Questions tagged [quantum-chromodynamics]

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

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The 1-loop anomalous dimension of massless quark field for $SU(N)$ gauge theory with $n_f$ quark flavours

Considering $SU(N)$ gauge theory with $n_f$ massless quarks I want to find the anomalous dimension to order of 1-loop of the massless quark field, that defined by: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
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What are clover fermions?

I've seen the term been used quite a lot when reading about lattice gauge theory calculations. So far what I've gathered is the following, from this source [1]. Lorentz invariance of the action is ...
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What is the matrix form of the gluon field strength tensor?

For electromagnetism, the matrix form $$\Bbb{F}^{\mu \nu}=\begin{pmatrix} 0 & E_x/c, & E_y/c & E_z /c \\ -E_x/c & 0 & B_z & -B_y \\ -E_y /c & -B_z & 0 & B_x \\ -...
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How do Fermi-Dirac statistics contribute to fermions in the Pauli Exclusion Principle?

So I’m doing some research on Quantum Chromodynamics and I've come to an area in which I’m having some trouble arriving at a conclusive answer. Apparently the Pauli exclusion principle states that no ...
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Proton Proton Collisions Cross Section Plot by Stirling

I am struggling to understand some details of the cross section plot by Stirling that is very often shown when talking about LHC physics. See e.g. here: http://www.hep.ph.ic.ac.uk/~wstirlin/plots/...
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Proving time-reversal symmetry property of GPD's

I am having a bit of trouble showing some the following: $$ H(x, \xi, t) \overset{\text{time reversal}}{=} H(x, -\xi, t) $$ where $$ H(x, \xi, t) = \frac{1}{2}\int_{-\infty}^{\infty}\frac{dz^-}{2\pi}e^...
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Number of gluons inside a proton/neutron

In the model of constituent quarks, of course very different of the picture of QFT about what a QCD proton/neutron is, protons are made of 3 quarks. However, how many gluons are inside a proton? After ...
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Why chiral symmetry of quark fields has to be associated to flavor, not color?

Chirality itself arises only from the spinor field, irrelevant with the flavor or color. Why is it so that every time chiral symmetry is discussed, the symmetry group is always decomposed into $SU(N_f)...
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Physical interpretation of hadron distribution amplitudes

A parton fragmentation function can be interpreted as the probability that a final state hadron originated from that particular hadron. A parton distribution function can be interpreted as the ...
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Why aren't all quarks clumped together in one giant hadron?

As far as I am aware, the strong interaction is attractive only, and its carrier, the gluon, is massless meaning it has unlimited range. If this is the case, how come we only observe quarks in pairs ...
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Confinement in 3+1 dimensions from confinement in 2+1 dimensions

It is well known that Yang-Mills theories in $2+1$ dimensions exhibit the color confinement property. This property is characterized by the average of a Wilson loop that is the exponential of a term ...
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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: $$\langle F\tilde{F},F\tilde{F}\rangle_{q \...
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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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Soft-gluon of scattering amplitude

The question from Scattering Amplitudes in Gauge Theory and Gravity page 46, equation (2.120) from which I can't get a consistent formula. I just calculate A3(gff) which two fermion and one gluon $A_n\...
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Why are the parity quantum numbers of low lying hadrons what they are?

So you can get the flavour and angular momentum from the $SU(3)_F$ symmetry and rotational symmetry respectively but I haven't seen how these models predict the parity of these states (and similarly ...
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Do gluons mediate the interactions between different flavors of quark?

From some of the quite professional sources (Basics from QCD by CERN; QCD from PDG), the QCD lagrangian is written in the form of $$ L = \Sigma_{f} \; \bar{\psi}^{(f)} i \gamma^\mu D_\mu \psi^{(f)} + ...
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Is the Yukawa potential the more accurate potential to describe nucleons nucleons interactions?

According the Wikipedia the Yukawa potential is of the form: $$ V_{\text {Yukawa }}(r)=-g^{2} \frac{e^{-\alpha m r}}{r} $$ I know that the best theory to describe nucleons nucleons interaction is ...
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How does one measure the handedness of quarks considering that they don't exist freely?

Question is fairly straightforward as stated: How does one measure the handedness of quarks considering that they don't exist freely?
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What are chromoelectric and chromomagnetic fields?

Are they the normal electric and magnetic fields from Maxwell fields? Or are they just the corresponding components from $G_{\mu\nu}^a$ (the gluon fields), say chromoelectric fields are simply $G_{0i}^...
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Do antiparticles have their own Fermi surface?

I am trying to understand Fig. 1 of this paper, which shows a quark-antiquark pair forming in a model of QCD with chemical potential: Is the implication that antiquarks have their own Fermi surface, ...
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How to find the explicit value of the fermion vacuum expectation value?

In the derivation for Goldstone modes, a pdf I found online (scipp.ucsc.edu/~dine/ph222/goldstone_lecture.pdf) says it's believed the above-mentioned expectation value $\langle \bar{ \psi} \psi \...
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Schwartz loop result in $\bar{c}b\rightarrow \bar{u}d$ EFT

I am trying to reproduce the result of equation $(31.97)$ of Schwart's book Quantum field theory and the Standard Model. The results involves the calculation of the following diagram where the ...
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How many colors really are there in QCD?

In abelian gauge theory (electrodynamics), the matter fields transform like (please correct me if I am wrong) $$ |\psi\rangle\rightarrow e^{in\theta(x)}|\psi\rangle\tag{1} $$ under a gauge ...
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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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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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Is there any meaningful notion of a probability distribution for the number of quark-antiquark pairs in a hadron?

A hadron (such a proton) can be thought of as being composed of a large (but fluctuating) number of quark-antiquark pairs. As far as I understand it, the situation (say for a proton, for definiteness) ...
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Are the arrangements of quarks in hadron ground-state wavefunctions rotationally symmetric?

The Hamiltonian of quantum chromodynamics (like the rest of the Standard Model) is rotationally symmetric. My question is whether these space symmetries are spontaneously broken in the ground state of ...
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$SU(2)$ gauge SUSY with Affleck-Dine-Seiberg term

Consider SUSY gauge theory with $SU(2)$ group and matter fields $Q$ and $\bar{Q}$ in fundamental and anti-fundamental representations correspondently and the following superpotential: $$W=\frac{{\...
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How to define the parton distribution function of the antiquark?

So I can define the quark distribution function within a hadron as $$ f_{\psi/h}(x)=\frac{1}{2}\int\frac{dz^-}{2\pi}e^{ixP^+z^-} \langle h(p)|\bar{\psi}(0)\gamma^+\psi(z^-)|h(p)\rangle|_{z^2=0} $$ ...
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How to derive quark-antiquark parton distribution relation?

This is kind of similar to this post here How to define the parton distribution function of the antiquark? with no response. I basically want to derive the following; $f_q(x) = -f_{\bar{q}}(-x)$ where ...
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5d nonabelian gauge theory or 5d QCD explicit $\beta$-function

Question: Are there some derived $\beta$-function formula $$ \beta(g) = \frac{\partial g}{\partial \log(\mu)} $$ for nonabelian gauge theory in the 5-dimensional spacetime at some energy scale $\mu$ ...
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Is there a differential equation describing the wavefunction of a hadron?

In Newtonian Physics there's a differential equation describing the motion of multiple bodies in orbit around each other. In non relativistic quantum mechanics there's a differential equation ...
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How is the colour quantum number not conserved in this process?

I stumbled upon this CERN article, where I found this diagram describing the process $gg \rightarrow HH$: I'm still new to QCD, and I don't see how a coloured gluon can decay into colourless final ...
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How do I derive this Ward-type identity?

I am trying to derive a Ward-type identity between amplitudes involving $\bar\psi \sigma_{\mu\nu}\gamma_5\psi$, $\bar \psi \gamma_\mu \gamma_5 \psi$, and $\bar \psi \gamma_5 \psi$ in QCD (diagonal ...
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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-...
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How can the strong nuclear force (QCD) be considered to violate chirality, but not parity?

Chirality is related to parity, correct? It is a form of 'parity'? So, How can the strong force violate chirality symmetry, but only the weak force violates parity symmetry? I am confused about the ...
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Can the process gluon + gluon $\rightarrow$ 2 Higgs proceed in the following way in the standard model?

At order $g_s^2$, usually only a triangle quark loop and box diagram are considered, I was wondering, is there some reason that excludes these diagrams from the possible standard model channels?
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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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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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Color factor in Breit-Wigner formula

We are given the Breit-Wigner formula for the process $ud\rightarrow W\rightarrow e\nu$ as $$\sigma=\frac{1}{N_c^2}\frac{2J_W+1}{(2J_u+1)(2J_d+1)}\frac{4\pi}{s}\frac{\Gamma_{ud}\Gamma_{e\nu}}{(\sqrt{s}...
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The heat bath algorithm for $SU(3)$ lattice gauge field

I'm studying lattice gauge theory and succeeded in simulating $U(1)$, $SU(2)$ with a heat bath algorithm. However, I have difficulty in applying the algorithm to $SU(3)$. I refer to Gattringer and ...
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Extensions of the BCFW recursion relations

In their "original" form the BCFW recursion relations are used to calculate tree-level (color-ordered) $n$-gluon amplitudes. However is it possible to extend this formalism to more general ...
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Does the path of a Wilson line in a quark-correlator matter?

Consider a gauge-invariant quark correlation function nested inside an arbitrary state $|p\rangle$ $$\langle p |\bar \psi(z)_{\alpha,a}\left( W_{\Gamma}(z,0)\right)_{ab}\psi(0)_{\beta,b}|p\rangle \...
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Applications of the BCFW recursion formula

I am currently trying to understand the BCFW-recursion formula. My problem is that I do not fully understand when I can apply the formula/which amplitudes it covers: As I understand the formula so far,...
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Why are Delta baryons called “Delta isobars”?

A lot of people seem to call the $\Delta$ baryon "Delta isobar", however there is no mention of "isobar" on its Wikipedia page. Am I missing something? Why do people use the term &...
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Which quarks can form vacuum condensates?

I faintly remember the rule of thumb that only the up, down and strange quarks can form condensates because their mass is below the QCD scale $\Lambda_\text{QCD}$. But why is that? Where‘s the ...
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Parke-Taylor formula and MHW-amplitudes

In Matthew Schwartz Quantum Field Theory and Standard Model the author presents the Parke-Taylor formula $\tilde{M}(1^+2^+...j^-...k^-...n^+) = \frac{\langle j k \rangle^4}{\langle 1 2 \rangle \...
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Problems understanding the BCFW recursion formula

I am currently reading through the chapter about the spinor helicity formalism in Schwartz Quantum Field Theory and Standart Model. In the chapter 27.6 (On-shell recursion) the author introduces the ...
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What is an $n$-gluon amplitude?

What exactly is meant when we speak of an n-gluon amplitude? For example, in case of $n = 6$: Does the $6$-gluon amplitude refer to all possible diagrams that involve six gluons (which means e.g. ...
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What is pion condensation (or hadron condensation in general)?

I found some references, for instance here and here, but I still don't really understand the concept of why it happens, or why it's interesting. In particular, I'd like to know: What is hadron ...

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