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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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Why hasn't QCD fed back to nuclear engineering?

A recent commenter on one of my questions noted that Fermi could take a tour of a modern nuclear powerplant and not be suprised by anything, and I believe that. I also think this shouldn't be the case,...
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How many quark flavor quantum numbers are really needed?

Several authors I've consulted recently use six separate flavor quantum numbers for the six observed flavors of quarks when constructing their QCD Lagrangians That seems excessive when three "family" ...
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How does the instanton break the $U(1)_A$ symmetry in QCD?

The $U(1)_A$ symmetry in QCD is anomalous. Its supposed to be broken by the instantons. Can anyone physically describe how does that happen?
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How and why is the pentaquark stable if it consists of 4 quarks and an antiquark?

If matter and antimatter annihilate each other, why is the pentaquark stable since quarks are matter and the antiquark is antimatter?
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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 ...
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How do we know that gluons have no electric charge?

Since the W boson carries electric charge and there is no a priori reason that massless electrically charged bosons cannot exist, I'm wondering if the lack of gluon electric charge has been confirmed ...
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QCD flavor gauging?

I ran across this old post: What the heck is the sigma (f0) 600? The question author is explaining his understanding of the spectrum of QCD in terms of various interesting things like chiral symmetry ...
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QCD Trace Anomaly and Mass

In the paper in equations 4 and 5, some of the mass of the nucleons comes from the "trace anomaly" of the QCD energy-momentum tensor (as described in the paragraph following these equations). Is there ...
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What is the twist 2 sector of nucleonic parton distributions? (edit: i think i answered it)

I am on the evolution of transversity distributions in QCD. And in the papers everyone talks about twist 2 sector and leading twist corrections. I can't find anything about twist. Do they talk about ...
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How can we have a quark condensate without a quark potential?

The QCD quark Lagrangian in the chiral limit is $$ L_q = i \bar{q}{\not D} q $$ which possesses a global $SU(3)_L \times SU(3)_R$ symmetry. I've read many places that this is symmetry is ...
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Clarification about confinement of colour charged objects

In lecture today we were reviewing the QCD lagrangian, and discussing hadronic wavefunctions. My lecturer said that QCD alone allows for states of colored hadrons, however because we do not see ...
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Why does literature list the strong coupling at the scale of the Z-boson's mass?

In the 2004 edition of the book "QCD as a Theory of Hadrons" by S. Narison, the author provides a value for the strong coupling at a scale of the mass of the Z boson, $$ \alpha_s (M_Z) = 0.1181 \pm ...
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Ghosts use in the calculus of the scattering matrix

When you perform the calculus of $S$ matrix in, for instance, QCD maybe you need to add ghosts in external legs or internal loops. E.g.: $q\bar{q} \rightarrow gg$ needs 2 ghosts diagrams with ghosts ...
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A Naive Question about Gauge Theory

I am suffering from a question I encountered from the lecture notes of gauge theory by David Tong. The problem comes from page 67 on the gauge fixing in back-ground gauge method. In David Tong's ...
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Why quarks in the fundamental and gluons in the adjoint?

I have been told that in gauge theories “fermionic matter goes in the fundamental rep of $SU(N)$, while gauge fields go in the adjoint rep”. I understand how this works, and for instance, in QCD,...
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Wilson loop and Polyakov loop

As I understand, the Wilson line is the operator $W(x) = P\exp(i\int_{xi}^{xf} A.dx)$, where $P$ is path ordering. The Polyakov loop $P(x)$ on the other hand is the trace of the Wilson loop $W(x)$ ...
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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 and gluons 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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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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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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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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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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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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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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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 ...