antiquarks with anticolor charges. Are there also antiquarks that instead carry color charges?
Basically, which of these lists describes the types of quarks that there are:
List one:
...
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Euclidean LQCD not on a lattice?
How much the idea of calculating Euclidean path integrals in LQCD is fundamentally tied to using formulations based on the discretized spacetime lattice?
In computational approaches to quantum many-...
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How does the on-shell (OS) scheme work if we assume mass to be zero?
When calculating the self-energy correction of a massless quark up to one loop, I get
$$i\Sigma(p)=i\frac{\alpha_s}{4\pi}C_F/\!\!\!{p}\left[\frac{1}{\varepsilon_{\text{UV}}}-\gamma+\ln(4\pi)+1+\ln(\...
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Can $\gamma^5$ matrices be ignored in $q\bar{q}\to ZZ$ processes?
In the $q\bar{q}\to ZZ$ process, the following Feynman diagram in LO appears:
This means for each vertex, the Feynman amplitude contains a term proportional to $(g_V-g_A\gamma^5)$, which makes $D$-...
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Why are two gluons needed for Feynman diagram?
Why do we need two gluons for the decay $$\pi^-+ p\rightarrow\pi^-+n+\pi^+\:\:?$$
If we have always the gluon $$\frac{1}{\sqrt{2}}(r\bar{r}-g\bar{g})$$ it should be possible with only one gluon
...
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