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Takahiro Kubota

Publications and source records attributed to Takahiro Kubota.

At least 19 recordsLinked to original sources
arXiv2026

Gauge fields in the presence of the electroweak bubble wall

The gauge field theory of the standard electroweak model in the presence of the electroweak bubble wall is investigated with a view to its applications to microscopic phenomena, which are believed to have occurred during the phase transition in the early universe. The asymptotic fields are defined anew so that the effects of the position-dependent Higgs condensate are taken into account through the position-dependent $W$ and $Z$ boson masses. A novel method of massive gauge field quantization in the $R_ξ$-gauge with $ξ=1$ is proposed for the case of the position-dependent masses. Our procedure is based on the eigenfunction expansion method associated with second-order differential operators, i.e., a sort of generalized Fourier expansion. The commutation relations of creation and annihilation operators of various wave propagation modes are given in terms of what is known as the spectral function. The decoupling of unphysical states from the physical S-matrix is also investigated along the line of Kugo-Ojima's quartet mechanism on the basis of the BRST symmetry. It is pointed out that one of the quartet fields is not merely the unphysical scalar field but should be a linear combination of the unphysical scalar and the gauge fields. The physical and unphysical polarizations of the gauge field waves are unambiguously distinguished and this will help us evaluate the friction caused by the physical polarization states of $W$ and $Z$ boson waves on the bubble wall during the phase transition in the early universe.

hep-ph↗
arXiv2024

Green's functions in the presence of a bubble wall

Field theoretical tools are developed so that one can analyze quantum phenomena such as transition radiation that must have occurred during the Higgs condensate bubble expansion through plasma in the early universe. Integral representations of Bosonic and Fermionic propagators are presented for the case that particle masses are varied continuously during the passage through the bubble wall interface between symmetry-restored and symmetry-broken regions. The construction of propagators is based on the so-called eigenfunction expansion method associated with self-adjoint differential operators, developed by Weyl, Stone, Titchmarsh, Kodaira and several others. A novel method of field quantization in the presence of the bubble wall is proposed by using the spectral functions introduced in constructing the two-point Green's functions.

hep-th↗
arXiv2021

Heavy particle non-decoupling in flavor-changing gravitational interactions

The flavor-changing gravitational process d --> s + graviton, is evaluated at the one-loop level in the standard electroweak theory with on-shell renormalization. The results we present in the 't Hooft-Feynman gauge are valid for on- and off-shell quarks and for all external and internal quark masses. We show that there exist non-decoupling effects of the internal heavy top quark in interactions with gravity. A naive argument taking account of the quark Yukawa coupling suggests that the amplitude of the process d --> s + graviton in the large top quark mass limit would possibly acquire an enhancement factor $m_{t}^{2}/M_{W}^{2}$, where $m_{t}$ and $M_{W}$ are the top quark and the W-boson masses, respectively. In practice this leading enhancement is absent in the renormalized amplitude due to cancellation. Thus the non-decoupling of the internal top quark takes place at the $O(1)$ level. The flavor-changing two- and three-point functions are shown to satisfy the Ward-Takahashi identity, which is used for a consistency-check of the aforementioned cancellation of the $O(m_{t}^{2}/M_{W}^{2})$ terms. Among the $O(1)$ non-decoupling terms, we sort out those that can be regarded as due to the effective Lagrangian in which quark bilinear forms are coupled to the scalar curvature.

hep-ph↗
arXiv2021

Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation

Primordial cosmological perturbations are the seeds that were cultivated by inflation and the succeeding dynamical processes, eventually leading to the current Universe. In this work, we investigate the behavior of the gauge-invariant scalar and tensor perturbations under the general extended disformal transformation, namely, $g_{μν} \rightarrow A(X,Y,Z)g_{μν} + Φ_μΦ_ν$, where $X \equiv -\tfrac{1}{2}ϕ^{;μ}ϕ_{;μ}, Y \equiv ϕ^{;μ}X_{;μ}, Z \equiv X^{;μ}X_{;μ} $ and $Φ_μ\equiv Cϕ_{;μ} + DX_{;μ}$, with $C$ and $D$ being a general functional of $(ϕ,X,Y,Z)$. We find that the tensor perturbation is invariant under this transformation. On the other hand, the scalar curvature perturbation receives a correction due the conformal term only; it is independent of the disformal term at least up to linear order. Within the framework of the full Horndeski theory, the correction terms turn out to depend linearly on the gauge-invariant comoving density perturbation and the first time-derivative thereof. In the superhorizon limit, all these correction terms vanish, leaving only the original scalar curvature perturbation. In other words, it is invariant under the general extended disformal transformation in the superhorizon limit, in the context of full Horndeski theory. Our work encompasses a chain of research studies on the transformation or invariance of the primordial cosmological perturbations, generalizing their results under our general extended disformal transformation.

gr-qc↗
arXiv2018

Heavy Particle Signatures in Cosmological Correlation Functions with Tensor Modes

We explore the possibility to make use of cosmological data to look for signatures of unknown heavy particles whose masses are on the order of the Hubble parameter during the time of inflation. To be more specific we take up the quasi-single field inflation model, in which the isocurvaton $σ$ is supposed to be the heavy particle. We study correlation functions involving both scalar ($ζ$) and tensor ($γ$) perturbations and search for imprints of the $σ$-particle effects. We make use of the technique of the effective field theory for inflation to derive the $ζσ$ and $γζσ$ couplings. With these couplings we compute the effects due to $σ$ to the power spectrum $\langle ζζ\rangle $ and correlations $\langle γ^{s} ζζ\rangle$ and $\langle γ^{s_{1}} γ^{s_{2}} ζζ\rangle $, where $s$, $s_{1}$ and $s_{2}$ are the polarization indices of gravitons. Numerical analyses of the $σ$-mass effects to these corrlations are presented. It is argued that future precise observations of these correlations could make it possible to measure the $σ$-mass and the strength of the $ζσ$ and $γζσ$ couplings. As an extension to the $N$-graviton case we also compute the correlations $\langle γ^{s_{1}} \cdots γ^{s_{N}} ζζ\rangle $ and $\langle γ^{s_{1}} \cdots \cdots γ^{s_{2N}} ζζ\rangle $ and their $σ$-mass effects. It is suggested that larger $N$ correlation functions are useful to probe larger $σ$-mass .

hep-th↗
arXiv2017

Adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation

We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruh's model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of $ e $-folds. As in the result for the canonical inflation, the regularized power spectrum tends to the "bare" power spectrum as the Universe expands during (and even after) inflation. This work justifies the use of the "bare" power spectrum in standard calculation in the most general context of slow-roll single-field inflation involving non-minimal coupling and varying speed of sound.

gr-qc↗
arXiv2016

The double-soft limit in cosmological correlation functions and graviton exchange effects

The graviton exchange effect on cosmological correlation functions is examined by employing the double-soft limit technique. A new relation among correlation functions that contain the effects due to graviton exchange diagrams in addition to those due to scalar-exchange and scalar-contact-interaction, is derived by using the background field method and independently by the method of Ward identities associated with dilatation symmetry. We compare these three terms, putting small values for the slow-roll parameters and $(1-n_{s}) = 0.042$, where $n_{s}$ is the scalar spectral index. It is argued that the graviton exchange effects are more dominant than the other two and could be observed in the trispectrum in the double-soft limit. Our observation strengthens the previous work by Seery, Sloth and Vernizzi, in which it has been argued that the graviton exchange dominates in the counter-collinear limit for single field slow-roll inflation.

hep-th↗
arXiv2015

Logarithmic divergences in the $k$-inflationary power spectra computed through the uniform approximation

We investigate a calculation method for solving the Mukhanov-Sasaki equation in slow-roll $k$-inflation based on the uniform approximation (UA) in conjunction with an expansion scheme for slow-roll parameters with respect to the number of $e$-folds about the so-called \textit{turning point}. Earlier works on this method has so far gained some promising results derived from the approximating expressions for the power spectra among others, up to second order with respect to the Hubble and sound flow parameters, when compared to other semi-analytical approaches (e.g., Green's function and WKB methods). However, a closer inspection is suggestive that there is a problem when higher-order parts of the power spectra are considered; residual logarithmic divergences may come out that can render the prediction physically inconsistent. Looking at this possibility, we map out up to what order with respect to the mentioned parameters several physical quantities can be calculated before hitting a logarithmically divergent result. It turns out that the power spectra are limited up to second order, the tensor-to-scalar ratio up to third order, and the spectral indices and running converge to all orders. This indicates that the expansion scheme is incompatible with the working equations derived from UA for the power spectra but compatible with that of the spectral indices. For those quantities that involve logarithmically divergent terms in the higher-order parts, existing results in the literature for the convergent lower-order parts calculated in the equivalent fashion should be viewed with some caution; they do not rest on solid mathematical ground.

gr-qc↗
arXiv2015

Adiabatic regularisation of power spectra in $k$-inflation

We look at the question posed by Parker et al. about the effect of UV regularisation on the power spectrum for inflation. Focusing on the slow-roll $k$-inflation, we show that up to second order in the Hubble and sound flow parameters, the adiabatic regularisation of such model leads to no difference in the power spectrum apart from certain cases that violate near scale invariant power spectra. Furthermore, extending to non-minimal $k$-inflation, we establish the equivalence of the subtraction terms in the adiabatic regularisation of the power spectrum in Jordan and Einstein frames.

gr-qc↗
arXiv2014

Observational Equivalence Using Schedulers for Quantum Processes

In the study of quantum process algebras, researchers have introduced different notions of equivalence between quantum processes like bisimulation or barbed congruence. However, there are intuitively equivalent quantum processes that these notions do not regard as equivalent. In this paper, we introduce a notion of equivalence named observational equivalence into qCCS. Since quantum processes have both probabilistic and nondeterministic transitions, we introduce schedulers that solve nondeterministic choices and obtain probability distribution of quantum processes. By definition, the restrictions of schedulers change observational equivalence. We propose some definitions of schedulers, and investigate the relation between the restrictions of schedulers and observational equivalence.

cs.LO↗
arXiv2014

Linear programming analysis of the $R$-parity violation within EDM-constraints

The constraint on the $R$-parity violating supersymmetric interactions is discussed in the light of current experimental data of the electric dipole moment of neutron, $^{129}$Xe , $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules. To investigate the constraints without relying upon the assumption of the dominance of a particular combination of couplings over all the rest, an extensive use is made of the linear programming method in the scan of the parameter space. We give maximally possible values for the EDMs of the proton, deuteron, $^3$He nucleus, $^{211}$Rn, $^{225}$Ra, $^{210}$Fr, and the $R$-correlation of the neutron beta decay within the constraints from the current experimental data of the EDMs of neutron, $^{129}$Xe, $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules using the linear programming method. It is found that the $R$-correlation of the neutron beta decay and hadronic EDMs are very useful observables to constrain definite regions of the parameter space of the $R$-parity violating supersymmetry.

hep-ph↗
arXiv2013

R-parity violating supersymmetric Barr-Zee type contributions to the fermion electric dipole moment with weak gauge boson exchange

The contribution of the R-parity violating trilinear couplings in the supersymmetric model to the fermion electric dipole moment is analyzed at the two-loop level. We show that in general, the Barr-Zee type contribution to the fermion electric dipole moment with the exchange of W and Z bosons is not small compared to the currently known photon exchange one with R-parity violating interactions. We will then give new upper bounds on the imaginary parts of R-parity violating couplings from the experimental data of the electric dipole moments of the electron and of the neutron. The effect due to bilinear R-parity violating couplings, which needs to be investigated separately, is not included in our analyses.

hep-ph↗
arXiv2012

R-parity violating supersymmetric contributions to the neutron beta decay at the one-loop level

The contribution of the R-parity violating minimal supersymmetric standard model to the neutron beta decay at the one-loop level is investigated. It is found that the baryon number and R-parity violating interactions contribute to the D correlation through one-loop corrections, while the tree level prediction is vanishing. The Fierz interference term is also investigated at the one-loop level by considering the lepton number and R-parity violating interactions. We show that future experimental progress can provide us with better constraints on some of the combinations of R-parity violating couplings.

hep-ph↗
arXiv2012

The Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling

The method of a conformal transformation is applied to a general class of single field inflation models with non-minimal coupling to gravity and non-standard kinetic terms, in order to reduce the cosmological perturbative calculation to the conventional minimal coupling case to all orders in perturbation theory. Our analysis is made simple by the fact that all perturbation variables in the comoving gauge are conformally invariant to all orders. The structure of the vacuum, on which cosmological correlation functions are evaluated, is also discussed. We show how quantization in the Jordan frame for non-minimally coupled inflation models can be equivalently implemented in the Einstein frame. It is thereafter argued that the general N-point cosmological correlation functions (of the curvature perturbation) are independent of the conformal frame.

gr-qc↗
arXiv2011

Constraint on R-parity violating MSSM at the one-loop level from CP-odd N-N interaction

Minimal supersymmetric standard model with R-parity violation (RPVMSSM) contributes to the P-, CP-odd four-quark interaction. The P-, CP-odd four-quark interaction is constrained by the new 199Hg EDM experimental data. It is then possible to constrain R-parity violating (RPV) couplings from the 199Hg EDM data. In this talk, we analyze the RPV contribution to the P-, CP-odd four- quark interaction at the one-loop level to give constraints on RPV parameters.

hep-ph↗
arXiv2010

One-loop analysis of the four-Fermi contribution to the atomic EDM within RPVMSSM

The contribution in the R-parity violating (RPV) Minimal Supersymmetric Standard Model (MSSM) to the electric dipole moment (EDM) of $^{199}$Hg at the one-loop level is evaluated. At the one-loop level, the $^{199}$Hg EDM receives RPV contribution whose couplings are of a different type from the tree level analysis. This contribution is shown to be constrained by using the limit to the CP-odd electron-nucleon (e-N) interaction given by the recent result of $^{199}$Hg EDM experiment.

hep-ph↗
arXiv2010

Galilean Conformal Algebra in Two Dimensions and Cosmological Topologically Massive Gravity

We consider a realization of the Galilean conformal algebra (GCA) in two dimensional space-time on the AdS boundary of a particular three dimensional gravity theory, the so-called cosmological topologically massive gravity (CTMG), which includes the gravitational Chern-Simons term and the negative cosmological constant. The infinite dimensional GCA in two dimensions is obtained from the Virasoro algebra for the relativistic CFT by taking a scaling limit $t\to t$, $x\toεx$ with $ε\to 0$. The parent relativistic CFT should have left and right central charges of order $\mathcal{O}(1/ε)$ but opposite in sign in the limit $ε\to 0$. On the other hand, by Brown-Henneaux's analysis the Virasoro algebra is realized on the boundary of AdS$_3$, but the left and right central charges are asymmetric only by the factor of the gravitational Chern-Simons coupling $1/μ$. If $μ$ behaves as of order $\mathcal{O}(ε)$ under the corresponding limit, we have the GCA with non-trivial centers on AdS boundary of the bulk CTMG. Then we present a new entropy formula for the Galilean field theory from the bulk black hole entropy, which is a non-relativistic counterpart of the Cardy formula. It is also discussed whether it can be reproduced by the microstate counting.

hep-th↗