Questions tagged [quantum-chromodynamics]

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

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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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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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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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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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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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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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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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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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Does pionium decay in massless QCD?

The bound state of ${\pi}^+ {\pi}^-$ is called Pionium. Is Pionium an Electromagnetic bound state or a Strong Force one? then Why? Does such a bound state last forever if one works in QCD with ...
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'If the spin of a particle has a positive projection on its direction of motion then it is called left-handed; otherwise, it is right-handed.' Huh?

From Wikipedia's article on quantum chromodynamics, theory section: "If the spin of a particle has a positive projection on its direction of motion then it is called left-handed; otherwise, it is ...
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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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Time Reversal Invariance of Electrical Dipole Moment

I'm reading from PDG the Tests of Discrete Space-Time Symmetries; we have the following row: Time Reversal (T) Invariance $e$ electric dipole moment $< 0.11 \times e^{-28} e\, \text{cm}$, $\text{...
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Evolution of the proton without external interactions

I've been thinking about the possibility of the proton evolving without external interactions and came up with the following problem. Let's say we have an isolated proton and therfore the Lagrangian ...
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Soft-gluon of scattering amplitude

The question from “Scattering Amplitudes in Gauge Theory and Gravity” page 46,(2.120) that I can't get a consistent formula. I just calculate A3(gff) which two fermion and one gluon An[..., f(i-1)+ ,i−...
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$U(1)_A$ effects on the baryons?

We know that the axial $U(1)_A$ is anomalous thus not a global symmetry. Therefore there is no direct associated pseudo goldstone boson for $U(1)_A$. This makes the $\eta'$ much more massive than the ...
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Low energy strong coupling asymptotic

The low-energy behavior ($Q^2<\text{1GeV}^2$) of the strong interaction coupling constant predicted by LFHQCD, $\alpha_S = \pi \exp(-Q^2/4\kappa^2) $, where $\kappa=M_\rho/\sqrt{2}$, is in ...
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How many extra dimensions needed to model the Strong interaction with a Kaluza-Klein extended theory?

The blog / video (See: https://backreaction.blogspot.com/2021/04/does-universe-have-higher-dimensions.html - Does the Universe have Higher Dimensions? Sabine Hossenfelder's blog) is discussing the ...
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How to decompose tensor products of $SU(3)$ representations? [duplicate]

Formally, one can arrange the quark flavors in a $SU(n)$ fundamental representation. One can then do tensor products for flavor and spin to construct other representations like baryons and mesons. An ...
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Do quarks annihilate into photons or virtual gluons?

I initially assumed a quark and its anti quark would annihilate into 2 photons (like electrons with positrons) and this does seem to be the case at least sometimes (e.g. For $\pi^0$s). However in our ...
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Do the “$SU(3)$ colors” live in a 3-dimensional vector space?

Previously I asked a question about the visualized colors: Do the "colors" live in a 3-dimensional vector space? (My earlier question is unfortunately closed) Now I like to ask the “$SU(3)$ ...
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Why we multiply the quark contribution term by 7/8 while calculating the degrees of freedom for QGP?

Why we multiply the quark contribution term by 7/8 while calculating the degrees of freedom for two flavour QGP? That is, g = 7/8 (2×2×2×3) + 2 × 8 Why there is a factor factor of 7/8 ?
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What is the good choice for QCD scale to use when trying to estimate the time of hadronization of a $b$ quark?

The time of hadronisation of a particle is typically : $\tau_{hadronization}=\frac{1}{\Lambda_{QCD}}$. What is the good choice for QCD scale ($\Lambda_{QCD}$) to use when trying to estimate the time ...
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In the deconfinement phase, there are absolutely no interactions between the particles?

The Wikipedia article on Deconfinement says: "In physics, deconfinement (in contrast to confinement) is a phase of matter in which certain particles are allowed to exist as free excitations, ...
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How does the strong force increase in attraction as particles move farther away?

I have heard that the strong force can be imagined similar to a rubber band, where the farther you extend the ends, the harder they pull themselves back together. My question is how? From what it ...
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What is “Colombia Plot” in reference to lattice QCD?

In High Energy Physics papers, I often see a diagram as shown below: I am still studying Quantum Field Theory, and I could not understand the only reference I could find about this plot: https://...
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What is meant by the “Leading Log Approximation” in the context of the steep rise in gluon distribution at small bjorken x?

I am taking a course in QCD, and we're learning about Regge Theory, Pomeron exchange and structure functions. I want to know what is meant by the leading log approximation in the context of the gluon ...
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How does the electroweak interaction and QCD form $SU(2)$ and $SU(3)$?

I'm trying to get a foothold into quantum field theory from a mathematical background. I see the use of $SU(2)$ and $SU(3)$ in gauge theory and wonder the following questions to help me bring QFT ...
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Jet Reconstruction: $k_{T}$-, anti-$k_{T}$ and Cambridge/Aachen in Comparison

In this paper, the following plot is shown: If we had had a perfect algorithm that would give us a perfect cone, would we see perfect circles in the $\phi-y$ plane that is shown, where $y$ is the ...
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Understanding Jet Clustering: Why is only $p_{T}$ used?

Let's only consider iterative jet clustering algorithms. Famous ones are the $k_{T}$ ($p = 1$), anti-$k_{T}$ ($p = -1$) and Cambridge/Aachen ($p = 0$) jet reconstruction algorithms. All these ...
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If having a finite action for Maxwell or Yang-Mills theory, $A_μ$ goes to a pure gauge configuration?

I had an empirical understanding that --- If we like to have a finite action for Maxwell or Yang-Mills theory, so that the field strengh $F_{μν}$ must go to zero at space-time infinity, meaning that $...
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Lattice spacing in lattice QCD

It is known that the lattice spacing in lattice QCD is not an external parameter and needs to be calculated, also the lattice beta parameter scales the lattice spacing ($a$) and goes as a function of ...
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What is instanton effect in QCD?

In the context of the Peccei-Quinn Symmetry in solving the Strong CP problem, it is said that the Axion develops a mass due to QCD instanton effects below $\Lambda_{QCD}$, which is very much ...
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Structure function in DIS calculation step

There is one step in the calculation that I am not understanting, but there are many things to present so one can understand and help me: i)$k^2$ and $k_T^2$ are small, so can be neglected; ii)$k^\mu=\...
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Factorization of squared amplitudes and the QCD splitting functions

When defining splitting functions from the Feynman rules, one makes use of the factorization of amplitudes. For definiteness, consider the process $$ a\,X \rightarrow b\,v\, X \rightarrow b\,W, $$ ...
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Why is the $SU(4)$ group not suitable for describing color symmetry?

How to demonstrate that the $SU(4)$ group cannot be a group of symmetry of a color charge?
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Normalisation of QCD Lagrangian

In QCD, and more generally in representations of $\mathfrak{su}(N)$, there is a freedom to choose the normalisation of the generators, $$ \mathrm{Tr} \, \left[R(T^a) R(T^b)\right] = T_R \delta^{ab}.\...
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Color function for tetraquark

The color function for tetraquark configuration $(qq)(\bar{q}\bar{q})$ is shown following: $$ \zeta_1=\frac{1}{2\sqrt6}[(rb+br)(\bar{b}\bar{r}+\bar{r}\bar{b})+(gr+rg)(\bar{g}\bar{r}+\bar{r}\bar{g})+(...
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Is there any progress in the study of the relationship between Rubik's cube and quark?

After Golomb discovered the relationship between Rubik's cube and quark, Anthony E. Durham improved it. Is there a link to Anthony E. Durham's work? May be the principal bundles can explain the ...
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How to calculate the chiral condensate from wilson fermions in lattice qcd?

In lattice qcd, respective more specifically in (1+1)-dimensional massless schwinger model on a lattice, iam trying to reproduce the chiral condensate by using correct constructed wilson overlap ...
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Abelian theories with more than one charge

I have a question about the non-abelian character of QCD. In order to write a gauge-invariant Lagrangian, there must be a term with the strength tensor $X^{\mu\nu}_{a}X_{\mu\nu}^{a}$ where $$ X^a_{\mu\...
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Avoiding unnecessary calculations when deriving Feynman rules

I'm trying to understand some principle behind deriving Feynman rules for QCD, i.e. avoid unnecessary calculations. Setup Assuming we have a gloun field $A_\mu^a$, fermion fields $\psi$ and ghosts $c^...
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Collinear factorisation in QCD: why can we multiply probabilities?

In the collinear factorisation equation for a QCD cross-section, schematically $$ \sigma_{AB\to X} = f^A_a \otimes \hat{\sigma}_{ab\to X} \otimes f^B_b , $$ we essentially convolute the probability ...
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What experimental evidence is there for quarks constantly changing colors?

In other words, why is it believed that the quarks are constantly changing colors? This question answers why theoretically but I'm curious what experimental observation prompted this theoretical piece ...

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