Parameters in the electroweak theory

This series of papers deals with the problem of finding relations between the parameters of the Standard Model of Glashow, Weinberg and Salam. In this first paper, the method of point splitting, suitably modified, is proposed as a useful regularization. When applied to quantum electrodynamics, this point-split regularization is indeed found to have desirable properties. More specifically, to one loop, the photon is shown to remain massless and the photon-photon scattering amplitude gauge invariant. In the following papers, this point-split regularization is applied to the electroweak theory. In the second paper, a first mass relation is obtained from the quadratic divergences. In the third paper, a second mass relation is found from the Higgs interactions. From these two relations, the masses of the Higgs boson and the top quark are determined theoretically for the Standard Model asm _H =190GeV andm _t =120GeV.Work supported in part by the Norwegian Research Council for Science and the Humanities     

Final results from DELPHI on the searches for SM and MSSM neutral Higgs bosons

These final results from DELPHI searches for the Standard Model (SM) Higgs boson, together with benchmark scans of the Minimal Supersymmetric Standard Model (MSSM) neutral Higgs bosons, used data taken at centre-of-mass energies between 200 and 209 GeV with a total integrated luminosity of 224 pb^-1. The data from 192 to 202 GeV are reanalysed with improved b-tagging for MSSM final states decaying to four b-quarks. The 95% confidence level lower mass bound on the Standard Model Higgs boson is 114.1 GeV/c ². Limits are also given on the lightest scalar and pseudo-scalar Higgs bosons of the MSSM.Received: 7 March 2003, Revised: 30 September 2003, Published online: 3 December 2003     

Search for the Standard Model Higgs boson with the OPAL detector at LEP

This paper summarises the search for the Standard Model Higgs boson in e ⁺ e ^- collisions at centre-of-mass energies up to 209 GeV performed by the OPAL Collaboration at LEP. The consistency of the data with the background hypothesis and various Higgs boson mass hypotheses is examined. No indication of a signal is found in the data and a lower bound of 112.7 Gev/c² is obtained on the mass of the Standard Model Higgs boson at the 95% CL. Received: 13 March 2002 / Revised version: 9 October 2002 / Published online: 13 December 2002     

Radiative corrections to the scalar Higgs masses in a non-minimal supersymmetric Standard Model

We calculate the dominant one-loop radiative corrections arising from quark-squark loops to the mass squared matrix of theCP-even Higgs bosons in a non-minimal supersymmetric Standard Model containing two Higgs doublets and a Higgs singlet chiral superfield using one-loop effective potential approximation. We use this result to evaluate upper and lower bounds on the radiatively corrected masses of all the scalar Higgs bosons as a function of the parameters of the model. We find that the one-loop radiative corrections are substantial only for the lightest Higgs boson of the model and can push its mass beyond the reach of LEP. We also calculate an absolute upper bound on the mass of the radiatively corrected lightest Higgs boson and compare it with the corresponding bound in the minimal supersymmetric Standard Model.     

Searches for invisibly decaying Higgs bosonswith the DELPHI detector at LEP

Searches for H Z production with the Higgs boson decaying into an invisible final state were performed using the data collected by the DELPHI experiment at centre-of-mass energies between 188 GeV and 209 GeV. Both hadronic and leptonic final states of the Z boson were analysed. In addition to the search for a heavy Higgs boson, a dedicated search for a light Higgs boson down to 40 GeV/c² was performed. No signal was found. Assuming the Standard Model HZ production cross-section, the mass limit for invisibly decaying Higgs bosons is 112.1 GeV/c² at 95% confidence level. An interpretation in the Minimal Supersymmetric extension of the Standard Model (MSSM) and in a Majoron model is also given.Received: 2 September 2003, Revised: 10 November 2003, Published online: 15 January 2004     

Recent results from LEP

Recent results from the LEP collider at CERN are presented: on the identification of e ⁺ e ⁻ → W ⁺ W ⁻ and the determination of the W mass and width and limits on its anomalous couplings; the search for the Standard Model and non-minimal Higgs; search for SUSY and other new particles. Fits to all electroweak data leading to predictions of the Higgs mass within the Standard Model are presented.     

Enhanced di-photon Higgs signal in the Next-to-Minimal Supersymmetric Standard Model

In the Next-to-Minimal Supersymmetric Standard Model, CP-even Higgs bosons can have masses in the range of 80–110 GeV in agreement with constraints from LEP due to their sizeable singlet component. Nevertheless their branching ratio into two photons can be more than 10 times larger than the one of a Standard Model Higgs boson of similar mass due to a reduced coupling to b quarks. This can lead to a spectacular enhancement of the Higgs signal rate in the di-photon channel at hadron colliders by a factor 6. Corresponding scenarios can occur in the Next-to-Minimal Supersymmetric Standard Model for a relatively low Susy breaking scale.     

The probable fate of the Standard Model

Extrapolating the Standard Model to high scales using the renormalisation group, three possibilities arise, depending on the mass of the Higgs boson: if the Higgs mass is large enough the Higgs self-coupling may blow up, entailing some new non-perturbative dynamics; if the Higgs mass is small the effective potential of the Standard Model may reveal an instability; or the Standard Model may survive all the way to the Planck scale for an intermediate range of Higgs masses. This latter case does not necessarily require stability at all times, but includes the possibility of a metastable vacuum which has not yet decayed. We evaluate the relative likelihoods of these possibilities, on the basis of a global fit to the Standard Model made using the Gfitter package. This uses the information about the Higgs mass available directly from Higgs searches at LEP and now the Tevatron, and indirectly from precision electroweak data. We find that the ‘blow-up’ scenario is disfavoured at the 99% confidence level (96% without the Tevatron exclusion), whereas the ‘survival’ and possible ‘metastable’ scenarios remain plausible. A future measurement of the mass of the Higgs boson could reveal the fate of the Standard Model.     

Higgs boson properties in the Standard Model and its supersymmetric extensions

We review the realization of the Brout–Englert–Higgs mechanism in the electroweak theory and describe the experimental and theoretical constraints on the mass of the single Higgs boson expected in the minimal Standard Model. We also discuss the couplings of this Higgs boson and its possible decay modes as functions of its unknown mass. We then review the structure of the Higgs sector in the minimal supersymmetric extension of the Standard Model (MSSM), noting the importance of loop corrections to the masses of its five physical Higgs bosons. Finally, we discuss some non-minimal models. To cite this article: J. Ellis et al., C. R. Physique 8 (2007).     

Precise prediction for the mass of the lightest Higgs boson in the MSSM

The leading diagrammatic two-loop corrections are incorporated into the prediction for the mass of the lightest Higgs boson, m_h, in the Minimal Supersymmetric Standard Model (MSSM). The results, containing the complete diagrammatic one-loop corrections, the new two-loop result and refinement terms incorporating leading electroweak two-loop and higher-order QCD contributions, are discussed and compared with results obtained by renormalization group calculations. Good agreement is found in the case of vanishing mixing in the scalar quark sector, while sizable deviations occur if squark mixing is taken into account.     

Higgs bosons in nonlinearly realized supersymmetry

Using the formatlism developed by Samuel and Wess a general form of the Higgs potential in nonlinearly realized supersymmetric extention of the Standard Model in curved space is constructed. In flat space limit we derive bounds for Higgs boson masses and mass relations. Comparisons to the linear supersymmetric models MSSM and NMSSM are made.     

The Higgs boson: shall we see it soon or is it still far away?

The status of the Higgs boson mass in the Standard Model and its supersymmetric extensions is reviewed and the perspectives of Higgs searches are discussed. The parameter space of the Minimal Supersymmetric Standard Model (MSSM) is analysed with the emphasis on the lightest Higgs mass. The infrared behaviour of renormalization group equations for the parameters of MSSM is examined and infrared quasi-fixed points are used for the Higgs mass predictions. They strongly suggest the Higgs mass to be lighter than 100 or 130 GeV for low and high tan β scenarios, respectively. Extended models, however, allow one to increase these limits for low tan β up to 50%.     

Search for Higgs bosons in {\rm e^+e^-} collisions at 183 GeV

The data collected by the OPAL experiment at GeV were used to search for Higgs bosons which are predicted by the Standard Model and various extensions, such as general models with two Higgs field doublets and the Minimal Supersymmetric Standard Model (MSSM). The data correspond to an integrated luminosity of approximately 54 pb. None of the searches for neutral and charged Higgs bosons have revealed an excess of events beyond the expected background. This negative outcome, in combination with similar results from searches at lower energies, leads to new limits for the Higgs boson masses and other model parameters. In particular, the 95% confidence level lower limit for the mass of the Standard Model Higgs boson is 88.3 GeV. Charged Higgs bosons can be excluded for masses up to 59.5 GeV. In the MSSM, GeV and GeV are obtained for , no and maximal scalar top mixing and soft SUSY-breaking masses of 1 TeV. The range is excluded for minimal scalar top mixing and GeV. More general scans of the MSSM parameter space are also considered. Received: 27 October 1998 / Published online: 19 February 1999     

Gauge symmetry and supersymmetry in the Higgsless standard model

The group SO(6) ⊗ SO(5) is shown to be the gauge group as well as supersymmetry group of a four dimensional superstring model. Here, we discuss how supersymmetry is realised in 4-dimensions and further, we successfully reproduce the gauge symmetry results. Using the SO(6) ⊗ SO(5) group, all the known aspects of the string theory are obtained. The model reduces to the Standard Model which has the capability of containing the ingredients of a successful theory of the present day physics. However, there are no Higgs in the model.     

Search for neutral Higgs bosons in Z0 decays using the OPAL detector at LEP

A search for neutral Higgs bosons has been performed using the full sample of Z⁰ decays collected by the OPAL detector at LEP up to 1995. The data were taken at centre-of-mass energies between 88 GeV and 95 GeV and correspond to an integrated luminosity of approximately 160 pb^?1. The present search addresses the processes Z⁰→H⁰Z* and h⁰Z*, where H⁰ is the Higgs boson predicted by the Standard Model and h⁰ the lightest neutral scalar Higgs boson predicted in the framework of the Minimal Supersymmetric Standard Model. For the virtual Z⁰ boson, Z*, the following decay channels are considered: Z*→vv?, e⁺e^? and μ⁺μ^?. Two candidate events have been found in the vv?H⁰ channel and one in the μ⁺μ^?H⁰ channel. Combined with earlier searches, the present search excludes the SM Higgs boson, at the 95% confidence level (CL), from the mass range below 59.6 GeV. In the framework of the Minimal Supersymmetric Standard Model, allowing a wide range of variation for most relevant model parameters, a 95% CL lower limit of 44.3 GeV is obtained for the mass of the h⁰ boson. Combined with earlier direct searches for the Higgs boson pair production process Z⁰→h⁰A⁰ and with measurements of the Z⁰ line shape, a 95% CL lower limit of 23.5 GeV is obtained for the mass of the pseudoscalar Higgs boson A⁰, assuming tan β≥ 1.     

Effective two Higgs doublets in nonminimal supersymmetric models

The Higgs sectors of supersymmetric extensions of the Standard Model have two doublets in the minimal version (MSSM), and two doublets plus a singlet in two others: with (UMSSM) and without (NMSSM) an extra U(1)′. A very concise comparison of these three models is possible if we assume that the singlet has a somewhat larger breaking scale compared to the electroweak scale. In that case, the UMSSM and the NMSSM become effectively two-Higgs-doublet models (THDM), like the MSSM. In this approach the well-known upper mass bounds on the lightest CP-even neutral Higgs boson can be derived in a very simple and transparent way.     

Standard Model without elementary scalars and high energy Lorentz violation

If Lorentz symmetry is violated at high energies, interactions that are usually non-renormalizable can become renormalizable by weighted power counting. Recently, a CPT invariant, Lorentz violating extension of the Standard Model containing two scalar-two fermion interactions (which can explain neutrino masses) and four fermion interactions (which can explain proton decay) was proposed. In this paper we consider a variant of this model, obtained suppressing the elementary scalar fields, and argue that it can reproduce the known low-energy physics. In the Nambu–Jona-Lasinio spirit, we show, using a large N _c expansion, that a dynamical symmetry breaking takes place. The effective potential has a Lorentz invariant minimum and the Lorentz violation does not reverberate down to low energies. The mechanism generates fermion masses, gauge-boson masses and scalar bound states, to be identified with composite Higgs bosons. Our approach is not plagued by the ambiguities of approaches based on non-renormalizable vertices. The low-energy effective action is uniquely determined and predicts relations among parameters of the Standard Model.     

Top quark mass in exophobic Pati-Salam heterotic string model

We analyse the phenomenology of an exemplary exophobic Pati-Salam heterotic string vacuum, in which no exotic fractionally charged states exist in the massless string spectrum. Our model also contains the Higgs representations that are needed to break the gauge symmetry to that of the Standard Model and to generate fermion masses at the electroweak scale. We show that the requirement of a leading mass term for the heavy generation, which is not degenerate with the mass terms of the lighter generations, places an additional strong constraint on the viability of the models. In many models a top quark Yukawa may not exist at all, whereas in others two or more generations may obtain a mass term at leading order. In our exemplary model a mass term at leading order exist only for one family. Additionally, we demonstrate the existence of supersymmetric F- and D-flat directions that give heavy mass to all the colour triplets beyond those of the Standard Model and leave one pair of electroweak Higgs doublets light. Hence, below the Pati-Salam breaking scale, the matter states in our model that are charged under the observable gauge symmetries, consist solely of those of the Minimal Supersymmetric Standard Model.     

Is it possible to estimate the Higgs mass from the CMB power spectrum?

General Relativity and Standard Model are considered as a theory of dynamical scale symmetry with definite initial data compatible with the accepted Higgs mechanism. In this theory the Early Universe behaves like a factory of electroweak bosons and Higgs scalars, and it gives a possibility to identify three peaks in the Cosmic Microwave Background power spectrum with the contributions of photonic decays and annihilation processes of primordial Higgs, W and Z bosons in agreement with the QED coupling constant, Weinberg’s angle, and Higgs’ particle mass of about 118 GeV. The text was submitted by the authors in English.     

Chargino decays in the complex MSSM: a full one-loop analysis

We evaluate two-body decay modes of charginos in the Minimal Supersymmetric Standard Model with complex parameters (cMSSM). Assuming heavy scalar quarks we take into account all decay channels involving charginos, neutralinos, (scalar) leptons, Higgs bosons and Standard Model gauge bosons. The evaluation of the decay widths is based on a full one-loop calculation including hard and soft QED radiation. Special attention is paid to decays involving the Lightest Supersymmetric Particle (LSP), i.e. the lightest neutralino, or a neutral or charged Higgs boson. The higher-order corrections of the chargino decay widths involving the LSP can easily reach a level of about ±10%, while the corrections to the decays to Higgs bosons are slightly smaller, translating into corrections of similar size in the respective branching ratios. These corrections are important for the correct interpretation of LSP and Higgs production at the LHC and at a future linear e ⁺ e ⁻ collider. The results will be implemented into the Fortran code FeynHiggs.