Accurate prediction of electroweak observables and impact on the Higgs mass bound

I discuss the importance of the O(g^4 m_t^2/\mw^2) corrections to the effective electroweak angle and Mw in the indirect determination of the Higgs mass. I emphasize the r\^ole of a very precise Mw measurement on the Mh estimate.Comment: 9 pages, LaTex, uses appb.sty. Talk presented at the Zeuthen Workshop on Elementary Particle Theory "Loops and Legs in Gauge Theories" Rheinsberg, Germany, April 19-24, 199

Topics in Electroweak Physics

We briefly discuss five topics in Precision Electroweak Physics: i) the recently proposed Effective Scheme of Renormalization, ii) evidence for electroweak bosonic corrections derived from the radiative correction Delta_r_eff, iii) an approach to estimate the scale of new physics in a hypothetical Higgs-less scenario, iv) simple and accurate formulae for s^2_eff, M_W, Gamma_l, and their physical applications, v) a recent proposal concerning the field renormalization constant for unstable particles.Comment: 5 pages, talk presented at the International Symposium Radcor 2002, September 8-13, Kloster Banz, German

Two-loop heavy top effects on the MZ-MW interdependence

The O(alpha^2 mt^2/mw^2) correction to the relation between G_\mu and the vector boson masses is computed in the MSbar scheme, and the results are used to investigate the magnitude of the effect on the theoretical prediction of mw and sin^2\theta_\msbar(mz) from alpha, G_\mu, and mz.Comment: 11 pages, LaTeX, includes 1 LaTeX figure, uses equations.sty and cite.sty, one minor comment and interpolation function for variable mtop added, no change in the result

The role of the top quark in the stability of the SM Higgs potential

I discuss the stability of the SM scalar potential in view of the discovery of a Higgs boson with mass around 125 GeV. The role played by the top quark mass in the choice between the full stability and the metastability conditions is analyzed in detail. The present experimental value of the top mass do not support the possibility that the SM potential is stable up to the Planck scale but favor an electroweak vacuum sufficiently long-lived to be metastable.Comment: 7 pages, 6 figures. To appear on the Proceedings of LC13 Workshop: exploring QCD from the infrared regime to heavy flavour scales at B-factories, the LHC and a Linear Collider, 16-20 September 2013, ECT*, Villa Tambosi, Villazzano (TN), Ital

Consistency Condition for the Pinch Technique Self-Energies at Two Loops

A simple and testable necessary condition for the gauge independence of the Pinch Technique self-energies at two loops is discussed. It is then shown that, in the case of the $Z$ and $W$ self-energies, the condition is indeed satisfied by the Papavassiliou-Pilaftsis formulation.Comment: 7 pages, Latex, 1 PostScript figur

The electroweak form factor \hat{\kappa}(q^2) and the running of \sin^2 \hat{\theta}_W

Gauge independent form factors \rho^(e; e) and \hat{\kappa}^(e; e)(q^2) for Moller scattering at s << m_W^2 are derived. It is pointed out that \hat{\kappa}^(e; e) is very different from its counterparts in other processes. The relation between the effective parameter \hat{\kappa}^(e; e)(q^2,\mu) \sin^2 \hat{\theta}_W(\mu) and \sin^2 \theta_eff is derived in a scale-independent manner. A gauge and process-independent running parameter \sin^2 \hat{\theta}_W (q^2), based on the pinch-technique self-energy a_{\gamma Z} (q^2), is discussed for all q^2 values. At q^2=0 it absorbs very accurately the Czarnecki-Marciano calculation of the Moller scattering asymmetry at low s values, and at q^2 = m^2_Z it is rather close to \sin^2 \theta_eff. The q^2 dependence of \sin^2 \hat{\theta}_W (q^2) is displayed in the space and time-like domains.Comment: A new paragraph has been inserted at the beginning of the discussion in Section

Constraints on the trilinear Higgs self coupling from precision observables

We present the constraints on the trilinear Higgs self coupling that arise from loop effects in the $W$ boson mass and the effective sine predictions. We compute the contributions to these precision observables of two-loop diagrams featuring an anomalous trilinear Higgs self coupling. We explicitly show that the same anomalous contributions are found if the analysis of $m_{ \scriptscriptstyle W}$ and \mbox{\sin^2 \theta^{{\rm lep}}_{{\rm eff}}} is performed in a theory in which the scalar potential in the Standard Model Lagrangian is modified by an (in)finite tower of $(\Phi^\dagger \Phi)^n$ terms with $\Phi$ the Higgs doublet. We find that the bounds on the trilinear Higgs self coupling from precision observables are competitive with those coming from Higgs pair production.Comment: 23 pages, 4 figures; V2: References added, version published on JHE

Two Loop Electroweak Bosonic Corrections to the Muon Decay Lifetime

A review of the calculation of the two loop bosonic corrections to $\Delta r$ is presented. Factorization and matching onto the Fermi model are discussed. An approximate formula, describing the quantity over the interesting range of Higgs boson mass values from 100 GeV to 1 TeV is given.Comment: 5 pages, 3 figures, minor corrections, to appear in the proceedings of the RADCOR 2002/Loops and Legs in Quantum Field Theory workshop, Kloster Banz, Germany, 8-13 Sep 200

The first Hochschild cohomology as a Lie algebra

In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, we show that if the quiver has no parallel arrows and no loops then the first Hochschild cohomology is solvable. For quivers containing loops, we determine easily verifiable sufficient conditions for the solvability of the first Hochschild cohomology. We apply these criteria to show the solvability of the first Hochschild cohomology space for large families of algebras, namely, several families of self-injective tame algebras including all tame blocks of finite groups and some wild algebras including most quantum complete intersections.Comment: 17 pages, v3: substantial rewrit