Questions tagged [quantum-chromodynamics]

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

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What are the differences between FFN, VFN, GMVFN and ZMVFN PDF schemes in QCD?

What are the differences between the fixed flavour number (FFN), variable flavour number (VFN), general-mass variable flavour number (GMVFN) and zero-mass variable flavour number (ZMVFN) schemes for ...
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What is mass factorisation?

I know that for some observables in QCD, e.g. inclusive DIS cross sections, one can use factorisation by writing said observable as a convolution of hard scattering coefficients with PDFs. But what is ...
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What are extrinsic and intrinsic flavour production?

In terms of Feynman diagrams, what are extrinsic and intrinsic flavour production? See for example this paper this paper (p.2).
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How exactly do quarks suppress gluon fluctuations?

In both this Veritasium Video and this answer it is said that Quarks suppress gluon fluctuations, thus creating a so-called 'flux tube' which is what binds the gluons together (as explained in both ...
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Misunderstanding the dimension of QCD

From my point of view, the definition of the tension tensor is contradictory. $$F_{\mu \nu}=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu} +ig[A_{\mu},A_{\nu}]$$ $$[A_{\mu}]=\frac{1}{cm \times g};[F_{\...
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What happens to an electron when it radiates a photon?

I recently came across this Feynman diagram: For a more simplistic diagram, I suppose even this would be adequate: As you can see in these diagrams, they radiate these virtual photons. The virtual ...
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What is the formula that hadronization is not able to be resolved using pertubation theory?

(New in particle physics background in Computer science) I read (source: https://www.slac.stanford.edu/econf/C990809/docs/webber.pdf) that hadronization is not well undestood because pertubation ...
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Can mesons be in $b \overline{b}$, $r \overline{r}$, $g \overline{g}$ states?

Can a meson be in a pure $b \overline{b}$, $r \overline{r}$, $g \overline{g}$ state or does it have to be in the $\frac{1}{\sqrt{3}}\left(b \overline{b}+r \overline{r}+g \overline{g}\right)$ state? ...
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Negative running coupling constant in QCD?

Considering the one-loop running coupling constant in QCD: $$\alpha_s(\mu) = \frac{a_s(\mu_0)}{1 + \frac{33-2f}{6 \pi}ln\left( \frac{\mu}{\mu_0}\right)}$$ where f is the number of quarks flavours with ...
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What’s the basic procedure to draw a QCD phase diagram?

Could someone recommend a book/resource where I can find a detailed way of sketching out a QCD temperature-chemical potential phase diagram using gap equations (eg. equations 35-37 or 39-40 as given ...
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Understanding $\rm SU(3)$ Gauge Invariance Through a Perturbation Theory

Here I am modifying the field theory approach, since I never taken a course on Quantum Field Theory. I am exploring Gauge Invariance in $\rm SU(3)$ by the following approach (which technically is ...
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How is the difference in ground and excited state of baryons masses explained within QCD and SM?

How is the difference in ground and excited state of baryons masses ($\Sigma$ and $\Sigma^*$, $\Xi$ and $\Xi^*$ for example) explained within QCD and SM? Is it possible to calculate (predict) this ...
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1answer
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Is Compton Scattering the “Abelian limit” of $qg \rightarrow qg$?

I have calculated the average over initial and sum over final states of the squared amplitude for both Compton scattering $e^-\gamma \rightarrow e^-\gamma$ (QED) and quark-gluon scattering $qg \...
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What are the correct QCD Feynman diagrams for jets or hadronization?

In many drawings for jets or hadronization there are outgoing individual quark or gluon lines from which hadrons seem to emerge. But this is wrong: a color-neutral hadron cannot emerge from a single ...
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QCD quark self-energy, is the propagator momentum in the right direction?

For the quark self-energy diagram the amplitude is giving by: The fermion propagator is given by $\frac{i}{\not p + l}$ in the lecture. It is not supposed to be $\frac{i}{\not p - l}$? It's seems ...
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Quark propagator

I was reading about Large N QCD, and specifically, T Hooft Double line notation, when I stumbled across the quark propagator- $$\langle \psi^a (x) \overline{\psi^b}(y) \rangle = \delta^{ab} S(x-y) $$ ...
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The investigation of particles in constant chromomagnetic field

The problem of the particle in the external magnetic field is one of the most famous and oldest problems in quantum mechanics. Hamiltonian of the particle in the constant magnetic field is: $$ \mathbf{...
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1answer
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Meson masses difference

I am reading some group theory applied to QCD and they show how by using the lightest 3 quarks in the $l=0$ state we get 9 pseudoscalar mesons and 9 vector mesons. The difference in masses between the ...
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1answer
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$C$-conjugation of a gluon

In some explanations about the OZI rule ( for example at page 38 here), I found that gluons have definite eigenvalue of the charge conjugation operator $C$. The eigenvalue is $-1$. How can this result ...
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Amplitude of quark$+$antiquark $\rightarrow$ ghost$+$antighost in QCD

Since the BRST charge operator commutes with the Hamiltonian of QCD, a physical state such as $q+\bar q$ should not be allowed to evolve into an unphysical one like $\chi+\bar\chi$, where these two ...
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$qg \rightarrow qg$: Spinor Helicity Formalism

I am calculating the cross-section for quark gluon to quark gluon scattering in the spinor helicity formalism. This process has contributions from the Mandelstam channels $s$, $t$ and $u$. Using the ...
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Calculating the Nambu-Gorkov propagator (given its inverse) for quarks

I am working through this paper on the calculation of a Nambu-Gorkov propagator, could someone explain how did we reach the next step right after equation (16)?
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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 ...
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QCD methods - Dirac trace, trace in color space, trace in flavor space

What is meant by the following terms in QCD - Dirac trace, trace in color space, trace in flavor space, etc. Could someone explain with an example (For eg. what's the diffrerence between something ...
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Calculating the quark propagator while dealing with the color, Dirac & flavor matrices all together

$S^+$ is a diagonal matrix in color space, and is given as : $S^+ = S_{rg} ^+ \hat{P_{rg}} + S_b ^+ \hat{P_b}, where, \hat{P_b} = 1_c - \hat{P_{rg}}$ is the projector on blue quarks, $\hat{P_{rg}}$ ...
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Deep inelastic scattering (DIS) and handbag diagram

Here, in page 11, you can see the so-called 'handbag' diagram that explains how a virtual photon emitted in a deep inelastic scattering (DIS) process interacts with a parton. I'm going to use this ...
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Infrared-safe and collinear-safe jet algorithms

A good algorithm for reconstructing jets in an experiment requires "infrared safety" and "collinear safety". This means that the configuration of the reconstructed jet must not ...
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1answer
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How to transform a given Lagrangian to a Nambu-Gorkov basis?

With reference to the Nambu (or famously, Nambu-Gorkov) transformation in this paper, could someone explain the reason behind using the 3rd Pauli matrix in the Lagrangian after equation (2.3) (would ...
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Deep inelastic electron-proton scattering amplitude

In 'QCD and collider Physics' book by Ellis, Stirling and Webber, chapter 4.2 'The parton model from field theory' there is this equation for the amplitude of the process $e^- (k) P \rightarrow e^- (k^...
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What determines whether free neutron decay results in the production of a neutral hydrogen atom?

Free neutrons (outside the nucleus) are known to be highly unstable with a mean lifetime of around 14 minutes and 40 seconds. Inside the neutron, which is composed of 1 up quark and 2 down quarks, a ...
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How does the mere movement of gluons keep quarks together?

You know the strong force (the one that keeps quarks together). Well it works by exchanging gluons right? So how does that force keep the quarks together? I mean you can imagine that process as three ...
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1answer
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Help to derive the inequality bounds $1/4\leq F_2^{\rm en}/F_2^{\rm ep}\leq 4$ (Halzen & Martin's exercise 9.7)

The structure functions $F_2^{\rm ep}$ and $F_2^{\rm en}$ for electron-proton and electron-neutron deep inelastic scattering deduced from the model of valence quarks and sea quarks of proton and ...
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Physical significance of the reality of an ${\bf N}$ representation: how the nature of interactions is affected?

Background The fundamental representation of ${\rm SU(N)}$ is denoted by ${\bf N}$ and the conjugate of the fundamental is denoted by ${\bar{\bf N}}$. If the representation ${\bf N}$ is related to ${\...
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Eight gluons, what are the properties of two of them?

If there are 8 gluons, and 6 of them can be represented as a color/anticolor pair (red/antiblue for example), that leaves 2 "other" gluons. How do these two gluons differ from each other? ...
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Effects of the discrete quotient of chiral symmetry group

For a theory of $N_f$ massless Dirac fermions coupled to a Yang-Mills field, the usual story is that we have a $U_L(N_f)\times U_R(N_f)$ symmetry, which is then expressed as $SU_L(N_f)\times SU_R(N_f) ...
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Why gluons don't have mass? [duplicate]

Which theoretical or experimental results provide us that we should calculate with massless gluon fields. Or in other words, what forbids gluons from having mass?
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What is the application of dimension $6$ representation of $SU(3)$ in particle physics?

As we know, the $uds$ transforms in fundamental representations of $SU(3)$. It has the antifundamental partner. According to representation theory, $$ \mathbf{3} \otimes \mathbf{\bar{3}}= \mathbf{8} \...
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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\...
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What does it mean by active quarks?

Do the active quarks mean valence quarks? Or we can also consider other quarks, like when there are offshell-quarks produced from gluons by pair production processes? For example: how the active quark ...
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Determining reduced graphs in perturbative QCD

I am reading "Foundations of perturbative QCD" by John Collins and I find it hard to determine the general form of reduced graphs (that is feynman graphs, where internal lines which do not ...
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Could a proton be produced using the dynamical Casimir effect?

According to the standard model, would it be theoretically possible to emit protons or other complex particles from the vacuum using the dynamical Casimir effect? Or is it only possible to emit ...
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Spatial Translation field operators in Non-Local Quark Bilinear

I am interested in studying a somewhat simple quantity at tree level $$ \langle p'|\bar{\psi}\Big(-\frac{z}{2}\Big)\gamma^{\mu}\psi\Big(\frac{z}{2}\Big)|p\rangle $$ where $|p\rangle$ is a fermion ...
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QCD energy scale $\Lambda_{\rm MS} $, $\Lambda_{\rm QCD}$, …?

Why there seems to be different conventions of QCD energy scales? Is that due to the running coupling? For example in Wikipedia https://en.wikipedia.org/wiki/Coupling_constant#QCD_scale: $$ \Lambda_{\...
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Is $\mu$ the renormalization or factorization scale in the DGLAP equations?

The DGLAP equations read $$\frac{\partial f_i(x,\mu^2)}{\partial\ln\mu^2}=\sum_j\int^1_x\frac{dz}{z}P_{ij}(z,\alpha_s(\mu^2))f_j\left(\frac{x}{z},\mu^2\right),$$ where the $f_i$ are the parton ...
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Why quarks are confined? Why can't they be found in unbound states?

No one has observed before a "free" quark, i.e. a quark in an unbound state. According to one paper, I read that $p\bar{p}$ collision produce unbound $t\bar{t}$ pair which quickly decay into ...
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Change of flavour in strong interactions?

Sorry if this question has been asked already but after researching I have found that quark flavour is not changed in the strong interaction. This confused me because how can a down and anti down ...
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Calculating strong coupling constant $\alpha_s$

I'm trying to find out how to calculate the value of strong coupling constant. but haven't found any exact answer, all I get is reference to perturbation theory. is there any exact defined formula to ...
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What evidence is there that bottom and top quarks come in 3 colors?

We know, because of baryons such as the triple-strange Omega baryon spin 3/2, that at least the quarks 'up', 'down', and 'strange' must come in 3 colors because of the Pauli exclusion principle. No ...
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Confusion among channel $u$ and channel $t$ in exclusive reactions

In the this paper (https://arxiv.org/abs/1203.4392), on page 2 it is said that Since DVCS amplitude is symmetric under $s \leftrightarrow u$ channel crossing, the CFFs and $^{S}C^i_{\cdots}$ ...
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How does the pion decay constant $f_{\pi}$ depend on the number of flavors $N_f$?

I know that for standard QCD with quarks, chiral symmetry breaking occurs for around 4 - 5 light/active quarks - i.e. pions, or generally pseudoscalar goldstone bosons, definitely appear in the ...

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