All Questions
Tagged with quantum-chromodynamics scattering
32
questions
1
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1
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267
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Why there is only $t$-channel for $u+\bar d\rightarrow u+\bar d$ scattering?
I am reading Griffith's textbook on particle physics about the $u+\bar d\rightarrow u+\bar d$ scattering for QCD. On page 285, it says there is only one possible channel ($t$-channel):
Why there are ...
- 1,783
0
votes
0
answers
41
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Does the scattering data, in any way, justify the simplistic picture of hadrons? [duplicate]
The structure of the neutron or the proton is extremely complicated. It is not a simple bound state of three valence quarks. However, the simplified picture allows us to explain various properties of ...
- 11.7k
1
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0
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135
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How do I calculate the Altarelli-Parisi splitting function for $g \rightarrow q\bar{q}$?
I'm trying to calculate the Altarelli-Parisi splitting function in the collinear limit for a gluon splitting into a quark-antiquark pair, but I keep getting stuck. Let $p$ and $k$ be the momenta for ...
- 43
2
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0
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38
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How to derive Collinear amplitude proportional to Born amplitude
In the collinear limit, the squared matrix element factorises into (for partons 4 and 5 going collinear)
\begin{eqnarray}
\overline{\sum}|M_3(1+2 \to 3+4+5)|^2 \approx \overline{\sum}|M_2(1+2 \to 3+4')...
1
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1
answer
118
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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 ...
- 387
0
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0
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55
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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 ...
- 1,597
1
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0
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147
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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\...
- 11
3
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0
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370
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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 ...
- 316
1
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2
answers
30
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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 ...
user248824
2
votes
1
answer
80
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Is Compton Scattering the "Abelian limit" of $qg \rightarrow qg$?
I have calculated the average over initial and sum over final states of the squared amplitude for both Compton scattering $e^-\gamma \rightarrow e^-\gamma$ (QED) and quark-gluon scattering $qg \...
- 321
1
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1
answer
370
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Deep inelastic scattering (DIS) and handbag diagram
Here, in page 11, you can see the so-called 'handbag' diagram that explains how a virtual photon emitted in a deep inelastic scattering (DIS) process interacts with a parton.
I'm going to use this ...
- 1,597
0
votes
0
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99
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Deep inelastic electron-proton scattering amplitude
In 'QCD and collider Physics' book by Ellis, Stirling and Webber, chapter 4.2 'The parton model from field theory' there is this equation for the amplitude of the process $e^- (k) P \rightarrow e^- (k^...
- 1,597
1
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1
answer
87
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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 ...
- 11.7k
1
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1
answer
133
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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 $^{S}C^i_{\cdots}$ ...
- 1,597
2
votes
0
answers
551
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Colour-ordering formula of QCD amplitudes (tree-level)
I have been studying colour-ordered amplitudes and spinor helicity formalism for a while. It is now apparent to me that I do not fully understand the 'master' formula which allows us to relate the ...
- 155
1
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1
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215
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Elimination of three gluon vertex
I am reading this paper by Dixon, where it is mentioned that one can diagrammatically compute the colour factor of certain Feynman graphs, such as shown in figure 1, where they expand a three gluon ...
- 302
3
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0
answers
70
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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 ...
- 2,921
3
votes
1
answer
87
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Notation: Dividing by a partial differential
Setup
Hi, I am working on a DIS scattering problem in the Light Cone Gauge, and this has me needing to calculate the currents. In doing this, I have come across the following equation
$$
t^a \...
1
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1
answer
187
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Drell-Yan process and factorization scale
What is the most relevant choice for the factorization scale of the Drell-Yan process? Can it be the invariant mass at the reaction threshold?
- 8,901
3
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0
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356
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Bjorken Scaling and the Parton Model
It is often said that Bjorken scaling of the deep inelastic structure functions
\begin{equation}
\nu W_2(\nu ,Q^2)\rightarrow F(x)
\end{equation}
(where $Q^2$ is the virtuality of the photon, $\nu=\...
- 2,270
2
votes
1
answer
370
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Parton distribution function and factorization scale
Consider some deep inelastic scattering $y f\to y f$, where $f$ is a parton inside a nucleon $N$, and $y$ is some particle. The cross-section is then
$$
\sigma_{\text{DIS}} = \int dx f_{N/f}(x,Q^{2})\...
- 8,901
7
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1
answer
338
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NMHV 5 Gluon Scattering (Elvang and Huang, Ex 3.11)
In Elvang and Huang's Scattering Amplitudes in Gauge Theory and Gravity, Exercise (3.10) (Exercise (3.11) in the printed version) asks the reader to construct the NMHV scattering amplitude of five ...
- 421
4
votes
1
answer
1k
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Callan-Gross relation validity
The inelastic electron-proton scattering cross section can be written as
$$\frac{d\sigma}{dE_2d\Omega}=\frac{\alpha^2}{4*E_1\sin^4{\frac{\theta}{2}}}(W_2\cos^2{{\frac{\theta}{2}}}+2W_1\sin^2{{\frac{\...
- 263
7
votes
1
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276
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What is the mathematical motivation for complexifying momenta in BCFW?
One of the first steps in obtaining the on-shell BCFW recursion relations is complexifying the momenta of the external particles. Now complexifying things is not unprecedented (the dispersion program ...
- 1,124
4
votes
2
answers
186
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How to compute scattering amplitude $\gamma\pi^+\to\pi^+\pi^0$
I wish to find the amplitude for process $\gamma\pi^+\to\pi^+\pi^0$ at low energies. I am familiar with the basic concepts and techniques of QFT but have never dealt with the scattering processes ...
- 1,586
2
votes
1
answer
5k
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Altarelli-Parisi Splitting Function $P_{qq}(z)$ vanishing integral if and only if quark flavour sum rules and equivalence
Question 1: I believe both questions are in the context of Deep Inelastic Scattering. I've been given the expression for $F_{2}^{ep}(x)=(\frac{2}{3})^2[u(x)+\bar{u}(x)]
+(\frac{1}{3})^2[d(x) + \bar{d}(...
- 23
3
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0
answers
194
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Conversion of QCD cross section formula
I'm writing a program to calculate NLO cross sections for semi-inclusive high-$p_T$ pion production in proton-proton-collisions for my bachelor thesis.
I've got a paper describing the production ...
- 337
16
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4
answers
4k
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Is forward scattering = no scattering?
What is forward scattering? If it is equivalent to no scattering, then why not call it "no scattering"?
- 5,569
19
votes
2
answers
3k
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Why Cronin Effect Happens?
I'm looking for explanation on Cronin effect but unfortunately there's no Wikipedia entry or self-contained paper to start from. The statement of this effect is that:
"At leading order, multiple ...
- 1,707
7
votes
1
answer
2k
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A certain gluon scattering amplitude
I am stuck with this process of calculating the tree-level scattering amplitude of two positive helicity (+) gluons of momentum say $p_1$ and $p_2$ scattering into two gluons of negative (-) helicity ...
- 4,619