New Renormalization Group Equations and the Naturalness Problem

Looking for an observable manifestation of the so-called unnaturalness of scalar fields we introduce a seemingly new set of differential equations for connected Green functions. These equations describe the momentum dependence of the Green functions and are close relatives to the previously known renormalization group equations. Applying the new equations to the theory of scalar field with $\phi^4$ interaction we identify a relation between the four-point Green function and the propagator which expresses the unnaturalness of the scalar field. Possible manifestations of the unnaturalness at low momenta are briefly discussed.Comment: 12 revtex pages; a coefficient has been corrected in eq. (34), four new references added; final version to appear in Phys. Rev.

Off-Shell Scattering Amplitudes for WW Scattering and the Role of the Photon Pole

We derive analytic expressions for high energy $2 \to 2$ off-shell scattering amplitudes of weak vector bosons. They are obtained from six fermion final states in processes of the type $e^+ e^- \to \bar\nu_e + (WW) + \nu_e \to \bar\nu_e + (l\nu)(l\nu) + \nu_e$. As an application we reconsider the unitarity bounds on the Higgs mass. Particular attention is given to the role of the photon exchange which has not been considered in earlier investigations; we find that the photon weakens the bound of the Higgs mass.Comment: 16 pages, 8 figure

Constraints on the excitations in the Strongly Coupled Standard Model

The Strongly Coupled Standard Model predicts a rich spectrum of excited states at the Fermi scale. We study the first radial excitations of the vector bosons. The inclusion of these new states affects the low energy phenomenology of the model. We put constraints on the effective couplings by performing a global fit with the electroweak observables, and we find that the excitations have to be rather decoupled from the low-energy states.Comment: 23 pages, 6 figures, uses RevTeX

Boosting Higgs discovery - the forgotten channel

Searches for a heavy Standard Model Higgs boson focus on the 'gold plated mode' where the Higgs decays to two leptonic Z bosons. This channel provides a clean signature, in spite of the small leptonic branching ratios. We show that using fat jets the semi-leptonic ZZ mode significantly increases the number of signal events with a similar statistical significance as the leptonic mode.Comment: 12 pages, 3 figure

The unit of electric charge and the mass hierarchy of heavy particles

We propose some empirical formulae relating the masses of the heaviest particles in the standard model (the W,Z,H bosons and the t quark) to the charge of the positron $e$ and the Higgs condensate v. The relations for the masses of gauge bosons m_W = (1+e)v/4 and m_Z=sqrt{(1+e^2)/2}*(v/2) are in excellent agreement with experimental values. By requiring the electroweak standard model to be free from quadratic divergencies at the one-loop level, we find: m_t=v/sqrt{2} and m_H=v/sqrt{2e}, or the very simple ratio (m_t/m_H)^2=e.Comment: 6 page

Low-Energy Effective Theory, Unitarity, and Non-Decoupling Behavior in a Model with Heavy Higgs-Triplet Fields

We discuss the properties of a model incorporating both a scalar electroweak Higgs doublet and an electroweak Higgs triplet. We construct the low-energy effective theory for the light Higgs-doublet in the limit of small (but nonzero) deviations in the rho parameter from one, a limit in which the triplet states become heavy. For small deviations in the rho parameter from one, perturbative unitarity of WW scattering breaks down at a scale inversely proportional to the renormalized vacuum expectation value of the triplet field (or, equivalently, inversely proportional to the square-root of the deviation of the rho parameter from one). This result imposes an upper limit on the mass-scale of the heavy triplet bosons in a perturbative theory; we show that this upper bound is consistent with dimensional analysis in the low-energy effective theory. Recent articles have shown that the triplet bosons do not decouple, in the sense that deviations in the rho parameter from one do not necessarily vanish at one-loop in the limit of large triplet mass. We clarify that, despite the non-decoupling behavior of the Higgs-triplet, this model does not violate the decoupling theorem since it incorporates a large dimensionful coupling. Nonetheless, we show that if the triplet-Higgs boson masses are of order the GUT scale, perturbative consistency of the theory requires the (properly renormalized) Higgs-triplet vacuum expectation value to be so small as to be irrelevant for electroweak phenomenology.Comment: Revtex, 11 pages, 7 eps figures included; references updated and three footnotes adde

Non locality and causal evolution in QFT

Non locality appearing in QFT during the free evolution of localized field states and in the Feynman propagator function is analyzed. It is shown to be connected to the initial non local properties present at the level of quantum states and then it does not imply a violation of Einstein's causality. Then it is investigated a simple QFT system with interaction, consisting of a classical source coupled linearly to a quantum scalar field, that is exactly solved. The expression for the time evolution of the state describing the system is given. The expectation value of any arbitrary ``good'' local observable, expressed as a function of the field operator and its space and time derivatives, is obtained explicitly at all order in the field-matter coupling constant. These expectation values have a source dependent part that is shown to be always causally retarded, while the non local contributions are source independent and related to the non local properties of zero point vacuum fluctuations.Comment: Submitted to Journal of Physics B: 16 pages: 1 figur

Leading quantum gravitational corrections to QED

We consider the leading post-Newtonian and quantum corrections to the non-relativistic scattering amplitude of charged spin-1/2 fermions in the combined theory of general relativity and QED. The coupled Dirac-Einstein system is treated as an effective field theory. This allows for a consistent quantization of the gravitational field. The appropriate vertex rules are extracted from the action, and the non-analytic contributions to the 1-loop scattering matrix are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitude are known to give the long range, low energy, leading quantum corrections, are used to construct the leading post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for two massive fermions with electric charge.Comment: 14 pages, 29 figures, format RevTex

Supersymmetric NLO QCD Corrections to Resonant Slepton Production and Signals at the Tevatron and the LHC

We compute the total cross section and the transverse momentum distribution for single charged slepton and sneutrino production at hadronic colliders including NLO supersymmetric and non-supersymmetric QCD corrections. The supersymmetric QCD corrections can be substantial. We also resum the gluon transverse momentum distribution and compare our results with two Monte Carlo generators. We compute branching ratios of the supersymmetric decays of the slepton and determine event rates for the like-sign dimuon final state at the Tevatron and at the LHC.Comment: 14 pages, LaTeX, 8 figures, uses REVTex

What is the discrete gauge symmetry of the R-parity violating MSSM?

The lack of experimental evidence for supersymmetry motivates R-parity violating realizations of the MSSM. Dropping R-parity, alternative symmetries have to be imposed in order to stabilize the proton. We determine the possible discrete R and non-R symmetries, which allow for renormalizable R-parity violating terms in the superpotential and which, at the effective level, are consistent with the constraints from nucleon decay. Assuming a gauge origin, we require the symmetry to be discrete gauge anomaly-free, allowing also for cancellation via the Green Schwarz mechanism. Furthermore, we demand lepton number violating neutrino mass terms either at the renormalizable or non-renormalizable level. In order to solve the mu problem, the discrete Z_N or Z_N^R symmetries have to forbid any bilinear superpotential operator at tree level. In the case of renormalizable baryon number violation the smallest possible symmetry satisfying all conditions is a unique hexality Z_6^R. In the case of renormalizable lepton number violation the smallest symmetries are two hexalities, one Z_6 and one Z_6^R.Comment: 25 pages, version to appear in PR