Questions tagged [partons]
A parton is a gluon, quark or antiquark in the eponymous model of scattering involving hadrons. In the hadron's infinite-momentum frame, incoming particles will be scattered instantaneously and incoherently, reducing the problem to a simple kernel convolved with parton distributions, at a particular physical scale (as probed by the inverse of the momentum transfer).
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OPE leading twist = collinear factorisation?
The operator product expansion systematically expands QFT interactions in terms of a sum of local operators.
Is the leading twist of this expansion identifiable with collinear factorisation and, if so,...
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Quark charges - parton-distribution function - factor 5/18
I got the following from Thomson’s Modern Particle Physics and some other sources.
The factor 5/18 distinguishing electron-DIS and neutrino scattering experiments is a basic proof for quarks and their ...
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Why is it that the Callan-Gross relation predicts that quark has spin 1/2?
I'm studying deep inelastic scattering, and currently at the part where they say the Callan-Gross relation:
$$F_1 (x) = \frac{1}{2x} F_x (x)$$
where $F_1$ and $F_2$ are the dimensionless structure ...
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What is a polarized/unpolarized parton?
In QCD physics, certain partonic distributions like Generalized Parton Distributions (GPDs) and Transverse Momentum Distributions (TMDs) are defined for the case where the parton is either unpolarized,...
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Are there equations for Parton Distribution Functions?
Are there actual equations for the Parton Distribution Functions for quarks and gluons? I've been looking high and low for theory-based papers about this and it seems like a wild goose chase at this ...
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Polarized structure functions and Bjorken sum rule
I'm trying to understand what the Bjorken sum rule and the polarized structure functions entering it are. I will use equation (2.3) here as a reference for asking the question.
In Peskin, I've only ...
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Are parton distribution functions non-negative?
Let $f_i(x)$ be a parton distribution function as known from QCD factorisation theorems. Is $f_i(x)$ non-negative for $0<x<1$? If so, how can this be seen from the definition of PDFs in terms of ...
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Is the pion valence PDF symmetric?
The positive-pion $\pi^+$ is comprised of 1 valence up-quark and 1 valence anti-down-quark. Assuming isospin symmetry, the parton distribution functions (PDFs) for these two valence quarks should be ...
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Parton Distribution Functions - Antiquarks?
In all the PDF plots that I have seen so far (e.g. https://arxiv.org/abs/1111.5452 Fig. $3$ and $4$) the PDFs for sea or charm quarks contained only the strange or charm quark, but not the $\bar{s}$ ...
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Parton, detector and particle level at LHC [closed]
What is the difference between parton, detector and particle level in high energy physics?
I found a similar question but I couldn't understand the explanation for detector and particle level given ...
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Paper showing evidence for Callan-Gross Relation
I am getting ready for a presentation and want to show a plot showing experimental evidence for the Callan-Gross relation. Are there any papers plotting this beyond 1970 across different $Q^2$ or ...
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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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Meaning of $\gamma^\pm$ in Parton Fragmentation Functions
I was just working through the paper Parton fragmentation functions and came across equation 12.
What do $\gamma^{+}$ and $\gamma^{-}$ mean? The text doesn't explain this at all.
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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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Does the path of a Wilson line in a quark-correlator matter?
Consider a gauge-invariant quark correlation function nested inside an arbitrary state $|p\rangle$
$$\langle p |\bar \psi(z)_{\alpha,a}\left( W_{\Gamma}(z,0)\right)_{ab}\psi(0)_{\beta,b}|p\rangle \...
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Is $\mu$ the renormalization or factorization scale in the DGLAP equations?
The DGLAP equations read
$$\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),$$
where the $f_i$ are the parton ...
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Collinear factorisation in QCD: why can we multiply probabilities?
In the collinear factorisation equation for a QCD cross-section, schematically
$$
\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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Why are sea quarks dominant only at low value of the Bjorken $x$ variable?
In electron proton deep inelastic scatterings, the sea quarks or gluon PDFs are only dominant at low value of $x$. Thomson explained this in his book Modern Particle Physics (see page 194) by arguing
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Deriving Callan-Gross from Parton Model
I want to derive the Callan-Gross relation from the parton model, not fom the Rosenbluth and Mott cross sections, but I am having some problems obtaining the textbook result. I am following M.D. ...
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What are extrinsic and intrinsic flavour production?
In terms of Feynman diagrams, what are extrinsic and intrinsic flavour production?
See for example this paper this paper (p.2).
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What are the differences between FFN, VFN, GMVFN and ZMVFN PDF schemes in QCD?
What are the differences between the fixed flavour number (FFN), variable flavour number (VFN), general-mass variable flavour number (GMVFN) and zero-mass variable flavour number (ZMVFN) schemes for ...
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Question about DGLAP evolution equation
I am reading chapter 32.2 of Schwartz's QFT book, where he defines the renormalized PDFs $f_i(x, \mu)$. This leads to an equation (32.48), which relates PDFs at different scales $\mu, \mu_1$:
$f_i(x,\...
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How to derive operator form of the parton distribution function
A similar question is found here in Stackexchange a year ago without any response.
I am following the formulation of the parton densities from the handbag diagram in Collins Handbook of Perturbative ...
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Textbook for parton distributions?
Are there any textbooks, or good pedagogical review articles, on the subject of parton distributions? I'm looking for such sources that cover all the standard topics, such as:
Generalized parton ...
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How are DGLAP splitting kernels probabilites for parton branchings?
In the literature on parton evolution one often reads that the DGLAP splitting kernels $P_{ij}$ represent the probabilities for a parton of type $j$ to split into a parton of type $i$ and another ...
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Is the starting distribution in the solution of DGLAP IR-bare?
On p.27 of this paper by John Collins, he says that when defining PDFs in terms of partonic number operators, one acquires an IR-divergent bare PDF (eq. 52). The residue of the IR-divergent term is ...
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Why is the convolution between hadron structure functions and PDFs defined this way?
Say you have the distribution function $\rho_i$ of a quark $i$ (depending on the momentum fraction of that quark), and a structure function $\hat{F}_i$ (depending on the "Bjorken variable" $...
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Proton Structure and Parton Distribution Function
I recently read a question about whether photons, electrons, neutrinos... are a part of the proton since there are these sea-quarks he learned about. And the answers were confusing to me because the ...
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Transverse momentum in partonic process $\gamma^\ast q\rightarrow qg$
Let $\hat{s}:=(q+p)^2$, $\hat{t}:=(k-p)^2$, $\hat{u}:=(p-p^\prime)^2$ be the Mandelstam variables of the partonic scattering process $\gamma^\ast(q) +q(p)\rightarrow q(p^\prime)+g(k)$, where the ...
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Transverse momentum in the parton model
Why is it so important that the partons in the parton model have low transverse momenta? And transverse to what anyway? I mean, basically one looks to justify breaking the hadronic subgraph in hadron-...
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Towards a matrix element definition of PDF
In Schwartz's book, 'Quantum Field Theory and the Standard Model' P.$696$, he starts to derive an expression for a parton distribution function in terms of matrix elements evaluated on the lightcone. ...
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How are the structure functions in Deep inelastic scattering measured?
I've been reading lots of different textbooks on the parton model and deep inelastic scattering and the discovery of quarks, and most of the time whenever I see a plot, it's about the measurement of ...
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Why do parton distribution functions not depend on the total momentum of the composite state?
When defining such quantity as the elastic form factor, I kinda understand why it turns out to be independent of the momentum of the charged particle, and only dependent on the momentum of the photon ...
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What are direct experimental evidences that quarks exist? [duplicate]
Now we have very established model of quarks explaining fundamental strong interaction. What are experimental proofs for existence of quarks and what is the name of physicist which made them?
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Why small $x$ corresponds to high energy process?
I just start to study Quantum Chromodynamics, I read in some references that small $x$ corresponds to process of high energy, but I cannot find a straightforward explanation.
In the case of electron ...
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Parton distribution function in terms of Fock space kets
To my understanding, I can (at least, formally) express the (unnormalized) PDF for a certain constituent of a composite state as
$$
f(x)=f\left(\dfrac{k}{K}\right)=\sum_j m_j^{(k)}|\langle\psi_j^{(k)}|...
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Integration of the splitting function
I have a problem performing the following integration provided in the paper by Catani and Seymour (arXiv: hep-ph/9605323) page 27. Given is the integral
$$
\mathcal{V}=\int_0^1 (z(1-z))^{-\epsilon} \...
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Drell-Yan process and factorization scale
What is the most relevant choice for the factorization scale of the Drell-Yan process? Can it be the invariant mass at the reaction threshold?
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Parton model and impulse approximation for the process $2\to 1$
Consider a process
$$
\tag 1 N+N\to X+\text{all},
$$
where $N$ are nucleons and $X$ is some massive particle. Assuming the parton model is valid and there is vertex $PP'X$, where $P,P'$ are partons ...
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Applicability of parton model at low factorization scale
Consider scattering process at partonic level occuring at low factorization scale $\mu^{2}\lesssim 1\text{ GeV}^{2}$ (for example, with the "hard" process $2\to 1$ with low mass produced particle, ...
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Deep Inelastic Scattering cross section: Smearing of the $F_2(x)$ graph and relation of form factors with Fourier Trasform of nucleon distibutions
Consider Deep Inelastic Scattering cross section
$$\frac{d^2 \sigma}{d \Omega d \nu}=(\frac{d \sigma}{d \Omega})|_{Mott} \{ W_2(Q^2,\nu)+2 W_1(Q^2,\nu) \tan^2(\theta/2) \}$$
It is said that the ...
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Computing the $p_{T}$ spectrum of hadrons in pp collisions by knowing the $p_{T}$ spectrum of quarks
Consider the differential quark production cross-section $d\sigma_{pp \to q\bar{q}}/d|\mathbf{p}_{T}|$, where $|\mathbf p_{T}|$ is the momentum transverse to the $pp$ beam line. Next, assume that the ...
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Bjorken Scaling and the Parton Model
It is often said that Bjorken scaling of the deep inelastic structure functions
\begin{equation}
\nu W_2(\nu ,Q^2)\rightarrow F(x)
\end{equation}
(where $Q^2$ is the virtuality of the photon, $\nu=\...
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Parton distribution function and factorization scale
Consider some deep inelastic scattering $y f\to y f$, where $f$ is a parton inside a nucleon $N$, and $y$ is some particle. The cross-section is then
$$
\sigma_{\text{DIS}} = \int dx f_{N/f}(x,Q^{2})\...
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Do electrons interact with gluons?
I know the straightforward answer to this question is no: electrons are leptons which by definition don't interact via the strong force, gluons are the mediators of the strong force and hence ...
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Leading order DGLAP evolution
Consider the leading-order (LO) DGLAP ((Dokshitzer–Gribov–Lipatov–Altarelli–Parisi) equation
$$x \mu^2 \frac{d xg(x,\mu^2)}{d\mu^2}= \alpha_s \int_x^1 dz P_{gg}(z) \frac{x}{z} g(\frac{x}{z}, \mu^2) + \...
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Parton model in experimental particle physics
In experimental particle physics, what does "parton-level" , "particle-level" and "detector-level" exactly mean ?
PS : detailed explanations, links, etc .. would be deeply appreciated
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Parton distribution function - dependence on $Q$?
In one of my previous questions I define the parton distribution function, following that of D.Stump as follows:
$f_i(x,Q^2)dx$ is the mean number of the $i$th type of patron with longitudinal ...
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Sea quark parton annihilation?
Consider the figure below1:
This can be read as follows (please correct me if I am wrong): two particles come in and 'fragment', a parton from each particle $C$ and $D$ annihilate to form the ...
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