Steps towards full two-loop calculations for 2 fermion to 2 fermion processes: running versus pole masses schemes

Recent progress in the calculation of the two-loop on-shell mass counterterms within the electroweak Standard Model (SM) for the massive particles are discussed. We are in progress of developing a package for full two-loop SM calculations of 2 -> 2 fermion processes, with emphasis on the analytical approach where feasible. The complete two-loop on-shell renormalization is implemented. Substantial progress has been made in calculating the master integrals. We are able to compute in an efficient and stable manner up to a few thousands of diagrams of very complex mass structure.Comment: 4 pages, 1 style file. To appear in the proceedings of 9th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 03), Tsukuba, Japan, 1-5 Dec 200

Improvements of the local bosonic algorithm

We report on several improvements of the local bosonic algorithm proposed by M. Luescher. We find that preconditioning and over-relaxation works very well. A detailed comparison between the bosonic and the Kramers-algorithms shows comparable performance for the physical situation examined.Comment: Talk presented at LATTICE96(algorithms), 3 pages, Latex, espcrc

Variations on Photon Vacuum Polarization

I provide updates for the theoretical predictions of the muon and electron anomalous magnetic moments, for the shift in the fine structure constant $\alpha(M_Z)$ and for the weak mixing parameter $\sin^2 \Theta_W(M_Z)$. Phenomenological results for Euclidean time correlators, the key objects in the lattice QCD approach to hadronic vacuum polarization, are briefly considered. Furthermore, I present a list of isospin breaking and electromagnetic corrections for the lepton moments, which may be used to supplement lattice QCD results obtained in the isospin limit and without the e.m. corrections.Comment: 10 pages, 4 figure

The Role of Mesons in Muon g-2

The muon anomaly $a_\mu=(g_\mu-2)/2$ showing a persisting 3 to 4 $\sigma$ deviation between the SM prediction and the experiment is one of the most promising signals for physics beyond the SM. As is well known, the hadronic uncertainties are limiting the accuracy of the Standard Model prediction. Therefore a big effort is going on to improve the evaluations of hadronic effects in order to keep up with the 4-fold improved precision expected from the new Fermilab measurement in the near future. A novel complementary type experiment planned at J-PARC in Japan, operating with ultra cold muons, is expected to be able to achieve the same accuracy but with completely different systematics. So exciting times in searching for New Physics are under way. I discuss the role of meson physics in calculations of the hadronic part of the muon g-2. The improvement is expected to substantiate the present deviation $\Delta a_\mu^{\rm New \ Physics}=\Delta a_\mu^{\rm Experiment}- \Delta a_\mu^{\rm Standard \ Model}$ to a 6 to 10 standard deviation effect, provided hadronic uncertainties can be reduce by a factor two. This concerns the hadronic vacuum polarization as well as the hadronic light-by-light scattering contributions, both to a large extent determined by the low lying meson spectrum. Better meson production data and progress in modeling meson form factors could greatly help to improve the precision and reliability of the SM prediction of $a_\mu$ and thereby provide more information on what is missing in the SM.Comment: 7 pages, 5 figure

Higgs inflation and the cosmological constant

The Higgs not only induces the masses of all SM particles, the Higgs, given its special mass value, is the natural candidate for the inflaton and in fact is ruling the evolution of the early universe, by providing the necessary dark energy which remains the dominant energy density. SM running couplings not only allow us to extrapolate SM physics up to the Planck scale, but equally important they are triggering the Higgs mechanism. This is possible by the fact that the bare mass term in the Higgs potential changes sign at about mu_0 = 1.4x10^16 GeV and in the symmetric phase is enhanced by quadratic terms in the Planck mass. Such a huge Higgs mass term is able to play a key role in triggering inflation in the early universe. In this article we extend our previous investigation by working out the details of a Higgs inflation scenario. We show how different terms contributing to the Higgs Lagrangian are affecting inflation. Given the SM and its extrapolation to scales mu>mu_0 we find a calculable cosmological constant V(0) which is weakly scale dependent and actually remains large during inflation. This is different to the Higgs fluctuation field dependent Delta V(phi), which decays exponentially during inflation, and actually would not provide a sufficient amount of inflation. The fluctuation field has a different effective mass which shifts the bare Higgs transition point to a lower value mu'_0 = 7.7x10^14 GeV. The vacuum energy V(0) being proportional to M_Pl^4 has a coefficient which vanishes near the Higgs transition point, such that the bare and the renormalized cosmological constant match at this point. The role of the Higgs in reheating and baryogenesis is emphasized.Comment: 39 pages, 25 figures, 1 table. Replacement: typos corrected, Eq (3) corrected, notation adjuste

About the role of the Higgs boson in the evolution of the early universe

After the discovery of the Higgs particle the most relevant structures of the SM have been verified and for the first time we know all parameters of the SM within remarkable accuracy. Together with recent calculations of the SM renormalization group coefficients up to three loops we can safely extrapolate running couplings high up in energy. Assuming that the SM is a low energy effective theory of a cutoff theory residing at the Planck scale, we are able to calculate the effective bare parameters of the underlying cutoff system. It turns out that the effective bare mass term changes sign not far below the Planck scale, which means that in the early universe the SM was in the symmetric phase. The sign-flip, which is a result of a conspiracy between the SM couplings and their screening/antiscreening behavior, triggers the Higgs mechanism. Above the Higgs phase transition the bare mass term in the Higgs potential must have had a large positive value, enhanced by the quadratic divergence of the bare Higgs mass. Likewise the quartically enhanced positive vacuum energy density is present in the symmetric phase. The Higgs system thus provides the large dark energy density in the early universe, which triggers slow-roll inflation, i.e. the SM Higgs is the inflaton scalar field. Reheating is dominated by the decay of the heavy Higgses into (in the symmetric phase) massless top/anti-top quark pairs. The new scenario possibly could explain the baryon-asymmetry essentially in terms of SM physicsComment: 19 pages, 6 figure

The Effective Fine Structure Constant at TESLA Energies

We present a new estimate of the hadronic contribution to the shift in the fine structure constant at LEP and TESLA energies and calculate the effective fine structure constant. Substantial progress in a precise determination of this important parameter is a consequence of substantially improved total cross section measurements by the BES II collaboration and an improved theoretical understanding. In the standard approach which relies to a large extend on experimental data we find \Delta \al_{\rm hadrons}^{(5)}(\mz) = 0.027896 \pm 0.000395 which yields \alpha^{-1}(\mz) = 128.907 \pm 0.054. Another approach, using the Adler function as a tool to compare theory and experiment, allows us to to extend the applicability of perturbative QCD in a controlled manner. The result in this case reads $\Delta\alpha^{(5)}_{\rm had}(M_Z^2) = 0.027730 \pm 0.000209$ and hence \alpha^{-1}(\mz) = 128.930 \pm 0.029. At TESLA energies a new problem shows up with the definition of an effective charge. A possible solution of the problem is presented. Prospects for further progress in a precise determination of the effective fine structure constant are discussed.Comment: 21 pages 6 figures 2 table

The hierarchy problem and the cosmological constant problem in the Standard Model

We argue that the SM in the Higgs phase does not suffer form a "hierarchy problem" and that similarly the "cosmological constant problem" resolves itself if we understand the SM as a low energy effective theory emerging from a cut-off medium at the Planck scale. We discuss these issues under the condition of a stable Higgs vacuum, which allows to extend the SM up to the Planck length. The bare Higgs boson mass then changes sign below the Planck scale, such the the SM in the early universe is in the symmetric phase. The cut-off enhanced Higgs mass term as well as the quartically enhanced cosmological constant term trigger the inflation of the early universe. The coefficients of the shift between bare and renormalized Higgs mass as well as of the shift between bare and renormalized vacuum energy density exhibit close-by zeros at some point below the Planck scale. The zeros are matching points between short distance and the renormalized low energy quantities. Since inflation tunes the total energy density to take the critical value of a flat universe Omega_tot=rho_tot/rho_crit=Omega_Lambda+Omega_matter+Omega_radiation}=1 it is obvious that Omega_Lambda today is of order Omega_tot given that 1>Omega_matter, Omega_radiation>0, which saturate the total density to about 26 % only, the dominant part being dark matter(21 %).Comment: 22 pages, 2 figure