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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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Feynman Parameters vs Passarino-Veltman reduction

I have computed the following one-loop integral: $$\int \frac{d^dp}{(2\pi)^d} \frac{p^{\mu}p^{\nu}}{(p+k)^2p^2}.$$ Using both Feynman Parameters and the Passarino-Veltman reduction. However, while I ...
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QCD vs. QED gauge invariance

Trying to understand the difference between QED and QCD gauge invariance treatment I found the following paper: https://arxiv.org/pdf/1101.3425.pdf I have the following questions: 1) I understand Eq....
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Why do quarks have colour?

I asked a question here a few days ago and got some fantastic answers so I'm going to continue. Let me preface this by saying I know quarks do not actually have 'colour', but colour is some sort of ...
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u-channel in $gg \rightarrow u\bar{u}$

I've seen that for the QCD process $gg \rightarrow u\bar{u}$, where $g$ is a gluon and $u, \bar{u}$ are the up quark and the corresponding antiquark, there is s, t and u channels. I perfectly ...
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Four-brackets (Hodges, Momentum Twistors)

I use the reference from Andrew Hodges, available at https://arxiv.org/abs/0905.1473. I am having trouble understanding his use of the four-bracket. I refer to equation 6 and equation 9, where he ...
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73 views

Comparison between $\rho^0$ and $J/\psi$ decay mode

Why must a hadronic decay of the $J/\psi$ meson include (at least) three gluons? Why is the decay mediated by a single gluon allowed for the $\rho^0$ meson?
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Invariance of Yang-Mills Lagrangian under charge conjugation

The Yang-Mills Lagrangian gauge invariant under an $SU(N)$ tranformation can be written as $${\cal L} = -\frac{1}{4}F_{\mu\nu}^i F^{i\ \mu\nu} \tag1$$ (Sum over $i$ implicit) This Lagrangian ...
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Question about DGLAP evolution equation

I am reading chapter 32.2 of Schwartz's QFT book, where he defines the renormalized PDFs $f_i(x, \mu)$. This leads to an equation (32.48), which relates PDFs at different scales $\mu, \mu_1$: $f_i(x,\...
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Effective field theories from QCD

Is there a way - at least formally - to derive theories like chiral perturbation theory or heavy baryon effective theory from QCD? As an example: is it possible first to introduce the effective ...
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QCD gluon physical polarisation sum in the three gluon vertex

In the Compton scattering quark($p_1$) + gluon ($q_1$)-> quark($p_2$) + gluon($q_2$), there is three gluon vertex contribution. If we choose the physical polarisation sum $\sum_{\lambda} \epsilon^a(\...
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Contribution from $u$-channel and $t$-channel processes in OPE analysis for deep inelastic scattering

In Ch.18 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.633 the moment sum rules for the deep inelastic form factors are discussed $$\int_0^1 dx x^{n-1}f_f^+(x,...
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Why is lattice QCD called non-perturbative?

Like, if you are approximating a smooth structure with a discrete lattice, isn't this like a perturbation from smooth space-time? If Feynman diagrams are a perturbative method, why are Feynamn ...
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62 views

How to think about color charged objects

When imagining color charged objects, I know we can treat color and anti-color much like electromagnetism. What I'm having trouble with is imagining the interaction of similarly coloured objects. Now ...
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1answer
92 views

Is color charge quantized?

I was reading this stackexchange question, and found the answer to my question not totally answered. Clearly there is color and anti-color in analogy to electric charge, and color charge clearly ...
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1answer
48 views

Does the external leg contraction of gluon in QCD carry group generator index?

While I am trying to compute the amplitude for the following Feynman diagram I realized that the external leg contraction of $g$ should carry group generator index $A$ or $B$, is that right? If so, ...
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What should I read to understand this question?

I understand the strong force as a Yang-Mills theory with $SU(3)$ color invariance. I understand that the quarks live in the fundamental representation of $SU(3)$ and that gluons live in the adjoint. ...
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The kinematic region for the operator product expansion

In Ch.18 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.613 the operator product expansion (OPE) is introduced $$\mathcal{O}_1(x)\mathcal{O}_2(0)\to \sum_n C_{...
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Temperature-dependence of quark potential in Abelian lattice gauge theory

I am working with Kapusta's "Finite-Temperature Field Theory" textbook, and am working through the first part of chapter 10. When building the correlator of the two quarks a distance $R$ apart in the ...
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If quarks can't be isolated in the first place, how did they become confined in the early universe?

On one hand, we know that quarks cannot exist in isolation. This is because the energy required to dissociate a quark-antiquark pair in a meson (or quarks in a hadron) will create a mesons (or hadrons)...
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Why is color confinement a difficult problem?

Assuming color force follows a constant rule of force instead of an inverse square rule of force. And that red, green and blue are all attracted to each other. Why is color confinement considered a ...
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One-loop correction to triple gluon vertex in QCD

I'm trying to calculate a one loop correction to the 3 gluon vertex, which is given by a circular correction, and another that's due to the 4 gluon vertex. However I'm unsure how the ghost fields ...
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1answer
92 views

Commutator of a quark current

In Quantum Chromodynamics, when we take the limit in which the u, d and s quarks have no mass, there exists a global symmetry $G \equiv SU(3)_L \otimes SU(3)_R$ in flavour space. The corresponding ...
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Feynman rule for 3-gluon vertex

I want to obtain the Feynman rule for the 3-gluon vertex, but looking at the result I don't really know how to tackle it. The relevant term in the Lagrangian is \begin{equation} \mathcal{L}_\text{...
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What macroscopic fields exist around color supercurrent?

For an ordinary superconductor such as Lead, charge supercurrent gives rise to a magnetic field around the whole material for low enough currents. At large enough currents, the superconductor will ...
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Questions on how Wilson loops relate to field & charge conservation, and lattice QFT

The path-ordered exponential from which the Wilson loop is traced is, crudely, $$ \prod (I+ A_\alpha dx^\alpha) = \mathcal{P}\,\mathrm{exp}(i \oint A_\alpha dx^\alpha )$$ which returns a matrix $\...
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Boundary bulk intuitive comparison between Planckian black holes and QCD jets

One of the key intuitions that we derive from trying to extrapolate QFT to the Planck scale is that when one tries to resolve features at those scales, you only get a larger uncertainty as your ...
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What is the relation between the Gribov problem and color confinement?

I have heard that the Gribov problem is in some way related to color confinement (For instance: Gribov copies and confinement). Although I understand what both the Gribov and confinement problems are, ...
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1answer
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Relation of vector and scalar matrix elements for hadronic transitions

Consider a matrix element $$ F_{\mu}(p_{h'}, p_{h}, \dots) = \langle h'(p_{h'})|\bar{q}_{i}\gamma_{\mu}q_{j}|p_{h}\rangle, $$ describing transition of some initial hadron $h$ that contains a quark $...
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Inclusive vs exclusive br fractions

Consider the inclusive process $$ q \to X, $$ where $q$ is the quark inside some hadron $H$, and $X$ is some fixed final state. Corresponding exclusive processes are $$ H \to X_{1}, \quad H \to X_{...
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2answers
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Does it really make sense to talk about the color of gluons?

It is my understanding that by enforcing SU(3) gauge invariance on our lagrangian of 3-colored quark fields, we are forced to accept the existence of 8 new massless vector fields, the gluons. The 8 ...
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Question about Gluon self energy diagram/symmetry factor

I am a qft beginner and have a question: In Peskin & Schroeder chapter 16.5 there is given an expression for a gluon self energy diagram: According to the feynman rules we get $\frac{1}{2} \int \...
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Isn't there a unique vacuum of the Yang-Mills quantum theory?

The theta vacua$^1$ of a Yang-Mills quantum theory are given by $$|\theta\rangle=\sum\limits_{n=-\infty}^{\infty}e^{in\theta}|n\rangle.$$ In Srednicki's Quantum Field Theory, he claims that the ...
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Integration of the splitting function

I have a problem performing the following integration provided in the paper by Catani and Seymour (arXiv: hep-ph/9605323) page 27. Given is the integral $$ \mathcal{V}=\int_0^1 (z(1-z))^{-\epsilon} \...
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How do we show that gluon-fields have color?

I understand how to derive the QCD lagrangian based on certain assumptions about Quark fields and $SU(3)$ gauge invariance and in the final expression one finds the term $(A_µ)^c*T_c$ where $T_c$ is ...
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What is the experimental evidence that the nucleons are made up of three quarks?

What is the experimental evidence that the nucleons are made up of three quarks? What is the point of saying that nucleons are made of quarks when there are also gluons inside it?
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How does the transition to turbulence happen in incompressible fluids?

The question is difficult to understand unless I explain why I am asking it. I would not really be interested in Fluid Dynamics if the transition to turbulent flow were not, at least approximately, ...
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2answers
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When/ how were/are quarks formed?

We know that all particles can eventually be converted into energy. We know also that electrons were and still are formed by pair production from a 1MeV photon. Do physicists have yet any idea how ...
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1answer
49 views

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\ \...
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Quark-Gluon Plasma vs QCD binding energy

The binding energy of nucleons is on the order of around 900 MEV. Yet, Quark-Gluon plasma is observed at around 175-300MEV. This doesn't seem to make any sense - how can only 300 MEV worth of energy ...
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Are the $N_f$ quarks in the coefficients of the beta function massless?

Consider the running of the strong coupling in QCD $$ \mu\frac{d}{d\mu}\alpha(\mu)=-\frac{1}{2\pi}\beta_0\alpha^2+\dots $$ there I have written the perturbative expansion of the beta function to ...
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Covariant Derivative in QCD: How does it act on gluons?

Let the covariant derivative be $$D_\mu = \partial_\mu + \text ig\ A_\mu^a t^a,\quad a=1,\ldots,8$$where $g$ is the bare QCD coupling, $A_\mu^a$ are the eight gluon fields and $t^a=\tfrac{1}{2}\lambda^...
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What is the Noether charge associated with the the color $SU(3)$ symmetry of QCD?

A version of the Noether's theorem applies to local gauge symmetries. What is the Noether's charge associated with a non-abelian gauge symmetry such as the color $SU(3)$ and how is that derived? I ...
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Four-fermion “contact” interactions differing from those arising from the Standard Model

In the 1998 article Compositeness Test at the FMC with Bhabha Scattering, it states that: It was pointed out that the existence of quark and lepton substructure will be signalled at energies well ...
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324 views

$\mathfrak{su}(3)$ structure constants

The $\mathfrak{su}(3)$ structure constants $f^{abc}$ are defined by $$[T^a,T^b] = i f^{abc} T^c,$$ with $T^a$ being the generators of the group $\mathrm{SU}(3)$. They are usually written out in a very ...
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At what stage is it necessary to introduce a field theory in the regeon-pomeron-odderon model of hadron interactions?

I've been reading some papers from G.F. Chew and S. C. Frautschi and they do not even bother to introduce the concept of "Field" when they describe hadron interactions. My impression is that they do ...
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How to “build” a proton

Sabine Hossenfelder in her column The End of Theoretical Physics As We Know It made the following statement: For example, we have a perfectly fine theory that describes the elementary particles ...
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Do Reggeons-Pomerons-Odderons offer an Universal picture of hadron interactions?

As far as I know, the total cross-sections of the following hadron interactions are well described by a single Reggeon trajectory and a single Pomeron (soft Pomeron) trajectory. It seems to work for ...
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2answers
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What are chromoelectric and chromomagnetic fields?

Are they the normal elctric and magnetic fields from Maxwell fields? Or are they just the corresponding components from $G_{\mu\nu}^a$ (the gluon fields), say chromoelectric fields are simply $G_{0i}^...
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What does that means? “QCD is a non-linear and non-trivial field theory?”

I know QCD is represented by the $SU(3)$ group and is non-abelian. Then, as a consequence QCD is a non-linear and non-trivial field theory. I would like to know why? and what does that means?
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Why are the elastic and total cross-section of $pp$ collisions increasing as the C.O.M. energy grows?

Well, that's about it. I don't find any reasonable explanation for this fact. Are they transversally expanding as the energy increases? Please, remember that strong interactions are short ranged and ...