arXiv subjects
Publications and source records attributed to D. N. Triantafyllopoulos.
We study the gluon content of a large nucleus (i) in the semi-classical McLerran-Venugopalan model and (ii) in the high energy limit as given by the quantum evolution of the Color Glass Condensate. We give a simple and qualitative description of the Cronin effect and high-pT suppression in proton-nucleus collisions.
In a previous publication, we have constructed a set of non-linear evolution equations for dipole scattering amplitudes in QCD at high energy, which extends the Balitsky-JIMWLK hierarchy by including the effects of fluctuations in the gluon number in the target wavefunction. In doing so, we have relied on the color dipole picture, valid in the limit where the number of colors is large, and we have made some further approximations on the relation between scattering amplitudes and dipole densities, which amount to neglecting the non-locality of the two-gluon exchanges. In this Letter, we relax the latter approximations, and thus restore the correct structure of the `triple-pomeron vertex' which describes the splitting of one BFKL pomeron into two within the terms responsible for fluctuations. The ensuing triple-pomeron vertex coincides with the one previously derived by Braun and Vacca within perturbative QCD. The evolution equations can be recast in a Langevin form, but with a multivariable noise term with off-diagonal correlations. Our equations are shown to be equivalent with the modified version of the JIMWLK equation recently proposed by Mueller, Shoshi, and Wong.
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.
We present a systematic, and fully analytic, study of the ratio R_{pA} between the gluon distribution in a nucleus and that in a proton scaled up by the atomic number A. We consider initial conditions of the McLerran-Venugopalan type, and quantum evolution in the Color Glass Condensate, with both fixed and running coupling. We perform an analytic study of the Cronin effect in the initial conditions and point out an interesting difference between saturating effects and twist effects in the nuclear gluon distribution. We show that the distribution of the gluons which make up the condensate in the initial conditions is localized at low momenta, but this particular feature does not survive after the quantum evolution. We demonstrate that the rapid suppression of the ratio R_{pA} in the early stages of the evolution is due to the DGLAP-like evolution of the proton, whose gluon distribution grows much faster than that in the nucleus because of the large separation between the respective saturation momenta. The flattening of the Cronin peak, on the other hand, is due to the evolution of the nucleus. We show that the running coupling effects slow down the evolution, but eventually lead to a stronger suppression in R_{pA} at sufficiently large energies.
We study the energy dependence of the saturation momentum in the context of the collinearly improved Leading and Next to Leading BFKL evolution, and in the presence of saturation boundaries. We find that the logarithmic derivative of the saturation momentum is varying very slowly with Bjorken-x, and its value is in agreement with the Golec-Biernat and Wusthoff model in the relevant x region. The scaling form of the amplitude for dipole-dipole or dipole-hadron scattering in the perturbative side of the boundary is given.
We study BFKL evolution and, in particular, the energy dependence of the saturation momentum in the presence of saturation boundaries limiting the region of linear BFKL evolution. In the case of fixed coupling evolution we confirm the previously found exponential term in $Q_s(Y)$ and determine the prefactor $Y$ and $α$ dependences. In the running coupling case we find $Y^{1/6}$ corrections to the $Y^{1/2}$exponential behavior previously known. Geometrical scaling of the scattering amplitude is valid in a wide-range of momenta for fixed coupling evolution and in a more restricted region for running coupling evolution.
The double well oscillator is used as a QCD-like model for studying the relationship between large order graphs and the instanton-antiinstanton solution. We derive an equation for the perturbative coefficients of the ground state energy when the number of 3 and/or 4-vertices is fixed and large. These coefficients are determined in terms of an exact``bounce'' solution. When the number of 4-vertices is analytically continued to be near the negative of half the number of 3-vertices the bounce solution approaches the instanton-antiinstanton solution and detremines leading Borel singularity.