Mueller’s dipole wave function in QCD: Emergent Koba-Nielsen-Olesen scaling in the double logarithm limit
Abstract
We analyze Mueller’s QCD dipole wave function evolution in the double logarithm approximation (DLA). Using complex analytical methods, we show that the distribution of the dipole in the wave function (gluon multiplicity distribution) asymptotically satisfies the Koba-Nielsen-Olesen (KNO) scaling, with a nontrivial scaling function f(z) with z = $$\frac{n}{n}$$. The scaling function decays exponentially as 2(2.55)2ze – $$\frac{z}{0.3917}$$ at large z, while its growth is log-normal as $$e^{–\frac{1}{2}ln^{2}z}$$ for small z. A detailed analysis of the Fourier-Laplace transform of f(z) allows for performing the inverse Fourier transform and accessing the nonasymptotic bulk region around the peak. The bulk and asymptotic results are shown to be in good agreement with the measured hadronic multiplicities in DIS, as reported by the H1 Collaboration at HERA in the region of large Q2. A numerical tabulation of f(z) is included. Remarkably, the same scaling function is found to emerge in the resummation of double logarithms in the evolution of jets. Using the generating function approach, we show why this is the case. The absence of KNO scaling in noncritical and super-renormalizable theories is briefly discussed. We also discuss the universal character of the entanglement entropy in the KNO scaling limit and its measurement using the emitted multiplicities in DIS and e+e– annihilation.
- Publication Date:
- Research Org.:
- Stony Brook Univ., NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1999287
- Alternate Identifier(s):
- OSTI ID: 2280606
- Grant/Contract Number:
- FG-88ER40388; FG02-88ER40388
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. D.
- Additional Journal Information:
- Journal Name: Physical Review. D. Journal Volume: 108 Journal Issue: 3; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Liu, Yizhuang, Nowak, Maciej A., and Zahed, Ismail. Mueller’s dipole wave function in QCD: Emergent Koba-Nielsen-Olesen scaling in the double logarithm limit. United States: N. p., 2023.
Web. doi:10.1103/PhysRevD.108.034017.
Liu, Yizhuang, Nowak, Maciej A., & Zahed, Ismail. Mueller’s dipole wave function in QCD: Emergent Koba-Nielsen-Olesen scaling in the double logarithm limit. United States. https://doi.org/10.1103/PhysRevD.108.034017
Liu, Yizhuang, Nowak, Maciej A., and Zahed, Ismail. Wed .
"Mueller’s dipole wave function in QCD: Emergent Koba-Nielsen-Olesen scaling in the double logarithm limit". United States. https://doi.org/10.1103/PhysRevD.108.034017.
@article{osti_1999287,
title = {Mueller’s dipole wave function in QCD: Emergent Koba-Nielsen-Olesen scaling in the double logarithm limit},
author = {Liu, Yizhuang and Nowak, Maciej A. and Zahed, Ismail},
abstractNote = {We analyze Mueller’s QCD dipole wave function evolution in the double logarithm approximation (DLA). Using complex analytical methods, we show that the distribution of the dipole in the wave function (gluon multiplicity distribution) asymptotically satisfies the Koba-Nielsen-Olesen (KNO) scaling, with a nontrivial scaling function f(z) with z = $\frac{n}{n}$. The scaling function decays exponentially as 2(2.55)2ze – $\frac{z}{0.3917}$ at large z, while its growth is log-normal as $e^{–\frac{1}{2}ln^{2}z}$ for small z. A detailed analysis of the Fourier-Laplace transform of f(z) allows for performing the inverse Fourier transform and accessing the nonasymptotic bulk region around the peak. The bulk and asymptotic results are shown to be in good agreement with the measured hadronic multiplicities in DIS, as reported by the H1 Collaboration at HERA in the region of large Q2. A numerical tabulation of f(z) is included. Remarkably, the same scaling function is found to emerge in the resummation of double logarithms in the evolution of jets. Using the generating function approach, we show why this is the case. The absence of KNO scaling in noncritical and super-renormalizable theories is briefly discussed. We also discuss the universal character of the entanglement entropy in the KNO scaling limit and its measurement using the emitted multiplicities in DIS and e+e– annihilation.},
doi = {10.1103/PhysRevD.108.034017},
journal = {Physical Review. D.},
number = 3,
volume = 108,
place = {United States},
year = {Wed Aug 16 00:00:00 EDT 2023},
month = {Wed Aug 16 00:00:00 EDT 2023}
}
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