Questions tagged [quantum-chromodynamics]

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

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Is it a coincidence that the maximum number of protons in a stable nucleus is on the order of $\alpha_s / \alpha_{EM}$?

The equivalent to the fine-structure constant for the strong interaction is about $\alpha_s \approx 0.5$ at the proton rest mass energy (and it runs pretty slowly with energy, so it's on this order ...
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Nielsen-Ninomiya Theorem on a 2+1 lattice

(a) In the paper on the proof of the Nielsen-Ninomiya theorem, it is shown for 1+1 and 3+1 lattices. Does the proof hold on lattices with even number of spatial dimensions (e.g 2 spatial + 1 time)? If ...
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Why is color screening in Quark Gluon Plasma not effective for light quarks mesons like pions?

The color screening of quarkonia states like $J/\psi$ (bound states of charm and anti-charm) and $\Upsilon$ (bound states of beauty and anti-beauty) is considered one signal of QGP (quark-gluon plasma)...
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Symmetry factor of gluon self-energy

In Peskin & Schroeder, p.523, they give the diagram contributing to the gluon self-energy that arises from the 3-gluon vertex, and they claim that the $1/2$ factor is a symmetry factor: How can ...
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Confusions with gluons. How many of them are there?

Gluons are bicolored objects. They are made out of one color and one anticolor. Therefore, there seems to be nine possible states $r\bar{r},r\bar{b},r\bar{g},b\bar{r},b\bar{b},b\bar{g},g\bar{r},g\bar{...
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Is QCD computable?

Are arbitrarily good approximations of the time evolution of any QCD system, given initial and boundary conditions, Turing computable? Can lattice QCD simulations be used to do so in theory? How ...
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A question about quarks and quantum chromodynamics

Penrose writes the following on pg 648 of his book "Road to Reality" How can we treat quarks as real particles, if they have the wrong spin-statistics relation? The way that this problem is dealt ...
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Measuring strong coupling constant

How can the strong coupling constant be measured?
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Asymptotic freedom and momentum exchange

Why is the momentum exchange very high for low distances? For sufficiently short distances or large exchanges of momentum https://en.wikipedia.org/wiki/Asymptotic_freedom While I think about ...
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How does the underlying symmetry of QCD imply the allowance of a 4-gluon vertex?

Quantum chromodynamics allows for a four-gluon vertex such as this, in a diagram Such a vertex would never be allowed in quantum electrodynamics, which has an underlying U(1) gauge symmetry. I know ...
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Is is cheating to use alpha strong (instead of V_QCD) to argue that there is asymptotic freedom of QCD?

For asymptotic freedom of QCD, people give the argument that alpha_strong decreases at high energy (thus there is freedom at low distance). But if we make the reasoning on the QCD potential, for ...
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Why do mesons decay?

Why do mesons decay shortly while baryons are more stable? And why do mesons decay, meaning that there are unstable, while they formed because meson is more stable than the two corresponding quarks? ...
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Is the asymptotic value (at high energy) of alpha strong null or non null?

If it is non null then why do we say that there is asymptotic freedom. Freedom would mean alpha strong equal zero
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Is the QCD potential really monotonic ? How does it prevent two quarks from meson to annihilate?

The QCD potential is made of two terms -(4/3) * alpha_s / r that describes the short distance and the term +k*r that describes the long distance Of course, alpha is a function of energy, so it is ...
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How can we reconcile the many different models in QCD that make inconsistent assumptions/claims?

For example, we have quark models, shell models, cluster models, etc. which seem to admit to different interpretations regarding nuclear structure and dynamics. Is there a way to resolve the fact that ...
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Theta-dependence of QCD quark condensate for $m=0$

I'm trying to understand the $\theta$-dependence of the following expression for the quark condensate in QCD, $$ \langle \bar{\psi}\psi\rangle = - \Sigma \cos(\theta)$$ taken from Eqs. (5) and (7) ...
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Could the Odderon intercept be equal to $\alpha_\mathbb {O}(0)=0.813$? [closed]

The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space): $$\beta=\beta'=0.813(9)$$ $$\nu_\perp=0.584(5)...
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If quarks don't exist individually how can we say baryons are made up of three quarks?

We know the composite subatomic particles are made up of odd number of quarks (at least 3 for baryons ) or combination of quarks and antiquarks (mesons). My question is if they don't exist ...
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What does QCD look like in higher dimensions?

It was pointed out as a comment on my question on atomic physics in higher dimensions that that question implicitly rests on an assumption that QCD, and thus the structure of atomic nuclei, is pretty ...
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A Question about Wave-Function Renormalization Factor in SQCD

Here, I have a question about the one-loop computation of the wave-function renormalization factor in SQCD. According to Seiberg duality, the following electric $\mathrm{SQCD}_{e}$ \begin{gather} ...
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What is the real problem in the free body problem?

Ions are produced when an EM neutral atom gains EM charge by gaining or losing electrons, by collision with other charged particles or photons. The study of such collisions is of fundamental ...
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How much color charge does a quark carry? [duplicate]

If we look at QED, we can say that an electron carries the charge $$Q_\text{electr.}=-e = -1.602\cdot 10^{-19}\text{ C}$$ so how can we extend this to quarks? Would, for instance, $$ Q_\text{red} = ...
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Why use $SU(3)$ and not $SL(3, \mathbb{R})$ for color charge? [duplicate]

Why do we use the group $SU(3)$ and not $SL(3, \mathbb{R})$ for color charge? As far as I can tell, the $SL(3, \mathbb{R})$ is volume and orientation preserving, by the fact that it has unit ...
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Understanding some lines from 't Hooft's paper on large-N QCD in 1+1d

In 't Hooft's paper "A two-dimensional model for mesons", the author shows that two-dimensional (1+1) QCD in the large-N limit interestingly gives a theory of mesons. 't Hooft calculates the "mesonic ...
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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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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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$U(N)$ & $SU(N)$ : 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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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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$\theta$ 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. ...