A. Patkós

Screened perturbation theory

A new perturbative scheme is proposed for the evaluation of the free energy density of field theories at finite temperature. The screened loop expansion takes into account exactly the phenomenon of screening in thermal propagators. The approach is tested in the N-component scalar field theory at 2-loop level and also at 3-loop in the large-N limit. The perturbative series generated by the screened loop expansion shows much better numerical convergence than previous expansions generated in powers of the quartic coupling

Gauge boson masses in the 3D, SU(2) gauge-Higgs model

Abstract We study gauge boson propagators in the symmetric and symmetry broken phases of the 3D, SU(2) gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading to a non-vanishing mass for the gauge bosons. We find that the W-boson screening mass drops in the symmetry broken phase when approaching the critical temperature. In the symmetric phase the screening mass stays small and is independent of the scalar-gauge coupling (the hopping parameter). Numerical results coincide with corresponding calculations performed for the pure gauge theory. We find mw = 0.35(1)g2T in this phase which is consistent with analytic calculations based on gap equations. This is, however, significantly smaller than masses extracted from gauge-invariant vector boson correlation functions. As internal consistency check we also have calculated correlation functions for gauge-invariant operators leading to scalar and vector boson masses. Finite lattice size effects have been systematically analyzed on lattices of size L2 × Lz with L = 4 – 24 and Lz = 16 – 128.

Hierarchy of effective field theories of hot electroweak matter

A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over nonstatic modes leads to an effective theory containing a gauge field [ital A][sub [ital i]][sup [ital a]], an adjoint Higgs field [ital A][sub 0][sup [ital a]], and the fundamental Higgs field [phi][sub [alpha]]. We carry out the integration in the one-loop approximation, study renormalization effects, and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Second, because of the existence of well-separated thermal mass scales, [ital A][sub 0][sup [ital a]] can be integrated over, and finally also [phi][sub [alpha]], leaving an effective theory of the [ital A][sub [ital i]][sup [ital a]]. In the analysis of the subsequent models particular attention is paid to the screening of the magnetic fluctuations due to the integrated-out degrees of freedom.

Series expansion solution of the Wegner-Houghton renormalisation group equation

The momentum independent projection of the Wegner-Houghton renormalisation group equation is solved with power series expansion. Convergence rate is analyzed for then-vector model. Further evidence is presented for the first order nature of the chiral symmetry restoration at finite temperature in QCD with 3 light flavors.

Critical exponents of defective Ising models and the U(1) Kac-Moody-Virasoro algebras

At the bulk critical point, the quantum Ising chain with defects is studied. The spectrum is generated from the unitary representations of the U(1) Kac-Moody-Virasoro algebra of central charge c = 1. A generalized formula for the leading finite-size correction to the ground-state energy is obtained, which is related to the magnitude of the Casimir effect.

The ising quantum chain with defects. I: The exact solution

The Ising quantum chain with n arbitrarily placed defects is solved exactly. At the bulk critical point, the model is conformally invariant if and only if the defects form a commensurate structure. The central charge is obtained and is found to be a discontinuous function of the distances of the defects, while the critical exponents (generalized corner exponents) depend continuously on the positions of the defects. It is argued that the discontinuous behavior of the central charge is a general feature not restricted to the Ising model.

Critical Higgs mass and temperature dependence of gauge boson masses in the SU(2) gauge Higgs model

Abstract We study the effective 3-D SU(2) Gauge-Higgs model at finite temperature for Higgs-masses in the range from 60 GeV up to 100 GeV. The first order electroweak phase transition weakens with increasing Higgs-mass and terminates at a critical end-point. For Higgs-mass values larger than about m H,c = 75.4(6) GeV the thermodynamic signature of the transition is described by a crossover. Close to this Higgs-mass value we investigate the vector boson propagator in Landau gauge. The calculated W-boson screening masses are compared with predictions based on gap equations.

Effective scalar field theory for the electroweak phase transition

We investigate an effective model for the finite temperature symmetry restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the 3 + 1 dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a 3-dimensional O(4) ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, mH = 37 GeV, considered in the present investigation, we find a discontinuous symmetry restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first order phase transition as compared to the mean field treatment, demonstrating that nonperturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first order transition could result only from non-perturbative effects related to the gauge degrees of freedom.

Spin-dependent deep inelastic electron-proton scattering

Abstract The two spin-dependent structure functions in electroproduction cross sections are investigated asymptotically. It is suggested that the amplitude for spin-dependent virtual Compton scattering at large space-like photon masses is controlled by the dominant J -plane singularities and the constitution of the electric current. Experimental and theoretical implications of this conjecture are discussed.

Partial path integration of quantum fields: Two loop analysis of the SU(2) gauge Higgs model at finite temperature

Abstract High temperature reduction of the SU(2) Higgs model is realised by partially integrating its partition function. Various approximate forms of the effective theory resulting from the integration over non-static fields and the static electric potential are analysed. Also non-polynomial and non-local terms are allowed. Consistency of the perturbative solution is ensured by new types of induced counterterms. Perturbative phase transition characteristics are presented in the Higgs mass range 30–120 GeV, and compared to results of other perturbative approaches.