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Systematics of geometric scaling
High Energy Physics - Phenomenology · Submitted 31 Oct 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant.
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The abstract, sentence by sentence
Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the original definition, or \log(Q^2)-\lambda \sqrt{Y}, which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. A ``Quality Factor'' (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept \lambda. Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the original definition, or \log(Q^2)-\lambda \sqrt{Y}, which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. | method 0.58 | 0.84 | 0.06 | hedged possibility 0.50 |
| s1 | A ``Quality Factor'' (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept \lambda. | method 0.73 | 0.88 | 0.04 | asserted 1.00 |
| s2 | Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. | result 0.94 | 0.90 | 0.52 | asserted 1.00 |
| s3 | A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation. | result 0.63 | 0.89 | 0.34 | hedged possibility 0.54 |
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The paper
Original abstract
Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the original definition, or \log(Q^2)-\lambda \sqrt{Y}, which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. A ``Quality Factor'' (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept \lambda. Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation.
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References
How the literature uses it
9 arXiv papers cite this in 16 sentences
Papers citing it · 7 sentences without a confident label
Uses its method or tool 4 papers
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In order to be as model independant as possible, we used the quality factor method [ref] , allowing to test the validity of scaling variables without any assumption concerning the shape of the scaling function.
Systematic Analysis of Scaling Properties in Deep Inelastic Scattering · Conclusions · 1.00
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In order to compare the quality of the different scalings and to check if the DIS cross sections $∼F_2 / Q^2$ depend mainly on the $τ$ variable or not, it is useful to introduce the concept of Quality Factor [ref] (QF) while the explicit form of the $τ$ dependence is not known.
Studies of scaling properties in deep inelastic scattering · The Quality Factor · 0.99
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For a set of points $(u_i, v_i)$, where $u_i$'s are ordered, we introduce $QF$ as follows [ref]
Geometric Scaling of $F_2$ and $F_2^c$ in data and QCD Parametrisations · The Quality factor method · 0.98
Compares with it 1 paper
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Nevertheless, the values of the scaling parameters and the $χ^2$ values for the ratios are very close to the results of Ref. [ref] obtained by completely different method based on the “quality factor” [ref] .
Scaling laws of elastic proton-proton scattering differential cross sections · Summary and conclusions · 1.00
Cites it as background 1 paper
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More detailed investigations of scaling behavior in inclusive DIS events are provided in [ref] .
Geometric scaling in leading neutron events at HERA · INTRODUCTION · 0.96
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