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Questions tagged [quantum-chromodynamics]

Quantum-ChromoDynamics (QCD) is the quantum field theory believed to describe the strong nuclear force.

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Asymptotic Freedom QCD

I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
Gogoman96 X's user avatar
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QCD parton shower hard scale

Currently I'm studying parton showers from QCD and I'm having trouble with understanding how the hard scale $Q$ is related to the virtuality and energy of the parent parton. The Sudakov factor $\Delta(...
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Why does an all connected diagram contribute to two-point function?

I am recently reading E.Witten's review for $1/N$ expansion of QCD. In there, considering the main contribution of quark bilinears like $\bar{q}q$, then He mentions that in free field theory there is ...
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Why the kinetic term of the Hamiltonian has to be positive definite for well-posed time evolution?

I was going through this paper on QCD chaos, where in Appendix B (page 10), for equation B12: $$\frac{\mathcal{S}}{\mathcal{T}}= \int \mathrm{d}t\sum _{n=0,1} \left(\dot{c}_n^2-c_n^2 \omega _n^2\right)...
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Evidence of more generations in the QCD beta function

We know that the beta function for QCD is $$ \beta = -\left(11 - \dfrac{2N_f}{3}\right), $$ where $N_f$ is the number of fermions in the theory. We have $\beta_{\text{SM}} = -7$. Now, my question is, ...
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Is color charge internal symmetry or global symmetry?

I was told the color charge in the standard model could not be observed directly. This sounded like the gauge field $\vec A$ in the electromagnetism. However, it is a discrete charge and does have ...
ShoutOutAndCalculate's user avatar
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Visualization of a gauge field with non-null winding number

In QCD you may add the term $\mathcal{L}_{\theta} = \theta\dfrac{g^2}{16\pi^2} \text{Tr}F\tilde{F}$, which turns out to be a total derivative. Now, it can be proven that the action of this lagrangian ...
Gabriel Ybarra Marcaida's user avatar
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How is the mass distributed in ordinary matter?

How is the mass distributed in ordinary matter? In the ordinary things around us, we know that most of the mass is in the cores of the atoms, the electrons around it contributing only a very small ...
Jos Bergervoet's user avatar
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Spinor-helicity formalism: relationship between 1 and 2 reference vector setups

The spinor-helicity formalism is usually set up so that for a massless vector boson (photon or gluon) with momentum $k$ an arbitrary reference momentum $p$ is introduced and the corresponding ...
Fetchinson0234's user avatar
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$SU(3)$ color charge

Is the color charge the Noether charge due to the "global" $SU(3)$ symmetry of the QCD Lagrangian, or is it due to the "local" symmetry of the QCD Lagrangian?
Flying Ostrich's user avatar
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Can an electron be produced inside a proton?

We know that inside a proton there is a sea of quarks, antiquarks and gluons. This happens as the valence quarks emit gluons which then split into a quark-antiquark pairs. These pairs become gluons ...
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What makes electric and magnetic fields in Yang-Mills theories gauge co-variant?

Specifically in QCD, why is it so?
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Wilson loop is not an element of $\mathrm{SU}(3)$ in color deconfinement

The center symmetry in QCD comes from the $$a\ \mathcal{P}\mathrm{exp}\left(ig_s \int_C dx^\mu \ A_\mu(x)\right) a^{-1} = \mathcal{P}\mathrm{exp}\left(ig_s \int_C dx^\mu \ A_\mu(x)\right),$$ where $C$ ...
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Understading dimensions in quark bilinears

I have encountered myself with the following definition for $\pi$-fields as quark bilinears: $$ \pi^a = i\bar{q}\tau^a \gamma_5 q \ ,\quad\text{with }\ q = \left(\begin{array}{c}u\\d\end{array}\right) ...
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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 $\...
Gabriel Ybarra Marcaida's user avatar
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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 ...
quantumology's user avatar
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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}...
Gabriel Ybarra Marcaida's user avatar
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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 ...
zixuan feng's user avatar
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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 ...
Gabriel Ybarra Marcaida's user avatar
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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 = \...
Gabriel Ybarra Marcaida's user avatar
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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....
Banach Caccioppoli's user avatar
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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 ...
Xiaan YuanTian's user avatar
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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: ...
blacktopshaman's user avatar
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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 $D$-...
Ozzy's user avatar
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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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Quantum Chromodynamics (QCD) Prediction of Proton Mass

I’m trying to understand the prediction of the proton mass according to Quantum Chromodynamics (QCD). I know that the proton is composed of quarks and gluons, and that the mass of the proton is not ...
Amirhossein Rezaei's user avatar
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Uniquness of the vacuum in a theory with/without mass gap

Context I read the note Light Cone Quantization and Perturbationwritten by Guillance Beuf. He gives a argument in section 3.3.2, p17, 2nd paragraph : In particular, in a theory with a mass gap, ...
Steven Chang's user avatar
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Solving for gluon propagator in axial gauge

I know the two-point function is given by: $$ \Gamma^{A_\mu^a A_\nu^b}(p) = -i \delta^{ab} (g_{\mu \nu} p^2 - p_\mu p_\nu + \frac{1}{\zeta}n^\mu n^\nu) $$ and I am looking to solve for the inverse of ...
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What is the meaning of twist in OPE?

In Operator Product Expansion (such as explained in Peaking) there appear a quantity for an operator called twist, defined to be $d-s$ where $d$ is the scaling dimension of the operator and $s$ is it'...
Fabio Canedo's user avatar
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Deriving gluon propagator in axial gauge

I am currently checking my work against an answer and I understand most of it except I am having difficulty understanding the signs in a particular part. The question is as follows: (a) Derive the ...
Aidan's user avatar
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Is there any physical reason behind the choice of Lie group in a Yang-Mills theory?

A Yang-Mills theory can be constructed for any Lie group that is compact and semisimple. The motivation behind this is discussed in this question. Is there any physical reason we choose $SU(3)$ or $U(...
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When can colour charge indices be equated?

I'm currently studying QFT and QCD for the first time and I have a question about the colour charge indices given below. I was asked the following question: (a) Derive the Feynman rule for the 3-...
Aidan's user avatar
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What is vector meson dominance and why is that related to QCD having a repulsive potential?

At long distances QCD is said to give rise to attractive force between nucleons by pion exchange and to give rise to repulsive force at short distance mediated by vector mesons. Is there a ...
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Subleading correction to the gluon propagator in large $N$ expansion

I was reading Callan, Coote and Gross' paper on 2-dimensional QCD, where they show that the model that 't Hooft proposes in his work indeed produces quark confinement. In section VIII, they analyze ...
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Possible cases of matter fields for $SU(2)$ theory which retains asymptotic freedom?

Let us assume $4$ spacetime dimensions. QCD, the $SU(3)$ gauge theory with quarks as the matter fields, have the asymptotic freedom property as long as there are 16 quark flavors of mass below the ...
Keith's user avatar
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Difference between $ SU(3)$ and $ SU(3)_c $ group

I am reading quark model. I don't understand what's the meaning of a color $SU(3)$ or $SU(3)_c$ group and how it differs from a general $SU(3)$ group. Please elaborate.
Sagar K. Biswal's user avatar
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Parton distribution functions and virtual particles

Parton distribution functions are distributions of quarks and gluons inside the nucleon, but besides the three valence quarks, they are virtual particles right? So if virtual particles are just a ...
rafa's user avatar
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Does anywhere exist a document of solutions to Collins' Foundations of Perturbative QCD?

I and some classmates are recently teaching ourselves the famous book Foundations of Perturbative QCD by John Collins via a form of regular peer reading group. We find that exercises in this book are ...
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When do pairs of quarks form jets vs mesons?

For certain processes with low momentum transfer, such as the Kaon decay shown below, quarks will form bound states of mesons. Whereas for higher momentum-transfer processes, such as the decay of an ...
Jackson Burzynski's user avatar
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Using Compton scattering to derive the deep inelastic cross-section for the parton model

In the second volume of The Quantum theory of Fields, Weinberg provides the inelastic cross-section for the scattering of an electron from a nucleon with four momentum $p$ based on the parton model: $$...
agc's user avatar
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How relevant is the electric charge of quarks within hadrons?

Given that each quark flavor has a particular electric charge (i.e., either +2/3 or -1/3): how do these charges effect the internal dynamics of hadrons? Do the attractive and repulsive effects of ...
Thor Ether's user avatar
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Deriving Euler-Lagrange Equations in Light-Front Quantization from the Heisenberg Equation

I'm delving into light-front quantization, with a focus on understanding the roles of good and bad fermions. Using Collins' formulation in Foundations of Perturbative QCD, we define the projectors as: ...
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How can dense quark matter stabilize wormholes?

I have read in several articles, such as https://www.sciencedirect.com/science/article/abs/pii/S0577907323000266 and https://arxiv.org/abs/1403.0771 that dense quark matter can stabilize wormholes. ...
Peter's user avatar
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QCD in Coulomb Gauge Kernel Expansion

I was re-reading the Hamiltonian QCD in Coulomb gauge section in Particle Physics and Introduction to Field Theory by T.D. Lee and I was trying to understand better the form of the Coulomb kernel that ...
Christian's user avatar
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Why is it justified to focus on gauge transformations constant at spatial infinity in QCD instantons?

In the context of Yang-Mills theories and QCD instantons, much of the literature and conventional treatment hinges on the consideration of gauge transformations that remain constant at spatial ...
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Beyond sexaquarks?

There are some candidates for tetraquarks, pentaquarks or even now sexaquarks/hexaquarks. But, I wonder, what are the highest molecular quark states taking into account QCD? Are there heptaquarks, ...
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