Questions tagged [quantum-chromodynamics]

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

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Regge theory and $SU(3)$ mass formula

In a video interview, Murray Gell-Mann states (at 40 seconds) "I have wondered all this time, and I still wonder, whether the straightness of those [Regge] trajectories, and the accuracy of the ...
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Pion mass in theta vacuum

Does the mass of the charged pion depend on the QCD vacuum angle? I've seen it said---e.g., in these TASI lectures---that when the quark mass matrix is real and there is a nonzero QCD vacuum angle $\...
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Why don't green and anti-green gluons immediately annihilate each other?

I can't believe I haven't found an answer elsewhere..... I have read repeatedly about blue/anti-blue gluons, etc., but no reason as to why they don't destroy each other immediately..... Or maybe ...
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Color symmetries in variant QCD

Suppose we only have two colors, for example, red (R) and blue (B) to construct the wave functions of baryons and mesons and that the color symmetry is SU (2) and not SU (3). In this situation, ...
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How do soft Pomerons become hard?

The exchange of soft Pomerons (and Reggeons) ($\alpha_R(0)=0.55$ and $\alpha_P(0)=1.08$) seem to describe total hadron-hadron cross sections pretty well in the Regge limit. See, for example: https://...
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How does the strong interaction “create” the nuclear force?

I’ve recently read that the strong interaction, that holds the quarks together to form protons and neutrons, also creates a residual force called the nuclear force, which holds the neutrons and ...
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What happens to large gauge transformations in gauges different from the temporal gauge?

There are already several questions regarding the meaning and definition of large gauge transformations. Discussions of large gauge transformations typically only happen in the context of the ...
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Implications of momenta sign conventions in QCD Feynman rules

In QCD, the Feynman rules for the vertices are usually presented with all momenta pointing inward. For the total amplitude of a given process, does this also affect the signs of the momenta taken in ...
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Why does the axion solve the CP problem?

I don't understand why the CP violating term in QCD vanishes when we introduce the axion. The term is $$\left(\frac{a}{f_a}+\theta\right)G\tilde{G}$$ It is claimed that $\left\langle a\right\rangle=-\...
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Sufficient and Necessary Conditions for Chiral Symmetry Breaking

In their 2005 paper, the authors write (just below eq. 3.19) we see that a non-zero value of $F_0$ is a necessary and sufficient criterion for spontaneous chiral symmetry breaking. On the other ...
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1answer
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Longitudinal polarization of gluons in loop

I have a short question about the possible gluon polarization in loop diagrams. For external gluons, we only want the 2 transverse polarizations. In Peskin-Schroeder it is explained that in Feynman-...
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Why do parton distribution functions not depend on the total momentum of the composite state?

When defining such quantity as the elastic form factor, I kinda understand why it turns out to be independent of the momentum of the charged particle, and only dependent on the momentum of the photon ...
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An invariant of the gauge group $G$ that is totally symmetric with three indices in the adjoint representation

In Ch.19 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.680 the property of a quantity $$\mathcal{A}^{abc}=\mathrm{tr}\left[t^a\{t^b,t^c\}\right]\tag{19.132}$$ ...
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Instantons, renormalization, and the Schwinger Model

Instantons in QCD contribute to the up, down, and strange quark masses (see, e.g., Georgi and McArthur (1981) or Kaplan and Manohar (1986)). Some papers claim that this contribution is equivalent to ...
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Would Color Confinement apply in higher dimensions?

As I understand it color confinement comes from the fact that as the distance between two color charges increases the color potential energy increases, instead of decreasing, and the energy needed to ...
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1answer
76 views

$U(N)$ & $SU(N)$ : What's the conceptual difference in Gauge Theory?

I know the mathematical difference that one means $ absolutevalue(det) = 1$ and one means det = 1 (rotation) and that ones the subgroup of the other and so on. But: has a local/gauged $SU(3)$ ...
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Why do we have 3 quantum colours?

I understand the need to invoke colour as another quantum state to explain the observation of uuu ddd and sss baryons. I just wanted to know if there was some other property which explains why we only ...
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How is the chiral condensate estimated from the pion decay constant?

In low-energy QCD, there are several dimensionful quantities that come up. Writing the chiral condensate as $$\langle \Omega | \bar{q}_{Ri} q_{Lj} | \Omega \rangle = - v^3 \exp \left(\frac{2 i \pi^a(...
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How Is Are Parton Distribution Functions (PDFs) Determined In Practice And In Theory?

I have put my actual questions in bold normal font, and the rest of this question clarifies what I mean to be asking, especially in terms of the depth and kinds of information I am looking for. ...
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Why small $x$ corresponds to high energy process?

I just start to study Quantum Chromodynamics, I read in some references that small $x$ corresponds to process of high energy, but I cannot find a straightforward explanation. In the case of electron ...
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1answer
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Topological theta-term as a background electric/magnetic field?

The topological $\theta$-term in the Schwinger model (1+1-dimensional QED) can be interpreted as a background electric field, as explained in Chapter 7.1.2 of Tong's lecture notes. The same holds true ...
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About the mass of the particles

Studying Higgs mechanism in EW theory and QCD I have a couple of questions that I would like to clarify: 1) The quark mass term in QCD Lagrangian should come from Higgs mechanism in EW sector of SM. ...
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Polarized structure functions and Bjorken sum rule

I'm trying to understand what the Bjorken sum rule and the polarized structure functions entering it are. I will use equation (2.3) here as a reference for asking the question. In Peskin, I've only ...
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Mass term in QCD is not hermitian? [duplicate]

Accordingly to the result $$ (\bar{\psi}\psi)^\dagger = (-1)\bar{\psi}\psi \tag1$$ coming from the fact that fields with and without bar anti-commutes, you can deduce that the QCD mass term $$ -m\...
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2answers
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$\theta$ angle QCD technically natural

Why exactly does the observed smallness of the $\theta$-angle in QCD constitute a fine-tuning problem? I thought that the content of 't Hooft's technical naturalness was exactly that a parameter is ...
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Why Aren't Hadron Masses More Useful In Determining Standard Model Constant Values?

Some of the most exquisitely precise experimental measurements in all of physics are the masses of the various hadrons. Consider these examples: the proton mass is known to eleven significant digits. ...
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Are theta vacua topologically protected?

In discussions of Yang-Mills instantons it is often stated that one should sum in the path integral over all contributions of fluctuations around all the topologically distinct vacua labelled by ...
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How much of the proton's mass is due to the Higgs field?

The proton mass is 938 MeV. People often claim that (A) The proton is a bound state of two up quarks and one down quark, with the three quarks contributing a total rest mass of $2 \times (2.2 \text{...
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1answer
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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?