Questions tagged [quantum-chromodynamics]

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

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11
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345 views

Is the QCD Lagrangian without a $\theta$-term invariant under large gauge transformations?

In his book "Quantum field theory", Kerson Huang states that we need to add the term $$\frac{i\theta}{32\pi^2}G_{\mu\nu}^a \tilde{G}_{\mu\nu}^a$$ to the Lagrangian, to make it invariant under large ...
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Why does strong interaction increase with distance?

I read numerous times that strong interaction increases with distance. But how can one actually derive the force-distance relation from the lagrangian (quark field + gluon field + gauge coupling)? ...
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351 views

Lattice QCD and the 5th dimension

I was digging into the Nielsen-Ninomiya Theorem and doubler fermions, as well as solutions to these problems using Domain Wall Fermions and overlap lattice fermions, both of which make effective use ...
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Does quark color contribute to “spin degeneracy” for QGP calculations?

Like the title say, does quark color matter in counting contributions in a early universe plasma (QGP), as when adding up the total plasma energy density, or is it just spin? The book I have (Pathria) ...
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166 views

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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Question about the vacua of the Standard Model

This question is probably based on a misunderstanding. Please correct me if I'm wrong, and if unclear, I'll try to put it in a clearer language. In Yang-Mills theory such as the theory of strong ...
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126 views

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. ...
6
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242 views

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 ...
6
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208 views

Final-state baryons in $p \bar p$ collisions in Pythia

I'm trying to simulate inclusive $\chi_c$ production in $p \bar p$ collisions at very low energies (~ 5.5 GeV) using Pythia8 event generator. Leaving aside problems bounded with applicability of ...
6
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174 views

Can quark-gluon plasma ever be close to an ideal gas of asymptotically free quarks?

The question inspired by an upcoming colloquim at UCB. A naive interpretation of quark asymptotic freedom seems to imply that at high enough energies they should be weakly interacting. On the other ...
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149 views

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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182 views

From $U(3)$ to $SU(3)\times U(1)$ Color symmetry. There is a “gluon” photon-like?

Suppose that $U(3)$ was the gauge group. We can decompose this as $U(3)=U(1)\times SU(3)$, which implies that in addition to the $SU(3)$ that has eight generators corresponding to eight gluons, there ...
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No mixing in light cone perturbation theory

In hep-ph/0609090, Triumvirate of Running Couplings in Small-x Evolution, Kovchegov et. al. calculated the running coupling correction to the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and ...
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543 views

How to integrate over rapidity for Parton Luminosities in LHC?

I want to make a comparison of parton luminosities between Tevatron and LHC. According to Factorization theorem the cross section in hadron colliders, as long as the partonic cross section has $\hat \...
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Which explanation of the OZI rule is correct (or most important)?

The OZI rule states that a QCD diagram is suppressed if it can be cut into two by only cutting gluon lines (the precise wording is addressed in the question What is the precise statement of the OZI ...
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Is there some truth to the “vacuum as bubbling soup” story?

There are many discussions on this site about the nature and reality of vacuum fluctuations. The general consensus seems to be that this it falls into the Lie-to-Laymen category. On the other hand, ...
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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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181 views

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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92 views

What is the relation between the Gribov problem and color confinement?

I have heard that the Gribov problem is in some way related to color confinement (For instance: Gribov copies and confinement). Although I understand what both the Gribov and confinement problems are, ...
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111 views

Which of the Wightman axioms are not incorporated by four dimensional quantum Yang-Mills?

I am trying to understand the quantum Yang-Mills existence problem but the best I have seen so far is the statement that there is no known interacting relativist field theory in four dimensions which ...
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316 views

Can the On-Shell Scheme be used for QCD?

I am reading a textbook on QFT and it mentions that the on-shell scheme cannot be used for QCD. Could someone explain the on-shell renormalization scheme in a bit more detail, plus why QCD cannot be ...
4
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286 views

Is the physical mass of the electron a gauge invariant quantity?

In Lattice, one cannot calculate gauge non-invariant quantities, such as the quark mass. This is because one averages over the gauge and gets 0. One way to get around the issue is to fix the gauge. ...
4
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104 views

Number of baryons in the Skyrme model

In QCD, the Eightfold Way organizes the number of baryons with respect to their flavor and color quantum numbers: for three light $(u,d,s)$ quark constituents, a spin-(1/2) baryon octet and a spin-(3/...
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339 views

Beta function for non-Abelian gauge theory with both fermionic and bosonic matter fields

Consider a non-Abelian gauge theory with both fermionic $\psi$ and bosonic $\phi$ matter fields in 4D, which may be called a QCD-Higgs model, $$L=-\frac{1}{4 g^2}F_{\mu\nu}F^{\mu\nu}+\bar{\psi}i\gamma^...
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Perturbative coupling for QFT

I'm confused about the definition of a perturbative coupling for QFT that it should be less than 4 $\pi$, because the higher order corrections comes of order $\lambda/(4 \pi)$ .. Now why QCD is not ...
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Strong force equivalent of electricity?

Could colour charges be manipulated into something analogous to the flow of electricity, and if so, would there be any situation in which circuits of this kind would be useful? For example, given a ...
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696 views

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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269 views

Unitarity of the S-matrix and Feynman Diagrams

There are several questions on the unitarity of the S matrix, but unfortunately non of them answers directly the following question. The S matrix is unitary and that can be proven by the fact that ...
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65 views

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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Does the number of left handed chiral quark superfields always equal half the number of quark flavours?

In Weinberg's "The Quantum Theory of Fields Vol III" page 267 we're told that $n_f = 2N_f$. Where $n_f$ are the number of flavours and $N_f$ is the number of left chiral quark superfields (or the ...
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1answer
105 views

Photon-Gluon annihilation in QCD

I am starting to learn about QCD, and I wanted to calculate the squared matrix elements for photon-gluon annihilation into a quark and an anti-quark. However, I am having trouble writing down the ...
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How can I visualize the oxygen nuclear charge density?

Oxygen has 8 protons and 8 neutrons. Based on the nuclear shell model, protons should pair with anti-parallel protons to create singlet spin states, and neutrons should similarly pair with anti-...
3
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1answer
193 views

How do $\theta$-terms not violate gauge invariance?

In the context of QCD (and more generally, any quantum gauge theory in even dimensions), the $\theta$-term is $$ \frac{\theta}{8\pi^2}\langle F_A\wedge F_A\rangle = \frac{\theta}{32\pi^2}\langle F_A^{\...
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79 views

Asymptotic states in strongly-coupled QFTs

In QFT the asymptotic states play a very important role, as they are the basis on which we decompose our in-states and out-states when we calculate correlation functions. However, I have not been ...
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79 views

Is the starting distribution in the solution of DGLAP IR-bare?

On p.27 of this paper by John Collins, he says that when defining PDFs in terms of partonic number operators, one acquires an IR-divergent bare PDF (eq. 52). The residue of the IR-divergent term is ...
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113 views

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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51 views

Topological number and gauge invariance

In QCD or other non-abelian gauge theories, we come across infinitely many vacua that are gauge equivalent but have different topological numbers. We then say that the instanton solution is tunnelling ...
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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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251 views

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} ...
3
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301 views

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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47 views

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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58 views

Effective field theories from QCD

Is there a way - at least formally - to derive theories like chiral perturbation theory or heavy baryon effective theory from QCD? As an example: is it possible first to introduce the effective ...
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123 views

How do we show that gluon-fields have color?

I understand how to derive the QCD lagrangian based on certain assumptions about Quark fields and $SU(3)$ gauge invariance and in the final expression one finds the term $(A_µ)^c*T_c$ where $T_c$ is ...
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190 views

Bjorken Scaling and the Parton Model

It is often said that Bjorken scaling of the deep inelastic structure functions \begin{equation} \nu W_2(\nu ,Q^2)\rightarrow F(x) \end{equation} (where $Q^2$ is the virtuality of the photon, $\nu=\...
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What is the physical meaning of Lie congruence classes?

Any weight $\lambda$ characterising a representation of $\mathfrak{su}(N)$ is an element of one of the $N$ congruence classes defined by (ref.1) $$ \lambda_1+2\lambda_2+\cdots+(N-1)\lambda_{N-1}\quad\...
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190 views

Formal definition of gauge field and spinors in QFT

I am trying to pin down what spaces a spinor and gluon gauge field exactly occupy. I know that the spinor is a quantity $\psi_{i\alpha f}(\vec x, t)$ where $i$ is a color index in the fundamental ...
3
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342 views

Mass gap v.s. classical nonlinear Yang-Mills waves

Why people said (Witten, p. 11), "For Yang-Mills theory. the mass gap is the reason that we do not see classical nonlinear Yang-Mills waves. They are a good approximation only under inaccessible ...
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266 views

Why is QCD hard to solve if I know the beta functions?

Why is it still hard to solve QCD if we know the beta functions of the coupling? Aren't only the loops causing problems? And am I not able to write every possible interaction exact at tree-level with ...
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68 views

Cronin enhancement in p-A collisions

What is the physical picture behind Cronin enhancement in proton-nucleus collisions at intermediate transverse momentum?
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131 views

How can we see that there is superconductivity/superfluidity in the boundary theory in the holographic principle?

For example in the models for holographic superconductors we can calculate the conductivity. Also there is an energy gap. I can understand that it describes a superconductor. However I have also heard ...

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