Semi-Analytic Calculation of the Gravitational Wave Signal From the Electroweak Phase Transition for General Quartic Scalar Effective Potentials

Upcoming gravitational wave (GW) detectors might detect a stochastic background of GWs potentially arising from many possible sources, including bubble collisions from a strongly first-order electroweak phase transition. We investigate whether it is possible to connect, via a semi-analytical approximation to the tunneling rate of scalar fields with quartic potentials, the GW signal through detonations with the parameters entering the potential that drives the electroweak phase transition. To this end, we consider a finite temperature effective potential similar in form to the Higgs potential in the Standard Model (SM). In the context of a semi-analytic approximation to the three dimensional Euclidean action, we derive a general approximate form for the tunneling temperature and the relevant GW parameters. We explore the GW signal across the parameter space describing the potential which drives the phase transition. We comment on the potential detectability of a GW signal with future experiments, and physical relevance of the associated potential parameters in the context of theories which have effective potentials similar in form to that of the SM. In particular we consider singlet, triplet, higher dimensional operators, and top-flavor extensions to the Higgs sector of the SM. We find that the addition of a temperature independent cubic term in the potential, arising from a gauge singlet for instance, can greatly enhance the GW power. The other parameters have milder, but potentially noticeable, effects.Comment: accepted by JCAP, revisions: removed turbulence contribution, minor changes to experimental sensitivity, fixed various minor typos and text revisions, added references, made it clear we consider only detonations; 17 pages, 4 figures, revtex

Isotope shift calculations for atoms with one valence electron

This work presents a method for the ab initio calculation of isotope shift in atoms and ions with one valence electron above closed shells. As a zero approximation we use relativistic Hartree-Fock and then calculate correlation corrections. The main motivation for developing the method comes from the need to analyse whether different isotope abundances in early universe can contribute to the observed anomalies in quasar absorption spectra. The current best explanation for these anomalies is the assumption that the fine structure constant, alpha, was smaller at early epoch. We test the isotope shift method by comparing the calculated and experimental isotope shift for the alkali and alkali-like atoms Na, MgII, K, CaII and BaII. The agreement is found to be good. We then calculate the isotope shift for some astronomically relevant transitions in SiII and SiIV, MgII, ZnII and GeII.Comment: 11 page

Magnetic Fields at First Order Phase Transition: A Threat to Electroweak Baryogenesis

The generation of the observed baryon asymmetry may have taken place during the electroweak phase transition, thus involving physics testable at LHC, a scenario dubbed electroweak baryogenesis. In this paper we point out that the magnetic field which is produced in the bubbles of a first order phase transition endangers the baryon asymmetry produced in the bubble walls. The reason being that the produced magnetic field couples to the sphaleron magnetic moment and lowers the sphaleron energy; this strengthens the sphaleron transitions inside the bubbles and triggers a more effective wash out of the baryon asymmetry. We apply this scenario to the Minimal Supersymmetric extension of the Standard Model (MSSM) where, in the absence of a magnetic field, successful electroweak baryogenesis requires the lightest CP-even Higgs and the right-handed stop masses to be lighter than about 127 GeV and 120 GeV, respectively. We show that even for moderate values of the magnetic field, the Higgs mass required to preserve the baryon asymmetry is below the present experimental bound. As a consequence electroweak baryogenesis within the MSSM should be confronted on the one hand to future measurements at the LHC on the Higgs and the right-handed stop masses, and on the other hand to more precise calculations of the magnetic field produced at the electroweak phase transition.Comment: 16 pages, 4 figures. Minor corrections and references added to match published versio

Nine-Propagator Master Integrals for Massless Three-Loop Form Factors

We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin-Barnes representation which we use to compute the coefficients of the Laurent expansion in epsilon. Using Riemann zeta functions of up to weight six, we give fully analytic results for one integral; for a second, analytic results for all but the finite term; for the third, analytic results for all but the last two coefficients in the Laurent expansion. The remaining coefficients are given numerically to sufficiently high accuracy for phenomenological applications.Comment: 15 pages, 2 figures. Minor modifications and reference added. Matches published versio

Logarithmic two-loop corrections to the Lamb shift in hydrogen

Higher order $(\alpha/\pi)^2 (Z \alpha)^6$ logarithmic corrections to the hydrogen Lamb shift are calculated. The results obtained show the two-loop contribution has a very peculiar behavior, and significantly alter the theoretical predictions for low lying S-states.Comment: 14 pages, including 2 figures, submitted to Phys. Rev. A, updated with minor change

Semiclassical force for electroweak baryogenesis: three-dimensional derivation

We derive a semiclassical transport equation for fermions propagating in the presence of a CP-violating planar bubble wall at a first order electroweak phase transition. Starting from the Kadanoff-Baym (KB) equation for the two-point (Wightman) function we perform an expansion in gradients, or equivalently in the Planck constant h-bar. We show that to first order in h-bar the KB equations have a spectral solution, which allows for an on-shell description of the plasma excitations. The CP-violating force acting on these excitations is found to be enhanced by a boost factor in comparison with the 1+1-dimensional case studied in a former paper. We find that an identical semiclassical force can be obtained by the WKB method. Applications to the MSSM are also mentioned.Comment: 19 page

Spin fluctuations in the quasi-two dimensional Heisenberg ferromagnet GdI_2 studied by Electron Spin Resonance

The spin dynamics of GdI_2 have been investigated by ESR spectroscopy. The temperature dependences of the resonance field and ESR intensity are well described by the model for the spin susceptibility proposed by Eremin et al. [Phys. Rev. B 64, 064425 (2001)]. The temperature dependence of the resonance linewidth shows a maximum similar to the electrical resistance and is discussed in terms of scattering processes between conduction electrons and localized spins.Comment: to be published in PR

The Orbital Order Parameter in La0.95Sr0.05MnO3 probed by Electron Spin Resonance

The temperature dependence of the electron-spin resonance linewidth in La0.95Sr0.05MnO3 has been determined and analyzed in the paramagnetic regime across the orbital ordering transition. From the temperature dependence and the anisotropy of linewidth and $g$-value the orbital order can be unambiguously determined via the mixing angle of the wave functions of the $e_{\rm g}$-doublet. The linewidth shows a similar evolution with temperature as resonant x-ray scattering results

Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering

We describe in detail the calculation of the two-loop corrections to the QED Bhabha scattering cross section due to the vacuum polarization by heavy fermions. Our approach eliminates one mass scale from the most challenging part of the calculation and allows us to obtain the corrections in a closed analytical form. The result is valid for arbitrary values of the heavy fermion mass and the Mandelstam invariants, as long as s,t,u >> m_e^2.Comment: 43 pages, 8 figures; added reference

On a two-loop crossed six-line master integral with two massive lines

We compute the two-loop crossed six-line vertex master integral with two massive lines in dimensional regularisation, and give the result up to the finite part in D-4. We focus in particular on the purely analytical calculation of the boundary condition which we derive from a three-fold Mellin-Barnes representation. We also describe how the computation of the boundary condition is used to derive three non-trivial relations among harmonic polylogarithms of the sixth root of unity.Comment: 10 pages, 1 figure. References added, minor modifications. Matches published versio