Low-energy impact of a heavy Higgs boson sector

The effective theory which characterizes the low-energy sensitivity of the minimal Weinberg-Salam model to a heavy Higgs boson sector is shown to be the gauged SU(2)_L × U(1) non-linear θ model. This theory is the limit of the Weinberg-Salam model as the Higgs boson mass, M_H, is removed (M_H → ∞). Using the symmetry properties of the non-linear theory, along with a power-counting analysis, we are able to classify low-energy observables according to their sensitivity to the regulator (M_H). At one loop, the greatest sensitivity is a logarithmic dependence on the Higgs boson mass. The M_H dependent corrections to some specific, experimentally accessible observables are calculated, and other possible applications of this technique are discussed.     

The higgs boson mass from precision electroweak data

We present a new global fit to precision electroweak data, including new low- and high-energy data and analyzing the radiative corrections arising from the minimal symmetry breaking sectors of the Standard Model (SM) and its supersymmetric extension (MSSM). It is shown that present data favor a Higgs mass ofO(M _z):M _H=76 _?50 ⁺¹⁵² GeV. We confront our analysis with (meta) stability and perturbative bounds on the SM Higgs mass, and the theoretical upper bound on the MSSM Higgs mass. Present data do not discriminate significantly between the SM and MSSM Higgs mass ranges. We comment in passing on the sensitivity of the Higgs mass determination to the values ofα(M _z) andα _s(M _z).     

Ultra heavy fermion bound states via Higgs exchange

We study the characteristic features of the ultra heavy fermion bound state via Higgs exchange. The constraint under which such a bound state occurs is presented. For a typical example of Higgs and fermion mass, M_H≅ 100 GeV / c² and M_F≅ 700 GeV/c², the wave function at the origin of the bound states via Higgs exchange becomes about 100 times larger than that via gluon exchange.     

On the role of the higgs mechanism in present electroweak precision tests

Based on the observablesM _W, Γ _l ,s _W ^?2 (M _Z ² ), we evaluate the parameters Δx, Δy and ε at one-loop level within an electroweak massive vector-boson theory, which does not employ the Higgs mechanism. The theoretical results are consistent with the experimental ones on Δx, Δy, ε. The theoretical prediction for Δy coincides with the standard-model one (apart from numerically irrelevant terms which vanish forM _H→∞). Nonrenormalizability only affects Δx and ε, which differ from the standard-model results by the replacement logM _H→log Λ for a heavy Higgs mass,M _H (where Λ denotes an effective UV cut-off).     

Numerical tests of the electroweak phase transition and thermodynamics of the electroweak plasma

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass M_H ≅ 34 GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to L_t = 5. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.     

Upper bounds on higgs boson masses

The low energy perturbative consistency of various models of electroweak interactions is discussed in the limit of large Higgs boson massesM _H . In each case an upper bound onM _H is found.     

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.     

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.     

Improving the heavy-Higgs four-charged-lepton signature

Assuming the Higgs scalar boson H⁰ of the standard model has mass m_H>2M_Z, we show that the popular four-lepton decay signature H⁰→ZZ→ℓ₁⁺ℓ₁⁻ℓ₂⁺ℓ₂⁻ at the SSC can be significantly enhanced relative to the continuum ZZ background by requiring high transverse momentum for at least one Z. The calculated signal is sensitive to the top quark mass.     

Another calculation of the Higgs mass and the top mass from the principles of H. B. Nielsen: m H ≅ 163GeV for M t ≅ 190GeV

We calculate the Higgs mass and the top mass starting from the principle that there are two, essentially degenerate minima in the Higgs effective potential; the second is at about the Planck energy scale M _P = 1.2 × 10¹⁹ GeV. Thus the parameter of the quartic self-coupling λ _h vanishes, as does β _λH at M _P. The new element is the addition of a quantum interaction term which couples the square of the Higgs field to the square of a pseudoscalar field, in the domain of the energy scale between about 10¹⁴ GeV and M _P. We modify β _λH at one loop. The pseudoscalar field which is introduced may be the field which is responsible for a spontaneous breakdown of discrete symmetry — for CP noninvariance at an energy scale of (10¹⁵–10¹⁶) GeV. The result is then a closer value for m _H ? 163 GeV for the top pole-mass M _t ? 190 GeV; both values are now close to the electroweak scale parameter $\langle {\phi _H}\rangle /\sqrt 2 = 175{\text{ GeV}}$ . In terms of dimensionless running coupling parameters, which determine the masses near to the electroweak scale, we get $\sqrt {{\lambda _H}} \cong 0.06$ and $gt/\sqrt 2 \cong 0.72$ , values that are close to each other and close to unity.     

Constraints on large-extra-dimensions model through 125 GeV Higgs pair production at the LHC

Based on the analysis of 5?fb^?1 of data at the LHC, the ATLAS and CMS collaborations have presented evidence for a Higgs boson with a mass in the 125 GeV range. We consider the 125 GeV neutral Higgs pair production process in the context of large-extra-dimensions (LED) model including the Kaluza?CKlein (KK) excited gravitons at the LHC. We consider the standard model (SM) Higgs pair production in gluon?Cgluon fusion channel and pure LED effects through graviton exchange as well as their interferences. It is shown that such interferences should be included; the LED model raises the transverse momentum (P _t ) and invariant mass (M _HH ) distributions at high scales of P _t and M _HH of the Higgs pair production. By using the Higgs pair production we could set the discovery limit on the cutoff scale M _S up to 6 TeV for ??=2 and 4.5 TeV for ??=6.     

Integrating out the standard Higgs field in the path integral

We integrate out the Higgs boson in the electroweak standard model at one loop and construct a low-energy effective Lagrangian assuming that the Higgs mass is much larger than the gauge-boson masses. Instead of applying diagrammatical techniques, we integrate out the Higgs boson directly in the path integral, which turns out to be much simpler. By using the background-field method and the Stueckelberg formalism, we directly find a manifestly gauge-invariant result. The heavy-Higgs effects on fermionic couplings are derived, too. At one loop the log M_H terms of the heavy-Higgs limit of the electroweak standard model coincide with the UV-divergent terms in the gauged non-linear σ-model, but vertex functions differ in addition by finite constant terms. Finally, the leading Higgs effects to some physical processes are calculated from the effective Lagrangian.     

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.     

Degenerate Higgs andZ Boson at LEP200

We investigate the problem of detecting the Higgs boson ifM _H ≈M _z at LEP200, the main problem being the large background fromZZ production. Since this background should be accurately calculable, we estimate that the existence of the Higgs can be established with about 3 fb^?1 of integrated luminosity. We also discuss how the signal can be improved if efficient tagging ofb quarks is available.     

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.     

Relativity,noncommutative geometry,renormalization and particle physics

A. Connes and A. Chamseddine have proposed a new geometric version of the standard model including a noncommutative relativity action. We present a systematic analysis of the relations among masses and coupling constants in these approaches. At the tree level, for a given top mass, the Higgs mass m_H is constrained to lie in an interval. Moreover, playing with the noncommutative gauge couplings, we compare the influence of the Higgs mass renormalization in these effective theories. The existing intersection is m_H = 188–201 GeV.     

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.     

Nambu sum rule in the NJL Models: from superfluidity to top quark condensation

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid ³He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ～ 325 GeV. They together satisfy the Nambu sum rule M ₁ ² + M ₂ ² = 4M _t ² , where M _t ～ 174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is ～210 GeV. In this case the Nambu sum rule is 2M ₁ ² + 2M ₂ ² = 4M _t ² . In addition, the properties of the Higgs modes in superfluid ³He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule M ₊ ² + M _? ² = 4M _t ² .     

Virtual very heavy top effects in LEP/SLC precision measurements

We estimate the O(α_s) strong interaction virtual corrections to the very heavy top (m_t = 200 GeV) virtual effects in several observable quantities to be measured in the near future in high precision experiments at LEP/SLC. In the cases of the measurements of M_w and of the longitudinal polarization asymmetry A_LR on Z₀ resonance we conclude that these corrections cannot be neglected, being of a size which is comparable with the effect coming from a possibly large Higgs mass, M_H≅1 TeV.     

Production on heavy Higgs bosons ate + e −-colliders

The production of Higgs bosons in the mass range of 200 GeV/c²<M _H <1TeV/c ² ate ⁺ e ^? super colliders is studied. We consider the possibilities to detect Higgs bosons via their decays into vector boson pairs. Single particle distributions of vektor bosons arising from this decay are compared with background reactions. We find, that the signal of Higgs bosons with masses up to 60- GeV/c² should be visible over the background already at \(\sqrt s = 1\) TeV, provided that the vektor bosons can be identified via their hadronic decay modes.