Gluon density and functions from BK equation with local impact parameter dependence in DIS on nuclei

Bondarenko, S.

doi:10.1016/j.nuclphysa.2011.01.025

“…[124]). An impact-parameter dependence was also introduced [125][126][127] that was already missing in the GBW model.…”

Section: Dipole Models and Geometric Scalingmentioning

confidence: 99%

Quantum chromodynamics at high energy and statistical physics

Munier

¹

2009

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When hadrons scatter at high energies, strong color fields, whose dynamics is described by quantum chromodynamics (QCD), are generated at the interaction point. If one represents these fields in terms of partons (quarks and gluons), the average number densities of the latter saturate at ultrahigh energies. At that point, nonlinear effects become predominant in the dynamical equations. The hadronic states that one gets in this regime of QCD are generically called ``color glass condensates''. Our understanding of scattering in QCD has benefited from recent progress in statistical and mathematical physics. The evolution of hadronic scattering amplitudes at fixed impact parameter in the regime where nonlinear parton saturation effects become sizable was shown to be similar to the time evolution of a system of classical particles undergoing reaction-diffusion processes. The dynamics of such a system is essentially governed by equations in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, which is a stochastic nonlinear partial differential equation. Realizations of that kind of equations (that is, ``events'' in a particle physics language) have the form of noisy traveling waves. Universal properties of the latter can be taken over to scattering amplitudes in QCD. This review provides an introduction to the basic methods of statistical physics useful in QCD, and summarizes the correspondence between these two fields and its theoretical and phenomenological implications.Comment: 92 pages, review paper. v2: a few mistakes corrected at various places, some parts clarified. To be published in Phys. Re

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“…The solution of the nonlinear evolution equation for the high energy factorizable unintegrated gluon density enters for example the formula for the proton structure function, which at leading α s ln(1/x) reads: The impact factors S T , and S L are obtained as matrix elements from the process γ * + g * → q q with inclusion of appropriate phase space factors, the sum runs over quark flavours. In the massless case the full impact factor reads (see also [19] for massive case):…”

Section: Nonlinear Equation For High Energy Factorizable Unintegratedmentioning

confidence: 99%

“…In this model the gluon density falls too fast at large k 2 as compared to perturabative QCD pattern but nevertheless it models quite well bulk properties of physics of saturation. It has also correct asymptotics and is frequently used as initial distributions for evolution equations [19,32]. Applying the formula (A.3) to F(x, k 2 ) = NcS ⊥ 2π 2 αs k 2 /Q 2 s (x)e −k 2 /Q 2 s (x) we obtain Φ(x, k 2 ) = S ⊥ 2 Γ(0, k 2 /Q 2 s ) (A.7)…”

Section: Jhep12(2012)033mentioning

confidence: 99%

Resummation in nonlinear equation for high energy factorizable gluon density and its extension to include coherence

Kutak

¹

2012

J. High Energ. Phys.

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Motivated by forthcoming p-Pb experiments at Large Hadron Collider which require both knowledge of gluon densities accounting for saturation and for processes at a wide range of p t we study basic momentum space evolution equations of high energy QCD factorization. Solutions of those equations might be used to form a set of gluon densities to calculate observables in generalized high energy factorization. Moreover in order to provide a framework for predictions for exclusive final states in p-Pb scattering with high p t we rewrite the equation for the high energy factorizable gluon density in a resummed form, similarly to what has been done in [1] for the BK equation. The resummed equation is then extended to account for colour coherence. This introduces an external scale to the evolution of the gluon density, and therefore makes it applicable in studies of final states.

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“…[130]). An impact-parameter dependence was also introduced [131][132][133] that was already missing in the GBW model.…”

Section: Dipole Models and Geometric Scalingmentioning

confidence: 99%

Quantum chromodynamics at high energy and noisy traveling waves

Munier

2012

Preprint

0

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When hadrons scatter at high energies, strong color fields, whose dynamics is described by quantum chromodynamics (QCD), are generated at the interaction point. If one represents these fields in terms of partons (quarks and gluons), the average number densities of the latter saturate at ultrahigh energies. At that point, nonlinear effects become predominant in the dynamical equations. The hadronic states that one gets in this regime of QCD are generically called "color glass condensates".Our understanding of scattering in QCD has benefited from recent progress in statistical and mathematical physics. The evolution of hadronic scattering amplitudes at fixed impact parameter in the regime where nonlinear parton saturation effects become sizable was shown to be similar to the time evolution of a system of classical particles undergoing reaction-diffusion processes.The dynamics of such a system is essentially governed by equations in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, which is a stochastic nonlinear partial differential equation. Realizations of that kind of equations (that is, "events" in a particle physics language) have the form of noisy traveling waves. Universal properties of the latter can be taken over to scattering amplitudes in QCD.This review provides an introduction to the basic methods of statistical physics useful in QCD, and summarizes the correspondence between these two fields and its theoretical and phenomenological implications. RésuméLors de la diffusion de hadrons à haute énergie, d'intenses champs de couleur, dont la dynamique est décrite par la chromodynamique quantique (QCD), sont créés au point d'interaction. Si on représente ces champs en termes de partons (quarks et gluons), la densité de ces derniers sature à très haute énergie. Les effets non-linéaires deviennent alors dominants dans les équations dynamiques. Les états hadroniques que l'on obtient dans ce régime de la QCD sont génériquement appelés "condensat de verre de couleur".Notre compréhension de la diffusion en QCD a bénéficié de progrès récents en physique statistique et en physique mathématique. On a montré que l'évolution des amplitudes de diffusion hadronique à paramètre d'impact fixé dans le régime dans lequel les effets non-linéaires de saturation des densités de partons deviennent importants est semblable à l'évolution temporelle d'un système de particules classiques soumis à des processus de type réaction-diffusion. La dynamique d'un tel système est essentiellement gouvernée par des équations dans la classe d'universalité de l'équation de Fisher-Kolmogorov-Petrovsky-Piscounov stochastique, qui est une équation aux dérivées partielles stochastique et non-linéaire. Les réalisations de telles équations (c'est-à-dire les événements, dans un langage de physique des particules) ont la forme d'ondes voyageuses bruitées. Les propriétés universelles de celles-ci peuvent être transposées aux amplitudes d'interactions en QCD.Ce mémoire est une introduction aux méthodes de physique s...

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Gluon density and functions from BK equation with local impact parameter dependence in DIS on nuclei

Cited by 5 publications

References 65 publications

Quantum chromodynamics at high energy and statistical physics

Quantum chromodynamics at high energy and statistical physics

Resummation in nonlinear equation for high energy factorizable gluon density and its extension to include coherence

Quantum chromodynamics at high energy and noisy traveling waves

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