2. As an important preliminary step for the eventual order g^6 computation
of the QCD pressure we together with Y. Schröder (MIT) published a
high-precision evaluation of the four-loop skeleton graphs of
three-dimensional field theories [hep-ph/0311323]. The calculation was
based on constructing systems of difference equations for the graphs and
subsequestly solving them by applying a novel algorithm developed by S.
Laporta (Bologna). It is anticipated that our results will be of use not
only to the QCD community but also in the context of condensed matter
theory.
3. The calculation of the phase diagram of the electroweak theory was extended by considering
how a finite net lepton number density (= finite chemical potentials for leptons) affects the
system [hep-ph/0303019]. This was done by generalizing
the succesful effective field theory methods to finite chemical potentials. Since the form of the
effective theory is unaffected by the chemical potentials, the same nonperturbative calculations can
be used to deduce the phase diagram as in the absence of chemical potentials. We observed that the
critical temperature increases and, more importantly, the value of the Higgs boson mass corresponding to the critical
end point of the first order phase transition line decreases as the chemical potentials are increased.
4. The number of gluons produced in a heavy-ion collision in the
McLerran-Venugopalan classical field model was computed numerically
[hep-ph/0303076]. The calculation corrected an error of a factor of two in
earlier calculations by Krasnitz, Nara and Venugopalan, showing that the
classical field model fits in with realistic scenarios for understanding
the transverse energy and multiplicity observed at RHIC.
5. One of the characteristic features of any plasma is screening. While the screening of gluonic operators in hot
QCD is a well-studied subject, the large systematic errors related to light dynamical fermions have so far prevented
the reliable determination of mesonic and baryonic screening correlators on the lattice. Together with M. Laine, we
calculated the next-to-leading order correction to mesonic screening masses in perturbation theory using effective
field theory methods, and found a gauge invariant, IR safe result
[hep-ph/0311268] that differs qualitatively from the
previous lattice studies.
1. The project of computing the free energy of hot quark-gluon
plasma nonperturbatively at
any energies has been advanced significantly by the computation of the
coefficient of the g^6 log(g) term in the perturbative expansion of
the free energy by Kajantie, Laine, Rummukainen and Schröder
[hep-ph/0211321]. This is actually the last coefficient calculable
by perturbative means; beyond that only fully numerical methods seem
to be the only method for obtaining first-principle results. Historically,
it is notable that the previous and the only other logarithmic term,
of order g^4 log(g), was also computed in Helsinki by T. Toimela
already in 1983. New progress was only possible due to the development
of new techniques of symbolic computation.
2. The quark number susceptibility of hot quark-gluon plasma
physically characterises how easy it is to produce quark-antiquark
pairs. For the theoretical analysis of its measurements by
numerical lattice Monte Carlo techniques one needs its
perturbative expansion. This has been known only up to order
g^4 log(g), also thanks to T. Toimela. Now the terms of order g^4,
g^5 and g^6 log(g) have been computed in one clean sweep by
A. Vuorinen [hep-ph/0212283].
1. The most ambitious project, started already in 1999, has
been developing a first-principle numerical method of
controllable accuracy to compute
the equation of state for QCD matter from about 2Tc to practically
infinite temperatures, using effective field theory methods. This is
a purely theoretical effort since experiments cannot conceivably
probe temperatures above about 10Tc, but it is a pure ab initio
computation in QCD and as such very important. The work is carried
out jointly with Mikko Laine (now at CERN, Geneva), Kari Rummukainen (now
at Nordita, Copenhagen) and York Schröder (now at MIT, Boston). The
general outline of the method has been published in Physical
Review Letters [hep-ph/0109100]
but the detailed implementation is technically
very complicated and demands extensive numerical simulations
(Rummukainen) at equally extensive symbolic computations (Schröder).
One might add that expressions with of the order of 10 million terms
easily appear at intermediate stages of the computation. As a spin-off
we also have
developed general diagrammatic techniques, presented in
[hep-ph/0109100]
2. With coworkers in Jyväskylä we
have already some time ago suggested (Eskola, Kajantie, Ruuskanen,
Tuominen, [hep-ph/9909456])
that the growth of
the number of produced partons in nuclear
collisions at small transverse
momenta is inhibited at sufficiently large densities. Based on the
conjecture of saturation and on a subsequent isentropic expansion
stage, we have predicted particle multiplicities for central
A+A collisions at various nucleon numbers A
and total energies s. The first results from
RHIC indeed confirmed our prediction amazingly well, both in absolute
magnitude and in the energy dependence.
This model has been further applied to various new phenomena in
Eskola, Kajantie, Tuominen,
hep-ph/0009246 and hep-ph/0106330.
3. Our particle physics-motivated field theories have also led
us to apply the same techniques to a prototype condensed matter theory:
the Ginzburg-Landau model in three dimensions. This is well known as the
coarse-grained theory of superconductivity. Surprisingly, it is not
precisely known what this theory says about the properties of the
transition in the type II region, which corresponds to high Tc
superconductors. This probably is not relevant for real-life
superconductors, since they are not really sensitive to quantum
fluctuations, but is a very relevant question about the theory
itself. It namely also answers the question whether the theory
could alternatively be described by a dual theory, in which
non-local vortices of the GL theory have become local fields, and
which perhaps could be more easily solved.
We (also Laine, Neuhaus (now in Bielefeld),
Rajantie (now at Cambridge), Rummukainen) have, in spite of
extensive simulations, not been able to solve the problem, the
dynamics is so involved that definite final conclusions cannot be drawn.
Tentative ones were reported in
hep-lat/0110062.