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Towards a New Global QCD Analysis: Solution to the Non-Linear Equation at Arbitrary Impact Parameter
High Energy Physics - Phenomenology · Submitted 6 Jan 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim A numerical solution is presented for the non-linear evolution equation that governs the dynamics of high parton density QCD.
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The abstract, sentence by sentence
A numerical solution is presented for the non-linear evolution equation that governs the dynamics of high parton density QCD. It is shown that thesolution falls off as $e^{-b/R}$ at large values of the impact parameter $b$. The power-like tail of the amplitude appears in impact parameter distributions only after the inclusion of dipoles of size larger than the target, a configuration for which the non-linear equation is not valid. The value, energy and impact parameterof the saturation scale $Q_s(y=\ln(1/x),b)$) are calculated both for fixed and running QCD coupling cases. It is shown that the solution exhibits geometrical scaling behaviour. The radius of interaction increases as the rapidity in accordance with the Froissart theorem. The solution we obtain differs from previous attempts, where an anzatz for $b$ behaviour was made. The solutions for running and fixed $\as$ differ. For running $\as$ we obtain a larger radius of interaction (approximately twice as large), a steeper rapidity dependence, and a larger value of the saturation scale.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A numerical solution is presented for the non-linear evolution equation that governs the dynamics of high parton density QCD. | contribution 0.94 | 0.93 | 0.15 | asserted 1.00 |
| s1 | It is shown that thesolution falls off as $e^{-b/R}$ at large values of the impact parameter $b$. | result 1.00 | 0.92 | 0.22 | asserted 1.00 |
| s2 | The power-like tail of the amplitude appears in impact parameter distributions only after the inclusion of dipoles of size larger than the target, a configuration for which the non-linear equation is not valid. | result 0.74 | 0.75 | 0.18 | asserted 1.00 |
| s3 | The value, energy and impact parameterof the saturation scale $Q_s(y=\ln(1/x),b)$) are calculated both for fixed and running QCD coupling cases. | result 0.69 | 0.93 | 0.09 | asserted 1.00 |
| s4 | It is shown that the solution exhibits geometrical scaling behaviour. | result 1.00 | 0.91 | 0.17 | asserted 1.00 |
| s5 | The radius of interaction increases as the rapidity in accordance with the Froissart theorem. | result 0.96 | 0.84 | 0.19 | asserted 1.00 |
| s6 | The solution we obtain differs from previous attempts, where an anzatz for $b$ behaviour was made. | contribution 0.63 | 0.69 | 0.10 | asserted 1.00 |
| s7 | The solutions for running and fixed $\as$ differ. | result 0.99 | 0.85 | 0.08 | asserted 1.00 |
| s8 | For running $\as$ we obtain a larger radius of interaction (approximately twice as large), a steeper rapidity dependence, and a larger value of the saturation scale. | result 1.00 | 0.95 | 0.20 | asserted 1.00 |
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Original abstract
A numerical solution is presented for the non-linear evolution equation that governs the dynamics of high parton density QCD. It is shown that thesolution falls off as $e^{-b/R}$ at large values of the impact parameter $b$. The power-like tail of the amplitude appears in impact parameter distributions only after the inclusion of dipoles of size larger than the target, a configuration for which the non-linear equation is not valid. The value, energy and impact parameterof the saturation scale $Q_s(y=\ln(1/x),b)$) are calculated both for fixed and running QCD coupling cases. It is shown that the solution exhibits geometrical scaling behaviour. The radius of interaction increases as the rapidity in accordance with the Froissart theorem. The solution we obtain differs from previous attempts, where an anzatz for $b$ behaviour was made. The solutions for running and fixed $\as$ differ. For running $\as$ we obtain a larger radius of interaction (approximately twice as large), a steeper rapidity dependence, and a larger value of the saturation scale.
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2 arXiv papers cite this in 3 sentences
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Cites it as background 1 paper
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Unfortunately, as far as we know there exist only two papers (see Ref. [ref] ) where the numerical solutions were found to BK equation including $b$ dependence.
Non-linear equation: energy conservation and impact parameter dependence · Impact parameter dependence · 0.82
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