Renormalization group evolution of the CKM matrix

We compute the renormalization of the complete CKM matrix in the scheme and perform a renormalization group analysis of the CKM parameters. The calculation is simplified by studying only the Higgs sector, which for the -function of the CKM matrix is at one loop the same as in the full Standard Model. The renormalization group flow including QCD corrections can be computed analytically using the hierarchy of the CKM parameters and the large mass differences between the quarks. While the evolution of the Cabibbo angle is tiny and increase sizably. We compare our results with the ones in the full Standard Model. Received: 24 October 1998 / Revised version: 16 February 1999 / Published online: 15 April 1999     

An estimate of the Higgs boson mass in two loop approximation in a noncommutative differential geometry

An estimation of the Higgs boson mass is performed by numerically solving the renormalization group equations in the two loop approximation based on the condition for SU(2), U(1) gauge and the Higgs quartic coupling constants, respectively. This condition is introduced in the new scheme of our noncommutative differential geometry (NCG) for the reconstruction of the standard model. However, contrary to GUT without supersymmetry, the grand unification of coupling constants is not realized in this scheme. The physical mass of the Higgs boson depends strongly on the top quark mass through the Yukawa coupling of the top quark in the functions. The two loop effect lowers the numerical value calculated within the one loop approximation by several GeV. The Higgs boson mass varies from 150.93 GeV to 167.96 GeV corresponding to . We find GeV for GeV and GeV for GeV. Received: 16 July 1997 / Published online: 23 February 1998     

Higgs bosons in the left–right model

The model with the gauge group, containing one bidoublet and two triplets in the Higgs sector, is considered. The link between the constants determining the physical Higgs boson interactions and the neutrino oscillation parameters is found. It is shown that the observation of the ultrahigh-energy neutrinos with the help of the processes , gives us information on the singly charged Higgs bosons. The processes of the doubly charged Higgs bosons production, , are investigated. From the point of view of detecting the neutral Higgs bosons the process of the electron–muon recharge is studied. Received: 29 January 1999 / Revised version: 20 September 1999 / Published online: 3 February 2000     

The b \to X_s \gamma rate and Higgs boson limits in the constrained minimal supersymmetric model

New NLO calculations have become available using resummed radiative corrections. Using these calculations we perform a global fit of the supergravity inspired constrained minimal supersymmetric model. We find that the resummed calculations show similar constraints as the LO calculations, namely that only with a relatively heavy supersymmetric mass spectrum of (1 TeV) the b– Yukawa unification and the rate can coexist in the large scenario. The resummed calculations are found to reduce the renormalization scale uncertainty considerably. The low scenario is excluded by the present Higgs limits from LEP II. The constraint from the Higgs limit in the plane is severe, if the trilinear coupling at the GUT scale is fixed to zero, but is considerably reduced for . The relatively heavy SUSY spectrum required by corresponds to a Higgs mass of GeV in the CMSSM. Received: 14 February 2001 / Revised version: 22 March 2001 / Published online: 29 June 2001     

An efficient renormalization group improved implementation of the MSSM effective potential

In the context of MSSM, a novel improving procedure based on the renormalization group equation is applied to the effective potential in the Higgs sector. We focus on the one-loop radiative corrections computed in Landau gauge by using the mass independent renormalization scheme . Thanks to the decoupling theorem, the well-known multimass scale problem is circumvented by switching to a new effective field theory every time a new particle threshold is encountered. We find that, for any field configuration, there is a convenient renormalization scale at which the loop expansion respects the perturbation series hierarchy and the theory retains the vital property of stability. Received: 31 August 1999 / Revised version: 22 March 2000 / Published online: 23 October 2000     

Constraints on the Higgs boson mass from direct searches and precision measurements

We combine, within the framework of the standard model, the results of Higgs search experiments with the information coming from an accurate theoretical calculation and precision measurements to provide a probability density function for the Higgs mass, from which all numbers of interest can be derived. The expected value is around 160–170 GeV, with an expectation uncertainty, quantified by the standard deviation of the distribution, of about 60–80 GeV. The median of the distribution is 150 GeV, while 75% of the probability is concentrated in the region GeV. The 95% probability upper limit turns out to be around 300 GeV. Received: 18 February 1999 / Published online: 28 September 1999     

Implications of the precision data for very light Higgs Boson scenarios in 2HDM(II)

We present an up-to-date analysis of the constraints the precision data impose on the (CP-conserving) Two Higgs Doublet Model of type II with emphasis on the possible existence of very light neutral (pseudo)scalar Higgs boson with mass below 20–30 GeV. We show that even in the presence of such light particles, the 2HDM(II) can describe the electroweak data with the precision comparable to that given by the SM. Particularly interesting lower limits on the mass of the lighter neutral CP-even scalar are obtained in the scenario with light CP-odd Higgs boson and large . Received: 8 June 1999 / Published online: 14 October 1999     

(Non)decoupling of the Higgs triplet effects

We consider the electroweak theory with an additional Higgs triplet at one loop, using the hybrid renormalization scheme based on α_EM, G_F and M_Z as input observables. We show that in this scheme loop corrections can in a natural way be split into a standard model part and corrections due to “new physics”. The latter, however, do not decouple in the limit of an infinite triplet mass parameter, if the triplet trilinear coupling to the SM Higgs doublets grows with the triplet mass. For electroweak observables computed at one loop this effect can be attributed to the radiative generation in this limit of a nonvanishing vacuum expectation value of the triplet. We also point out that whenever tree level expressions for the electroweak observables depend on vacuum expectation values of scalar fields other than the standard model Higgs doublet, a tadpole contribution to the “oblique” parameter T should in principle be included. The origin of nondecoupling is discussed also on the basis of symmetry principles in a simple scalar field theory.     

Quantum effects on t\rightarrow H^{+}\,b in the MSSM: a window to “virtual” supersymmetry?

We analyze the one-loop effects (strong and electroweak) on the unconventional top quark decay mode within the MSSM. The results are presented in the on-shell renormalization scheme with a physically well motivated definition of . The study of this process at the quantum level is useful to unravel the potential supersymmetric nature of the charged Higgs emerging from that decay. As compared with the standard mode , the corrections to are large, slowly decoupling and persist at a sizeable level even for all sparticle masses well above the LEP 200 discovery range. As a matter of fact, the potential size of the SUSY effects, which amount to corrections of several ten percent, could counterbalance the standard QCD corrections and even make them to appear with the “wrong” sign. Therefore, if the charged Higgs decay of the top quark is kinematically allowed – a possibility which is not excluded by the existing measurements of the branching ratio at the Tevatron – it could be an invaluable laboratory to search for “virtual” supersymmetry. While a first significant test of these effects could possibly be performed at the upgraded Tevatron, a more precise verification would most likely be carried out in future experiments at the LHC. Received: 18 April 1997 / Revised version: 18 June 1997     

The Higgs sector of the minimal supersymmetric standard model including radiative corrections

We discuss the Higgs sector of the minimal supersymmetric standard model including effects of radiative corrections. The formalism is explained in detail for computing radiative corrections to the masses and the coupling constants of the Higgs bosons. The radiative corrections to the masses are studied in the on-shell renormalization scheme. The radiative corrections to the mixing angles between the two CP-even Higgs bosons and the Higgs self-coupling constants are investigated in a simple procedure. The explicit analytic expressions are given for the radiative corrections due to the loops containing the top and bottom quarks and their superpartners. Simple approximate formulae are derived from the analytic expressions obtained in the on-shell renormalization scheme. We numerically study the effects of radiative corrections on the mass of the lighter Higgs boson and the mixing angles between the two CP-even Higgs bosons.     

Renormalization and symmetry conditions in supersymmetric QED

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov–Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms. Received: 23 July 1999 / Published online: 14 October 1999     

Low-energy vortex dynamics in Abelian Higgs systems

The low-energy dynamics of the vortices of the Abelian Chern–Simons–Higgs system is investigated from the adiabatic approach. The difficulties involved in treating the field evolution as motion on the vortex moduli space in this system are shown. Another two generalized Abelian Higgs systems are discussed with respect to their vortex dynamics at the adiabatic limit. The method works well, and we find bound states in the first model and scattering at right angles in the second system. Received: 9 October 1998 / Revised version: 12 December 1998 / Published online: 18 June 1999     

Renormalization group estimate of the hadronic decay width of the Higgs boson

The total hadronic decay width of the Weinberg-Salam type Higgs boson is estimated in QCD for the Higgs boson mass much larger than the ordinary hadronic mass scale, by use of the operator product expansion and renormalization group equation. We give an explicit formula for the decay width in terms of quark masses including strong interaction corrections up to the next-to-leading order. A numerical analysis of the hadronic decay width of the Higgs boson is made in the six-quark model. The next-to-leading order correction is found to be significant, e.g., 30-20% of the leading term for m_H of oue interest, m_H ? 1 TeV. Application of our scheme to the decay rates of heavy Higgs bosons of other types is also discussed.     

The one-loop renormalization of the MSSM Higgs sector and its application to the neutral scalar Higgs masses

The structure of the Higgs sector in the minimal supersymmetric standard model is reviewed at the oneloop level. An on-shell renormalization scheme of the MSSM Higgs sector is presented in detail together with the complete list of formulae for the neutral Higgs masses at the one-loop level. The results of a complete one-loop calculation for the mass spectrum of the neutral MSSM Higgs bosons and the quality of simpler Born-like approximations are discussed for sfermion and gaugino masses in the range of the electroweak scale.     

Two-loop renormalization group restrictions on the standard model and the fourth chiral family

In the framework of the two-loop renormalization group, the restrictions on the Higgs mass from the electroweak vacuum stability and from the absence of the strong coupling are refined, while the more precise value of the top mass is taken into account. When the SM cutoff is equal to the Planck scale, the Higgs mass must be GeV and GeV, where the corridor is the theoretical one and the errors are due to the top-mass uncertainty. The SM two-loop functions are generalized to the case with massive neutrinos from extra families. The requirement of self-consistency of the perturbative SM as an underlying theory up to the Planck scale excludes a fourth chiral family. Under the precision-experiment restriction GeV, the fourth chiral family, if alone, is excluded even when the SM is regarded as an effective theory. Nevertheless a pair of chiral families constituting a vector-like one could exist. Received: 2 September 1998 / Revised version: 4 January 1999 / Published online: 28 September 1999     

Determining SUSY parameters in chargino pair-production in e^+e^- collisions

In most supersymmetric theories, charginos , mixtures of charged color-neutral gauginos and higgsinos, belong to the class of the lightest supersymmetric particles. They are easy to observe at colliders. By measuring the total cross sections and the left–right asymmetries with polarized electron beams in , the chargino masses and the gaugino–higgsino mixing angles can be determined. From these observables the fundamental SUSY parameters can be derived: the SU(2) gaugino mass , the modulus and of the higgsino mass parameter, and , the ratio of the vacuum expectation values of the two neutral Higgs doublet fields. The solutions are unique; the CP-violating phase can be determined uniquely by analyzing effects due to the normal polarization of the charginos. Received: 3 December 1998 / Published online: 27 April 1999     

A generalized Slavnov-invariant Abelian Higgs-Kibble model

The supersymmetric structure of the Becchi-Rouet-Stora invariance is used for investigating the Abelian Higgs-Kibble model. It allows for a symmetric photon mass M, in which case a massless scalar state corresponding to the Goldstone model belongs to the physical sector. If M = 0, i.e. the photon mass is generated by the Higgs mechanism, this state is decoupled from the physical sector, as usual. The BPHZ renormalization procedure is used.     

Masses and couplings of the lightest Higgs bosons in (M + 1)SSM

We study the upper limits on the mass of the lightest and second lightest CP even Higgs bosons in the (M + 1)SSM, the MSSM extended by a gauge singlet. The dominant two loop contributions to the effective potential are included, which reduce the Higgs masses by GeV. Since the coupling R of the lightest Higgs scalar to gauge bosons can be small, we study in detail the relations between the masses and couplings of both lightest scalars. We present upper bounds on the mass of a ”strongly” coupled Higgs (R < 1/2) as a function of lower experimental limits on the mass of a ”weakly” coupled Higgs (R < 1/2). With the help of these results, the whole parameter space of the model can be covered by Higgs boson searches. Received: 7 September 1999 / Published online: 12 July 2002     

平流扩散差分方程的新正定性重整化方案设计和试验

质量守恒是平流扩散差分方程所必须满足的基本性质,但是由于差分格式不具有正定性(positive-definite),因此在积分过程中负质量的产生会导致总质量不守恒.针对这一问题,本文从负质量产生的物理意义出发,提出了一个简单有效的新正定性重整化方案,通过点源平流扩散试验表明,该方案不但解决了平流扩散差分方程的正定性问题,同时保证了总质量守恒性.与WRF模式中采用的"重整化方案"相比,具有物理含义清楚、并且简单易行的优点.