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

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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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39 views

Does quantum chromodynamics imply continuous space? [duplicate]

I am thinking it does. That's because a pillar of quantum chromodynamics is renormalization, which is itself due to the assumption that electrons are point particles (having no extent). A point ...
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26 views

How can we calculate pion decay constant in Chiral Perturbation Theory ?

Above diagram is an one-loop contribution to the Pion decay constant $f_\pi$. For example in this paper (Eq.7) they have written down the pion decay constant to one loop, but the calculation is not ...
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Is there some no-go theorem for $D=9$ Kaluza Klein QCD+EM?

While QCD is a typical product of AdS/CFT and some other research trends in extra dimensions, I have never found in the literature an example producing the non-chiral part of the standard model, ...
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Massive Gauge Bosons without Higgs Effect

In a possible theory like our Standard model but without a Higgs i.e.: $$ \mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}] $$ where $b,f$ run over the typical ...
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153 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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43 views

Axion domain walls and QCD phase transition

Now it is known that QCD phase transition corresponds to crossover. This it seems that no topological defects is produced during phase transition. Do axion domain walls arise during QCD phase ...
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1answer
47 views

QCD Color Structure relation [closed]

i want to proof the following relation : \begin{equation} t^a t^b \otimes t^a t^b = \frac{2}{N_C} \delta^{ab} \mathbb{1} \otimes \mathbb{1} - \frac{1}{N_C} t^a \otimes t^a \end{equation} Right now I ...
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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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23 views

What tell us know that Parton distributions and Fragmentation function are non-perturbative part of QCD?

I read some document I see Parton distributions and Fragmentation function are non-perturbative part of QCD. Have document tell about that?.
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41 views

Supersymmetric chiral QCD resource recommendations?

I want somebody to recommend me where I can read about supersymmetric chiral QCD.
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38 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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16 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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29 views

Why is shown three-gluon diagram a two-loop diagram?

Why is this QCD diagram a two-loop and not a three-loop diagram? Thanks for your help!
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1answer
97 views

Why is the chiral symmetry only $SU(3) \times SU(3)$ and not $SU(6)$?

In the limit where the masses vanish, low energy QCD has a well known chiral symmetry (see http://arxiv.org/abs/hep-ph/0505265 for a very extensive review, and pg 19 for the section relevant for my ...
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49 views

Are topological vacua of QCD Lorentz invariant?

Are topological vacua of QCD Lorentz invariant or they mix under boosts?
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1answer
60 views

Strong force between quarks that are out of causal contact

This is a rather artificial scenario, but it has been bugging me lately. Background Due to the confinement in QCD, quarks are bound in color-neutral configurations. Any attempt to separate a quark ...
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62 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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1answer
114 views

Counting degrees of freedom in spinor-helicity formalism

Just a couple of quick questions about the spinor-helicity formalism. We start with $p^\mu$ and $\epsilon^\mu$, so we have eight degrees of freedom. Then we have that $p^\mu p_\mu = 0$ and that ...
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1answer
69 views

Quark-gluon plasma: status [closed]

Can we say that a QGP has been observed or is there only suggestive evidence? Is the idea that string theory, through the AdS/CFT correspondence, could help to understand this new state of matter ...
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1answer
73 views

How to compute scattering amplitude $\gamma\pi^+\to\pi^+\pi^0$

I wish to find the amplitude for process $\gamma\pi^+\to\pi^+\pi^0$ at low energies. I am familiar with the basic concepts and techniques of QFT but have never dealt with the scattering processes ...
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40 views

How to count completely symmetric wavefunctions can be made by 6 (u, d, s, $\bar{u},\bar{d},\bar{s}$) quarks to form Baryons (i.e., 3 particle state)?

(Excluding antisymmetric part i.e., colour part) Peskin said 6 (particles + Anti-Particles) "guys" make (6(i.e., total "guys") x7x8)/(3x2)= 56 total symmetric state. How? There are 10 (decuplate) ...
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20 views

Hadron Annihilation - what happens with the constituents

When a Hadron and its antimatter equivalent annihilate, what happens to the QCD "soup" (for lack of an appropriate term) from each? Eg, the valence quarks in a proton - antiproton event, to they pair ...
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51 views

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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48 views

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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154 views

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 [closed]

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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1answer
65 views

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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51 views

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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1answer
70 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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25 views

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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56 views

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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27 views

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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83 views

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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1answer
58 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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75 views

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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1answer
78 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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1answer
93 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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1answer
42 views

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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89 views

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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1answer
152 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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54 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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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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1answer
124 views

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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33 views

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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1answer
158 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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3answers
149 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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58 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 ...