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

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CP-Symmetry of the axion field and decay constant

In the $U(1)$-Peccei-Quinn-Symmetry an axion field $a$ is introduced in order to solve the strong CP-Problem. It is said, that below a certain scale $f_{a}$ this symmetry is broken and you are able to ...
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How far can we separate two bound quarks?

If we try to separate two quarks bound into a meson or a hadron, the energy in the gluon field eventually will be large enough to spawn a quark-antiquark pair. How far can we stretch that gluon ...
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Sudakov double logarithm

I have calculated a few NLO corrections in QED and in the final result the Sudakov double logarithms have always canceled. So I thought that they have no physical meaning. On the other hand I have ...
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A Question about a $U(1)_{B-L}$

I know I can write the QCD lagrangian like this: $$ \mathcal{L} = (i\bar{q}_{R} \gamma_{\mu}\partial_{\mu} {q}_{R} + i\bar{q}_{L}\gamma_{\mu}\partial_{\mu} {q}_{L}) + \text{other terms} $$ When ...
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Klein Gordon, Dirac, Proca [closed]

How do we know these equations : Klein-Gordon, Dirac, Proca is for spin 0, spin 1/2 , spin 1? How did people find Klein Gordon doesn't work for spin 1/2?
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color structure of a QCD Feynman diagram

I am trying to find a color structure of a Feynman diagram in QCD. I understand that for the diagram shown (left) we read from the double line notation diagram (right) , that the color structure is $ ...
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How many glueballs are there?

As I understand there are eight types of gluons (linear combinations of color/anticolor pairs with varying amplitudes) which can combine (for very short periods) to form glueballs. If there were no ...
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Can glueballs, consisting of massles gluons, get a mass without reference to a Higgs field? [duplicate]

Glueballs, the by the standard model predicted combinations of short-lived combinations of massless gluons, have a mass between 1.4 and 5 (MeV). But where is this mass coming from? From interaction ...
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Equality of renormalized coupling constant

I want to show, that the renormalized coupling constants of a SU(N) Yang-Mills field with fermions included, are all equal. In the most textbooks it is written, that this could been shown by the ...
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Semileptonic decay amplitude

I'm trying to do past exam papers and I am absolutely failing understand some things. I would very much appreciate any insights/intuition you have. The part I'm struggling is here: In the first ...
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18 views

Pion decay from chiral anomaly

I have to compute the decay rate of the process: $$ \pi^{0} \rightarrow \gamma \gamma $$ with 4-momenta $P \rightarrow K_{1}+K_{2},$ by the means of the following effective Lagrangian, coming from ...
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How would one go about drawing a Feynman diagram of color screening and anti-screening in QCD?

Title really explains this one. I'm not sure how to put together a diagram of the lowest order for colour screening and anti-screening in QCD. Seems to be a lack of diagrams for this in the ...
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Physical meaning of the chiral condensate in QCD

Considering the QCD Lagrangian in the chiral limit, where all the quarks masses are set to zero. Then the Lagrangian has the following chiral symmetry: $$ SU(L)_{V} \times SU(L)_{A} \times U(1)_{V} ...
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Is there a preferred mode of exchange of gluons?

Red , Blue and Green quarks are colorless when put together and thus the color of the proton remains colorless.In principle quarks can exchange colorless gluons to keep quarks together. Quarks can ...
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Some questions about QCD [closed]

About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD. 1, Why do we need to solve QCD ...
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Pion-pion scattering amplitude with an effective Lagrangian

I have to compute the scattering amplitude at tree level for the process $$ \pi^{a}\pi^{b} \rightarrow \pi^{c}\pi^{d} $$ with an interaction given by what is written in the square brackets of the ...
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Computation of theta-term from triangle diagram

The chiral $U(1)$ anomaly in QCD can be calculated exactly by one-loop Feynman diagrams, for example by the famous triangle diagram. I am currently performing the computation to get a better ...
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Is even the perturbative expansion of the QCD beta function expected to be divergent?

The usual QCD folklore tells us that perturbative expansions are (at best) asymptotic. Recently a colleague of mine told me that the expansion of the beta function is thought to be convergent because, ...
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Why do we exclude the quark condensate in the OPE?

In every QCD paper I open people say that in the OPE, the lowest order non-trivial condensate is the gluon condensate, whose dimensions are 4. Nonetheless, I knowof the existence of the quark ...
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Why have our eyes not evolved to see “gluons”? [closed]

Bit of a random question...photons are the propagators for QED, and we rely on photons to see the world around us. The gluon is the propagator in QCD. Why have our eyes not evolved to see gluons ...
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Constant electric background field from theta-term in QCD?

The theta-term of $1+1$ dimensional QED corresponds to a constant electric background field. Does the theta-term of QCD also induce a constant electric background field, which could be measurable in ...
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what is the analog of electronics for quarks or protons?

Is there an equivalent field for quarks or for protons as there is electronics for electrons where you can build engineer and mess around with things? May be even hack ?
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Resummation of large logarithms in effective field theory

I am trying to learn about the ideas of large-logarithms in effective field theory from a set of notes. However the following paragraph is confusing me: This doesn't seem quite right to me. Surely ...
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Are the properties assigned to quarks meaningful?

Suspect this may have been asked before, but can't find it. My question is: If you can never have a free quark, what sense does it make to attribute properties to them, since you can never ...
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Which properties control the strength of strong interactions?

Does the strong nuclear force depend on mass, charge or spin? Accordingly, can we order neutron-neutron, proton-proton and neutron-proton pairs by the strength of the strong force between them?
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Literatur recommendations for QCD Self study [duplicate]

Im a Computer Science Student with String physisch background, nur vety wrack formal Math Education In physisch the most advanced Theorie coursr I Tool was Quantum statistics, nur I have absolutely no ...
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Does an instanton couple equally to all flavors?

Do gravitational / electroweak / QCD / ... instantons couple equally to all fermion flavors? For example, do QCD instantons distinguish between the different quark flavors? Edit, due to comment ...
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Can glueball be created by electron-positron colliders?

Since electrons and positrons are leptons, which don't experience strong interaction, and glueballs are unadulterated entities of quantum chromodynamics. Does that mean hadron colliders are better at ...
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relative minus sign in radiation of gluon jets

I am trying to calculate the cross-section for electron-positron annihilation into a quark-antiquark pair and a gluon. I find that I need a relative minus sign between the two contributing diagrams in ...
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60 views

Why group elements associated with gauge transformations of finite action field configurations in QCD don't depend in $r$?

I am reading the chapter on instantons in Coleman's Aspects of Symmetry. I am puzzled by an argument i don't quite follow. In section 3.2, Coleman considers configurations of the gauge field with ...
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Gluon to quark scattering

I am trying to calculate the $g g\to q \bar q$ amplitude but am finding it intractably complex. I have determined that there are only two independent polarizations that contribute non-zero ...
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Would the existence of more than 16 quark flavors make QCD deconfinning?

Consider the QCD beta function. Its expansion in powers of the coupling is $$\beta(\mu)=-(\beta_0a(\mu)+\beta_1a^2(\mu)+\ldots)$$ where $a=\alpha/4\pi$. For simplicity let's neglect everything but ...
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Why do we say that gluons carry color charge?

We know that gluons are Lie algebra $su(3)$-valued one-form fiels $A_{\mu}$. And because of $[A_\mu,A_\nu]$ does not vanish generally for the non-Abelian case, gluons have self-interactions. Now how ...
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Confirming an inconsistency of the Balitsky-Kovchegov equation between references

I'm comparing the form of the Balitsky-Kovchegov equation, which describes the splitting of low-momentum gluons, between different references, and I'm finding an inconsistency: most sources (1, 2, 3, ...
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Where did Schwinger term come from?

Where did Schwinger term in the commutation relation of current density and charge density come from?
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Callan-Symanzik equation for the QCD scattering cross section of the $e^{-}e^{+}\to q\bar{q}$ process

In Peskin and Schroeder (Section 17.2) it is stated without derivation that the scattering cross section for the $e^{-}e^{+}\to q\bar{q}$ process obeys the following Callan-Symanzik equation: $$ ...
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NMHV Helicity Amplitudes.

Looking for NMHV amplitudes with 2 gluons and two fermion pairs. This paper presents compact formulas for these amplitudes that look like that: $ \frac{<13>^3\ [46]^3\ [5|3+2|1>}{t_1^{[3]}\ ...
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Why are there eight different types of gluons? [duplicate]

I read somewhere that are different types or ''colors'' of gluons, how can this be? There are 3 colors - red, blue and green - and this seems to make 9 differen types: red anti-red, red anti-blue, ...
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What is a “dynamically generated scale” physically?

A theory like QCD with massless quarks in four dimensions has no explicit mass parameters in its classical Lagrangian. At the quantum level however, instead a mass scale Λ is generated dynamically at ...
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Continuum of lattice QCD is free?

I am having a hard time getting to grips with the statement that $$g_{0}(a) \to 0 \text{ as } a \to 0$$ where $g_{0}$ is the bare coupling in lattice QCD and $a$ the lattice spacing. How come this ...
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Perturbative QCD application iin FAIR

In FAIR CBM scenario i.e at high density will be perturbative QCD applicable?
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Doubts about quark confinement, the pole mass and the quark gluon plasma

I have seen written a few times that the notion of a pole mass for a quark contradicts the quark confinement picture and that non-perturbatively it is expected that the quark pole mass be infinite. ...
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Calculation of divergences of Feynman diagram

In Peskin Schroeder, while considering gluon diagrams for $\beta$-function in QCD, they say that we can calculate the divergent part of loop diagram taking limit of zero external momenta - e.g. for ...
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Why there aren't gluons with charges like $b b$ or $ r r$? [duplicate]

Well it seems like it's a simple/stupid question, but I'm really interesting in such good explanation! Thank you!!
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Why there aren't gluons with charges like $b b$ or $r r$?

So my principal question is the one in the object above. But then I have another question related. Supposing I have a $bg$ gluon. How may I write it in the octet basis? Thank you for your help!!
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Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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Obtaining the correlator of harmonic oscillator

The two point function for harmonic oscillator can be written as $$\langle \langle x(t_1)x(t_2) \rangle \rangle =\frac{\int Dx(t) x(t_1)x(t_2) e^{-S(x)}}{\int Dx(t) e^{-S(x)}} \tag{21} \, .$$ In ...
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Yang-Mills theories, confinement and chiral symmetry breaking

I was thinking about hadrons in general Yang-Mills theories and I have some doubts that I'd like to discuss with you. Suppose that we have a Yang-Mills theory that, like QCD, tend to bind quarks ...
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Topological susceptibility in QCD and corresponding pole

The topological susceptibility in QCD (here I've used path integral approach, and hence I will neglect all contact terms) is defined as $$ \kappa (p) \equiv \lim_{y \to 0}\int d^{4}x ...
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Names for various color indices in QCD

In Quantum Chromodynamics with $\mathrm{SU}(3)$ there are at least two types of color indices: Indices $a$, $b$, … that index the eight generators of the group $\mathrm{SU}(3)$. In some sense they ...