Michael Lublinsky

Towards a symmetric approach to high energy evolution: Generating functional with pomeron loops

Abstract We derive an evolution equation for the generating functional which accounts for processes for both gluon emission and recombination. In terms of color dipoles, the kernel of this equation describes evolution as a classical branching process with conserved probabilities. The introduction of dipole recombination allows one to obtained closed loops during the evolution, which should be interpreted as pomeron loops of the BFKL pomerons. In comparison with the emission, the dipole recombination is formally 1 / N c 2 suppressed. This suppression, nevertheless, is compensated at very high energies when the scattering amplitude tends to its unitarity bound.

In pursuit of Pomeron loops: The Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation and the Wess-Zumino term

We derive corrections to the JIMWLK equation in the regime where the charge density in the hadronic wave function is small. We show that the framework of the JIMWLK equation has to be significantly modified at small densities in order to properly account for the noncommutativity of the charge density operators. In particular the weight function for the calculation of averages can not be real, but is shown to contain the Wess-Zumino term. The corrections to the kernel of the JIMWLK evolution which are leading at small density are resummed into a path ordered exponential of the functional derivative with respect to the charge density operator, thus hinting at intriguing duality between the high and the low density regimes.

Angular correlations in gluon production at high energy

We present a general, model independent argument demonstrating that gluons produced in high energy hadronic collision are necessarily correlated in rapidity and also in the emission angle. The strength of the correlation depends on the process and on the structure/model of the colliding particles. In particular we argue that it is strongly affected (and underestimated) by factorized approximations frequently used to quantify the effect.

From target to projectile and back again : Self-duality of high-energy scattering evolution in QCD

We prove that the complete kernel for the high-energy evolution in QCD must be self-dual. The relevant duality transformation is formulated in precise mathematical terms and is shown to transform the charge density into the functional derivative with respect to the single-gluon scattering matrix. This transformation interchanges the high and the low density regimes. We demonstrate that the original Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner kernel, valid at large density, is indeed dual to the low density limit of the complete kernel derived recently in hep-ph/0501198.

Balitsky's hierarchy from Mueller's dipole model and more about target correlations

Abstract High energy scattering formulated as a classical branching process is considered within the framework of the QCD dipole model. Starting from Muellers generating functional, we derive the high energy evolution law for the scattering amplitude. The amplitudes evolution is given by an infinite hierarchy of linear equations equivalent to the Balitskys chain reduced to dipole operators. This new derivation of the hierarchy is the central result of the Letter. We also comment about target correlations which prevent the hierarchy from being expressed as the Balitsky–Kovchegov equation in closed form.

Small x Phenomenology - summary of the 3rd Lund Small x Workshop in 2004

A third workshop on small-x physics, within the Small-x Collaboration, was held in Hamburg in May 2004 with the aim of overviewing recent theoretical progress in this area and summarizing the experimental status.

Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner evolution at next to leading order.

The Jalilian-Marian,Iancu, McLerran, Weigert, Leonidov, Kovner (JIMWLK) Hamiltonian for high energy evolution of QCD amplitudes is presented at the next-to-leading order accuracy ins. The form of the Hamiltonian is deduced from the symmetries and the structure of the hadronic light cone wavefunction and by comparing the rapidity evolution of the quark dipole and the three-quark singlet states with results available in the literature. The next-to-leading corrections should allow for more robust phenomenological applications of perturbative saturation approach. It is believed that at high energy gluons saturate in perturbative regime. The idea of perturbative gluon saturation was first suggested and discussed in detail in (1). To date there exist numerous phenomenological applications of this idea to DIS, heavy ion collisions and proton-proton collisions at the LHC (2). These applications are based on the Balitsky-Kovchegov (BK) non-linear evolution equation (3, 4), which at large Nc describes the growth of the gluon density with energy and the gluon saturation. The more general approach to the calculation of high energy hadronic amplitudes is known as the Jalilian-Marian,Iancu, McLerran, Weigert, Leonidov, Kovner (JIMWLK) evolution. The JIMWLK Hamiltonian (5) is the limit of the QCD Reggeon Field Theory (RFT), applicable for computations of high energy scattering amplitudes of dilute (small parton number) projectiles on dense (nuclei) targets. In general it predicts the rapidity evolution of any hadronic observable O via the functional equation of the form

One gluon, two gluon: multigluon production via high energy evolution

We develop an approach for calculating the inclusive multigluon production within the JIMWLK high energy evolution. We give a formal expression of multigluon cross section in terms of a generating functional for arbitrary number of gluons n. In the dipole limit the expression simplifies dramatically. We recover the previously known results for single and double gluon inclusive cross section and generalize those for arbitrary multigluon amplitude in terms of Feynman diagramms of Pomeron - like objects coupled to external rapidity dependent field s(?). We confirm the conclusion that the AGK cutting rules in general are violated in multigluon production. However we present an argument to the effect that for doubly inclusive cross section the AGK diagramms give the leading contribution at high energy, while genuine violation only occurs for triple and higher inclusive gluon production. We discuss some general properties of our expressions and suggest a line of argument to simplify the approach further.

Single inclusive particle production in proton-nucleus collisions at next-to-leading order in the hybrid formalism

We reconsider the perturbative next-to-leading calculation of the single inclusive hadron production in the framework of the hybrid formalism, applied to hadron production in proton-nucleus collisions. Our analysis, performed in the wave function approach, differs from the previous works in three points. First, we are careful to specify unambiguously the rapidity interval that has to be included in the evolution of the leading-order eikonal scattering amplitude. This is important, since varying this interval by a number of order unity changes the next-to-leading order correction that the calculation is meant to determine. Second, we introduce the explicit requirement that fast fluctuations in the projectile wave function which only exist for a short time are not resolved by the target. This Ioffe time cutoff also strongly affects the next-to-leading order terms. Third, our result does not employ the approximation of a large number of colors. Our final expressions are unambiguous and do not coincide at next-to-leading order with the results available in the literature.

Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic quantum Reggeon field in this theory is the unitary matrix R which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of s — channel gluons. The eigenstates have a natural interpretation in terms of the t — channel exchanges. Studying the single s — channel gluon sector we find the eigenstates which include the reggeized gluon and five other colored Reggeons. In the two (s — channel) gluon sector we study only singlet color exchanges. We find five charge conjugation even states. The bound state of two reggeized gluons is the standard BFKL Pomeron. The intercepts of the other Pomerons in the large N limit are 1+ωP = 1+2ω where 1+ω is the intercept of the BFKL Pomeron, but their coupling in perturbation theory is suppressed by at least 1/N2 relative to the double BFKL Pomeron exchange. For the [27,27] Pomeron we find 2\omega