The Standard Model as a noncommutative geometry: the low-energy regime

We render a thorough, physicist's account of the formulation of the Standard Model (SM) of particle physics within the framework of noncommutative differential geometry (NCG). We work in Minkowski spacetime rather than in Euclidean space. We lay the stress on the physical ideas both underlying and coming out of the noncommutative derivation of the SM, while we provide the necessary mathematical tools. Postdiction of most of the main characteristics of the SM is shown within the NCG framework. This framework, plus standard renormalization technique at the one-loop level, suggest that the Higgs and top masses should verify 1.3 m_top ≲ m_H ≲ 1.73 m_top.     

Correlations and static energies in the standard Higgs model

Correlations in the W-boson and Higgs boson channels and the static energy of an external SU(2) doublet charge pair are investigated by Monte Carlo calculations in the SU(2) lattice gauge theory with a scalar Higgs doublet field. The mass ratio m_W/m_H and the shape of the static potential are used to obtain information on the renormalization group trajectories in the three-dimensional coupling constant space. As a function of an appropriately chosen varibale, the measured quantities are, within errors, independent from the scalar self-coupling (λ) in a wide range 0.1 ⩽ λ ⩽ ∝. In the Higgs phase, a lower bound m_W/m_H ⩾ (1.0 ± 0.3) is obtained for the ratio of the Higgs boson mass to the W-boson mass.     

Associated production of heavy Higgs boson with top quarks

Associated production of a heavy Higgs boson (m_H > 100 GeV) with top quarks at Juratron energies is studied. It is natural to differentiate between the “light” (2m_t < m_H < 2m_W) and “heavy” (m_H > 2m_W) Higgs search. It is assumed that the mass value of the top quarks is in the interval m_t ≈ 30–80 GeV. m_W is the W-boson mass. If m_H < 2m_W a dangerous background is given by the QCD production of four top quarks. We have calculated the cross sections for both the Higgs production and the background reaction. The disappointing result found is that the background is overwhelmingly large. However the Higgs search in this mass region is not hopeless. The associated production of the Higgs boson with a W-boson may have a clear experimental signature, its background given by the reaction $\text{p}\text{+}\text{p}\text{→}\text{W}\text{+}\text{t}\text{+}\text{t}$ might be suppressed. The difficulty with this mechanism is that the rate is rather low. If m_H > 2m_W the background is different and its contribution is expected to be small. The associated production of a Higgs boson with a pair of top quarks might be a useful method in the Higgs search in this case.     

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 cut-off dependence of the Higgs meson mass and the onset of new physics in the standard model

The scaleΛ ^cut before which the Weinberg-Salam model is expected to break down is predicted as the function of the Higgs meson massm _H by using two different approximate, but non-perturbative renormalization group procedures. The first scheme is the “local potential approximation”, the second is Wilson's recursion relation. For values of the functionΛ ^cut =Λ ^cut(m _H) of the order of the Higgs mass itself, we get an absolute upper bound onm _H . The conceptual background of these problems is discussed in detail.     

Associated production of intermediate-mass Higgs particle with a large-pT jet at SSC energy

We calculate the higher-order Higgs particle production process gg→gH for a large top-quark mass (2m_t > m_H). We compute the resulting associated cross section for intermediate-mass Higgs particle (m_W<m_H<2m_W) at SSC, followed by its dominant decay mode into a bottom-quark pair. At large p_T the cross section becomes comparable to that of the QCD background while remaining sufficiently large for detection at SSC.     

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.     

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.     

Flavour non-conservation induced by Higgs particle exchange inSU(2)L×SU(2)R×U(1) model

The VEV of the Higgs field inSU(2)_L×SU(2)_R×U(1) model is discussed in the context of the flavour changing neutral currents. The lower bound of Higgs particle mass is found (m _H ?3 TeV).     

Cosmic-ray induced vacuum decay in the standard model

In the standard model, if the Higgs boson mass, m_H, and the top quark mass, m_t, satisfy the relationship m_t≳95GeV + 0.60 m_H, then the vacuum is unstable. However, if the top quark mass is less than 190 GeV, then the lifetime is greater than the age of the universe. There is thus a large region of parameter space in which the vacuum is unstable, but sufficiently long-lived. We examine the possibility that high energy cosmic ray collisions could induce the decay of the vacuum, and show that this region of parameter space can be excluded.     

On the metastability of the Standard Model vacuum

If the Higgs mass m_H is as low as suggested by present experimental information, the Standard Model ground state might not be absolutely stable. We present a detailed analysis of the lower bounds on m_H imposed by the requirement that the electroweak vacuum be sufficiently long-lived. We perform a complete one-loop calculation of the tunnelling probability at zero temperature, and we improve it by means of two-loop renormalization-group equations. We find that, for m_H=115 GeV, the Higgs potential develops an instability below the Planck scale for m_t>(166±2) GeV, but the electroweak vacuum is sufficiently long-lived for m_t<(175±2) GeV.     

On the lattice approach to the maximum Higgs boson mass

If the triviality upper bound on the Higgs boson mass m_H occurs for strong self-coupling, inferring properties of the Higgs from the euclidean propagator is in principle theoretically difficult whether in coordinate or momentum space. In that case, common methods of identifying m_H in lattice field theory simulations may produce a value for which is at best distantly related to the true upper limit. We discuss some shortcomings and ambiguities of recent results suggesting that the maximum occurs for weak coupling and emphasize potential complications due to finite-size and non-Lorentz-invariant effects of the lattice. The situation is illustrated by reference to the behavior in an analytically soluble approximation based on a 1/N expansion.     

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.     

Upper bounds on Higgs-Boson masses in the Weinberg-Salam model with three Higgs doublets

In the Weinberg-Salam model with three Higgs doublets, the positivity of masses and tree graph unitarity applied on Higgs scattering lead to the following upper bounds on Higgs masses: m_H1^±, m_H2^± < 883 GeV, m_H1⁰ < 500 GeV, m_H2⁰, m_H3⁰ < (958–1633) GeV, m_H4⁰, m_H5⁰ < (360–883) GeV.     

Bound on the Higgs boson mass with no zero-charge behaviour in a magnetic field

The upper boundm<280 GeV/c² on the Higgs boson mass is obtained by considering the requirement that the electroweak theory must be consistent in a magnetic fieldH. The restriction emerges naturally by studying the effective potential in a magnetic field as a function of mass, and the values ofm when there is no zero-charge, in the fieldsH～H ₀=M _w ² /e are obtained.     

A comparison of direct and indirect determinations of the masses of the Higgs Boson and the top quark

The indirect estimation of the Higgs Boson mass from electroweak radiative corrections within the Standard Model is compared with the directly measured value obtained by the ATLAS and CMS Collaborations at the CERN LHC collider. Treating the direct measurement of m_H as input, the Standard Model indirect estimation of the top-quark mass is also obtained and compared with its directly measured value. A model-independent analysis finds an indirect value of m_H of ■70 GeV, below the directly measured value of 125.7±0.4 GeV and an indirect value:m_t = 177.3±1.0 GeV, above the directly measured value: 173.21±0.87 GeV. A goodness-of-fit test to the Standard Model using all Z-pole observables and mW has a χ~2 probability of ■2%. The reason why probability values about a factor of ten larger than this, and indirect estimates of m H about 30 GeV higher, have been obtained in recent global fits to the same data is recalled.     

Four weak gauge boson production at photon linear collider and heavy Higgs signal

We study the signals and backgrounds for a heavy Higgs boson in the processes γγ → WWWW, γ → WWZZ at the proton linear collider. The results are based on the complete tree-level SM calculation for these reactions. We show that the invariant mass spectrum of central WW, ZZ pairs is sensitive to the signal from Higgs boson with a mass up to 1 TeV linear collider for integrated luminosity of 300 fb⁻¹. At 1.5 TeV PLC Higgs boson with a mass up to 700 GeV can be studied. The nonresonant longitudinal gauge boson scattering (m_H = ∞) can be detected in photon-photon collisions at e⁺e⁻ center-of-mass energy of 3 TeV.     

Simplified parametric scenarios of the Minimal Supersymmetric Standard Model after the discovery of the Higgs boson

Constraints on the parameter space of theMinimal Supersymmetric StandardModel (MSSM) that are imposed by the experimentally observed mass of the Higgs boson (m_H = 125 GeV) upon taking into account radiative corrections within an effective theory for the Higgs sector in the decoupling limit are examined. It is also shown that simplified approximations for radiative corrections in theMSSM Higgs sector could reduce, to a rather high degree of precision, the dimensionality of the multidimensionalMSSM parameter space to two.     

Effective gauge theory and the effect of heavy quarks in Higgs boson decays

A general framework is given for evaluating the contributions of as yet undiscovered heavy quarks to the gluonic decay rate of the Weinberg-Salam type Higgs boson. Since the Yukawa coupling of the Higgs boson to a quark pair is proportional to the quark mass, loop graphs involving heavy quarks have a non-vanishing effect on the gluonic decay width of the Higgs boson. This effect of heavy quarks with massesM _j(j=t,...) much greater than the Higgs boson massm _H is calculated in an effective gauge theory. The effects of two different kinds of large logarithms, lnM _j ² /μ m _h ² /μ ² are separated and summed up by the renormalization group method. It is found that the higher order QCD corrections are large and that the gluonic contribution to the hadronic decay width is significant if there are more than three generations. The Higgs decay width can therefore be used to probe the number of generations of heavy quarks.     

MSSM Higgs searches in multi-b-jet final states at the LHC

This paper discusses the possibility to observe a signal from MSSM Higgs boson decays into final states containing four b-jets. Two specific channels are considered: bb?H and bb?A production with H,A → bb?, for large values of m_H, m_A and tan β, and H → hh → bb?bb? decays for 150 GeV < m_H < 2m_t and for low values of tan β. Both channels are difficult to extract because of the very large reducible and irreducible QCD backgrounds. Even with an ultimate integrated luminosity, expected per LHC experiment, of 3 · 10⁵ pb^-1, the region of the MSSM parameter space covered by these channels does not extend the reach beyond that accessible to other channels that were studied in the past. Nevertheless, their observation would help in constraining the couplings and branching ratios of the MSSM Higgs bosons.