Renormalization of scalar quartic and Yukawa couplings in unified gauge theories based onE 6

Renormalization group equations for scalar and Yukawa couplings in gauge theories based on the exceptional groupE ₆ are analyzed. Asymptotic freedom is possible only for a limited set of scalar fields, and then only if several fermion generations are present. The infrared behavior of the scalar quartic coupling constants is striking: they are necessarily driven out of the region of positivity of the classical potential. Some useful group theoretic relations inE ₆ are given in an Appendix.     

Renormalization group constraints on unified gauge theories

Renormalization group constraints on the behavior of Yukawa and scalar quartic couplings in unified gauge theories are examined. Yukawa couplings are generally asymptotically free whenever the gauge couplings are, but scalar quartic couplings can be asymptotically free only for simple scalar multiplets in large groups with large fermion content. The infrared behavior of Yukawa and scalar quartic couplings implied by the renormalization group equations has interesting and phenomenologically useful consequences: infrared fixed points (or quasifixed points) lead to bounds on masses of fermions and scalars, while scalar quartic couplings can be driven out of the domain of positivity of the classical potential, with possible implications for patterns of symmetry breaking.     

Two-loop results from improved one loop computations

A nonperturbative method is proposed for the approximative solution of the exact evolution equation which describes the scale dependence of the effective average action. It consists of a combination of exact evolution equations for independent couplings with renormalization group improved one loop expressions of secondary couplings. Our method is illustrated by an example: We compute the β-function of the quartic coupling λ of anO(N) symmetric scalar field theory to order λ³ as well as the anomalous dimension to order λ² using only one loop expressions and find agreement with the two loop perturbation theory. We also treat the case of very strong coupling and confirm the existence of a “triviality bound”.     

A one-loop renormalization group analysis of the Gelmini-Roncadelli model

A one-loop renormalization group analysis is presented of the Gelmini-Roncadelli model of neutrino mass generation via an extended Higgs sector. We are unable to find values for the quartic scalar couplings at the W mass scale which cause the combined Higgs-gauge couplings to evolve to a stable fixed point of the renormalization group. As a consequuence this model may well be “trivial” in the same sense as λφ⁴ theory is believed to be in four dimensions.     

Where to look for solving the gauge hierarchy problem?

A mass of the Higgs boson close to 126 GeV may give a hint that the standard model of particle physics is valid up to the Planck scale. We discuss perspectives for the solution of the gauge hierarchy problem at high scales. Scenarios with an ultraviolet fixed point have predicted a Higgs boson mass very close to 126 GeV if the fixed point value of the quartic scalar coupling is small. In this case the top quark pole mass should be close to 172 GeV.     

Leptoquarks in lepton-quark collisions

Low-energy experiments permit the existence of leptoquarks with masses of order 100 GeV and couplings to quark-lepton pairs as large as gauge couplings. We study systematically the signatures of all possible scalar and vector leptoquarks in electron (positron)-proton collisions. Clear evidence for leptoquarks would be narrow peaks in the x-distributions of inclusive neutral and charged current processes. At HERA one will be able to explore the mass range up to 300 GeV through direct production, and even somewhat beyond the CM energy of 314 GeV through virtual effects. Conversely, leptoquarks with masses of 200 GeV can be discovered for couplings as small as 10⁻³ α_em.     

Two-loop renormalization group equations in a general quantum field theory: (III). Scalar quartic couplings

The two-loop β-functions for the scalar quartic couplings are computed in a general renormalizable quantum field theory with scalar, $\text{spin}\text{-}\text{1}\text{2}$, and (vector) gauge fields associated with a general gauge group G, using dimensional regularization and modified minimal subtraction (^?MS). A more explicit form is given for the two-loop β-function of the quartic coupling of the Higgs doublet in the minimal QCD electroweak theory based on SU(3) × SU(2) × U(1).     

Limits to possible scalar-boson mass and coupling from e+e− collisions

Measurements of e⁺e^? → e⁺e^? at 2.8 GeV are reported and interpreted in terms of limits for the mass and coupling of a possible scalar boson of the type introduced in recent renormalizable models of weak interactions. In particular, in the Georgi-Glashow scheme of leptons we find that the scalar boson mass must be larger than 10 GeV for an m_W = 10 GeV (m_W mass of the W-boson) and of 6.5 GeV for m_W = 15 GeV. Alternatively its coupling is extremely weak.     

A soft origin for CKM-type CP violation

We present a two-Higgs-doublet model, with a Z₃ symmetry, in which CP violation originates solely in a soft (dimension-2) coupling in the scalar potential, and reveals itself solely in the CKM (quark mixing) matrix. In particular, in the mass basis the Yukawa interactions of the neutral scalars are all real. The model has only eleven parameters to fit the six quark masses and the four independent CKM-matrix observables. We find regions of parameter space in which the flavour-changing neutral couplings are so suppressed that they allow the scalars to be no heavier than a few hundred GeV.     

Unifying darko-lepto-genesis with scalar triplet inflation

We present a scalar triplet extension of the standard model to unify the origin of inflation with neutrino mass, asymmetric dark matter and leptogenesis. In presence of non-minimal couplings to gravity the scalar triplet, mixed with the standard model Higgs, plays the role of inflaton in the early Universe, while its decay to SM Higgs, lepton and dark matter simultaneously generate an asymmetry in the visible and dark matter sectors. On the other hand, in the low energy effective theory the induced vacuum expectation value of the triplet gives sub-eV Majorana masses to active neutrinos. We investigate the model parameter space leading to successful inflation as well as the observed dark matter to baryon abundance. Assuming the standard model like Higgs mass to be at 125–126 GeV, we found that the mass scale of the scalar triplet to be ?O(10⁹) GeV$?O({10}^9)\text{GeV}$ and its trilinear coupling to doublet Higgs is ?0.09 so that it not only evades the possibility of having a metastable vacuum in the standard model, but also lead to a rich phenomenological consequences as stated above. Moreover, we found that the scalar triplet inflation strongly constrains the quartic couplings, while allowing for a wide range of Yukawa couplings which generate the CP asymmetries in the visible and dark matter sectors.     

A search for leptoquark bosons and lepton flavor violation in e^+ p collisions at HERA

A search for new bosons possessing couplings to lepton-quark pairs is performed in the H1 experiment at HERA using 1994 to 1997 data corresponding to an integrated luminosity of pb. First generation leptoquarks (LQs) are searched in very high neutral (NC) and charged (CC) current data samples. The measurements are compared to Standard Model (SM) expectations from deep-inelastic scattering (DIS). A deviation in the spectrum previously observed in the 1994 to 1996 dataset at GeV remains, though with less significance. This deviation corresponded to a clustering in the invariant mass spectrum at GeV which is not observed with the 1997 dataset alone. The NC DIS data is used to constrain the Yukawa couplings of first generation scalar and vector LQs in the Buchmüller–Rückl–Wyler effective model. Scalar LQs are excluded for masses up to 275 GeV for a coupling of electromagnetic strength, . A sensitivity to coupling values is established for masses up to 400 GeV for any LQ type. The NC and CC DIS data are combined to constrain for arbitrary branching ratios of the LQ into eq in a generic model. For a decay branching ratio into pairs as small as 10%, LQ masses up to 260 GeV are ruled out for . LQs possessing couplings to mixed fermion generations, which could lead to signals of lepton flavor violation (LFV), are searched in events with a high transverse momentum or . No or event candidate is found that is compatible with LQ kinematics. Constraints are set on the Yukawa coupling involving the and lepton in a yet unexplored mass range. Received: 2 July 1999 / Published online: 28 September 1999     

Signatures of lower-scale gauge coupling unification in the standard model due to extended Higgs sector

The gauge coupling unification can be achieved at a unification scale around 5×10¹³ GeV if the Standard Model scalar sector is extended with extra Higgs-like doublets. The relevant new scalar degrees of freedom in the form of chiral Z* and W* vector bosons might “be visible” already at about 700 GeV. Their eventual preferred coupling to the heavy quarks explains the non observation of these bosons in the first LHC run and provides promising expectation for the second LHC run.     

Radiative corrections to the Higgs potential in the LH model

In this work we compute the radiative corrections to the Higgs mass and the Higgs quartic couplings coming from the Higgs sector itself and the scalar fields φ in the Littlest Higgs (LH) model. The restrictions that the new contributions set on the parameter space of the models are also discussed. Finally, this work, together with our three previous papers, complete our program addressed to compute the relevant contributions to the Higgs low-energy effective potential in the LH model and the analysis of their phenomenological consequences.     

Mass of the Higgs boson in the standard model with four generations

We study the functional behavior of the quartic scalar coupling in the standard model with four generations. From the assumed boundedness of its ratio to theU(1) gauge coupling and the stability of the Higgs potential under radiative corrections, we derive upper and lower bounds on the Higgs-boson mass as functions of the fourth-generation fermion masses. We also obtain a solution in which the Higgs-boson mass is determined as a function of the other masses of the model.     

Spontaneous breakdown of CP in left right symmetric models

We show that it is possible to obtain spontaneous CP violation in the minimal SU(2)_L × SU(2)_R × U(1)_{B -L}, i.e. in a left right symmetric model containing a bidoublet and two triplets in the scalar sector. For this to be a natural scenario, the non-diagonal quartic couplings between the two scalar triplets and the bidoublet play a fundamental role. We analyze the corresponding Higgs spectrum, the suppression of FCNC’s and the manifestation of the spontaneous CP phase in the electric dipole moment of the electron.     

Search for single leptoquark and squark production in electron-photon scattering at $\sqrt{s_{\rm ee}}=189$ GeV at LEP

A search for first generation scalar and vector leptoquarks (LQ) as well as for squarks () in R-parity violating SUSY models with the direct decay of the into Standard Model particles has been performed using ee collisions collected with the OPAL detector at LEP at an ee centre-of-mass energy of 189 GeV. The data correspond to an integrated luminosity of about 160 pb. The dominant process for this search is , where a photon, which has been radiated by one of the beam electrons, serves as a source of quarks. The numbers of selected events found in the two decay channels are in agreement with the expectations from Standard Model processes. This result allows to set lower limits at the 95% confidence level on the mass of first generation scalar and vector leptoquarks, and of squarks in R-parity violating SUSY models. For Yukawa couplings to fermions larger than , the mass limits range from 121 GeV to GeV ( GeV to GeV) depending on the branching ratio of the scalar (vector) leptoquark state. Furthermore, limits are set on the Yukawa couplings for leptoquarks and for squarks, and on as a function of the scalar leptoquark/squark mass. Received: 22 May 2001 / Published online: 25 January 2002     

Grand unification with local supersymmetry

We study general conditions for obtaining spontaneous breaking of local supersymmetry in N = 1 supergravity coupled to supersymmetric matter. We consider in particular the coupling of N = 1 supergravity to grand unified theories like SU(5) and study the conditions which must be met in order to obtain a realistic model. Specific models are built in which local supersymmetry is broken at a scale √M_Wm_p ～ 10¹⁰ GeV. This breaking of supersymmetry is only detected at low energies through soft terms breaking explicitly the global supersymmetry. These soft terms (scalar masses, gaugino masses and trilinear scalar couplings) are renormalized at low energies according to the renormalization group. The (mass)² of the Higgs doublet evolve towards negative values at low energies giving rise to SU(2) × U(1) breaking as a radiative effect of local supersymmetry breaking. We finally point out the possible relevance of non-renormalizable superpotentials for the problem of fermion masses.     

Exploring effects of strong interactions in enhancing masses of dynamical origin

A previous study of the dynamical generation of masses in massless QCD is considered from another viewpoint. The quark mass is assumed to have a dynamical origin and is substituted for by a scalar field without self-interaction. The potential for the new field background is evaluated up to two loops. Expressing the running coupling in terms of the scale parameter μ, the potential minimum is chosen to fix m _top=175 GeV when μ ₀=498 MeV. The second derivative of the potential predicts a scalar field mass of 126.76 GeV. This number is close to the value 114 GeV, which preliminary data taken at CERN suggested to be associated with the Higgs particle. However, the simplifying assumptions limit the validity of the calculations done, as indicated by the large value of a = \frac g²4p=1.077 \alpha=\frac {g^{2}}{4\pi}=1.077 obtained. However, supporting statements about the possibility of improving the scheme come from the necessary inclusion of weak and scalar field couplings and mass counterterms in the renormalization procedure, in common with the seemingly needed consideration of the massive W and Z fields, if the real conditions of the SM model are intended to be approached.     

A scalar-fermion model in the limit of infinitely heavy fermions

As a first step in the non-perturbative study of a chiralU(1)?U(1) Yukawa-model with explicit mirror fermions the limit of infinite bare fermion mass is considered. Non-perturbative information is obtained from 14th order scalar hopping parameter expansion, which is confronted with high statistics numerical data. A remarkable universality of the upper bound for the renormalized quartic coupling is observed. A new kind of first order phase transition surface is localized, which is characterized by a large jump in the average field length.