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

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

Dropping rho and A_1 Meson Masses at Chiral Phase Transition in the Generalized Hidden Local Symmetry

We study the chiral symmetry restoration using the generalized hidden local symmetry (GHLS) which incorporates the rho and A_1 mesons as the gauge bosons of the GHLS and the pion as the Nambu-Goldstone boson consistently with the chiral symmetry of QCD. We show that a set of parameter relations, which ensures the first and second Weinberg's sum rules, is invariant under the renormalization group evolution. Then, we found that the Weinberg's sum rules together with the matching of the vector and axial-vector current correlators inevitably leads to {\it the dropping masses of both rho and A_1 mesons} at the symmetry restoration point, and that the mass ratio as well as the mixing angle between the pion and A_1 meson flows into one of three fixed points.Comment: 17 pages, 7 figures; references added and discussions expande

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

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

Two-photon exchange in elastic electron-nucleon scattering

A detailed study of two-photon exchange in unpolarized and polarized elastic electron--nucleon scattering is presented, taking particular account of nucleon finite size effects. Contributions from nucleon elastic intermediate states are found to have a strong angular dependence, which leads to a partial resolution of the discrepancy between the Rosenbluth and polarization transfer measurements of the proton electric to magnetic form factor ratio, G_E/G_M. The two-photon exchange contribution to the longitudinal polarization transfer P_L is small, whereas the contribution to the transverse polarization transfer P_T is enhanced at backward angles by several percent, increasing with Q^2. This gives rise to a small, ~3% suppression of G_E/G_M obtained from the polarization transfer ratio P_T/P_L at large Q^2. We also compare the two-photon exchange effects with data on the ratio of e^+ p to e^- p cross sections, which is predicted to be enhanced at backward angles. Finally, we evaluate the corrections to the form factors of the neutron, and estimate the elastic intermediate state contribution to the ^3He form factors