scholarly journals Solving the high energy evolution equation including running coupling corrections

2007 ◽  
Vol 75 (12) ◽  
Author(s):  
Javier L. Albacete ◽  
Yuri V. Kovchegov
Keyword(s):  
Evolution Equation ◽  
High Energy ◽  
Energy Evolution ◽  
Running Coupling

NONLINEAR EVOLUTION AT SMALL x WITH IMPACT PARAMETER DEPENDENCE

2011 ◽  
Vol 04 ◽  
pp. 67-73
Author(s):  
JEFFREY J. BERGER
Keyword(s):  
Evolution Equation ◽  
Structure Function ◽  
Numerical Solution ◽  
Impact Parameter ◽  
Qualitative Agreement ◽  
Nonlinear Evolution ◽  
Hera Data ◽  
Saturation Scale ◽  
Running Coupling ◽  
Small X

Nonlinear evolution at small x was evaluated numerically with full dependence on impact parameter using the BK equation. several distinct behaviors were found and are presented for the leading logarithmic kernel in the BK evolution equation with both fixed and running coupling. The value of the saturation scale at various dipole sizes was found to agree with analytic expectations. Calculation of the F2structure function from the numerical solution of the evolution with running coupling were then compared to the HERA data and qualitative agreement found. The agreement is improved with inclusion of soft contributions and these are discussed.

scholarly journals More remarks on high energy evolution

2006 ◽  
Vol 767 ◽  
pp. 171-188 ◽  
Author(s):  
A. Kovner ◽  
M. Lublinsky
Keyword(s):  
High Energy ◽  
Energy Evolution

Smallx EVOLUTION OF MULTI-POINT CORRELATORS OF WILSON LINES

2011 ◽  
Vol 04 ◽  
pp. 20-25
Author(s):  
JAMAL JALILIAN-MARIAN
Keyword(s):  
Evolution Equation ◽  
Evolution Equations ◽  
Scattering Amplitude ◽  
High Energy ◽  
Point Function ◽  
Forward Scattering Amplitude ◽  
Angular Correlations ◽  
Small X ◽  
Dipole Scattering ◽  
Inclusive Processes

At high energy (small x) n-point coorelators of Wilson lines appear in calculation of physical observables. The energy dependence of these observables is determined by the solution of the evolution equations these correlators satisfy. The most common correlator is the two-point function, the imaginary part of the forward scattering amplitude of a quark anti-quark dipole scattering on a target. This appears in structure functions in DIS as well as single inclusive hadron production in proton-nucleus collisions. Higher point correlators of Wilson lines appear in less inclusive processes, such as two-hadron angular and rapidity correlations and satisfy the Balitski-JIMWLK evolution equation. Here we derive the evolution equation satisfied by the six point correlator of Wilson lines which appears in di-hadron angular correlations in proton-nucleus collisions at high energy.

scholarly journals A Langevin equation for high-energy evolution with pomeron loops

2005 ◽  
Vol 756 (3-4) ◽  
pp. 419-467 ◽  
Author(s):  
E. Iancu ◽  
D.N. Triantafyllopoulos
Keyword(s):  
Langevin Equation ◽  
High Energy ◽  
Energy Evolution

scholarly journals On systematic effects in the numerical solutions of the JIMWLK equation

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Salvatore Calì ◽  
Krzysztof Cichy ◽  
Piotr Korcyl ◽  
Piotr Kotko ◽  
Krzysztof Kutak ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
High Energy ◽  
Gluon Density ◽  
Longitudinal Momentum ◽  
Coupling Constant ◽  
Longitudinal Momentum Fraction ◽  
Running Coupling ◽  
Systematic Effects ◽  
Gluon Distributions ◽  
Comprehensive Study

AbstractIn the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian–Marian–Iancu–McLerran–Weigert–Leonidov–Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation. In this paper, we present a comprehensive study of systematic effects associated with the numerical framework, in particular the ones related to the inclusion of the running coupling. We consider three proposed ways in which the running of the coupling constant can be included: “square root” and “noise” prescriptions and the recent proposal by Hatta and Iancu. We implement them both in position and momentum spaces and we investigate and quantify the differences in the resulting evolved gluon distributions. We find that the systematic differences associated with the implementation technicalities can be of a similar magnitude as differences in running coupling prescriptions in some cases, or much smaller in other cases.

scholarly journals Angular correlations and high energy evolution

2011 ◽  
Vol 84 (9) ◽  
Author(s):  
Alex Kovner ◽  
Michael Lublinsky
Keyword(s):  
High Energy ◽  
Energy Evolution ◽  
Angular Correlations

scholarly journals Energy evolution in many-particle quantum hydrodynamics of spinning plasmas

2016 ◽  
Vol 30 (04) ◽  
pp. 1650023
Author(s):  
Mariya Iv. Trukhanova
Keyword(s):  
Evolution Equation ◽  
Thermal Energy ◽  
Schrodinger Equation ◽  
Fundamental Equation ◽  
Quantum Evolution ◽  
Energy Evolution ◽  
Quantum Hydrodynamics ◽  
Spinning Particles ◽  
Energy Current ◽  
The Many

In this paper, we develop a quantum hydrodynamics (QHD) method for the research of the quantum evolution of a system of spinning particles. We derived the fundamental equation for charged and neutral spinning particles — the energy evolution equation from the many-particle microscopic Schrödinger equation with a spin–spin and Coulomb modified Hamiltonian. We derive the spin contributions to the energy evolution equation, thermal energy and thermal energy current.

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