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Numerical studies of correlation and discreteness in non-linear QCD evolution

N. Armesto. Numerical studies of correlation and discreteness in non-linear QCD evolution. Low x Meeting IST, Lisbon, June 28th-July 1st 2006. N éstor Armesto Departamento de Física de Partículas and IGFAE Universidade de Santiago de Compostela and José Guilherme Milhano CENTRA, IST

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Numerical studies of correlation and discreteness in non-linear QCD evolution

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  1. N. Armesto Numerical studies of correlation and discretenessin non-linear QCD evolution Low x Meeting IST, Lisbon, June 28th-July 1st 2006 Néstor Armesto Departamento de Física de Partículas and IGFAE Universidade de Santiago de Compostela and José Guilherme Milhano CENTRA, IST and Departamento de Física, Universidade do Algarve 1

  2. N. Armesto Contents 1. Motivation. 2. Numerical method. 3. Results: * Evolution. * Scaling. * y-dependence of Qs. * Dispersion of the wave front. 4. Conclusions. Phys. Rev. D73 (2006) 114003 (hep-ph/0601132); see the talks by A. Kovner, E. Iancu, E. Levin, C. Marquet, L. Motyka, S. Munier, G. Soyez, D. Triantafyllopoulos,... 2 Numerical studies on correlation and discreteness in non-linear QCD evolution

  3. N. Armesto 1. Motivation (I) • Until now, most of our knowledge of high-energy QCD evolution comes from B-JIMWLK: asymmetric situation of dilute-dense scattering. • Most of it concerns the mean-field approximation: BK; corrections to BK known to be small (Rummukainen, Weigert, '04). • y- and A-dependence of Qs, geometrical scaling, behavior of the travelling front,... both analytically (FKPP) and numerically understood. • Running coupling effects, kinematical constraints,... (---> NLL BK?: Balitsky; Kovchegov, Weigert) examined: vanishing A-dependence, slower y-dependence of Qs, still geometrical scaling. h(k)=k2Df(k) 3 Numerical studies on correlation and discreteness in non-linear QCD evolution

  4. N. Armesto 1. Motivation (II) • In the last three years, the limitations of B-JIMWLK have been debated: dense-dense situation unavoidable for high enough energies ---> inclusion of Pomeron loops, discreteness in gluon emission, fluctuations. 2-->1 vertex known, dense- dilute duality, dipole limit,... • Analogy with statistical mechanics: sFKPP equation in the limit of weak fluctuations (noise), numerical studies conclude that: * At small rapidities, mean field ~ OK but the y-evolution of Qs is slower and the region of geometrical scaling smaller. * At large rapidities, dispersion in the position of the wave fronts increases: diffusive scaling. Poor men's idea: is it possible to get something from a modified BK? 4 Numerical studies on correlation and discreteness in non-linear QCD evolution

  5. N. Armesto 2. Numerical method (I) in the local approximation (no b-dependence). BK evolved upto y=(asNc/p)Y=10 (Y~50): 4th-orderRunge-Kutta, Gauss- Chebyshev quadrature,... numerical accuracy better than 1%. • Initial conditions: * GBW-like * MF (A, Salgado, Wiedemann, '05) Results independent from these (supercritical) IC, in the following we will use only MF, d=1. 5 Numerical studies on correlation and discreteness in non-linear QCD evolution

  6. N. Armesto 2. Numerical method (II) a) Averaging procedure(Iancu, Mueller, Munier, '04; Kovner, Lublinsky, '05): * Linear: * Logarithmic: D, D l=0.01, 0.1, 1, 10, 100; all momenta in GeV * (y-)Log with increasing dispersion (sFKPP): 284 points log-sampled in b) Cut-off evolution(Iancu, Mueller, Munier, '04): f(k) ----> f(k) q[f(k)-k] in BK k proportional to 1/as, but unknown constant: k=0.002, 0.01, 0.05 6 Numerical studies on correlation and discreteness in non-linear QCD evolution

  7. N. Armesto log linear No change in slope: where is the mixing? cut-off 3. Results: evolution log y-log Steeper slope 7 Numerical studies on correlation and discreteness in non-linear QCD evolution

  8. N. Armesto log linear y-log cut-off 3. Results: scaling • Scaling violations: • ~ 10 % for individual configs. • (Albacete et al. ’04). • Smaller for cut-off. • Of the same order for averages • with D=100. • Larger for averages with D=y. 8 Numerical studies on correlation and discreteness in non-linear QCD evolution

  9. N. Armesto No effect of averaging d ~ k-0.1 3. Results: y-dependence of Qs linear log y-log 9 Numerical studies on correlation and discreteness in non-linear QCD evolution

  10. N. Armesto Log-dispersion stable except for D=y (but limited by sampling space in Qs0) 3. Results: dispersion of the wave front log log y-log y-log 10 Numerical studies on correlation and discreteness in non-linear QCD evolution

  11. N. Armesto 4. Conclusions • We have attempted naive modifications of mean field BK evolution: averaging over initial conditions, and cut off the high kt tails. • None of them fully reproduces the expectations from sFKPP: * The cut-off version leads to slower y-evolution of Qs, but to better scaling; the solutions fall steeper than standard BK. * The averaging procedure shows configuration mixing and, for the case with a dispersion increasing with y, to a log-spreading in the wave fronts. • A combination of both may show the results expected from sFKPP but does not look simple. • The evaluation of the actual impact of 'beyond B-JIMWLK-K' at accessible rapidities is a key open problem from the numerical point of view. 11 Numerical studies on correlation and discreteness in non-linear QCD evolution

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