The main goal of Ultrarelativistic heavy ion collisions (URHIC) is to verify the phase transition from Quark-Gluon Plasma (QGP) to Hadron gas (HG), as predicted by the first-principles calculations of Quantum Chromodynamics (QCD). Also the detailed properties of the strongly interacting matter are to be determined. The field is guaranteed to remain very active and to have a solid future at least for the next 15 years: the first experimental results are now being obtained from the colliding-beams experiments at the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory (BNL, NY, USA), and the ALICE experiment dedicated to URHIC at the Large Hadron Collider in CERN will start in 2006.

The Finnish theory groups working with QCD matter and phenomenology of URHIC belong to the leading ones in this field since 1980. Traditionally, the groups have been in close contact: collaboration between Helsinki (Kajantie's group) and Jyväskylä (Ruuskanen's group) has been frequent from the beginning of the field, and also the contacts to Oulu (Suhonen's group) have been active. The groups in Helsinki and Jyväskylä have now even more concretely joint their efforts in forming the new URHIC project at the Theory Programme of HIP (1.1.2002-). Also the connection to other projects at the Theory Programme of HIP, Particle phenomenology and Cosmology in particular, and to the ALICE project in the Nuclear Matter Programme is smooth. The groups have extensive international contacts, and especially the co-operation with the CERN/TH is maintained very active.

The research programme of the URHIC project covers the description of high energy nuclear collisions from the primary production of QCD quanta and the formation of the QGP to the final state observables. We focus on the phenomenology of URHIC and on the first-principles calculations of the properties of the QCD matter.

In the phenomenology of URHIC, our goal is to make as reliable computations as possible for various observables in the final state. These include both integrated quantities such as multiplicities and transverse energies, and more detailed particle spectra, cross sections for the hard probes of dense matter, and also rates for the potential signals of the QGP. In the computation of the primary production of quarks and gluons and hard probes, the basic tool is perturbative QCD. The space-time evolution of the produced QGP system with the QCD phase-transition included is describable in terms of relativistic hydrodynamics. On the other hand, the basic properties of the QGP we study without any phenomenological assumptions, relying on the QCD Lagrangian only. This leads in both analytical and numerical problems, where the latest computational techniques are needed.

The initial densities of the QGP produced in high energy AA collisions can be estimated based on perturbative QCD (pQCD). The recently completed next-to-leading order (NLO) computation of the minijet transverse energy production [Eskola, Tuominen, hep-ph/0002008] plays an important role in these estimates. We are currently extending this work to include other global average quantities that can be computed in NLO pQCD, such as the fully integrated minijet cross sections, and the production of net baryon number. Also the studies of fluctuations of these quantities, especially that of the transverse energy, have been already initiated.

Based on a conjecture of saturation of perturbatively produced gluons and on a subsequent isentropic expansion stage, we have recently suggested [Eskola, Kajantie, Ruuskanen, Tuominen, hep-ph/9909456; EKT, hep-ph/0009246] that the growth of the number of produced partons at small transverse momenta is inhibited at sufficiently large densities. Our predictions for the charged-particle multiplicities in central collisions agree with the first results from Au-Au collisions at RHIC at sqrt(s)/A= 56, 130 and 200 GeV amazingly well, both in absolute magnitude and in the sqrt(s) dependence. However, clearly much more work on the quantification of the underlying uncertainties and finding the limits of the approach is needed. These will be obtained from the studies already initiated on the centrality and rapidity dependence of the charged particles and transverse energies. Also the antibaryon-to-baryon ratio, which can be computed in the framework of pQCD+saturation+hydrodynamics, is on our working list.

An approach, complementary to the perturbative+saturation model is the use of classical equations of motion. It is complementary in that it emphasises small-p_T phenomena with large occupation numbers, permitting the description of the state of the system by a classical field. The relevant equations of motion can only be solved numerically and a code for doing this is being written. Codes and expertice acquired in this context will also be applied to time dependent electroweak and cosmological phenomena.

Computation of any hard process in nuclear collisions involves nuclear parton distributions (nPDF). The EKS98 parametrization [Eskola, Kolhinen, Salgado, hep-ph/9807297 ] based on a pQCD analysis of nPDF [Eskola, Kolhinen, Ruuskanen, hep-ph/9802350 ] in terms of the DGLAP equations is now in the PDFLIB library of CERN. Vesa Kolhinen defended his thesis on this subject on in October, 2001. Next, efforts will be made to extend our nPDF analysis to NLO pQCD in the future. Related to the studies of nPDF in general, K.J. Eskola is the convenor of a subgroup, ``PDFs, shadowing and pA'' in the series of CERN Workshops on Hard Probes of Dense Matter , taking place at the CERN/TH in 2001-2002.

The Helsinki-Jyväskylä group also has long traditions in the hydrodynamical description of the expanding nuclear system (Kajantie, Raitio, Ruuskanen, Kataja, Huovinen). This leads to interesting numerical computations which become more and more involved with increasing energy: many different scales enter. But also the physical interest is enhanced, the description should become better with increasing energy. We are currently combining the pQCD initial conditions with a realistic transversally expanding hydrodynamic description of both azimuthally symmetric and non-symmetric but longitudinally boost invariant systems. Boost non-invariant features will be studied in the future, too. Once the evolution of the system is correctly described and the global observables (N_ch,E_T) are known, signals from the expansion stage, such as elliptic flow, energy losses of high-p_T jets (collaboration with U.Wiedemann (CERN/TH) started in 8/2001 on this topic) in the QGP, and the emission of electromagnetic probes (Huovinen, Ruuskanen, Räsänen, [ nucl-th/0111052], and ongoing work ), can be predicted. Uncertainties, such as those due to the chemical equilibration of quarks and antiquarks, on the probes of the QGP will also be studied.

In addition to these only phenomenologically accessible phenomena, there are certain quantities which can be studied with controlled first-principle computations, either analytic or numerical or a combination of these two. An ongoing project (Kajantie, Laine, Rummukainen, Schröder, [ hep-ph/0007109], [ hep-lat/0110122]) is to extend analytic computation of the free energy of hot QCD as far as theoretically possible, to a limit beyond which one must proceed by numerical means. This requires complicated symbolic computations and it is difficult to estimate when they can be completed. The theoretical path is already well defined, though. These analytic studies will also be extended to the case of finite chemical potential, nonzero net baryon number density (Gynther, Vuorinen).