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

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What is quark transverse momentum?

When you google my question you get something on the order of 400 000 results but none of them explains how it is defined (No I didn't check them all). I know what the words quarks, transverse and ...
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93 views

Linear rising potential from a Gribov propagator

It is common wisdom that a gluon propagator (Gribov-)like $$ G(p^2)=\frac{a+bp^2}{cp^4+dp^2+e} $$ should give rise to a linear rising potential. So far, I have not seen a proof of this and I would ...
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108 views

QCD Parton Branching - Is the angle always negligible?

The GLAP equation describes the evolution of parton distribution under successive branchings. When branching takes place at a finite angle, the outgoing parton carries some finite transverse momentum. ...
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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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30 views

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 ...
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32 views

QCD-Process with superposition-particle

I am a total beginner with non-abelian gauges. To write down a process from a neutral pion ($\pi^0 = \frac{1}{\sqrt{2}}(u\overline{u}-d\overline{d})$) I expect to have to write it as this ...
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55 views

Theta-parameter vacuum energy

Suppose we have $\theta$-field in QCD (in a special case of constant $\theta$ it reduces to ordinary $\theta$ parameter): $$ \tag 1 Z_{\theta} = \int D[\psi_{QCD}]e^{iS}, $$ where $$ \tag 2 S = \int ...
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58 views

How do I decide when to use raised/lowered indices when calculating the amplitude of a Feynman diagram?

I am learning the Feynman rules for QCD. The book I am reading tells me that gluon propagators contribute a factor of $$\frac{-ig_{\mu\nu}\delta^{\alpha\beta}}{q^2}$$ However, in one of the ...
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Constant in Regge trajectory

The Regge trajectory in QCD is given by $$m=\sqrt{\frac{J}{\alpha}-\alpha_0},$$ where $m$ is the mass and $J$ is the angular momentum of the hadrons, $\alpha=(4\pi\sigma)^{-1}$ is the inverse QCD ...
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18 views

QCD condensate and lepton mass

I read that the QCD U(1) anomaly is caused by the QCD condensate giving rise to quark masses. Does the QCD condensate also give masses to leptons (electron, mu, tau, neutrinos), or are these masses ...
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27 views

Relation between renormalisation matrix and anomalous dimension

I need an relation between the renormalization constant matrix and the anamalous dimension matrix. Now I found the following derivation \begin{equation} \begin{split} \gamma (a_\mu) &= ...
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181 views

Pentaquark spin prediction

Is there a straightforward way to see what the spin of the recently-discovered pentaquark states should be, from the representation theory of $SU(3)\times SU(2)\subset SU(6)$? I can see that from the ...
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23 views

How is (if it is) gauge symmetry realized in chiral perturbation theory?

I often read that an effective field theory must have the symmetries of its UV completion. Chiral perturbation theory is an EFT of QCD. I know that the approximate chiral symmetry of QCD is realized ...
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52 views

Supersymmetric chiral QCD resource recommendations?

I want somebody to recommend me where I can read about supersymmetric chiral QCD.
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65 views

Mass and wave function renormalization In chiral perturbation theory

Before I put forward my actual question, I think it will be useful to set the context in a clear way and that involves my understanding of a few very basic things of Chiral Perturbation Theory. ...
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21 views

Neutron dipole moment and $\theta -$term

In many references is stated that by having QCD $\theta -$term, $$ L_{\theta} = \frac{g_{s}^{2}}{8 \pi^{2}}\theta F \wedge F, $$ we may compute the value of neutron dipole moment, $$ d \approx ...
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56 views

Are topological vacua of QCD Lorentz invariant?

Are topological vacua of QCD Lorentz invariant or they mix under boosts?
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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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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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87 views

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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59 views

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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67 views

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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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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140 views

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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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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266 views

What is anti-screening?

In his book "The Lightness of Being" Frank Wilczek (page 48) writes about screening and anti-screening. In screening, a bare charge attracts virtual particles of opposite charge which lessen the ...
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65 views

Generalization of relation between charge and magnetic moment

In classical theory, for electrons or protons, charge and angular momentum combine to give the magnetic moment. Does a similar consequence hold for the generalization of charge to other forces, like ...
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78 views

Color factor for squark-quark-antiquark vertex

I am trying to do a tree level calculation of cross section in a process that involves sbottom exchange. There is a $ \widetilde{b} q \bar{q} $ vertex, where $q$ and $\bar q$ are quark and anti-quark ...
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48 views

Quantum fluctuations in the non-relativistic limit

Is there any way to describe quantum fluctuations in ordinary quantum mechanics? For instance, a proton fluctuating into a proton-$\pi^0$ state and then back to a proton? What are the relevant ...
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74 views

't Hooft duality

I've studied something so I'm able to explain better what I'm thinking about. 't Hooft duality states: In a gauge theory with fields in the adjoint representation in presence of a mass gap only the ...
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126 views

Effective Field Theories of QCD

Recently, I am studying the online course Effective Field Theory provided by MIT OCW. Prof. Stewart gives a nice picture to summarize the effective theories: As a newbie in this field (I only have ...
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147 views

Is the axial gauge with a $\xi$ term useful in Yang-Mills theory?

i) Do people use axial gauge with a $\xi$ term? When $\xi\neq 0$, ghosts do not decouple, but maybe it's still useful? ii) Is it proved that the term $\frac 1 {2\xi}(n.A)^2$ in the Lagrangian does ...
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Color Force & Nuclear Force [closed]

I was wondering if the color force and nuclear force are both sub-forces of the Strong Interaction? If so is the Strong Interaction responsible for any other forces?
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Quark space tensor product Vs Angular momentum space tensor product

For two triplet angular momenta states, say $J=1$ and $I=1$, if we wanna look at it in the coupled basis $F=I+J$, we use the regular Angular Momentum rules: $$|I-J|\leq F\leq I+J,$$ and from that ...
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quarks annihilation process

I am appreciating particle physics and I read about mesons. In quark's model, mesons are pairs of quark-antiquark. Now I think that in general matter-antimatter annihilate and so I don't understand ...
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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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196 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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How do we know that nuclear physics corresponds to low energy QCD?

One often hears the phrase "most of nuclear physics is in the low energy regime of QCD, where strong coupling constant is large ...", with the following diagram being invoked: How does one know ...
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177 views

Reasons for choosing $SU(3)$ as the color group vs. $SO(4)$

What are the reasons that $SU(3)$ is used for QCD? Why wouldn't the simpler & smaller group $SO(4)$ make a better candidate?
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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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Is There Any Difference Between Strong Quarks Force and Strong Nuclear Force?

the spectrum of quarkonium and the comparison with positronium potential for the strong force is: $V(r) = - \frac{4}{3} \frac{\alpha_s(r) \hbar c}{r} + kr$ (where the constant $k$ determines the ...
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Has the mass of longitudinal and perpendicular spin 1 mesons been measured separately?

This might be a silly question. When the mass of a spin 1 meson is measured, is there a way to check whether it is the same for all polarizations? Is such a meson mass the same for longitudinal and ...
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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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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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23 views

Green function of squared chiral pseudoscalar in QCD

I need to compute the Green function $$ G(0) \equiv \int d^{4} x\int D[\text{QCD}]\bar{q}\gamma_{5}Mq(x)\bar{q}M\gamma_{5}q(0)e^{iS_{QCD}} \equiv $$ $$ \tag 1 \equiv \int d^{4}x\langle 0|T( ...
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Looking for a reference for $\gamma_a e^{a}_{\mu} D^\mu \gamma_b e^{b}_{\nu} D^\nu =D^\mu D_\mu - \tfrac{1}{4}R$

I am having trouble finding references for the following identities: Dirac Operator: $$ \gamma_a e^{a}_{\mu} D^\mu \gamma_b e^{b}_{\nu} D^\nu =D^\mu D_\mu - \tfrac{1}{4}R \tag{1} $$ QED Operator: $$ ...
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IBP Identities to solve differential equation

I am wondering if anyone has experience in using IBP( Integration by parts) identities in the evaluation of Feynman diagrams via differential equations? My question is that I can't seem to understand ...
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FESR: Relation Between Total Cross Section and Spectral Function

In the papers I am reading the total cross section of electrons, positron scattering into hadrons can always be written in terms of an integral of a weight function w(s) and the spectral function ...
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How to calculate thd average of a Wilson loop in LQCD?

I'm am trying to do the excercise in page 35 from Lepage's LQCD notes: http://arxiv.org/abs/hep-lat/0506036. I want to compute the thermal average of the Wilson loop of size $a\times a$, where $a$ is ...