arXiv subjects
Publications and source records attributed to M. Laine.
We review briefly the current status of thermal phase transitions within the Standard Model and its simplest extensions. We start with an update on QCD thermodynamics, then discuss the electroweak phase transition, particularly in supersymmetric extensions of the Standard Model, and end with a few remarks on the cosmological constraints that thermal phase transitions might impose on even higher scale particle physics.
We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible ("skeleton") expansion. The regrouping leads to skeletons containing only free propagators, together with "ring diagrams" containing all the self-energy insertions. As a consequence, relatively few diagrams need to be drawn and integrations carried out at any single stage of the computation and, in low dimensions, overlapping ultraviolet/infrared subdivergences can be cleanly isolated. As an illustration we enumerate the graphs contributing to the 4-loop free energy in QCD, explicitly in a continuum and more compactly in a lattice regularization.
For the pressure (or free energy) of QCD, four-dimensional (4d) lattice data is available at zero baryon density up to a few times the critical temperature $T_c$. Perturbation theory, on the other hand, has serious convergence problems even at very high temperatures. In a combined analytical and three-dimensional (3d) lattice method, we show that it is possible to compute the QCD pressure from about $2 T_c$ to infinity. The numerical accuracy is good enough to resolve in principle, e.g., logarithmic contributions related to 4-loop perturbation theory.
We study the critical behaviour of the three-dimensional U(1) gauge+Higgs theory (Ginzburg-Landau model) at large scalar self-coupling λ(``type II region'') by measuring various correlation lengths as well as the Abrikosov-Nielsen-Olesen vortex tension. We identify different scaling regions as the transition is approached from below, and carry out detailed comparisons with the criticality of the 3d O(2) symmetric scalar theory.
We discuss the effective action for QCD gauge fields at finite temperatures and densities, obtained after integrating out the hardest momentum scales from the system. We show that a non-vanishing baryon density induces a charge conjugation (C) odd operator to the gauge field action, proportional to the chemical potential. Even though it is parametrically smaller than the leading C even operator, it could have an important effect on C odd observables. The same operator appears to be produced by classical kinetic theory, allowing in principle for a non-perturbative study of such processes.
There has been recent interest in new types of topological defects arising in models with compact extra dimensions. We discuss in this context the old statement that if only SU(N) gauge fields and adjoint matter live in the bulk, and the coupling is weak, then the theory possesses a spontaneously broken global Z(N) symmetry, with associated domain wall defects in four dimensions. We discuss the behaviour of this symmetry at high temperatures. We argue that the symmetry gets restored, so that cosmological domain wall production could be used to constrain such models.
One suggestion for determining the properties of QCD at finite temperatures and densities is to carry out lattice simulations with an imaginary chemical potential whereby no sign problem arises, and to convert the results to real physical observables only afterwards. We test the practical feasibility of such an approach for a particular class of physical observables, spatial correlation lengths in the quark-gluon plasma phase. Simulations with imaginary chemical potential followed by analytic continuation are compared with simulations with real chemical potential, which are possible by using a dimensionally reduced effective action for hot QCD. We find that for imaginary chemical potential the system undergoes a phase transition at |mu/T| \approx pi/3, and thus observables are analytic only in a limited range. However, utilising this range, relevant information can be obtained for the real chemical potential case.
Using a three-dimensional (3d) effective field theory and non-perturbative lattice simulations, we study the MSSM electroweak phase transition with two dynamical Higgs doublets. We first carry out a general analysis of spontaneous CP violation in 3d two Higgs doublet models, finding that this part of the parameter space is well separated from that corresponding to the physical MSSM. We then choose physical parameter values with explicit CP violation and a light right-handed stop, and determine the strength of the phase transition. We find a transition somewhat stronger than in 2-loop perturbation theory, leading to the conclusion that from the point of view of the non-equilibrium constraint, MSSM electroweak baryogenesis can be allowed even for a Higgs mass mH \approx 115 GeV. We also find that small values of the mass parameter mA (\lsim 120 GeV), which would relax the experimental constraint on mH, do not weaken the transition noticeably for a light enough stop. Finally we determine the properties of the phase boundary.
The strict coupling constant expansion for the free energy of hot QCD plasma shows bad convergence at all reasonable temperatures, and does not agree well with its 4d lattice determination. This has recently lead to various refined resummations, whereby the agreement with the lattice result should improve, at the cost of a loss of a formal agreement with the coupling constant expansion and particularly with its large infrared sensitive ``long-distance'' contributions. We show here how to resum the dominant long-distance effects by using a 3d effective field theory, and determine their magnitude by simple lattice Monte Carlo simulations.
Standard theories of electroweak interactions are based on the concept of a gauge symmetry broken by the Higgs mechanism. If they are placed in an environment with a sufficiently high temperature, the symmetry gets restored. It turns out that the characteristics of the symmetry restoring phase transition, such as its order, are important for cosmological applications, such as baryon asymmetry generation. We first briefly review how, by a combination of analytic and numerical methods, the properties of the phase transition can be systematically resolved for any given type of a (weakly interacting) Higgs sector. We then summarise the numerical results available for the Standard Model, and present a generic model independent statement as to how the Higgs sector should differ from the Standard Model for the properties of the transition to be very different. As an explicit example, we discuss the possibilities available for a strong transition in the experimentally allowed parameter region of the Minimal Supersymmetric Standard Model.
We use a perturbatively derived effective field theory and three-dimensional lattice simulations to determine the longest static correlation lengths in the deconfined QCD plasma phase at high temperatures (T\gsim 2 Tc) and finite densities (μ\lsim 4 T). For vanishing chemical potential, we refine a previous determination of the Debye screening length, and determine the dependence of different correlation lengths on the number of massless flavours as well as on the number of colours. For non-vanishing but small chemical potential, the existence of Debye screening allows us to carry out simulations corresponding to the full QCD with two (or three) massless dynamical flavours, in spite of a complex action. We investigate how the correlation lengths in the different quantum number channels change as the chemical potential is switched on.
In many extensions of the Standard Model, finite temperature computations are complicated by a hierarchy of zero temperature mass scales, in addition to the usual thermal mass scales. We extend the standard thermal resummations to such a situation, and discuss the 2-loop computations of the Higgs effective potential, and an effective 3d field theory for the electroweak phase transition, without carrying out high or low temperature expansions for the heavy masses. We also estimate the accuracy of the temperature expansions previously used for the MSSM electroweak phase transition in the presence of a heavy left-handed stop. We find that the low temperature limit of dealing with the left-handed stop is accurate up to surprisingly high temperatures.
We study with lattice Monte Carlo simulations the relation of global O(2) symmetry breaking in three dimensions to the properties of a geometrically defined vortex loop network. We find that different definitions of constructing a network lead to different results even in the thermodynamic limit, and that with typical definitions the percolation transition does not coincide with the thermodynamic phase transition. These results show that geometrically defined percolation observables need not display universal properties related to the critical behaviour of the system, and do not in general survive in the field theory limit.
Placing a high-Tc superconductor in an increasing external magnetic field, the flux first penetrates the sample through an Abrikosov vortex lattice, and then a first order transition is observed by which the system goes to the normal phase. We discuss the cosmological motivation for considering the electroweak phase transition in the presence of an external magnetic field, the analogies this system might have with the superconductor behaviour described above, and in particular whether at large physical Higgs masses, corresponding to the high-Tc regime, an analogue of the vortex phase and an associated first order phase transition could be generated.
We complete an existing result for how the baryon asymmetry left over after a period of full thermal equilibrium depends on different lepton asymmetries.
We solve the equations of motion for a CP violating phase between the two Higgs doublets at the bubble wall of the MSSM electroweak phase transition. Contrary to earlier suggestions, we do not find indications of spontaneous ``transitional'' CP violation in the MSSM. On the other hand, in case there is explicit CP violation in the stop and chargino/neutralino sectors, the relative phase between the Higgses does become space dependent, but only mildly even in the maximal case. We also demonstrate that spontaneous CP violation within the bubble wall could occur, e.g., if the Higgs sector of the MSSM were supplemented by a singlet. Finally we point out some implications for baryogenesis computations.
We study with lattice Monte Carlo simulations the interactions and macroscopic behaviour of a large number of vortices in the 3-dimensional U(1) gauge+Higgs field theory, in an external magnetic field. We determine non-perturbatively the (attractive or repelling) interaction energy between two or more vortices, as well as the critical field strength H_c, the thermodynamical discontinuities, and the surface tension related to the boundary between the Meissner phase and the Coulomb phase in the type I region. We also investigate the emergence of vortex lattice and vortex liquid phases in the type II region. For the type I region the results obtained are in qualitative agreement with mean field theory, except for small values of H_c, while in the type II region there are significant discrepancies. These findings are relevant for superconductors and some models of cosmic strings, as well as for the electroweak phase transition in a magnetic field.
We define a non-local gauge-invariant Green's function which can distinguish between the symmetric (confinement) and broken (Higgs) phases of the hot SU(2)xU(1) electroweak theory to all orders in the perturbative expansion. It is related to the coupling of the Chern-Simons number to a massless Abelian gauge field. The result implies either that there is a way to distinguish between the phases, even though the macroscopic thermodynamical properties of the system have been observed to be smoothly connected, or that the perturbative Coleman-Hill theorem on which the argument is based, is circumvented by non-perturbative effects. We point out that this question could in principle be studied with three-dimensional lattice simulations.