Oleg L. Veretin

Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision

We perform a manifestly gauge-independent analysis of the vacuum stability in the standard model including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the Higgs self-coupling and its beta function in the modified minimal-subtraction scheme and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the standard model be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with the Monte Carlo mass quoted by the Particle Data Group at the 1.3σ level.

Strong-coupling constant with flavor thresholds at five loops in the modified minimal-subtraction scheme.

We present in analytic form the matching conditions for the strong-coupling constant alphas(nf) (mu) at the flavor thresholds to four loops in the modified minimal-subtraction scheme. Taking into account the present knowledge on the coefficient beta4 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a five-loop formula for alphas(nf) (mu) together with appropriate relationships between the asymptotic scale parameters Lamda(nf) for different numbers of flavors nf.

Bosonic corrections to Delta r at the two loop level

The details of the recent calculation of the two-loop bosonic corrections to the muon lifetime in the Standard Model are presented. The matching on the Fermi theory is discussed. Renormalisation in the on-shell and in the MS scheme is studied and transition between the schemes is shown to lead to identical results. High precision numerical methods are compared with mass difference and large mass expansions.

Two-loop sunset diagrams with three massive lines

Abstract In this paper, we consider the two-loop sunset diagram with two different masses, m and M, at spacelike virtuality q 2 = − m 2 . We find explicit representations for the master integrals and an analytic result through O ( ɛ ) in d = 4 − 2 ɛ space–time dimensions for the case of equal masses, m = M .

Electroweak corrections to Z-boson hadroproduction at finite transverse momentum

We calculate the full one-loop electroweak radiative corrections, of O(α 2 αs ), to the cross section of single Z-boson inclusive hadroproduction at finite transverse momentum (pT ). This includes the O(α) corrections to Z + j production, the O(αs ) corrections to Z + γ production, and certain QCD-electroweak interference contributions involving a single quark trace. We recover the QCD and purely weak corrections and study the QED corrections and the QCD-electroweak interference contributions for the first time. We also consider direct and resolved photoproduction in elastic and inelastic scattering. We present pT and rapidity distributions for the experimental conditions at the Fermilab Tevatron and the CERN LHC and assess the significance of the various contributions.

Two-Loop Formfactors in Theories with Mass Gap and Z-Boson Production

Abstract The non-factorizable two-loop corrections to the formfactor both for a U ( 1 ) × U ( 1 ) and a SU ( 2 ) × U ( 1 ) gauge theory with massive and massless gauge bosons respectively are evaluated at arbitrary momentum transfer q 2 . The asymptotic behaviour for q 2 → ∞ is compared to a recent calculation of Sudakov logarithms. The result is an important ingredient for the calculation of radiative corrections to Z -boson production at hadron and lepton colliders.

Heavy mass expansion, light by light scattering and the anomalous magnetic moment of the muon

Contributions from light-by-light scattering to (g_\mu-2)/2, the anomalous magnetic moment of the muon, are mediated by the exchange of charged fermions or scalar bosons. Assuming large masses M for the virtual particles and employing the technique of large mass expansion, analytical results are obtained for virtual fermions and scalars in the form of a series in (m_\mu /M)^2. This series is well convergent even for the case M=m_\mu. For virtual fermions, the expansion confirms published analytical formulae. For virtual scalars, the result can be used to evaluate the contribution from charged pions. In this case our result confirms already available numerical evaluations, however, it is significantly more precise.

Two-loop electroweak threshold corrections in the Standard Model

We study the relationships between the basic parameters of the on-shell renormalization scheme and their counterparts in the MS scheme at full order O(� 2 ) in the Standard Model. These enter as threshold corrections the renormalization group analyses underlying, e.g., the investigation of the vacuum stability. To ensure the gauge invariance of the parameters, in particular of the MS masses, we work in

mr: A C++ library for the matching and running of the Standard Model parameters

We present the C++ program library mr that allows us to reliably calculate the values of the running parameters in the Standard Model at high energy scales. The initial conditions are obtained by relating the running parameters in the MS¯ renormalization scheme to observables at lower energies with full two-loop precision. The evolution is then performed in accordance with the renormalization group equations with full three-loop precision. Pure QCD corrections to the matching and running are included through four loops. We also provide a Mathematica interface for this program library.

Low-mass Higgs decays to four leptons at one loop and beyond

The ongoing searches for Higgs-boson signals in data taken at the CERN LHC and the Fermilab Tevatron crucially rely on the decay channels H -> Z l l and H -> W l nu. We present a precision study of the partial widths of these decay channels including the full one-loop electroweak corrections and the dominant contributions at two and three loops, of O(G_F^2 m_t^4), O(G_F m_t^2 alpha_s), and O(G_F m_t^2 alpha_s^2). Since the invariant mass of the off-shell intermediate boson is relatively low in the mass window 115 GeV < m_H < 129 GeV of current interest, lepton mass effects are relevant, especially for the tau lepton.