Narrow Results

We present a mini-review of the present constraints of the large extra dimension scenario. We show many experiments and considerations that can constrain the fundamental scale of the large extra dimension. We observe that constraints come from collider experiments are much weaker than those of astrophysical and cosmological considerations. When the number of extra dimension n is smaller than four, the constraint is so strong that the large extra dimension scenario cannot solve hierarchy problem. But when n ≥ 4 there is still possibility that it can solve the hierarchy problem.

We pursue the possibility of the scenario in which the Higgs field is identified with the extra-space component of a bulk gauge field. The space–time we take is M⁴ ⊗ S¹/Z₂. We show that a nontrivial Z₂-parity assignment allows some of the extra-space component to have radiatively induced vev, which strongly modifies the mass spectrum and gauge symmetry of the theory, realized by orbifolding. In particular we investigate the dynamical mass generation of zero-mode fermion and spontaneous gauge symmetry breaking due to the vev. The gauge theories we adopt are a prototype model SU(2) and SU(3) model, of special interest as the realistic minimal scheme to incorporate the standard model SU(2) × U(1).

We propose a phenomenological solution to the electroweak hierarchy problem. It predicts no new particles beyond those in the Standard Model. The Higgs is arbitrarily massive and slow-roll inflation can be implemented naturally. Loop corrections will be negligible even for large cutoffs.

In order that nonsupersymmetric quiver gauge theories can satisfy naturalness requirements to all orders of perturbation theory, one expects a global symmetry similar to, but different from, supersymmetry. Consistent with the generalized no-go theorem published by Haag et al. in 1975, we suggest a generalization of supersymmetry to a misaligned supersymmetry where fermionic generators do not commute with gauge transformations. An explicit form for the corresponding field transformations is suggested.

We propose a new solution to problems of the hierarchy and smallness of the cosmological constant using the TeV scale of the Standard Model in a new framework of the higher-order gravity.

The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments, it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarchy problem without necessity to introduce any artificially large numbers. Quantum mechanical model illustrating this scenario is presented.

We study the hierarchy problem on the four- and five-branes which are constructed by attaching a circle and a sphere to the standard three-brane, respectively. The effective masses in their excited spectra on these extended dimensional branes imply intriguing characteristics associated with the quantization of the compact circular and spherical manifolds. In particular, their lightest effective masses are shown to suppress exponentially with respect to the Planck mass, similar to the three-brane case. We also investigate the effective couplings in these extended dimensional branes.

We point out a possible mechanism by which the electroweak hierarchy problem can be avoided in the low energy effective quantum field theory. Assuming the existence of a UV complete underlying fundamental theory and treating the cutoff scale Λ of the effective field theory as a real physical scale we argue that the hierarchy problem would be solved if the coefficient in front of quadratic divergences vanished at the scale Λ, and if the effective theory mass parameters fixed at Λ by the fundamental theory were hierarchically smaller than Λ itself. While this mechanism most probably cannot work in the Standard Model if the scale Λ is to be close to the Planck scale, we show that it can work in a minimal extension (Conformal Standard Model) proposed recently for a different implementation of conformal symmetry breaking.

Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a nonvanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.

In this paper, we present a systematical study of braneworlds of string theory on S¹/Z₂. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold branes as its boundaries. We divide the whole set of the gravitational and matter field equations into two groups, one holds outside the two branes, and the other holds on them. By combining the Gauss–Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the four-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza–Klein (KK) modes. The mechanism of solving the hierarchy problem is essentially the combination of the large extra dimension and warped factor mechanisms together with the tension coupling scenario. With very conservative arguments, we find that the radion mass is of the order of 10^-2 GeV. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the four-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss–Codacci equations and Israel's junction conditions across a (D - 1)-dimensional hypersurface, which can be either spacelike or timelike.

We argue that presymmetry, a hidden predynamical electroweak quark–lepton symmetry that explains the fractional charges and triplication of families, must be extended beyond the Standard Model as to have a residual presymmetry that embraces partner particles and includes the strong sector, so accounting for the twin or mirror partners proposed to alleviate the naturalness problem of the weak scale. It leads to the full duplication of fermions and gauge bosons of the Standard Model independently of the ultraviolet completion of the theory, even if the Higgs particle is discarded by experiment, which adds robustness to twin and mirror symmetries. The established connection is so strongly motivated that the search for twin or mirror matter becomes the possible test of presymmetry. If the physics beyond the Standard Model repairs its left–right asymmetry, mirror symmetry should be the one realized in nature.

We extend a classically scale invariant model where the electroweak symmetry breaking is triggered by the dynamical chiral symmetry breaking in a hidden QCD sector, and a real singlet scalar $S$ mediates these two sectors. Our model can explain cosmic inflation without unitarity violation in addition. Slow-roll inflation occurs along a valley in scalar potential. In the original model, the coupling $-{\lambda }_{HS}$ between the Higgs field $H$ and $S$ is always negative and therefore, the potential has its valleys in $H$-$S$ mixed directions. For large value of the top Yukawa coupling $y_t$, the potential along the valley becomes negative since the Higgs quartic coupling ${\lambda }_H$ becomes negative at inflationary scale. Then slow-roll inflation cannot occur. For inflation to definitely occur, we render the coupling $-{\lambda }_{HS}$ positive at inflationary scale and consider the $S$-inflation case. This is achieved by introducing a new singlet scalar $\eta$ with the large coupling ${\lambda }_{H\eta }$ to $H$. By this extension, ${\lambda }_H$ can also always be positive, and we consider this case as the simplest case. We consider inflation with the nonminimal coupling ${\xi }_S$ between $S$ and gravity. Although ${\xi }_S$ is large such as ${\xi }_S\simeq {𝒪}(10^3)$, unitarity is not violated since couplings between $S$ and other fields are sufficiently small. $\eta$ is odd under a new symmetry $Z_2$ not to mix with $H$ regardless of largeness of ${\lambda }_{H\eta }$. Because of this symmetry, $\eta$ may have its relic abundance ${\mathrm{\Omega }}_{\eta }{ĥ}^2$ comparable with the observational value ${\mathrm{\Omega }}^{\mathrm{\text{obs}}}{ĥ}^2\simeq 0.12$ of the dark matter relic abundance. However, the spin-independent elastic cross-section ${\sigma }_{\mathrm{\text{SI}}}^{\eta }$ of $\eta$ exceeds the observational bound ${\sigma }_{\mathrm{\text{SI}}}^{\mathrm{\text{obs}}}\sim {𝒪}(10^{-47})$ cm². Hence, we impose the resonance condition $m_{\eta }\simeq m_S/2$ and reduce ${\mathrm{\Omega }}_{\eta }{ĥ}^2$ to much smaller than ${\mathrm{\Omega }}^{\mathrm{\text{obs}}}{ĥ}^2$. Constraints from the electroweak scale physics and inflationary scale physics are much strong, and the allowed parameter space is very narrow.

Our model (Refs. 1–7) with a complex action in a functional integral formulation with path integrals extending over all times, both past and future, is reviewed. Several numerical relations between coupling constants are presented as supporting evidence. The new evidence is that several more hitherto unexplained coincidences are explained by our model:

(1) The "scale problem" is solved because the Higgs field expectation value is predicted to be very small compared to say some fundamental scale, that might be the Planck scale.

(2) The Higgs VEV need not be just zero, but rather is predicted to be so that the running top-quark Yukawa coupling just is about to be unity at this scale; in this way the (weak) scale easily becomes "exponentially small." Instead of the top-Yukawa we should rather say the highest flavor Yukawa coupling here.

These predictions are only achieved by allowing the principle of minimization of the imaginary part of the action S_I(history) to a certain extent adjust some coupling constants in addition to the initial conditions.

If supersymmetric partners are not found at LHC it would strengthen the need for a "solution" to the hierarchy problem in our direction of an explanation via a fine-tuning scheme inside the Standard Model, from say minimizing "the imaginary part of the action" in our complex action model.

We discuss the physical implications of the extra space in higher-dimensional unification, and show that a large extra space requires an extremely small fine structure constant (of the order of 10^-42) for the Kaluza-Klein gauge boson, or else a huge violation of equivalence principle in 4-dimensional Einstein gravity. More importantly, the extra space generates the dilaton which represents the volume element of the extra space. We show that the scalar curvature of the extra space generates the dilaton mass, and that the dilaton mass determines the size of the extra space. Moreover, as a massive scalar graviton, the dilaton can be an excellent candidate of dark matter. Assuming that the dilaton is the dark matter, we estimate the lower bound of the scale of the extra space to be of 10^-9 m.

The discovery of the Higgs particle at around 126 GeV has given us a big hint towards the origin of the Higgs potential. The running quartic self-coupling decreases and crosses zero somewhere in the very high energy scale. It is usually considered as a signal of the instability of the standard model (SM) vacuum, but it can also indicate a link between the physics in the electroweak scale and the Planck scale. Furthermore, the LHC experiments as well as the flavor physics experiments give strong constraints on the physics beyond the SM. It urges us to reconsider the widely taken approach to the physics beyond the SM (BSM), namely the approach based on the gauge unification below the Planck scale and the resulting hierarchy problem. Motivated by the recent experiments, we first revisit the hierarchy problem and consider an alternative appoach based on a classical conformality of the SM without the Higgs mass term.

In this talk, I review our recent proposal of a B-L extension of the SM with a flat Higgs potential at the Planck scale.^1,2 This model can be an alternative solution to the hierarchy problem as well as being phenomenologically viable to explain the neutrino oscillations and the baryon asymmetry of the universe. With an assumption that the Higgs has a flat potential at the Planck scale, we show that the B-L symmetry is radiatively broken at the TeV scale via the Coleman-Weinberg mechanism, and it triggers the electroweak symmetry breaking through a radiatively generated scalar mixing. The ratio of these two breaking scales is dynamically determined by the B-L gauge coupling.