A Langevin equation for high energy evolution with pomeron loops

We show that the Balitsky-JIMWLK equations proposed to describe non-linear evolution in QCD at high energy fail to include the effects of fluctuations in the gluon number, and thus to correctly describe both the low density regime and the approach towards saturation. On the other hand, these fluctuations are correctly encoded (in the limit where the number of colors is large) in Mueller's color dipole picture, which however neglects saturation. By combining the dipole picture at low density with the JIMWLK evolution at high density, we construct a generalization of the Balitsky hierarchy which includes the particle number fluctuations, and thus the pomeron loops. After an additional coarse-graining in impact parameter space, this hierarchy is shown to reduce to a Langevin equation in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov (sFKPP) equation. This equation implies that the non-linear effects in the evolution become important already in the high momentum regime where the average density is small, which signals the breakdown of the BFKL approximation.Comment: 56 pages, 10 figure

Herança da senescência retardada em milho Inheritance of the delayed senescence in maize

O objetivo deste trabalho foi estudar a herança da senescência retardada em milho. Foram realizados cruzamentos dialélicos parciais entre 50 linhagens e cinco testadores. Os 250 cruzamentos resultantes, além de seis híbridos comerciais utilizados como testemunhas, foram avaliados em oito ambientes, no delineamento látice simples 16x16, com duas repetições por ambiente. Os cruzamentos dialélicos foram analisados utilizando o método 4 do modelo 1 de Griffing, adaptado para múltiplos ambientes. A contribuição da capacidade geral de combinação (CGC) para a expressão do caráter "stay-green" (69,06%) foi maior que a da capacidade específica de combinação (CEC) (30,94%), evidenciando que os efeitos aditivos são mais importantes que os efeitos não aditivos na expressão deste caráter. Tanto a CGC como a CEC interagiram significativamente com o ambiente, indicando que a seleção para este caráter deve ser realizada com base nas médias de experimentos em diversos ambientes.<br>The objective of this research was to study the inheritance of delayed senescence in maize. Partial diallel crosses among 50 inbred lines and five testers were made. The 250 crosses, along with six commercial hybrids used as checks, were evaluated at eight environments in lattices 16x16 with two replications per environment. The diallel crosses were analyzed following the method 4 model 1 of Griffing, extended to multiple environments. The contribution of the general combining ability (CGA) for the expression of the stay-green trait (69.06%) was greater than the specific combining ability (SCA) (30.94%), showing that additive effects are more important than non-additive effects for the expression of this trait. Both GCA and SCA interacted significantly with the environments, indicating that the selection for this trait should be based on the means across environments