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

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Callan-Symanzik equation for the QCD scattering cross section of the $e^{-}e^{+}\to q\bar{q}$ process

In Peskin and Schroeder (Section 17.2) it is stated without derivation that the scattering cross section for the $e^{-}e^{+}\to q\bar{q}$ process obeys the following Callan-Symanzik equation: $$ ...
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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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What is a “dynamically generated scale” physically?

A theory like QCD with massless quarks in four dimensions has no explicit mass parameters in its classical Lagrangian. At the quantum level however, instead a mass scale Λ is generated dynamically at ...
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Continuum of lattice QCD is free?

I am having a hard time getting to grips with the statement that $$g_{0}(a) \to 0 \text{ as } a \to 0$$ where $g_{0}$ is the bare coupling in lattice QCD and $a$ the lattice spacing. How come this ...
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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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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. ...
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Calculation of divergences of Feynman diagram

In Peskin Schroeder, while considering gluon diagrams for $\beta$-function in QCD, they say that we can calculate the divergent part of loop diagram taking limit of zero external momenta - e.g. for ...
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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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62 views

Why there aren't gluons with charges like $b b$ or $r r$?

So my principal question is the one in the object above. But then I have another question related. Supposing I have a $bg$ gluon. How may I write it in the octet basis? Thank you for your help!!
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Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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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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66 views

Yang-Mills theories, confinement and chiral symmetry breaking

I was thinking about hadrons in general Yang-Mills theories and I have some doubts that I'd like to discuss with you. Suppose that we have a Yang-Mills theory that, like QCD, tend to bind quarks ...
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36 views

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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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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39 views

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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Why do we need the strong interaction if we have Yukawa's meson theory?

How is Yukawa's theory of mesons different from the standard model's strong interaction? I mean if Yukawa's theory is complete then why do we need quarks and gluons?
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Why Conserved Current Should Not Need Renormalization?

May be this is trivial but I need to understand why the renormalization of conserved current is not necessary ? As for example, in this paper, they demand (2$^{nd}$ paragraph of the 2$^{nd}$ column in ...
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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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Why do protons not break into quarks?

I know that free a neutron breaks into a proton because a proton has less mass and energy. Then, why do protons not break into quarks, since they have even less energy? Or why do gluons join quarks? ...
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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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SU(3) Transformation behavior of hadronic wave function

We were given a “baryon” wave function $$ \sum_{i,j,k=1}^3 \epsilon_{ijk} q_i q_j q_k$$ which is supposedly invariant under SU(3) gauge transformations. The structure of those transformations was ...
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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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Chiral current VEV below the QCD scale

Let's have pure QCD. I know that after spontaneous symmetry breaking quark bilinear form are replaced by their averaged values: $$ \bar{q}_{i}q_{j} \to \langle \bar{q}_{i}q_{j}\rangle \approx ...
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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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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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Valence sea quarks parton distribution functions

There's somethin from Thomson (Modern Particle Physics) that I am a little mythed by. Section 8.4.3, eq. 8.3 is given as $$ ...
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References on Current Algebra

Although current algebra is out of usage from what I hear, I think I see lots of papers (especially dealing with strong interactions) with transition amplitude written with the currents (this is based ...
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Why doesn't the color force between two quarks have an inverse square law?

From what I understand the color force between two quarks doesn't decrease with distance. Why is it that the color force doesn't decrease with the square of the distance if there are three dimensions ...
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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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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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What does the discovery of a pentaquark signify?

at a particle collider a pentaquark was discovered. My question in short is what does the discovery of a pentaquark signify? Is there a theory that it supports or something like that?
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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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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 ...
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Spontaneous symmetry breaking of anomalous global abelian symmetries and $U(1)$ of QCD

Let me restate the $U(1)$ problem of QCD: Let us forget about the $s$ quark, and consider the $u$ and $d$ massless. This is a good approximation since $m_{u,d} \ll \Lambda_{QCD}$. Then ...
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Vector mesons as background gauge fields

Suppose we have some complicated fundamental theory of fermions and gauge fields which involves global chiral symmetry and global anomalies which breaks some subgroup of this symmetr. At some energy ...
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Topological susceptibility

In QCD we have strong CP violation (and hence a $\theta$-dependence of the theory) only if the topological susceptibility of the vacuum is nonzero: $<F\tilde{F},F\tilde{F}>_{q \rightarrow 0} ...
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Completeness Relations of Polarization Vectors in QCD

What are the completeness relations of the polarization vectors of (external) particles in QCD amplitude calculation? (I assume the polarization vectors depend on the gauge and even so still have some ...
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complicated QCD Color factor formula?

I was doing higher order calculations for purely gluonic system and came across complicated color factors like the product of six structure constants product ...
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why can't you simply evaluate QCD processes in a high kin energy frame

Asymptotic freedom says that QCD coupling becomes weak at high energies, right? Why can't you simply shift to a frame where our given particles have high kinetic energy, evaluate the process with weak ...
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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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Polarization Sums in QCD for the calculation of parton model splitting functions

Before i state the actual problem, here's a premise. In the case of a Spin 1 massive particle it's possible to demonstrate that $$\sum_{\lambda=0,\pm1}\epsilon_{\lambda}^{* \ ...
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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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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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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 ...