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

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Can we just replace the finite part of $Z_m$ in a renormalization scheme at leading order

Suppose that we have to determine the finite part of $Z_m$ how it differs from common schemes, but we are free to choose the other renormalization constants in QCD (at Leading order). Could we make ...
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Can we change the point form $\not p = m$ to $\not p = 0$ in on-shell renormalization scheme condition?

In the on-shell scheme, in QCD, one can impose the counterterms action to vanish the part of 1PI diagrams on external lines. The on-shell condition can be written as follows: \begin{equation} {\left. ...
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If proton spin emergence from quarks and gluons is mysterious, why is silver atom spin not?

A recent Scientific American article brought up an old issue, which is this: According to quantum chromodynamic models, the emergence of exactly 1/2 unit of spin in a proton (or a neutron, or any ...
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Matrix elements of four-quark operators [on hold]

In weak interaction phenomenology, especially in strangeness changing processes, effective four-quark operators are used. Such as $Q_1 = (\bar{s}_\alpha \gamma_\mu (1-\gamma_5) d_\alpha) ...
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Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?

Quantum chromodynamics, or QCD, is the theory describing the strong nuclear force. Carried by gluons, it binds quarks into particles like protons and neutrons. According to the theory, the tiny ...
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What does mathematical equivalence means here?

On Motls blog, http://motls.blogspot.com/2012/06/on-importance-of-conformal-field.html, while I was trying to understand what dimensional transmutation means, he said: I said that by omitting the ...
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56 views

Computation of the QCD vector two point function

I am following some notes on the computation of the vector two point function in QCD and I would like somebody to make some intermediate steps more explicit. Let's consider ...
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Problem in the derivation of the Ward identities

This is a follow up to my previous Phys.SE question. The last equation in that question is $$-a\frac{1}{k^2+i\eta}k^{\lambda}i\Pi_{\lambda\rho}(k)iD^{\rho\nu}(k)=0$$ which we can further simplify as ...
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Permissible combinations of colour states for gluons

My lecturer has said that there are 8 types of gluons (I'm assuming that the repetition of $r\bar{b}$ is a typo that is meant to be $r\bar{g}$) $$r\bar{b}, b\bar{r}, r\bar{g}, g\bar{r}, g\bar{b}, ...
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Computing the ratio of unpolarized QED and QCD cross section

How is the last equality of the equation $$ \frac{\sigma_{QCD}}{\sigma_{QED}}=\frac{1}{3*3}(tr T^a T^b)^2=\frac{2}{9} $$ derived, where $T^{a,b}$ are the basis matrices of SU(3)?
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Why is the strong CP term $ \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$ never considered for $SU(2)$ or $U(1)$ interactions?

The Lagrangian one would write down naivly for QCD is invariant under CP, which is in agreement with all experiments. Nevertheless, if we add the term \begin{equation} \theta \frac{g^2}{32 \pi^2} ...
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47 views

Experimental determination of $\Lambda_{QCD}$

I have a question about $\Lambda_{QCD}$, the energy scale at which there is a transition from the regime of perturbative QCD to quark confinement. How it is measured experimentally?
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Origin of the quark condensate VEV

Consider the QCD lagrangian : $$L_{QCD}=-\frac{1}{4}G^a_{\mu\nu}G^{a\mu\nu}+\sum\bar{\psi}_q(i\not{D}-m_q)\psi_q$$ Textbooks explain that this lagrangian is spontaneously broken by the VEV of quark ...
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Altarelli-Parisi Splitting Function $P_{qq}(z)$ vanishing integral if and only if quark flavour sum rules and equivalence

Question 1: I believe both questions are in the context of Deep Inelastic Scattering. I've been given the expression for $F_{2}^{ep}(x)=(\frac{2}{3})^2[u(x)+\bar{u}(x)] +(\frac{1}{3})^2[d(x) + ...
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87 views

Why does this proof show the gluon propagator comes from the first two terms?

I am reading the book "QCD: Renormalization for the Practitioner" and i am having trouble understanding something. In page 70 the gluon propagator is written as follows $$\begin{multline} ...
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Parameterization of an arbitrary element of $U(2)_L \times U(2)_R$ (Chiral symmetry with two quarks)

When you write down the Lagrangian for two quarks : \begin{equation} \mathcal{L}_\text{QCD}^0 = -\frac{1}{4} G_{\mu\nu}^a G^{a\mu\nu}+ \bar\Psi i \gamma^\mu D_\mu \Psi \end{equation} you find an ...
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Why are $SU(N)$ gauge theories easier to handle for $N\rightarrow \infty$?

I was wondering if there was a intuitive/heuristic argument to understand why generalizing the QCD gauge group $SU(3)$ to $SU(N)$ and taking $N\rightarrow \infty$ simplifies the analysis of the ...
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Interpretation of vector mesons in QCD

It is well-known that scalar mesons are interpreted as pseudogoldstone bosons which is connected with spontaneous broken $SU(3) \times SU(3)$ symmetry to $SU(3) \times SU(3) / SU(3)_{chiral}$. Is ...
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83 views

What are the equations for the weak and strong forces?

What are the equations for the strong and weak force, like how for the Electrostatics the equation is $F_c= k*Q*q/(r*r)$. I understand to an extend what the strong and weak forces are. However, I ...
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Difference between LO and NLO event generators?

I am performing undergraduate research in particle physics. In our research, we are using two event generators (PYTHIA8 and MC@NLO with HERWIG++) to study open bottom production. I am unsure of the ...
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Asymptotic behavior of Euclidean correlators in QCD

I am reading an old review paper (http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.65.1). In the beginning it makes the following statement (I copy with slightly different notation). If we ...
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Decay of some particle involved quarks vs mesons as outgoing states

Let's have decay width of some mother particle into the state which involves hadrons. For simplicity, let's assume that creation of hadrons (on diagram) is possible only through electroweak vertices ...
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Why do the quarks constantly change colors?

In a hadron the quarks constantly change colors.They,then exchange gluons to remain color neutral.For example a red quark becomes blue by emitting a red and anti blue gluon and then the blue quark ...
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Reference for the non-perturbative origin of the baryon masses

I'm looking for nice introductions to the non-perturbative generation of the baryon masses.
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How to compute this loop integral? [closed]

I have a gauge boson that splits into two scalars and the loop is closed by a gauge boson as shown in the picture. The incoming boson has $\mu$ index while the boson that runs in the loop has momentum ...
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Quark anti-quark pair creation. Do we need a gluon?

What is the difference between these diagrams? Is the presence of the gluon taken for granted in the second one? and EDIT: I just zoomed into the picture, it is not a single quark state. ...
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Instantons and confinement

Do instantons tell us something about behavior of QCD when lowering an energies? I.e., is it possible that instantons provide confinement? Are there some calculations which tell us that instantons ...
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Hard processes in particle collisions

This is in reference to a MC generator called Pythia, but has wider applicability because the phrases are used widely in particle phyiscs, even though I have not managed to find a clear, ...
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Do we know where newly formed quark-antiquark pairs come from in the process of hadronization?

The only explanations I have found are very vague, such as "spontaneously created from the vacuum" and because "it is more energetically favorable".
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The counting of all possible baryons quark combinations

I would like to ask how do you count the number of possible quark combination that could possibly exist in a baryon. I know certain spin symmetry or orbital momentum symmetry have to be conserved. But ...
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Why scattering of red and blue quark only involves $G_8^\mu$?

According to the author C. G. Tully (Particle physics in a nutshell), the scattering of a red and blue quark only involves $G_8^\mu$. How come this is so? I thought $G_3^\mu$ and $G_8$ only mediate ...
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Variation of the kinetic quark term of the QCD Lagrangian under gauge transformation

A simple kinetic quark term would look like $$\bar{\psi}(\gamma^{\mu}\partial_{\mu} - m){\psi}.$$ Imposing SU(3) symmetry the Dirac spinor transforms like $$\psi(x) \rightarrow \psi'(x) = e^{ig_s ...
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Colour decomposition in QCD

I am looking to compute the matrix element for the process gg -> u ubar at leading order. It is straightforward to calculate the non-colour part of the usual s, t and u channels. I will call these ...
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What are non-Abelian plasmas?

I know what a non-Abelian group is: a group whose operation does not obey commutativity. Does this have anything to do with a non-Abelian plasma? I'm not really looking at a specific paper, but I'll ...
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Are there new physics scenarios that predict low lying hadrons?

There is a significant ongoing experimental effort to search for new hadrons with masses in the GeV range. This is used to find the spectra of QCD bound states, with a particular emphasis on finding ...
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Why cross section of $e^+ e^- \to \bar{q} q$ is 3 times larger than $e^+ e^- \to \mu^+ \mu^-$?

I know the usual answer: quarks carry color charge (let us denote them r,g,b), antiquarks anti color charge, and since the initial state ($e^+ e^-$) does not carry any color charge (and color is ...
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Is it possible to calculate neutron half-life theoretically?

Is it possible to calculate neutron half-life theoretically? For example, from lattice QCD or something?
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QCD and QED with unlimited computational power - how precise are they going to be?

My question is about quantum algorithms for QED (quantum electrodynamics) computations related to the fine structure constants. Such computations (as explained to me) amounts to computing Taylor-like ...
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How to calculate D0->K+K- decay with QCD factorization?

I am studying the decay of D0->K+K- and I calculated the result of Branching Ratio by Naive QCD and I wrote all the equations for amplitude and branching Ration and Hamiltonian and... for this decay ...
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100 views

From which dimensionful constants does proton mass arise?

It is well known that the most of the proton (or any other hadron with light quarks) mass is not made up from quark masses, but it is dynamically generated by QCD mess inside. I've also heard that, ...
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Different ways of derivation of Gell-Mann-Okubo mass formula

Recently my teacher have told me that there are many ways of derivation of Gell-Mann-Okubo mass formula by using group representation theory (by using dynamical group etc). Where can I read about ...
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Strong CP Problem

So, as far as I know, the Strong CP Problem in QCD results from the theta angle term in the action: $i\theta\int_X F_\nabla\wedge F_\nabla$ where $\nabla$ is the gauge connection and $X$ is a manifold ...
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Has confinement been experimentally observed? [closed]

So, confinement has obviously been shown by lattice gauge theory to be a predicted aspect of QCD. However, to what extent has it been observed in experimental physics?
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Simplify QCD Lagrangian

How we can derive the electric charge of the field theory for each field? For example lets say that we have the u-quarks (3-colors) and electron that we know that has charge -e) free Lagrangian ...
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Why are the dineutron and diproton unbound?

It is known that there is no diproton and dineutron nuclei. Does this mean that two protons or neutrons are not actually attracted to each other? Even if the attraction was weak, wouldn't it cause ...
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Infrared divergences in QCD

As we know, we can remove infrared divergences by summing over all final states with arbitrary number of soft photons. But in QCD this does not work, since gluons are not "neutral" because they carry ...
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Charge conjugation matrix in baryon current

In his paper Calculation of baryon masses in quantum chromodynamics (ScienceDirect), B.L. Ioffe considers currents describing baryons. In equation (13) he gives an interpolating current for the isobar ...
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Measure of interaction of two quarks and Casimir operators [closed]

Let's have two quarks, which refers to representations of $r_{1}$ and $r_{2}$ of color symmetry group. They create bounded state which refers to the representation $r$. There is a statement that ...
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Uncharged Gluon Representation

I'm currently learning for an exam and in an old exam the question was posed: If Gluons were uncharged, under which representation would they transform? The ...
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Baryon in terms of quark fields – spinor index structure

What is the most general way to write down a current describing a baryon made from quarks $\psi_i^\alpha$? Let's say we suppress flavour indices but want to write colour $(i,j)$ as well as spinor ...