尾田 欣也

<jats:p>We investigate a gravitational model based on local Lorentz invariance and general coordinate invariance. The model incorporates classical scale invariance, which forbids dimensionful parameters, and the irreversible vierbein postulate, which enables continuous degenerate limits of the vierbein, both at a specific scale. Through the dynamics of the system, we demonstrate the simultaneous emergence of the Planck mass and a curved spacetime background.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>In models with non-minimal Higgs sectors, enforcing (near) Higgs alignment, necessary to prevent significant deviations in the Higgs boson coupling from the standard model prediction, causes a serious fine-tuning problem. We demonstrate that the Higgs alignment is naturally deduced from the multicritical point principle (MPP) in the general two Higgs doublet model while keeping non-zero CP-violating phases. Furthermore, we discuss the possibility of realizing the Yukawa alignment from the MPP, which is necessary to prevent flavor-changing neutral currents mediated by Higgs bosons at tree level, and find that it seems difficult to realize it by the MPP due to the non-diagonal structure of the CKM matrix.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Cosmological analysis of extended Jordan-Brans-Dicke (eJBD) gravity is presented in the Einstein metric frame in which gravitational interaction is readily understandable. Our formulation is the first systematic investigation of how to introduce lagrangian of standard particle physics in eJBD framework consistently with the general principle of spontaneously broken gauge symmetry, which makes it possible to confront eJBD-based cosmology with observational and laboratory bounds on time variation of parameters, masses, and coupling constants, caused by time evolution of eJBD fields. Decomposition of standard particle physics lagrangian into independent gauge invariant pieces is proposed to avoid serious conflict that may arise from standard lagrangian transformed from the Jordan frame. Independent conformal factors are assigned to each of five gauge invariant pieces. The formulation is most unambiguously made possible by defining fields having canonical kinetic terms that allow us to use the canonical quantization rule of field theory. This construction gives as one of its consequences the canonical eJBD field χ that couples to the universal fermion current, a linear combination of baryon and lepton number currents,  <jats:italic>∂<jats:sub>μχ</jats:sub> </jats:italic> (3 <jats:italic>j<jats:sup>μ</jats:sup> <jats:sub>B</jats:sub> </jats:italic> + <jats:italic>j<jats:sup>μ</jats:sup> <jats:sub>L</jats:sub> </jats:italic>), in addition to the conventional trace of the energy-momentum tensor. Field equation of eJBD field along with gravitational equation is analyzed by using a simplified polynomial class of potential and conformal functions, giving time evolution of radiation, matter and dark energy densities consistent with observations when an appropriate set of model parameters are used. Finite temperature corrections are further calculated to give temperature dependent terms in eJBD field potential.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Since electroweak symmetry is generally broken during inflation, the Standard Model Higgs field can become supermassive even after the end of inflation. In this paper, we study the non-thermal phase space distribution of the Higgs field during reheating, focusing in particular on two different contributions: primordial condensate and stochastic fluctuations. We obtain their analytic formulae, which agree with the previous numerical result. As a possible consequence of the non-thermal Higgs spectrum, we discuss perturbative Higgs decay during reheating for the case it is kinematically allowed. We find that the soft-relativistic and hard spectra are dominant in the decay rate of the stochastic fluctuation and that the primordial condensate and stochastic fluctuations decay almost at the same time.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The general scalar-tensor theory that includes all the dimension-four terms has parameter regions that can produce successful inflation consistent with cosmological observations. This theory is in fact the same as the Higgs-Starobinsky inflation, when the scalar is identified with the Standard Model Higgs boson. We consider possible dimension-six operators constructed from non-derivative terms of the scalar field and the Ricci scalar as perturbations. We investigate how much suppression is required for these operators to avoid disrupting the successful inflationary predictions. To ensure viable cosmological predictions, the suppression scale for the sixth power of the scalar should be as high as the Planck scale. For the other terms, much smaller scales are sufficient.</jats:p>

There is renewed attention to whether we can observe the decoherence effect in neutrino oscillation due to the separation of wave packets with different masses in near-future experiments. As a contribution to this endeavor, we extend the existing formulation based on a single 1D Gaussian wave function to an amplitude between two distinct 3D Gaussian wave packets, corresponding to the neutrinos being produced and detected, with different central momenta and spacetime positions and with different widths. We find that the spatial widths-squared for the production and detection appear additively in the (de)coherence length and in the localization factor for governing the propagation of the wave packet, whereas they appear as the reduced one (inverse of the sum of inverse) in the momentum conservation factor. The overall probability is governed by the ratio of the reduced to the sum.

<jats:title>Abstract</jats:title><jats:p>The gauge-invariant two-point function of the Higgs field at the same spacetime point can make a natural gauge-invariant order parameter for spontaneous gauge symmetry breaking. However, this composite operator is ultraviolet divergent and is not well defined. We propose using a gradient flow to cure the divergence from putting the fields at the same spacetime point. As a first step, we compute it for the Abelian Higgs model with a positive mass squared at the one-loop order in the continuum theory using the saddle-point method to estimate the finite part. The order parameter consistently goes to zero in the infrared limit of the infinite flow time.</jats:p>

Gravitational particle production is a minimal contribution to reheating the Universe after the end of inflation. To study this production channel, two different approaches have commonly been considered, one of which is based on the Boltzmann equation, and the other is based on the Bogoliubov transformation. Each of these has pros and cons in practice. The collision term in the Boltzmann equation can be computed based on quantum field theory in the Minkowski spacetime, and thus many techniques have been developed so far. On the other hand, the Bogoliubov approach may deal with the particle production beyond the perturbation theory and is able to take into account the effect of the curved spacetime, whereas in many cases one should rely on numerical methods, such as lattice computation. We show by explicit numerical and analytical computations of the purely gravitational production of a scalar that these two approaches give consistent results for particle production with large momenta during reheating, whereas the Boltzmann approach is not capable of computing particle production out of vacuum during inflation. We also provide analytic approximations of the spectrum of produced scalar with/without mass for the low momentum regime obtained from the Bogoliubov approach.

<jats:title>Abstract</jats:title><jats:p>We argue that double inflation may occur when a spectator field is non-minimally coupled to gravity. As a concrete example, we study a two-field inflationary model where the initial spectator field is non-minimally coupled to gravity while the initial inflaton field is minimally coupled. The non-minimal coupling results in the growth of the spectator field which, in turn, drives the second stage of inflation in a significant region of parameter space. The isocurvature fluctuations originating from the spectator field source adiabatic ones, and hence the spectator non-minimal coupling can modify the inflationary predictions for the spectral index and the tensor-to-scalar ratio even though the initial inflaton field is minimally coupled to gravity. We explicitly show that quadratic chaotic inflation can become viable by the introduction of the spectator non-minimal coupling.</jats:p>

<jats:title>Abstract</jats:title><jats:p>The multicritical-point principle (MPP) provides a natural explanation of the large hierarchy between the Planck and electroweak scales. We consider a scenario in which MPP is applied to the Standard Model extended by two real singlet scalar fields <jats:inline-formula><jats:alternatives><jats:tex-math>$$\phi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> and <jats:italic>S</jats:italic>, and a dimensional transmutation occurs by the vacuum expectation value of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\phi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>. In this paper, we focus on the critical points that possess a <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathbb {Z } }_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> symmetry <jats:inline-formula><jats:alternatives><jats:tex-math>$$S\rightarrow -S$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>→</mml:mo> <mml:mo>-</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> and all the other fields are left invariant. Then <jats:italic>S</jats:italic> becomes a natural dark matter (DM) candidate. Further, we concentrate on the critical points where <jats:inline-formula><jats:alternatives><jats:tex-math>$$\phi $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> does not possess further <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathbb {Z } }_2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> symmetry so that there is no cosmological domain-wall problem. Among such critical points, we focus on maximally critical one called CP-1234 that fix all the superrenormalizable parameters. We show that there remains a parameter region that satisfies the DM relic abundance, DM direct-detection bound and the current LHC constraints. In this region, we find a first-order phase transition in the early universe around the TeV-scale temperature. The resultant gravitational waves are predicted with a peak amplitude of <jats:inline-formula><jats:alternatives><jats:tex-math>$${ { \mathcal {O } } }(10^{-12})$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> at a frequency of <jats:inline-formula><jats:alternatives><jats:tex-math>$$10^{-2}{-}10^{-1}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>-</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> Hz, which can be tested with future space-based instruments such as DECIGO and BBO.</jats:p>

<jats:title>Abstract</jats:title><jats:p>We study <jats:inline-formula><jats:alternatives><jats:tex-math>$$R^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>-Higgs inflation in a model with two Higgs doublets in which the Higgs sector of the Standard Model is extended by an additional Higgs doublet, thereby four scalar fields are involved in the inflationary evolutions. We first derive the set of equations required to follow the inflationary dynamics in this two Higgs doublet model, allowing a nonminimal coupling between the Higgs-squared and the Ricci scalar <jats:italic>R</jats:italic>, as well as the <jats:inline-formula><jats:alternatives><jats:tex-math>$$R^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> term in the covariant formalism. By numerically solving the system of equations, we find that, in parameter space where a successful <jats:inline-formula><jats:alternatives><jats:tex-math>$$R^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>-Higgs inflation are realized and consistent with low energy constraints, the inflationary dynamics can be effectively described by a single slow-roll formalism even though four fields are involved in the model. We also argue that the parameter space favored by <jats:inline-formula><jats:alternatives><jats:tex-math>$$R^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula>-Higgs inflation requires nearly degenerate masses for <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_{\mathsf {H } }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>H</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_A$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_{ { \mathsf {H } }^{\pm } }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mo>±</mml:mo> </mml:msup> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, where <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathsf {H } }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>, <jats:italic>A</jats:italic>, and <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathsf {H } }^{\pm }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mo>±</mml:mo> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> are the extra CP even, CP odd, and charged Higgs bosons in the general two Higgs doublet model taking renormalization group evolutions of the parameters into account. Discovery of such heavy scalars at the Large Hadron Collider (LHC) are possible if they are in the sub-TeV mass range. Indirect evidences may also emerge at the LHCb and Belle-II experiments, however, to probe the quasi degenerate mass spectra one would likely require high luminosity LHC or future lepton colliders such as the International Linear Collider and the Future Circular Collider.</jats:p>

<jats:p>A correction to this paper has been published: <jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://doi.org/10.1140/epjc/s10052-020-08450-5">https://doi.org/10.1140/epjc/s10052-020-08450-5</jats:ext-link></jats:p>

We define a set of fully Lorentz-invariant wave packets and show that it spans the corresponding one-particle Hilbert subspace, and hence the whole Fock space as well, with a manifestly Lorentz-invariant completeness relation (resolution of identity). The position-momentum uncertainty relation for this Lorentz-invariant wave packet deviates from the ordinary Heisenberg uncertainty principle, and reduces to it in the non-relativistic limit.

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We propose a scenario of spontaneous leptogenesis in Higgs inflation with help from two additional operators: the Weinberg operator (Dim 5) and the derivative coupling of the Higgs field and the current of lepton number (Dim 6). The former is responsible for lepton number violation and the latter induces chemical potential for lepton number. The period of rapidly changing Higgs field, naturally realized in Higgs inflation during the reheating, allows large enhancement in the produced asymmetry in lepton number, which is eventually converted into baryon asymmetry of the universe. This scenario is compatible with high reheating temperature of Higgs inflation model.</jats:p>

In a transition amplitude of wave-packets, e.g., that of the $\Phi\to\phi\phi$ decay process, there are in and out time boundaries for the initial $\Phi$ and final $\phi\phi$ configurations, respectively, when the transition occurs in a finite time interval. In this Letter, we prove that the effect of the in time boundary of the $\Phi\to\phi\phi$ decay emerges from the $\phi\phi\to\Phi\to\phi\phi$ scattering amplitude that does not include the time boundaries for $\phi\phi$. This effect has been overlooked in the standard plane-wave formulation and can exhibit distinct phenomena in wide areas of science. We confirm the result in different integration orders. The result is also interpreted as a Stokes phenomenon in the Lefschetz-thimble decomposition.

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We investigate a model with two real scalar fields that minimally generates exponentially different scales in an analog of the Coleman-Weinberg mechanism. The classical scale invariance — the absence of dimensionful parameters in the tree-level action, required in such a scale generation — can naturally be understood as a special case of the multicritical-point principle. This two-scalar model can couple to the Standard Model Higgs field to realize a maximum multicriticality (with all the dimensionful parameters being tuned to critical values) for field values around the electroweak scale, providing a generalization of the classical scale invariance to a wider class of criticality. As a bonus, one of the two scalars can be identified as Higgs-portal dark matter. We find that this model can be consistent with the constraints from dark matter relic abundance, its direct detection experiments, and the latest LHC data, while keeping the perturbativity up to the reduced Planck scale. We then present successful benchmark points satisfying all these constraints: the mass of dark matter is a few TeV, and its scattering cross section with nuclei is of the order of 10<jats:sup><jats:italic>−</jats:italic>9</jats:sup> pb, reachable in near future experiments. The mass of extra Higgs boson <jats:italic>H</jats:italic> is smaller than or of the order of 100 GeV, and the cross section of <jats:italic>e</jats:italic><jats:sup>+</jats:sup><jats:italic>e</jats:italic><jats:sup><jats:italic>−</jats:italic></jats:sup> → <jats:italic>ZH</jats:italic> can be of fb level for collision energy 250 GeV, targetted at future lepton colliders.</jats:p>

<jats:title>Abstract</jats:title><jats:p>We study the correlation between the constraints on general two Higgs doublet model from Higgs inflation and from collider experiments. The parameter space receives meaningful constraints from direct searches at the large hadron collider and from flavor physics if <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_H$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>H</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_A$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, and <jats:inline-formula><jats:alternatives><jats:tex-math>$$m_{H^\pm }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> are in the sub-TeV range, where <jats:italic>H</jats:italic>, <jats:italic>A</jats:italic>, and <jats:inline-formula><jats:alternatives><jats:tex-math>$$H^\pm $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> are the CP even, CP odd, and charged Higgs bosons, respectively. We find that in the parameter region favored by the Higgs inflation, <jats:italic>H</jats:italic>, <jats:italic>A</jats:italic>, and <jats:inline-formula><jats:alternatives><jats:tex-math>$$H^\pm $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> are nearly degenerate in mass. We show that such near degeneracy can be probed directly in the upcoming runs of the Large Hadron Collider, while the future lepton colliders such as the International Linear Collider and the future circular collider would provide complementary probes.</jats:p>

We compute an $s$-channel $2\to2$ scalar scattering $\phi\phi\to\Phi\to\phi\phi$ in the Gaussian wave-packet formalism at the tree-level. We find that wave-packet effects, including shifts of the pole and width of the propagator of $\Phi$, persist even when we do not take into account the time-boundary effect for $2\to2$, proposed earlier. The result can be interpreted that a heavy scalar $1\to2$ decay $\Phi\to\phi\phi$, taking into account the production of $\Phi$, does not exhibit the in-state time-boundary effect unless we further take into account in-boundary effects for the $2\to2$ scattering. We also show various plane-wave limits.

Gravity can be regarded as a consequence of local Lorentz (LL) symmetry, which is essential in defining a spinor field in curved spacetime. The gravitational action may admit a zero-field limit of the metric and vierbein at a certain ultraviolet cutoff scale such that the action becomes a linear realization of the LL symmetry. Consequently, only three types of term are allowed in the four-dimensional gravitational action at the cutoff scale: a cosmological constant, a linear term of the LL field strength, and spinor kinetic terms, whose coefficients are in general arbitrary functions of LL and diffeomorphism invariants. In particular, all the kinetic terms are prohibited except for spinor fields, and hence the other fields are auxiliary. Their kinetic terms, including those of the LL gauge field and the vierbein, are induced by spinor loops simultaneously with the LL gauge field mass. The LL symmetry is necessarily broken spontaneously and hence is nothing but a hidden local symmetry, from which gravity is emergent.

We study the proton lifetime in the $SO(10)$ Grand Unified Theory (GUT), which has the left-right (LR) symmetric gauge theory below the GUT scale. In particular, we focus on the minimal model without the bi-doublet Higgs field in the LR symmetric model, which predicts the LR-breaking scale at around $10^{10\text{--}12}$ GeV. The Wilson coefficients of the proton decay operators turn out to be considerably larger than those in the minimal $SU(5)$ GUT model especially when the Standard Model Yukawa interactions are generated by integrating out extra vector-like multiplets. As a result, we find that the proton lifetime can be within the reach of the Hyper-Kamiokande experiment even when the GUT gauge boson mass is in the $10^{16\text{--}17}$ GeV range. We also show that the mass of the extra vector-like multiplets can be generated by the Peccei-Quinn symmetry breaking in a consistent way with the axion dark matter scenario.

We derive the Fermi's golden rule in the Gaussian wave-packet formalism of quantum field theory, proposed by Ishikawa, Shimomura, and Tobita, for the particle decay within a finite time interval. We present a systematic procedure to separate the bulk contribution from those of time boundaries, while manifestly maintaining the unitarity of the $S$-matrix unlike the proposal by Stueckelberg in 1951. We also revisit the suggested deviation from the golden rule and clarify that it indeed corresponds to the boundary contributions, though their physical significance is yet to be confirmed.

The observed Higgs mass indicates that the Standard Model can be valid up to near the Planck scale $M_\text{P}$. Within this framework, it is important to examine how little modification is necessary to fit the recent experimental results in particle physics and cosmology. As a minimal extension, we consider the possibility that the Higgs field plays the role of inflaton and that the dark matter is the Higgs-portal scalar field. We assume that the extended Standard Model is valid up to the string scale $10^{17}\,\text{GeV}$. (This translates to the assumption that all the non-minimal couplings are not particularly large, $\xi\lesssim 10^2$, as in the critical Higgs inflation, since $M_\text{P}/\sqrt{10^2}\sim 10^{17}\,\text{GeV}$.) We find a correlated theoretical bound on the tensor-to-scalar ratio $r$ and the dark matter mass $m_\text{DM}$. As a result, the Planck bound $r<0.09$ implies that the dark-matter mass must be smaller than 1.1\,TeV, while the PandaX-II bound on the dark-matter mass $m_\text{DM}>0.7\pm0.2\,\text{TeV}$ leads to $r\gtrsim 2\times10^{-3}$. Both are within the range of near-future detection. When we include the right-handed neutrinos of mass $M_\text{R}\sim 10^{14}$\,GeV, the allowed region becomes wider, but we still predict $r\gtrsim 10^{-3}$ in the most of the parameter space. The most conservative bound becomes $r>10^{-5}$ if we allow three-parameter tuning of $m_\text{DM}$, $M_\text{R}$, and the top-quark mass.

We propose a realization of cosmic inflation with the Higgs field when the Higgs potential has degenerate vacua by employing the recently proposed idea of hillclimbing inflation. The resultant inflationary predictions exhibit a sizable deviation from those of the ordinary Higgs inflation.

We present how to implement special relativity in computer games. The resultant relativistic world shows the time dilation and Lorentz contraction exactly, not only for the player but also for all the nonplayer characters, who obey the correct relativistic equation of motion according to their own accelerations. Causality is explicitly maintained in our formulation by use of the covariant velocities, proper times, worldlines, and light cones. Faraway relativistic scenes can be accurately projected onto the skydome. We show how to approximate a rigid body consisting of polygons, which is ubiquitous in computer games but itself is not a relativistically invariant object. We also give a simple idea to mimic the Doppler effect within the RGB color scheme.

We study a class of models in which the Higgs pair production is enhanced at hadron colliders by an extra neutral scalar. The scalar particle is produced by the gluon fusion via a loop of new colored particles, and decays into di-Higgs through its mixing with the Standard Model Higgs. Such a colored particle can be the top/bottom partner, such as in the dilaton model, or a colored scalar which can be triplet, sextet, octet, etc., called leptoquark, diquark, coloron, etc., respectively. We examine the experimental constraints from the latest Large Hadron Collider (LHC) data, and discuss the future prospects of the LHC and the Future Circular Collider up to 100TeV. We also point out that the 2.4$\sigma$ excess in the $b\bar b\gamma\gamma$ final state reported by the ATLAS experiment can be interpreted as the resonance of the neutral scalar at 300GeV.

We consider the prescription dependence of the Higgs effective potential under the presence of general nonminimal couplings. We evaluate the fermion loop correction to the effective action in a simplified Higgs-Yukawa model whose path integral measure takes simple form either in the Jordan or Einstein frame. The resultant effective action becomes identical in both cases when we properly take into account the quartically divergent term coming from the change of measure. Working in the counterterm formalism, we clarify that the difference between the prescriptions I and II comes from the counter term to cancel the logarithmic divergence. This difference can be absorbed into the choice of tree-level potential from the infinitely many possibilities, including all the higher-dimensional terms. We also present another mechanism to obtain a flat potential by freezing the running of the effective quartic coupling for large field values, using the nonminimal coupling in the gauge kinetic function.

We investigate the Higgs potential beyond the Planck scale in the superstring theory, under the assumption that the supersymmetry is broken at the string scale. We identify the Higgs field as a massless state of the string, which is indicated by the fact that the bare Higgs mass can be zero around the string scale. We find that, in the large field region, the Higgs potential is connected to a runaway vacuum with vanishing energy, which corresponds to opening up an extra dimension. We verify that such universal behavior indeed follows from the toroidal compactification of the nonsupersymmetric SO(16)×SO(16) heterotic string theory. We show that this behavior fits in the picture that the Higgs field is the source of the eternal inflation. The observed small value of the cosmological constant of our universe may be understood as the degeneracy with this runaway vacuum, which has vanishing energy, as is suggested by the multiple point criticality principle.

The observed Higgs mass MH=125.9±0.4GeV leads to the criticality of the standard model, that is, the Higgs potential becomes flat around the scale 10[17-18]GeV for the top mass 171.3 GeV. Earlier we proposed a Higgs inflation scenario in which this criticality plays a crucial role. In this paper, we investigate the detailed cosmological predictions of this scenario in light of the latest Planck and BICEP2 results. We also consider the Higgs portal scalar dark matter model, and compute the Higgs one-loop effective potential with the two-loop renormalization group improvement. We find a constraint on the coupling between the Higgs boson and dark matter which depends on the inflationary parameters.

We consider a possibility that the Higgs field in the Standard Model (SM) serves as an inflaton when its value is around the Planck scale. We assume that the SM is valid up to an ultraviolet cutoff scale Λ, which is slightly below the Planck scale, and that the Higgs potential becomes almost flat above Λ. Contrary to the ordinary Higgs inflation scenario, we do not assume the huge non-minimal coupling, of O(10[4]), of the Higgs field to the Ricci scalar. We find that Λ must be less than 5×10[17]GeV in order to explain the observed fluctuation of the cosmic microwave background, no matter how we extrapolate the Higgs potential above Λ. The scale 10[17]GeV coincides with the perturbative string scale, which suggests that the SM is directly connected with string theory. For this to be true, the top quark mass is restricted to around 171 GeV, with which Λ can exceed 10[17]GeV. As a concrete example of the potential above Λ, we propose a simple log-type potential. The predictions of this specific model for the e-foldings N[∗]=50–60 are consistent with the current observation, namely, the scalar spectral index is ns=0.977--0.983 and the tensor to scalar ratio 0<r<0.012–0.010. Other parameters, dns/dlnk, nt, and their derivatives, are also consistent.

We first review the current status of the top mass determination paying attention to the difference between the MS-bar and pole masses. Then we present our recent result on the bare Higgs mass at a very high ultraviolet cutoff scale.