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

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 \cite{Kutak:2011fu} 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.Comment: 14 pages, appendix added, accepted for publication in JHE

Next-to-leading and resummed BFKL evolution with saturation boundary

We investigate the effects of the saturation boundary on small-x evolution at the next-to-leading order accuracy and beyond. We demonstrate that the instabilities of the next-to-leading order BFKL evolution are not cured by the presence of the nonlinear saturation effects, and a resummation of the higher order corrections is therefore needed for the nonlinear evolution. The renormalization group improved resummed equation in the presence of the saturation boundary is investigated, and the corresponding saturation scale is extracted. A significant reduction of the saturation scale is found, and we observe that the onset of the saturation corrections is delayed to higher rapidities. This seems to be related to the characteristic feature of the resummed splitting function which at moderately small values of x possesses a minimum.Comment: 34 page

Nonlinear equation for coherent gluon emission

Motivated by the regime of QCD explored nowadays at LHC, where both the total energy of collision and momenta transfers are high, we investigate evolution equations of high energy factorization. In order to study such effects like parton saturation in final states one is inevitably led to investigate how to combine physics of the BK and CCFM evolution equations. In this paper we obtain a new exclusive form of the BK equation which suggests a possible form of the nonlinear extension of the CCFM equation

JIMWLK evolution in the Gaussian approximation

We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors Nc. This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it reproduces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite Nc. Any higher n-point function with n greater than or equal to 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.Comment: v2: 45 pages, 4 figures, various corrections, section 4.4 updated, to appear in JHE

On the Energy Dependence of the Dipole-Proton Cross Section in Deep Inelastic Scattering

We study the dipole picture of high-energy virtual-photon-proton scattering. It is shown that different choices for the energy variable in the dipole cross section used in the literature are not related to each other by simple arguments equating the typical dipole size and the inverse photon virtuality, contrary to what is often stated. We argue that the good quality of fits to structure functions that use Bjorken-x as the energy variable - which is strictly speaking not justified in the dipole picture - can instead be understood as a consequence of the sign of scaling violations that occur for increasing Q^2 at fixed small x. We show that the dipole formula for massless quarks has the structure of a convolution. From this we obtain derivative relations between the structure function F_2 at large and small Q^2 and the dipole-proton cross section at small and large dipole size r, respectively.Comment: 27 page

Fluctuations, Saturation, and Diffractive Excitation in High Energy Collisions

Diffractive excitation is usually described by the Good--Walker formalism for low masses, and by the triple-Regge formalism for high masses. In the Good--Walker formalism the cross section is determined by the fluctuations in the interaction. In this paper we show that by taking the fluctuations in the BFKL ladder into account, it is possible to describe both low and high mass excitation by the Good--Walker mechanism. In high energy $pp$ collisions the fluctuations are strongly suppressed by saturation, which implies that pomeron exchange does not factorise between DIS and $pp$ collisions. The Dipole Cascade Model reproduces the expected triple-Regge form for the bare pomeron, and the triple-pomeron coupling is estimated.Comment: 20 pages, 12 figure

Non-perturbative computation of double inclusive gluon production in the Glasma

The near-side ridge observed in A+A collisions at RHIC has been described as arising from the radial flow of Glasma flux tubes formed at very early times in the collisions. We investigate the viability of this scenario by performing a non-perturbative numerical computation of double inclusive gluon production in the Glasma. Our results support the conjecture that the range of transverse color screening of correlations determining the size of the flux tubes is a semi-hard scale, albeit with non-trivial structure. We discuss our results in the context of ridge correlations in the RHIC heavy ion experiments.Comment: 25 pages, 11 figures, uses JHEP3.cls V2: small clarifications, published in JHE

Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution

Results for the two real parton differential distributions needed for implementing a next-to-leading order (NLO) parton shower Monte Carlo are presented. They are also integrated over the phase space in order to provide solid numerical control of the MC codes and for the discussion of the differences between the standard $\bar{MS}$ factorization and Monte Carlo implementation at the level of inclusive NLO evolution kernels. Presented results cover the class of non-singlet diagrams entering into NLO kernels. The classic work of Curci-Furmanski-Pertonzio was used as a guide in the calculations.Comment: 34 pages, 3 figure

Ioffe Times in DIS from a Dipole Model Fit

We present a study of Ioffe times in deep inelastic electron-proton scattering. We deduce 'experimental' Ioffe-time distributions from the small-x HERA data as described by a particular colour-dipole-model fit. We show distributions for three representative gamma*-proton c.m. energies W and various values of the photon virtuality Q^2. These distributions are rather broad for transversely and very narrow for longitudinally polarised virtual photons. The Ioffe times for W=150 GeV, for example, range from around 1000 fm for Q^2=1 GeV^2 to around 10 fm for Q^2=100 GeV^2. Based on our results we discuss consequences for the limitations of applicability of the dipole picture.Comment: 20 page