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

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Charge in terms of wavefunctions

For a charged quantum particle, say, an electron or a quark, how in the particle's wavefunction is the electric charge represented? Is it truly possible to represent electric charge using the wave ...
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Top quark production questions

I am just looking on the TopQuark production via proton antiproton collision and strong interaction. There seem to be three basic possibilities. $q + \bar q \rightarrow Gluon \rightarrow t +\bar t ...
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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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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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Quarks and theory on nuclear forces [closed]

I wonder if there existed a complete theory describing the behaviour of quarks in nucleons and other baryons and mesons and the behaviour of gluons. Does QCD alredy describes it all in perfect detail ...
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118 views

The anticommutator of $SU(N)$ generators

For the Hermitian and traceless generators $T^A$ of the fundamental representation of the $SU(N)$ algebra the anticommutator can be written as $$ \{T^A,T^{B}\} = \frac{2N}{d}\delta^{AB}\cdot1_{d} + ...
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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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127 views

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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197 views

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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282 views

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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123 views

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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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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Construction of Bound states in Lattice QCD

How the proton state is found and renormalized in lattice QCD? Is there any literature shows the method step by step? What about other bound states in QCD if we somehow know their quantum numbers?
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Is this a photograph of Surface Plasmon Resonance?

Does this photograph depict surface plasmon resonance? PHOTO 1 - Ellipsometric style photograph produces blue-green and purple resonance waves from nanogold-like tubule. PHOTO 1 was cropped from ...
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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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109 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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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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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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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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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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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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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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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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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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249 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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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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Supersymmetric chiral QCD resource recommendations?

I want somebody to recommend me where I can read about supersymmetric chiral QCD.
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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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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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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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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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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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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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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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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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81 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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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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'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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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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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 ...