Pressure of the Standard Model Near the Electroweak Phase Transition

We extend our previous determination of the thermodynamic pressure of the Standard Model so that the result can be applied down to temperatures corresponding to the electroweak crossover. This requires a further resummation which can be cleanly organised within the effective theory framework. The result allows for a precise determination of the expansion rate of the Universe for temperatures around the electroweak crossover.Comment: 16 pages, 6 figures. v2: published versio

Pressure of the Standard Model at High Temperatures

We compute the pressure of the standard model at high temperatures in the symmetric phase to three loops, or to O(g^5) in all coupling constants. We find that the terms of the perturbative expansion in the SU(2) + Higgs sector decrease monotonically with increasing order, but the large values of the strong coupling constant g_s and the Yukawa coupling of the top quark g_Y make the expansion in the full theory converge more slowly. The final result is observed to be about 10% smaller than the ideal gas pressure commonly used in cosmological calculations.Comment: 30 pages, 4 figures. v2: one reference added, minor revisions, accepted for publication in JHE

Mesonic screening masses at high temperature and finite density

We compute the first perturbative correction to the static correlation lengths of light quark bilinears in hot QCD with finite quark chemical potentials. The correction is small and positive, with mu-dependence depending on the relative sign of chemical potentials and the number of dynamical flavors. The computation is carried out using a three-dimensional effective theory for the lowest fermionic Matsubara mode. We also compute the full correlator in free theory and find a rather complicated general mu-dependence at shorter distances. Finally, rough comparisons with lattice simulations are discussed.Comment: 24 pages, 5 figures, JHEP style. Minor corrections and clarifications, version to appear in JHE

The diagonal and off-diagonal quark number susceptibility of high temperature and finite density QCD

We study the quark number susceptibility of the hot quark-gluon plasma at zero and non-zero quark number density, using lattice Monte Carlo simulations of an effective theory of QCD, electrostatic QCD (EQCD). Analytic continuation is used to obtain results at non-zero quark chemical potential. We measure both flavor singlet (diagonal) and non-singlet (off-diagonal) quark number susceptibilities. The diagonal susceptibility approaches the perturbative result above 20T_c, but below that temperature we observe significant deviations. The results agree well with 4d lattice data down to temperatures 2T_c. The off-diagonal susceptibility is more prone to statistical and systematic errors, but the results are consistent with perturbation theory already at 10T_c.Comment: 21 pages, 8 figures. Published version, references added, conclusions unchange

Pressure to order g8∗log(g)g^8*log(g) in ϕ4\phi^4-theory at weak coupling

We calculate the pressure of massless $\phi^4$-theory to order $g^8\log(g)$ 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 $g^2$ 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 $g^2$. This contribution is a power series in $g$ starting at order $g^3$. The calculation of the hard part to order $g^6$ involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schr\"oder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order $g^6$ and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order $g^7$. 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 $g^8\log(g)$. Finally, we investigate the convergence of the perturbative series.Comment: 29 pages and 12 figs. New version: we have pushed the calculations to g^8*log(g) using the renormalization group to sum up log(g) from higher orders. Published in JHE

Three-loop matching coefficients for hot QCD: Reduction and gauge independence

We perform an integral reduction for the 3-loop effective gauge coupling and screening mass of QCD at high temperatures, defined as matching coefficients appearing in the dimensionally reduced effective field theory (EQCD). Expressing both parameters in terms of a set master (sum-) integrals, we show explicit gauge parameter independence. The lack of suitable methods for solving the comparatively large number of master integrals forbids the complete evaluation at the moment. Taking one generic class of masters as an example, we highlight the calculational techniques involved. The full result would allow to improve on one of the classic probes for the convergence of the weak-coupling expansion at high temperatures, namely the comparison of full and effective theory determinations of the spatial string tension. Furthermore, the full result would also allow to determine one new contribution of order O(g**7) to the pressure of hot QCD.Comment: 19 pages, 2 figures. v2: new Section 6 discussing applications, to match journal versio

Effect of environmental assessment on primary energy of modular prefabricated panel for building renovation in Portugal

While facing increasingly strict regulations regarding energy efficiency, the construction sector should also adopt sustainable solutions in terms of new constructions and renovations of buildings. In particular, energy renovation of existing buildings has specific technical and economic constraints that are generally addressed through implementation of new materials and building integrated systems, whose environmental impact should be considered when assessing the most adequate solution. Within the context of the More-Connect Project, which aims to develop modular prefabricated solutions for energy renovation of buildings, several renovation scenarios for a pilot building in Portugal were assessed using a methodology to compare the cost-effectiveness of renovation measures. The article explores the use of lifecycle assessment to analyse the effect of considering embodied primary energy in cost-effectiveness calculations.The MORE-CONNECT project is funded by the European Commission within the framework of the Horizon 2020 program

A fresh look on three-loop sum-integrals

In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified way using coherent notation. We do this for three important cases of massless bosonic three-loop vacuum sum-integrals that have been frequently used in the literature, and aim for a streamlined exposition as compared to the original evaluations. In passing, we speculate on options for generalization of the computational techniques that have been employed.Comment: 19 page

The Lower–Middle Jurassic of the Anholt borehole: implications for the geological evolution of the eastern margin of the Danish Basin

This study of Upper Pliensbachian – Bajocian/Bathonian deposits in a borehole drilled on the island of Anholt, Denmark incorporates sedimentology, biostratigraphy (palynomorphs and foraminifera), palaeomagnetism and coal petrology. The studied succession records a gradual change from marine inner shelf storm-influenced clays to mainly terrestrial sands, clays, and lignite containing a flora of mainly freshwater algae and pollen. The regression was initiated at the Pliensbachian–Toarcian boundary and marine influence ceased during Bajocian–Bathonian times; the regression thus took place earlier at Anholt than in the centre of the Danish Basin. The sediments in the Anholt borehole are referred to the Fjerritslev and Haldager Sand Formations. Although the Lower–Middle Jurassic boundary is commonly placed at the boundary between the two formations, our data indicate that at Anholt the upper Fjerritslev Formation (member F-IV) is of Aalenian age. The Lower–Middle Jurassic boundary occurs close to the boundary between members F-III and F-IV of the Fjerritslev Formation. In contrast to other Lower–Middle Jurassic successions in the North Sea region, smectites of inferred volcanic origin are preserved in the Anholt section, suggesting limited burial and hence less intense diagenetic illitisation or chloritisation of smectites. A down-hole increase in diagenetic influence is reflected by the increase down-section both in the thermal stability of kaolinite and in the vitrinite reflectance. Kaolinite of inferred authigenic origin forms a white powder in the quartz-dominated sands of the Haldager Sand Formation; this kaolinite is thermally very unstable and is interpreted to be of late diagenetic, post-uplift origin. The vitrinite reflectance data indicate that the Jurassic formations have been exposed to thermal maturation corresponding to burial to a depth of 1000–1200 m below their present depth. Post-maturation uplift of the order of 1 km probably occurred partly during Late Cretaceous – Paleocene inversion in the Kattegat area and partly during Oligocene–Recent regional uplift, the latter being the most important of the two uplift phases. Palaeomagnetic data indicate that the main carrier of magnetic remanence is fine-grained magnetite. The stable remanence shows a pronounced inclination shallowing, which is attributed to post-depositional compaction

Electroweak phase diagram at finite lepton number density

We study the thermodynamics of the electroweak theory at a finite lepton number density. The phase diagram of the theory is calculated by relating the full 4-dimensional theory to a 3-dimensional effective theory which has been previously solved using nonperturbative methods. It is seen that the critical temperature increases and the value of the Higgs boson mass at which the first order phase transition line ends decreases with increasing leptonic chemical potential.Comment: 16 pages, 14 figures, RevTex4, v2: references added, minor corrections, v3: small changes, references added, published in Phys. Rev.