Lars Kyllingstad

Four-loop screened perturbation theory

We study the thermodynamics of massless {phi}{sup 4}-theory using screened perturbation theory. In this method, the perturbative expansion is reorganized by adding and subtracting a thermal mass term in the Lagrangian. We calculate the free energy through four loops expanding in a double power expansion in m/T and g{sup 2}, where m is the thermal mass and g is the coupling constant. The expansion is truncated at order g{sup 7} and the loop expansion is shown to have better convergence properties than the weak-coupling expansion. The free energy at order g{sup 6} involves the four-loop triangle sum-integral evaluated by Gynther, Laine, Schroeder, Torrero, and Vuorinen using the methods developed by Arnold and Zhai. The evaluation of the free energy at order g{sup 7} requires the evaluation of a nontrivial three-loop sum-integral, which we calculate by the same methods.

Pion condensation in a two-flavour NJL model: the role of charge neutrality

We study pion condensation and the phase structure in a two-flavour Nambu–Jona-Lasinio model in the presence of baryon chemical potential μ and isospin chemical potential μI at zero and finite temperature. There is a competition between the chiral condensate and a Bose–Einstein condensate of charged pions. In the chiral limit, the chiral condensate vanishes for any finite value of the isospin chemical potential, while there is a charged pion condensate that depends on the chemical potentials and the temperature. At the physical point, the chiral condensate is always nonzero, while the charged pion condensate depends on μI and T. For T = μ = 0, the critical isospin chemical potential μcI for the onset of Bose–Einstein condensation is always equal to the pion mass. For μ = 0, we compare our results with chiral perturbation theory, sigma-model calculations and lattice simulations. Finally, we examine the effects of imposing electric charge neutrality and weak equilibrium on the phase structure of the model. In the chiral limit, there is a window of baryon chemical potential and temperature where the charged pions condense. At the physical point, the charged pions do not condense.

The chiral phase transition and the role of vacuum fluctuations

We investigate the chiral phase transition in the quark‐meson effective model using optimised perturbation theory to one loop. Certain terms in the free energy are frequently omitted in calculations, on the assumption that their contribution is negligible. We show that this is not necessarily the case, and that the order of the phase transition, as well as the critical temperature, depends heavily on which contributions are included.

Pressure to order

We calculate the pressure of massless 4-theory to order g8log (g) at weak coupling. The contributions to the pressure arise from the hard momentum scale of order T and the soft momentum scale of order gT. Effective field theory methods and dimensional reduction are used to separate the contributions from the two momentum scales: The hard contribution can be calculated as a power series in g2 using naive perturbation theory with bare propagators. The soft contribution can be calculated using an effective theory in three dimensions, whose coefficients are power series in g2. This contribution is a power series in g starting at order g3. The calculation of the hard part to order g6 involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schroder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order g6 and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order g7. The coefficients of the effective theory satisfy a set of renormalization group equations that can be used to sum up leading and subleading logarithms of T/gT. We use the solutions to these equations to obtain a result for the free energy which is correct to order g8log (g). Finally, we investigate the convergence of the perturbative series.

g^8*log(g)

We calculate the pressure of massless 4-theory to order g8log (g) at weak coupling. The contributions to the pressure arise from the hard momentum scale of order T and the soft momentum scale of order gT. Effective field theory methods and dimensional reduction are used to separate the contributions from the two momentum scales: The hard contribution can be calculated as a power series in g2 using naive perturbation theory with bare propagators. The soft contribution can be calculated using an effective theory in three dimensions, whose coefficients are power series in g2. This contribution is a power series in g starting at order g3. The calculation of the hard part to order g6 involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schroder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order g6 and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order g7. The coefficients of the effective theory satisfy a set of renormalization group equations that can be used to sum up leading and subleading logarithms of T/gT. We use the solutions to these equations to obtain a result for the free energy which is correct to order g8log (g). Finally, we investigate the convergence of the perturbative series.

in

The average phase factor of the QCD fermion determinant signals the strength of the QCD sign problem. We compute the average phase factor as a function of temperature and baryon chemical potential using a two-flavor NJL model. This allows us to study the strength of the sign problem at and above the chiral transition. It is discussed how the U(1)A anomaly affects the sign problem. Finally, we study the interplay between the sign problem and the endpoint of the chiral transition.

\phi^4

Abstract We study the thermodynamics of massless ϕ 4 -theory using screened perturbation theory, which is a way to systematically reorganise the perturbative series. The free energy and pressure are calculated through four loops in a double expansion in powers of g 2 and m / T , where m is a thermal mass of order gT . The result is truncated at order g 7 . We find that the convergence properties are significantly improved compared to the weak-coupling expansion.

-theory at weak coupling

We calculate the pressure of massless 4-theory to order g8log (g) at weak coupling. The contributions to the pressure arise from the hard momentum scale of order T and the soft momentum scale of order gT. Effective field theory methods and dimensional reduction are used to separate the contributions from the two momentum scales: The hard contribution can be calculated as a power series in g2 using naive perturbation theory with bare propagators. The soft contribution can be calculated using an effective theory in three dimensions, whose coefficients are power series in g2. This contribution is a power series in g starting at order g3. The calculation of the hard part to order g6 involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schroder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order g6 and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order g7. The coefficients of the effective theory satisfy a set of renormalization group equations that can be used to sum up leading and subleading logarithms of T/gT. We use the solutions to these equations to obtain a result for the free energy which is correct to order g8log (g). Finally, we investigate the convergence of the perturbative series.