Gaussian effective potential for the U(1) Higgs model

In order to investigate the Higgs mechanism nonperturbatively, we compute the Gaussian effective potential of the U(1) Higgs model (“scalar electrodynamics”). We show that the same simple result is obtained in three different formalisms. A general covariant gauge is used, with Landau gauge proving to be optimal. The renormalization generalizes the “autonomous” renormalization for λ?⁴ theory and requires a particular relationship between the bare gauge coupling e _B and the bare scalar self-coupling λ _B. When both couplings are small, then λ is proportional to e⁴ and the scalar/vector mass-squared ratio is of order e², as in the classic 1-loop analysis of Coleman and Weinberg. However, as λ increases, e reaches a maximum value and then decreases, and in this “nonperturbative” regime the Higgs scalar can be much heavier than the vector boson. We compare our results to the autonomously renormalized 1-loop effective potential, finding close agreement in the physical predictions. The main phenomenological implication is a Higgs mass of about 2 TeV.     

Space-time geometry and symmetry breaking

We look for solutions of the Einstein-Yang-Mills equations in a 4 + D dimensional space-time. We find solutions where the first 4 dimensions are a flat Minkowskian space-time, while the D others are a compact, space-like manifold of small size. Such solutions can be obtained for an arbitrary compact gauge group K and are invariant under a sub-group G of K related to the space-time geometry. This shows that 4 + D dimensional gravity can give a mechanism for the super-strong symmetry breaking needed in grand unified field theories without introducing Higgs scalars.     

Virtual effects of Higgs particles

The possibility of observing Higgs particles through virtual effects is considered in detail for a general gauge theory. The effect of charged Higgs particles on low-energy weak interaction processes, like muon decay, tau decay, nuclear beta decay, pion decay, and some higher-order processes is analyzed. The effect of flavor-changing neutral Higgs particles on rare decay modes of the muon and kaon, μe conversion, K^o-$\text{K}$^o and D^o-$\text{D}$^o mixing is also studied. We discuss constraints on possible extensions of the Weinberg-Salam model and experiments sensitive to their Higgs particles. In particular, we analyze the neutral Higgs which couple to fermions in the minimal SU(2)_L×SU(2)_R×U(1) model and find that they probably have mass greater than 100 GeV.     

Loop induced flavor changing neutral decays of the top quark in a general two-Higgs-doublet model

Decays of the top quark induced by flavor changing neutral currents (FCNC) are known to be extremely rare events within the Standard Model. This is so not only for the decay modes into gauge bosons, but most notably in the case of the Higgs channels, e.g., t→H_SM+c, with a branching fraction of 10⁻¹³ at most. Therefore, detection of FCNC top quark decays in a future high-energy, and high-luminosity, machine like the LHC or the LC would be an indisputable signal of new physics. In this paper we show that within the simplest extension of the SM, namely the general two-Higgs-doublet model, the FCNC top quark decays into Higgs bosons, t→(h⁰,H⁰,A⁰)+c, can be the most favored FCNC modes — comparable or even more efficient than the gluon channel t→g+c. In both cases the optimal results are obtained for Type II models. However, only the Higgs channels can have rates reaching the detectable level (10⁻⁵), with a maximum of order 10⁻⁴ which is compatible with the charged Higgs bounds from radiative B-meson decays. We compare with the previous results obtained in the Higgs sector of the MSSM.     

Solar neutrinos in models involving an extended Higgs sector

Neutrino oscillations in matter and in a magnetic field are investigated within models involving an extended Higgs sector. The left-right model containing a bidoublet and two triplets of Higgs fields (LRM) and the general two-Higgs-doublet model (GTHDM) are chosen by way of example. It is shown that the interaction of leptons with physical Higgs bosons can substantially change the pattern of oscillations in these models in relation to the predictions of the Standard Model (SM). Upper limits on the Yukawa coupling constants and on the Higgs boson masses are found in order to obtain maximum corrections to the SM solar-matter potential V ^SM. By using constraints on these parameters from the literature and those that are obtained here, it is possible to estimate corrections to V ^SM that come exclusively from charged Higgs bosons. The maximum value of these corrections is 40% of V ^SM within the LRM and 10% of V ^SM within the GTHDM. The entire body of information about the contributions of physical Higgs bosons to the solar-matter potential can be obtained by studying the Lorentz structure of the amplitudes for the reactions e ^? ν _l → e ^? ν _l′ at low energies.     

Review of searches for Higgs bosons and beyond the Standard Model Physics at the Tevatron

The energy frontier is currently at the Fermilab Tevatron accelerator, which collides protons and antiprotons at a center-of-mass energy of 1.96 TeV. The luminosity delivered to the CDF and DØ experiments has now surpassed the 4 fb^?1. This paper reviews the most recent direct searches for Higgs bosons and beyond-the-standard-model (BSM) physics at the Tevatron. The results reported correspond to an integrated luminosity of up to 2.5 fb^?1 of Run II data collected by the two Collaborations. Searches covered include the standard model (SM) Higgs boson (including sensitivity projections), the neutral Higgs bosons in the minimal supersymmetric extension of the standard model (MSSM), charged Higgs bosons and extended Higgs models, supersymmetric decays that conserve or violate R-parity, gauge-mediated supersymmetric breaking models, long-lived particles, leptoquarks, compositeness, extra gauge bosons, extra dimensions, and finally signature-based searches. Given the excellent performance of the collider and the continued productivity of the experiments, the Tevatron physics potential looks promising for discovery with the coming larger data sets. In particular, evidence for the SM Higgs boson could be obtained if its mass is light or near 160 GeV. The observed (expected) upper limits are currently a factor of 3.7 (3.3) higher than the expected SM Higgs boson cross section at m _H =115 GeV and 1.1 (1.6) at m _H =160 GeV at 95% C.L.     

Type IIB Green-Schwarz superstrings in AdS 5 × S 5 from the supercoset approach

We consider superstrings moving in the AdS ₅ × S ⁵ space-time and find their Green-Schwarz action using the supercoset approach based on the supergroup PSU(2, 2|4). We describe several parametrizations of the relevant supercoset and present the action in different κ-symmetry gauges. In particular, we discuss a gauge where all the fermionic coordinates corresponding to the conformal (S) supercharges are gauged away and also a light-cone type gauge where half of the Q and S supercoordinates are gauged away. The resulting action contains terms that are quadratic and quartic in fermions. In the flat-space limit, it reduces to the standard light-cone Green-Schwarz action. We comment on the possibility of fixing the bosonic light-cone gauge and of reformulating the action in terms of two-dimensional Dirac spinors.     

Induced Higgs couplings to neutral bosons in e+e− collisions

We calculate induced couplings of the type HV_γ in the standard model, where H is a Higgs meson and V is a virtual or real neutral gauge boson (Z⁰ or photon). Numerous applications are given for e⁺e^? collisions and various Higgs meson decays. The calculated rates are in general somewhat too low to make these processed an attractive way to search for the Higgs boson. However, once it has been found, it is argued that these processes should be studied experimentally since the induced couplings probe the structure of the gauge theory in an interesting way. In particular, it may be possible to infer the existence of one or more heavy fermion generations (of mass ?m_Z) by observing their virtual effects in radiative decays into Higgs particles. We also briefly treat the related coupling HV_γ with V a heavy quarkonium vector state.     

Neutral currents within beyond the standard model

We present new, model-independent analyses of the observables in low-energy neutral-current experiments in the neutrino-hadron, neutrino-electron, electron/muon-hadron and electron- muon/tau sectors. We combine them with the latest experimental measurements of the W and Z masses to make global fits in the context of the standard model and of superstring-inspired models. We find in the standard model that sin ²θ _w = 0.228 ± 0.004 if ϱ is fixed to be 1, whilst a two parameter fit yields sin ²θ _w = 0.229 ± 0.006 and ϱ = 1.001 ± 0.007. This new value of sin ²θ _w for ϱ = 1 lies uncomfortably outside the predicted region of the minimal SU(5) model, but is consistent with supersymmetric SU(5) models. In the minimal standard model with ϱ = 1 and equal Higgs and Z masses we find that m_t<168 GeV at the 90% confidence level. We establish lower bounds on the masses of additional neutral gauge bosons Z′ in three superstring-inspired models and upper limits on their mixing with the standard model Z ⁰. In particular, we find that m_Z′129 GeV at the 90% confidence level in a minimal rank-5 superstring-inspired model with canonical Higgs structure.     

Higgs boson physics in the s-channel at μ+μ− colliders

Techniques and strategies for discovering and measuring the properties of Higgs bosons via s-channel production at a μ⁺μ⁻ collider, and the associated requirements for the machine and detector, are discussed in detail. The unique feature of s-channel production is that, with good energy resolution, the mass, total width and partial widths of a Higgs boson can be directly measured with remarkable accuracy in most cases. For the expected machine parameters and luminosity the standard model (SM) Higgs boson h_SM, with mass ≲ 2m_W, the light h⁰ of the minimal supersymmetric standard model (MSSM), and the heavier MSSM Higgs bosons (the CP-odd A⁰ and the CP-even H⁰) can all be studied in the s-channel, with the heavier states accessible up to the maximal √s over a large fraction of the MSSM parameter space. In addition, it may be possible to discover the A⁰ and H⁰ by running the collider at full energy and observing excess events in the bremsstrahlung tail at lower energy. The integrated luminosity, beam resolution and machine/detector features required to distinguish between the h_SM and h⁰ are delineated.     

Strong and electroweak interactions and their unification with non-commutative space-time

Quantum field theories based on non-commutative space-time (NCQFT) have been extensively studied recently. However no NCQFT model which can uniquely describe the strong and electroweak interactions has been constructed. This prevents one to make a consistent and systematic study of non-commutative space-time. In this work we construct a NCQFT model based on the trinification gauge group . A unique feature of this model, that all matter fields (fermions and Higgs bosons) are assigned to (anti-) fundamental representations of the factor SU(3) groups, allows us to construct a NCQFT model for strong and electroweak interactions and their unification without ambiguities. This model provides an example which allows one to make a consistent and systematic study of non-commutative space-time phenomenology. We also comment on some related issues regarding extensions to E₆ and models. Received: 18 September 2002 / Revised version: 21 February 2003 / Published online: 5 May 2003     

Z′ mass limits,masses and coupling of higgs bosons,and Z′ decays in an E6 superstring based model

We demonstrate that current phenomenological constraints on Z-Z′ mixing for an E₆ grand unified group with low energy gauge group SU(2)_L×U(1)_Y×U(1)_Y, allow only a narrow range of Higgs vacuum expectation values consistent with possibilities favored by renormalization group expectations. Modest improvements in bounds on this mixing will lead to substantial bounds on the Z′ mass if alternative renormalization group solutions are not found. We then explore the constraints upon relations between Higgs masses in this model. In addition we explore the couplings of these Higgs to the gauge particles of the theory and emphasize the associated implications for Higgs detection in decays of the Z′.     

Heavy SUSY Higgs bosons at e + e − linear colliders

The production mechanisms and decay modes of the heavy neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model are investigated at future e ⁺ e ^? colliders in the TeV energy regime. We generate supersymmetric particle spectra by requiring the MSSM Higgs potential to produce correct radiative electroweak symmetry breaking, and we assume a common scalar mass m₀, gaugino mass m_1/2 and trilinear coupling A, as well as gauge and Yukawa coupling unification at the Grand Unification scale. Particular emphasis is put on the low tan β solution in this scenario where decays of the Higgs bosons to Standard Model particles compete with decays to supersymmetric charginos/neutralinos as well as sfermions. In the high tan β case, the supersymmetric spectrum is either too heavy or the supersymmetric decay modes are suppressed, since the Higgs bosons decay almost exclusively into b and τ pairs. The main production mechanisms for the heavy Higgs particles are the associated AH production and H ⁺H^? pair production with cross sections of the order of a few fb.     

ZN Gauge theories on a lattice and quantum memory

In the present paper we shall study (2+1)-dimensional Z_N gauge theories on a lattice. It is shown that the gauge theories have two phases, one is a Higgs phase and the other is a confinement phase. We investigate low-energy excitation modes in the Higgs phase and clarify relationship between the Z_N gauge theories and Kitaev’s model for quantum memory and quantum computations. Then we study effects of random gauge couplings (RGC) which are identified with noise and errors in quantum computations by Kitaev’s model. By using a duality transformation, it is shown that time-independent RGC give no significant effects on the phase structure and the stability of quantum memory and computations. Then by using the replica methods, we study Z_N gauge theories with time-dependent RGC and show that nontrivial phase transitions occur by the RGC.     

Effective potential methods and the Higgs mass spectrum in the MSSM

We generalize the analytical expressions for the two-loop leading-log neutral Higgs boson masses and mixing angles to the case of general left- and right-handed soft supersymmetry breaking stop and sbottom masses and left-right mixing mass parameters (m_Q, m_U, m_D, A_t, A_b). This generalization is essential for the computation of Higgs masses and couplings in the presence of light stops. At high scales we use the minimal supersymmetric standard model effective potential, while at low scales we consider the two-Higgs doublet model (renormalization group improved) effective potential, with general matching conditions at the thresholds where the squarks decouple. We define physical (pole) masses for the top quark, by including QCD self-energies, and for the neutral Higgs bosons, by including the leading one-loop electroweak self-energies where the top/stop and bottom/sbottom sectors propagate. For m_Q = m_U = m_D and moderate left-right mixing mass parameters, for which the mass expansion in terms of renormalizable Higgs quartic couplings is reliable, we find excellent agreement with previously obtained results.     

A disorder parameter that test for confinement in gauge theories with quark fields

We propose to use a suitably defined vortex free energy as a disorder parameter in gauge field theories with matter fields. It is supposed to distinguish between the confinement phase, massless phase(s) and Higgs phase where they exist. The matter fields may transform according to an arbitrary representation of the gauge group. We compute the vortex free energy by series expansion for a Z₂ Higgs model and for SU(2) lattice models with quark or Higgs fields in the fundamental representation at strong coupling (confinement phase), and for the Z₂ Higgs model in the range of validity of low-temperature expansions (Higgs phase). The results are in agreement with the expected behavior.     

A numerical estimate of the upper limit for the Higgs boson mass

TheSU (2) Higgs model with a scalar doublet field is studied by Monte Carlo calculations on 12⁴ and 16⁴ lattices. The gauge coupling is chosen to be similar in magnitude to the physical value in the standard model. The numerical results at large scalar self-coupling imply an upper limitm _H /m _W ?9 for the ratio of the Higgs boson mass to the W-mass.     

Anomalous magnetic moment of the muon in the left-right model

The effect of Higgs bosons on the anomalous magnetic moment of the muon is considered within the model that is based on the SU(2)_L×SU(2)_R×U(1)_B–L gauge group and which involves a bidoublet and two triplets of Higgs fields (left-right model). For the Yukawa coupling constants and the masses of Higgs bosons, the regions are found where the model leads to agreement with experimental results obtained at the Brookhaven National Laboratory (BNL) for the anomalous magnetic moment of the muon. In order to explore corollaries from the constraints obtained for the parameters of the Higgs sector, the processes e⁺e^? → μ⁺μ^?, τ⁺τ^? and μ⁺μ^? → μ⁺μ^?, τ⁺τ^? are considered both within the left-right model and within the model involving two Higgs doublets (two-Higgs-doublet model). It is shown that, if the mass of the lightest neutral Higgs boson does indeed lie in the range 3.1–10 GeV, as is inferred from the condition requiring the consistency of the two-Higgs-doublet model with the data of the BNL experiment, this Higgs boson may be observed as a resonance peak at currently operating e⁺e^? colliders (VEPP-4M, CESR, KEKB, PEP-II, and SLC). In order to implement this program, however, it is necessary to reduce considerably the scatter of energy in the e⁺ and e^? beams used, since the decay width of the lightest neutral Higgs boson is extremely small at such mass values. It is demonstrated that, in the case of the left-right model, for which the mass of the lightest neutral Higgs boson is not less than 115 GeV, the resonance peak associated with it may be detected at a muon collider.     

Deconstruction of gauge symmetry breaking by discrete symmetry and G unification

We deconstruct the non-supersymmetric SU(5) breaking by discrete symmetry on the space-time and in the Higgs mechanism deconstruction scenario. Also we explain the subtle point of how to exactly match the continuum results with the latticized results on the quotient space S ¹ /Z ₂ and . We also propose an effective deconstruction scenario and discuss the gauge symmetry breaking by the discrete symmetry on the theory space in this approach. As an application, we suggest the G^N unification where G^N is broken down to by the bifundamental link fields and the doublet-triplet splitting can be achieved. Received: 10 October 2002 / Revised version: 23 March 2003 / Published online: 13 May 2003 RID="a" ID="a" Current address: School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA e-mail: tli@sns.ias.edu RID="b" ID="b" e-mail: liutao@sas.upenn.edu     

Upper bound estimate for the Higgs mass from the lattice regularized Weinberg-Salam model

There are indications that, as a consequence of the trivality of the scalar φ⁴ theory, the Weinberg-Salam model is massive free field theory. However, considering theWS model as an effective field theory, an upper bound for the Higgs mass can exist. We have studied this phenomenon by simulating the SU(2) gauge Higgs model on a lattice. The results indicate that R_max = m_H/m_W|_max = 9.3 ± 1. However, serious finite size effects make it unfeasible to explore the region m_H ⩽ Λ_cutoff with Monte Carlo simulation.