This writeup is a compilation of the predictions for the forthcoming Heavy Ion Program at the Large Hadron Collider, as presented at the CERN Theory Institute ‘Heavy Ion Collisions at the LHC—Last Call for Predictions’, held from 14th May to 10th June 2007.

We present a new phenomenological model of the dipole scattering amplitude to demonstrate that the RHIC data for hadron production in d-Au collisions for all available rapidities are compatible with geometric scaling, just like the small-x inclusive DIS data. A detailed comparison with earlier geometric scaling violating models of the dipole scattering amplitude in terms of an anomalous dimension γ is made. In order to establish whether the geometric scaling violations expected from small-x evolution equations are present in the data a much larger range in transverse momentum and rapidity must be probed. Predictions for hadron production in p-P b and p-p collisions at LHC are given. We point out that the fall-off of the transverse momentum distribution at LHC is a sensitive probe of the variation of γ in a region where x is much smaller than at RHIC. In this way, the expectation for the rise of γ from small-x evolution can be tested.

We discuss the angular distribution of the lepton pair in the Drell-Yan process, hadron + hadron → γ * + X → l + + l − + X. This process gives information on the spin-density matrix ρ (q,q) of the annihilating quark-antiquark pair in q +q → l + + l − . There is strong experimental evidence that even for unpolarised initial hadrons ρ (q,q) is nontrivial, and therefore the quark-antiquark system is polarised. We discuss the possibilities of a general ρ (q,q) -which could be entangled-and a factorising ρ (q,q) . We argue that instantons may lead to a nontrivial ρ (q,q) of the type indicated by experiments.

We pursue the intriguing possibility that larger-size instantons build up diffractive scattering, with the marked instanton-size scale ρ ≈ 0.5 fm being reflected in the conspicuous "geometrization" of soft QCD. As an explicit step in this direction, the known instantoninduced cross sections in deep-inelastic scattering (DIS) are transformed into the familiar colour dipole picture, which represents an intuitive framework for investigating the transition from hard to soft physics in DIS at small x Bj . The simplest instanton (I) process without final-state gluons is studied first. With the help of lattice results, the qq-dipole size r is carefully increased towards hadronic dimensions. Unlike perturbative QCD, one now observes a competition between two crucial length scales: the dipole size r and the size ρ of the background instanton that is sharply localized around ρ ≈ 0.5 fm. For r > ∼ ρ , the dipole cross section indeed saturates towards a geometrical limit, proportional to the area π ρ 2 , subtended by the instanton. In case of final-state gluons, lattice data are crucially used to support the emerging picture and to assert the range of validity of the underlying IĪ-valley approach. As function of an appropriate energy variable, the resulting dipole cross section turns out to be sharply peaked at the sphaleron mass in the soft regime. The general geometrical features remain like in the case without gluons.

Phenomenological models of the dipole cross section that enters in the description of for instance deep inelastic scattering at very high energies have had considerable success in describing the available small-x data in both the saturation region and the so-called extended geometric scaling (EGS) region. We investigate to what extent such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in x of the dipole cross section in these momentum regions. We find that in the EGS region the BK equation yields results that are qualitatively different from those of phenomenological studies. In particular, geometric scaling around the saturation scale is only obtained at asymptotic rapidities. We find that in this limit, the anomalous dimension γ(r, x) of phenomenological models approaches a limiting function that is universal for a large range of initial conditions. At the saturation scale, this function equals approximately 0.44, in contrast to the value 0.628 commonly used in the models. We further investigate the dependence of these results on the starting distribution, the small-r limit of the anomalous dimension for fixed rapidities and the x-dependence of the saturation scale.

We consider the gauge-boson sector of a locally SU(2) × U(1) invariant effective Lagrangian with ten dimension-six operators added to the Lagrangian of the Standard Model. These operators induce anomalous three-and fourgauge-boson couplings and an anomalous γγH coupling. In the framework of this effective Lagrangian we calculate the helicity amplitudes and differential and total cross sections for the process γγ → W W at a photon collider. We give relations between different parts of the amplitudes that show which linear combinations of anomalous couplings are measurable in this reaction. The transformation properties of the differential cross section under CP are discussed. We find that three linear combinations of CP conserving and of CP violating couplings can be measured independently of the photon polarisation in γγ → W W .

We briefly report on the contribution of QCD-instantons to the phenomenon of saturation in deep-inelastic scattering (DIS) at small Bjorken-x. The explicitly known instanton gauge field serves as a concrete realization of an underlying nonperturbative saturation mechanism associated with strong classical fields. Two independent strategies were pursued, with consistent results: On the one hand, an approach starting from instanton-perturbation theory was considered and on the other hand, the scattering of a Wilson loop in an instanton gauge field background. In both cases, the conspicuous, intrinsic instanton size scale ρ ≈ 0.5 fm, as known from the lattice, turns out to determine the saturation scale.

We demonstrate that the RHIC data for hadron production in d-Au collisions for all available rapidities are compatible with geometric scaling. In order to establish the presence of scaling violations expected from small-x evolution a much larger range in transverse momentum and rapidity needs to be probed. We show that the fall-off of the transverse momentum distribution of produced hadrons at LHC is a sensitive probe of small-x evolution.It is well known that the small-x DIS data show geometric scaling [1]. This means that the cross section depends on Q 2 /Q 2 s (x) only, instead of Q 2 and x independently, where Q s (x) is known as the saturation scale. Since geometric scaling arises as a feature of saturation from nonlinear evolution equations, such as the BK equation [2], its occurrence is often seen as an indication of saturation. Here, we investigate this issue by studying the scaling properties of hadron collision data from RHIC at similarly small x.The small-x inclusive HERA data were shown to be well described by the phenomenological Golec-Biernat Wüsthoff (GBW) model for the dipole cross section [3]. In the GBW model, the cross section is given by σ = σ 0 N GBW (r t , x), where σ 0 ≃ 23 mb and the scattering amplitude N GBW is given bywhere r t is the dipole size. This amplitude depends on r 2 t Q 2 s (x) only, leading to a Q 2 /Q 2 s (x) dependence of the DIS cross section. Hence, the amplitude (1) incorporates geometric scaling. The saturation scale Q s (x) is parameterized as