Questions tagged [quantum-chromodynamics]

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

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Help to derive the inequality bounds $1/4\leq F_2^{\rm en}/F_2^{\rm ep}\leq 4$ (Halzen & Martin's exercise 9.7)

The structure functions $F_2^{\rm ep}$ and $F_2^{\rm en}$ for electron-proton and electron-neutron deep inelastic scattering deduced from the model of valence quarks and sea quarks of proton and ...
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Physical significance of the reality of an ${\bf N}$ representation: how the nature of interactions is affected?

Background The fundamental representation of ${\rm SU(N)}$ is denoted by ${\bf N}$ and the conjugate of the fundamental is denoted by ${\bar{\bf N}}$. If the representation ${\bf N}$ is related to ${\...
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Eight gluons, what are the properties of two of them?

If there are 8 gluons, and 6 of them can be represented as a color/anticolor pair (red/antiblue for example), that leaves 2 "other" gluons. How do these two gluons differ from each other? ...
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Effects of the discrete quotient of chiral symmetry group

For a theory of $N_f$ massless Dirac fermions coupled to a Yang-Mills field, the usual story is that we have a $U_L(N_f)\times U_R(N_f)$ symmetry, which is then expressed as $SU_L(N_f)\times SU_R(N_f) ...
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Why gluons don't have mass? [duplicate]

Which theoretical or experimental results provide us that we should calculate with massless gluon fields. Or in other words, what forbids gluons from having mass?
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What is the application of dimension $6$ representation of $SU(3)$ in particle physics?

As we know, the $uds$ transforms in fundamental representations of $SU(3)$. It has the antifundamental partner. According to representation theory, $$ \mathbf{3} \otimes \mathbf{\bar{3}}= \mathbf{8} \...
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Chiral symmetry in massless QCD

The QCD Lagrangian for two flavors is: $-\frac{1}{4} G\tilde{G}+i\bar{u}\displaystyle{\not} D u+i\bar{d} \displaystyle{\not} D d-m_u\bar{u} u-m_d\bar{d}d$ or alternaively $-\frac{1}{4} G\tilde{G}+i\...
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What does it mean by active quarks?

Do the active quarks mean valence quarks? Or we can also consider other quarks, like when there are offshell-quarks produced from gluons by pair production processes? For example: how the active quark ...
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Determining reduced graphs in perturbative QCD

I am reading "Foundations of perturbative QCD" by John Collins and I find it hard to determine the general form of reduced graphs (that is feynman graphs, where internal lines which do not ...
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Apparent ambiguity on delta function imposing constraint (Halzen 10.2)

In section 10.2 of Halzen and Martin's Quarks and Leptons, the authors express the cross section ratio $\sigma_T/\sigma_0$ of the process $\gamma^*$-proton in terms of the cross section of the ...
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Could a proton be produced using the dynamical Casimir effect?

According to the standard model, would it be theoretically possible to emit protons or other complex particles from the vacuum using the dynamical Casimir effect? Or is it only possible to emit ...
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Spatial Translation field operators in Non-Local Quark Bilinear

I am interested in studying a somewhat simple quantity at tree level $$ \langle p'|\bar{\psi}\Big(-\frac{z}{2}\Big)\gamma^{\mu}\psi\Big(\frac{z}{2}\Big)|p\rangle $$ where $|p\rangle$ is a fermion ...
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QCD energy scale $\Lambda_{\rm MS} $, $\Lambda_{\rm QCD}$, …?

Why there seems to be different conventions of QCD energy scales? Is that due to the running coupling? For example in Wikipedia https://en.wikipedia.org/wiki/Coupling_constant#QCD_scale: $$ \Lambda_{\...
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Is $\mu$ the renormalization or factorization scale in the DGLAP equations?

The DGLAP equations read $$\frac{\partial f_i(x,\mu^2)}{\partial\ln\mu^2}=\sum_j\int^1_x\frac{dz}{z}P_{ij}(z,\alpha_s(\mu^2))f_j\left(\frac{x}{z},\mu^2\right),$$ where the $f_i$ are the parton ...
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Why quarks are confined? Why can't they be found in unbound states?

No one has observed before a "free" quark, i.e. a quark in an unbound state. According to one paper, I read that $p\bar{p}$ collision produce unbound $t\bar{t}$ pair which quickly decay into ...
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Change of flavour in strong interactions?

Sorry if this question has been asked already but after researching I have found that quark flavour is not changed in the strong interaction. This confused me because how can a down and anti down ...
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Calculating strong coupling constant $\alpha_s$

I'm trying to find out how to calculate the value of strong coupling constant. but haven't found any exact answer, all I get is reference to perturbation theory. is there any exact defined formula to ...
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What evidence is there that bottom and top quarks come in 3 colors?

We know, because of baryons such as the triple-strange Omega baryon spin 3/2, that at least the quarks 'up', 'down', and 'strange' must come in 3 colors because of the Pauli exclusion principle. No ...
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Confusion among channel $u$ and channel $t$ in exclusive reactions

In the this paper (https://arxiv.org/abs/1203.4392), on page 2 it is said that Since DVCS amplitude is symmetric under $s \leftrightarrow u$ channel crossing, the CFFs and $^{S}C^i_{\cdots}$ ...
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How does the pion decay constant $f_{\pi}$ depend on the number of flavors $N_f$?

I know that for standard QCD with quarks, chiral symmetry breaking occurs for around 4 - 5 light/active quarks - i.e. pions, or generally pseudoscalar goldstone bosons, definitely appear in the ...
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Gluon radiation from a nucleon?

Due to the fact that neutrons and protons consist of quarks (i.e. are not really Dirac particles), their magnetic moments differ from the so-called "nuclear magneton" (i.e. the natural unit ...
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Connections between conformal field theory and particle physics

I'm wondering if one could use conformal field theory to predict any facts in (experimental) particle physics? I think CFT shares some similarities with QCD, but I'm not sure if one could use CFT to ...
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If quark current masses were equal, processes like $dd \to ss$ would be forbidden?

The QCD lagrangian has a $SU(N_{f})$ vectorial symmetry, which is explicitly broken by the difference in quark current masses. If this symmetry was exact ($m_{u}=m_{d}=m_{s}$...) the charges ...
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Recommend books for learning lattice QCD

I want to learn lattice QCD by myself, but I don't know how to start. Can you recommend some books for lattice QCD?
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Bern-Carrasco-Johansson (BCJ) Double Copy and Color-Kinematic duality

According to the wikipedia page on Strong Gravity, the theory is considered "non-mainstream", but from what I can gather there have been some very interesting progress and results since it ...
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How to understand observed electric quadrupole moment of deuteron?

Deuteron is p-n, so naively should have zero electric quadrupole moment. However, experimentally it turns out quite large: $0.2859\ e\cdot fm^2$ from https://en.wikipedia.org/wiki/Deuterium#...
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How to expand the QCD loops in terms of infrared scale for matching with heavy quark effective field theory

According to Manohar:"argument applies almost without change to a practical example,the derivation of the HQET Lagrangian to one-loop." on page 37 of the following paper on effective field ...
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Emergence of Dual Resonance model from QCD

This question is about getting to understand better what the Dual Resonance (DR) model actually managed to successfully predict or model from the nuclear interactions, in the context of understanding ...
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Altarelli-Parisi splitting functions

I had a problem when calculating the splitting functions for an off-shell emitting a quark and the problem goes like this. First, the kinematics, I had three four-vectors that were: $ p=(p_+,\frac{p^2}...
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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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Help on deriving the relationship between the quark and anti-quark parton distribution function

I know $f_{u/h}(x) = -f_{\bar{u}/h}(-x)$ where $$ f_{u/h}(x) = \frac{1}{2}\int\frac{dz^-}{2\pi}e^{ixP^+z^-} \langle h(p)|\bar{u}(0)\gamma^+[0;z]u(z)|h(p)\rangle |_{z^+=0,z_{\perp}=0} $$ where $[u;z] = ...
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How to average over colour factor for process gluon-quark scattering?

My question is how to average the color factors when calculating the magnitude of amplitude for gluon-quark scattering process, for example, how to average over color factor for $|\mathcal{M}_{a}|^{2}$...
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Conservation of left-handed quark current

I'm reading about the Operator Product Expansion in Gelis's A Stroll Through Quantum Fields section 7.4.2. As an example, he's using the product of currents $$A_1^\mu = \overline{d}_L\gamma^\mu u_L$, ...
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What is the QCD gluon field (mathematically)?

In QCD, the gluon field is described as $A^a_\mu$. In the covariant derivative for the Lagrangian, it is multiplied by the Gell-Mann $SU(3)$ generator matrices $\lambda_a$ ($a=1..8$) as $\lambda_aA^a_\...
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How to calculate the Feynman diagram under $SU(N_c)$ group?

I give my own answer below. I use the feynman rules for QCD directly to calculate the process: $qq'\rightarrow qq'$, where $q$ and $q'$ have different flavor. But I don't how to give my answer ...
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Are gravitons equivalent to extra localised lattice points?

So imagine space is a regular square mesh or lattice. In a theory like QCD, the photon lines are placed along the edges of this graph to form paths. The space is supposed to represent simple ...
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Can a gauge theory with $SU(2)_{left}*SU(2)_{additional}$ symmetry contain confinement?

Consider a gauge theory with $SU(2)_{left}*SU(2)_{additional}$ symmetry. By $additional$, I mean adding a new symmetry between an electron and a quark(like up quark and electron forming a doublet). ...
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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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How is $\Lambda_{\textrm{QCD}}$ relevant in the non-perturbative regime?

The famous $\Lambda_{\textrm{QCD}}$ parameter enters through the one-loop running of the QCD coupling, through a relation similar to the following: $$\alpha_S(Q^2)=\frac{\alpha_S(Q^2_0)}{1+b\ln(Q^2/Q^...
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Question about Renormalization of Ghosts in QCD in MS scheme

During a calculation of the Renormalization constant of the ghosts in QCD I stumbled over the following question: When I calculate the self-energy of the Faddeev-Popov ghosts in $SU(N)$ non-abelian ...
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How the non-existence of a color singlet gauge boson rules out $U(3)$ as a gauge group for th

On page 271 of his book Gauge Theories of the Strong, Weak and Electromagnetic Interactions, Quigg reasons that "In U(3) color gauge theory, the color-singlet gauge boson that occurs in the product $$...
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Classical chromodynamics force density vector

In classical electrodynamics there is a current and potential four-vector. The covariant force density in a charge continuum according to wikipedia is $f_\alpha=F_{\alpha\beta}J^\beta$ But I'm not ...
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Strong force coupling

My lecture notes write that the coupling constant for the strong force goes to infinity as the distance goes to infinity. However the range of the strong force is said to be small. If the strength ...
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Why do we need two gluons for the decay $ϕ \to 2K$?

The Feynman diagram for the decay $\phi \to K^+K^-$ usually depicts two gluons. (This can be seen e.g. on Wikipedia). Why do we need two gluons, instead of just one?
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Asymptotic states in strongly-coupled QFTs

In QFT the asymptotic states play a very important role, as they are the basis on which we decompose our in-states and out-states when we calculate correlation functions. However, I have not been ...
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Symmetry factor of a loop diagram with gauge-bosons

I have learnt in the lecture that the symmetry factor of the following diagram is 1/2: where the line corresponds to a gluon. But why is this the case? We get 1/2 from 2nd order in pertubation ...
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Calculation of splitting kernel

I want to calculate the DGLAP splitting kernel $P_{gq}$ to leading order from the following diagramm but I am stuck and need help on how to proceed. I find that the matrix element should be $$M_{n+1}=...
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What corresponds to the radial component of the axion potential?

An axion can be understood as an oscillation of the axion field in some potential. In the Higgs mechanism, there are 4 degrees of freedom. The Higgs boson is the radial oscillation and 3 remaining ...
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Permitted bound states in extended QCD color group $SU(4)$

I'm very much curious about the possible quark combinations to form bound states in $SU(4)$ QCD. We already know Wilson has proven that only colorless combinations can arise in $SU(3)$ of these ...
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Counting Structure Functions for Mesons

The decomposition of form factors between mesons and baryons can be written as $$ \langle \text{meson}(p') |j^{\mu}(x)| \text{meson}(p)\rangle = \frac{(p'+p)^{\mu}}{2\sqrt{E(p')E(p)}}F(Q^2) $$ $$ \...

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