Questions tagged [quantum-chromodynamics]

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

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Why is the convolution between hadron structure functions and PDFs defined this way?

Say you have the distribution function $\rho_i$ of a quark $i$ (depending on the momentum fraction of that quark), and a structure function $\hat{F}_i$ (depending on the "Bjorken variable" $...
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Understanding the proof of the “Photon-Decoupling Identity” for colour-ordered Yang-Mills amplitudes

Problem: To prove the Photon-Decoupling Identity for colour-ordered Yang-Mills amplitudes: $$0= A(1,2,3,...,n)+A(2,1,3,...,n)+...+A(2,3,...,1,n) \tag{1}$$ I know I must use $(2)$, which expresses ...
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Quark gluon plasma at arbitrarily high temperature

Does the quark-gluon plasma become weakly coupled at infinite temperature (due to asymptotic freedom), or does it maintain some non-perturbative behavior?
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$e^+e^- \to p^+p^-$ cross-section?

Does anyone know of a calculated or measured cross-section somewhere for $e^+e^-$ annihilation into a proton-antiproton pair, say at the LEP? Seems to me that it would be rather strongly energetically ...
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Is tree-level QCD on-shell constructible, with BCFW?

Is tree-level QCD on-shell constructible, with BCFW? Pure yang mills is on-shell constructible, what is one add into massless fermions?
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Color symmetry and flavor symmetry in QCD

In QCD, there is an SU(3) color symmetry for each flavor of quark as well as an SU(3) flavor symmetry for $u, d, s$ (although the latter is approximate). Why is there a gauge field for the SU(3) color ...
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Winding number of QCD vacuum

We know that QCD vacuum has instantons, which corresponds to tunneling process. Consider $SU(2)$ gauge theory without matter. We say that in the classical configuration of vacuum state $F^a_{\mu\nu}=0$...
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Decoupling of ghost fields in axial-gauge QCD

After quantizing QCD using the Faddeev-Popov "prescription", we end up with the original QCD Lagrangian plus the gauge-fixing term, \begin{equation} -\frac{1}{2\alpha}(n\cdot A)^2, \end{equation} and ...
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Models of confinement based on negative mass carriers

In the old Yukawa model of nuclear forces, it was proposed that short-range interactions were mediated by exchanges using massive force carriers (originally, mesons were proposed for this). If one ...
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What is the meaning of a flat metric invariant up to a Weyl factor?

When studying CFT I was told that: A conformal transformation is a spacetime transformation that leaves the flat metric invariant up to a Weyl factor. What is the meaning of leaving a metric ...
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Simple “toy-model”-like explanation of quark confinement (QCD) and accompanying math

I have a qualitative understanding of quantum chromodynamics within nucleons and between nucleons, but I do not understand the math behind some of the physics like quark confinement. What is the math ...
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Equations of motion of classical chromodynamics with Yang-Mills theory

I am currently reading a paper about classical chromodynamics: https://arxiv.org/abs/hep-th/0607203 However I have problems understanding equation (2) and (4) (2): \begin{equation} F_{\mu \nu}= \...
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Colour-ordering formula of QCD amplitudes (tree-level)

I have been studying colour-ordered amplitudes and spinor helicity formalism for a while. It is now apparent to me that I do not fully understand the 'master' formula which allows us to relate the ...
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Wick contraction for unperturbative fields

Say I want to calculate the transition amplitude of a meson to 2 photons using QED only: $$\langle \gamma(q1) \gamma(q2)|meson\rangle$$ I can start with normal perturbation theory: $$\langle \gamma(...
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1answer
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How do I calculate the amplitude of an $s$-channel Feynman diagram?

What is is the starting point to measure the amplitude in an $s$-diagram like the one below where two particles collide and create a propagator followed by the final product? I know that in $t$-...
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What is the meaning of the structure constant for the $\rm SU(3)$ group and how I can find its values? [duplicate]

To calculate the tree-level amplitude for: $$Z(p_1) + Z(p_2) \to Z(p_3) +Z(p_4)$$ I must take into the consideration, amongst other cases, the amplitude for: I know the values shown in another post ...
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How do I find the values for the structure constants ($f^{abc}$) of a gauge group?

How do I find the values for the structure constants ($f^{abc}$) of a gauge group, as a mean to find the tree-level amplitude for a process in which one of the tree-level diagrams is: the process ...
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Does the path of a Wilson line in a quark-correlator matter?

Consider a gauge-invariant quark correlation function nested inside an arbitrary state $|p\rangle$ $$\langle p |\bar \psi(z)_{\alpha,a}\left( W_{\Gamma}(z,0)\right)_{ab}\psi(0)_{\beta,b}|p\rangle \...
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Colour counting in $\mathrm{e}^++\mathrm{e}^-\to \mathrm{q}+\bar{\mathrm{q}}+\mathrm{g}$ final states

I want to calculate the cross section associated to the $\mathrm{e}^++\mathrm{e}^-\to \mathrm{q}+\bar{\mathrm{q}}+\mathrm{g}$ process as in the Feynman diagram (source) and the other one in which the ...
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1answer
310 views

Derivative of a Wilson Line

It's my first post on this website so please excuse any breaches of protocol that I'm unaware of. I've come across a formula for taking derivatives of Wilson Lines with respect to points on the path,...
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How does neutron radiation affects a body? [closed]

My question involves two aspects of the same thing: how does neutron radiation affect the particles in our body. • First of all: How does the effects happen, from a quantum perspective? • Second, ...
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What’s lacking in our understanding of the strong interaction?

As far as I’m aware, our understanding of the strong interaction and strong nuclear force is pretty good. We can explain how particles move and stick together with good models. But from what I can ...
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How to calculate the total cross section of a QCD process? (qq->gg)

I want to calculate the total cross section of various QCD processes (let's go with $q\bar{q}\rightarrow gg$ for this question) at tree level for some colliding hadrons at a certain energy (let's go ...
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Understanding interaction between two quarks

Two protons and two electrons repel each other as they have same charge. Protons and electrons attract each other since they are oppositely charged. A single proton is made up of two up and one down ...
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If nucleons are tied together are their quarks closer with each other than in the single nucleon?

If the volume of the core of an atom is the sum of the volumes of every single nucleon does this mean that quarks of two neighbouring neutrons are much closer than the quarks in each of the two ...
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How do I compute the amplitude for this QCD diagram?

Studying the following scattering process at a tree-level: $$\bar{q}^i (p_a) + q^j (p_b) \to \gamma(k_1) + \gamma(k_2)$$ Considering the “reduced” amplitude that is obtained by stripping away the ...
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Can one distinguish QED (or QCD) from QED (or QCD) plus higher field powers?

The Lagrangian of QED is based on minimal coupling; it contains a term proportional to $F_{\mu\nu}F^{\mu\nu}$ for the electromagnetic field. The QED Lagrangian is the simplest Lagrangian with U(1) ...
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Quark confinement mechanism

As far as I understood: Quark confinement states that observing individual quarks is not possible, color charged quarks are confined into hadrons. As we try to pull them apart, force between them ...
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What would the propagator of the Feynamn diagram for $\bar{q}q \to \gamma \gamma$ be?

I am trying to draw the Feynman diagram at tree-level for: $$\bar{q}q \to \gamma\gamma $$ but I don't seem to understand what sort of propagator fits this diagram? I have seen in some places that a ...
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36 views

Why do the soft QCD processes have non-perturbative nature?

I know that due to their non-perturbative nature, soft (i.e. low momentum transfer) QCD processes require phenomenological models that need to be tuned to data. However, I do not exactly understand ...
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Why there is no such a thing as colour moment?

I was busy google about different types of electric and magnetic dipole moment then a thought suddenly striked me, why there is no colour multipole moment?
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Calculating the pion decay constant in Chiral Perturbation Theory

I am trying to calculate the pion decay constant by following this paper [arXiv]. Since the decay constant is defined via $$ \langle 0| A_\mu (0) | \phi(p)\rangle = \text{i} p_\mu F_0 \tag{3.19}$$ ...
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Is there a closed form solution to the parallel DGLAP evolution equation

The parallel DGLAP evolution equation is given by $$t\frac{\partial f(x,t)}{\partial t} = \frac{\alpha_s(t)}{2\pi} \int_x^1 \frac{d\hat{x}}{\hat{x}} P_{qq}(\hat{x})f\left(\frac{x}{\hat{x}},t\right)$$ ...
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Kinematic region of Bjorken $x_B$ in Deep inelastic electron-proton scattering

I am considering DIS with an electron and a proton: $$ e^-(k) p^+(P) \rightarrow e^-(k') X(p_X) $$ I define $q = k-k'$ and $Q^2 = -q^2 > 0$. The variable $x_B = \frac{Q^2}{2P\cdot q}$ is should be ...
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Why is the self-energy for quarks in $d=2$ Large $N$ QCD only order $g^2$?

In an interesting article by 't Hooft , he is able to find the exact quark propagator, in the large $N$ limit of QCD. He finds that the full 1PI self-energy is given by: $$\Gamma(p)=-\frac{g^2}{2\pi} \...
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Why is a quarkonium any different from a meson?

Quarkonium states are bound states of a quark-antiquark pair but so do the mesons. What is the difference between a quarkonium (e.g., charmonium, and bottomonium) and a meson then? Why use a separate ...
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Transverse momentum in partonic process $\gamma^\ast q\rightarrow qg$

Let $\hat{s}:=(q+p)^2$, $\hat{t}:=(k-p)^2$, $\hat{u}:=(p-p^\prime)^2$ be the Mandelstam variables of the partonic scattering process $\gamma^\ast(q) +q(p)\rightarrow q(p^\prime)+g(k)$, where the ...
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What's the definition of $\bar\psi$ in QCD?

This is a two part question. What is the definition of $\bar\psi$ in QCD? In QED I know that $\bar\psi=\psi^\dagger\gamma^0$, but in QCD we also have flavor and/or color space. In particular, I'm ...
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How do gluons bind the quarks together within the hadrons and mesons?

I was trying to know about the strong nuclear force within the nucleus and the books and websites told me that it is the gluons which carry the force, and now I am curious how the gluons carry this ...
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QCD antiscreening

i'm trying to understand antiscreening in QCD. I'm following Peskin & Schroeder's Introduction to QFT and i'm having trouble to follow their argument. In section 16.17, p542-543, we get an ...
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Obtaining the effective Lagrangian for axions from the spontaneous breakdown of Peccei-Quinn symmetry

I am reading Section $3$ of this review titled The Strong CP Problem and Axions by R. D. Peccei and also the post here. A famous solution of the Strong CP problem in QCD is offered by the proposal of ...
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What is the matrix form of the gluon field strength tensor?

For electromagnetism, the matrix form $$\Bbb{F}^{\mu \nu}=\begin{pmatrix} 0 & E_x/c, & E_y/c & E_z /c \\ -E_x/c & 0 & B_z & -B_y \\ -E_y /c & -B_z & 0 & B_x \\ -...
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How do we derive the Hamiltonian of the Wilson Loop Action?

I'm reading Fradkin and Susskind's 1978 paper "Order and disorder in gauge systems and magnets" to try and understand how they derive the Hamiltonian for the U(1) compact lattice gauge theory. The ...
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On the Euclidean action for QCD

The Euclidean action for QCD reads, (see e.g., Eq. (45) in "ABC of instantons" by Novikov, Shifman, Vainshtein, and Zakharov) $$S_E=\int d^4 x\left[\frac{1}{4}G^a_{\mu\nu}G^a_{\mu\nu}+\psi^\dagger(-i\...
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Elimination of three gluon vertex

I am reading this paper by Dixon, where it is mentioned that one can diagrammatically compute the colour factor of certain Feynman graphs, such as shown in figure 1, where they expand a three gluon ...
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Why do we think that the $U(1)$ problem is solved by instantons?

It is usually thought that the $U(1)$ problem is solved when 't Hooft realized that instantons induce additional symmetry breaking of the $U(1)_A$ symmetry aside from the non-vanishing quark masses. ...
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4 top quark production Feynman diagrams

In this paper in figure 1 they show the lowest order Feynman diagrams for four top production. Isn't it possible to have a single 4-gluon vertex (getting rid of the gluon propagator in the second ...
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How do you reconcile quark masses with notion of confinement?

In trying to understand exactly what confinement means, I have been reading 't Hooft s original paper on 2D QCD at large $N$. In the paper he shows that the quark propagator pole is moved to infinity, ...
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QCD generating functional and QCD vacuum from nonperturbative to perturbative regime!

The complete generating functional in QCD (starting from the most general renormalizable, Lorentz invariant and gauge invariant Lagrangian) given by $$Z_\theta[J]=\int \mathcal{D}A \exp i\int d^4x~ {\...
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What's the difference between perturbative QCD, non-perturbative QCD, and gauge theory QCD?

I'm trying to get the ideal of QCD, and it turns out that there seems to be several versions, and some of which does not appear to agree with each other at a glance. What's the difference, and how ...

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