Criticality and Inflation of the Gauged B-L Model

We consider the multiple point principle (MPP) and the inflation of the gauged B-L extension of the Standard Model (SM) with a classical conformality. We examine whether the scalar couplings and their beta functions can become simultaneously zero at $\Lambda_{\text{MPP}}:=10^{17}$ GeV by using the two-loop renormalization group equations (RGEs). We find that we can actually realize such a situation and that the parameters of the model are uniquely determined by the MPP. However, as discussed in \cite{Iso:2012jn}, if we want to realize the electroweak symmetry breaking by the radiative B-L symmetry breaking, the self coupling $\lambda_{\Psi}$ of a newly introduced SM singlet complex scalar $\Psi$ must have a non-zero value at $\Lambda_{\text{MPP}}$, which means the breaking of the MPP. We find that the ${\cal{O}}(100)$GeV electroweak symmetry breaking can be achieved even if this breaking is very small; $\lambda_{\Psi}(\Lambda_{\text{MPP}})\leq10^{-10}$. Within this situation, the mass of the B-L gauge boson is predicted to be \begin{equation} M_{B-L}=2\sqrt{2}\times\sqrt{\frac{\lambda(v_{h})}{0.10}}\times v_{h}\simeq 696\hspace{1mm}\text{GeV},\nonumber\end{equation} where $\lambda$ is the Higgs self coupling and $v_{h}$ is the Higgs expectation value. This is a remarkable prediction of the (slightly broken) MPP. Furthermore, such a small $\lambda_{\Psi}$ opens a new possibility: $\Psi$ plays a roll of the inflaton \cite{Okada:2011en}. Another purpose of this paper is to investigate the $\lambda_{\Psi}\Psi^{4}$ inflation scenario with the non-minimal gravitational coupling $\xi\Psi^{2} {\cal{R}}$ based on the two-loop RGEs.Comment: 28 pages, 8 figures; some typos are corrected, Eq.(11) is corrected, the predicted mass of M_{B-L} has changed, RGEs are corrected, footnotes added, references added (v2); some typos are corrected, Eq.(26) is added, references added, version to appear in PTEP(v3

Reconsideration of the Coleman's Baby Universe

We reconsider the Coleman's mechanism that solves the Cosmological Constant Problem by the baby universes. We use the Lorentzian path integral and allow each universe has a different effective field theory and a vacuum. By using the probability distribution of coupling constants, it is shown that the cosmological constant of our universe does not necessary become small due to the effects of other universes.Comment: 13 pages, 3 figures; typos are corrected, and references are added (v3

RG-improvement of the effective action with multiple mass scales

Improving the effective action by the renormalization group (RG) with several mass scales is an important problem in quantum field theories. A method based on the decoupling theorem was proposed in \cite{Bando:1992wy} and systematically improved \cite{Casas:1998cf} to take threshold effects into account. In this paper, we apply the method to the Higgs-Yukawa model, including wave-function renormalizations, and to a model with two real scalar fields $(\varphi, h)$. In the Higgs-Yukawa model, even at one-loop level, Feynman diagrams contain propagators with different mass scales and decoupling scales must be chosen appropriately to absorb threshold corrections. On the other hand, in the two-scalar model, the mass matrix of the scalar fields is a function of their field values $(\varphi, h)$ and the resultant running couplings obey different RGEs on a different point of the field space. By solving the RGEs, we can obtain the RG improved effective action in the whole region of the scalar fields.Comment: 22 pages, 6 figure

Reheating-era leptogenesis

We propose a novel leptogenesis scenario at the reheating era. Our setup is minimal in the sense that, in addition to the standard model Lagrangian, we only consider an inflaton and higher dimensional operators. The lepton number asymmetry is produced not by the decay of a heavy particle, but by the scattering between the standard model particles. After the decay of an inflaton, the model is described within the standard model with higher dimensional operators. The Sakharov's three conditions are satisfied by the following way. The violation of the lepton number is realized by the dimension-5 operator. The complex phase comes from the dimension-6 four lepton operator. The universe is out of equilibrium before the reheating is completed. It is found that the successful baryogenesis is realized for the wide range of parameters, the inflaton mass and reheating temperature, depending on the cutoff scale. Since we only rely on the effective Lagrangian, our scenario can be applicable to all mechanisms to generate neutrino Majorana masses.Comment: 5 pages, 3 figures; published version(v2

Hillclimbing saddle point inflation

Recently a new inflationary scenario was proposed in arXiv:1703.09020 which can be applicable to an inflaton having multiple vacua. In this letter, we consider a more general situation where the inflaton potential has a (UV) saddle point around the Planck scale. This class of models can be regarded as a natural generalization of the hillclimbing Higgs inflation (arXiv:1705.03696).Comment: 5 pages, 3 figures; Report number added (v2

Note on general functional flows in equilibrium systems

We study the response of generating functionals to a variation of parameters (couplings) in equilibrium systems i.e. in quantum field theory (QFT) and equilibrium statistical mechanics. These parameters can be either physical ones such as coupling constants or artificial ones which are intentionally introduced such as the renormalization scale in field theories. We first derive general functional flow equations for the generating functional (grand-canonical potential) $W[J]$ of the connected diagrams. Then, we obtain functional flow equations for the one-particle irreducible ($1$PI) vertex functional (canonical potential) $\Gamma[\phi]$ by performing the Legendre transformation. By taking the functional derivatives of the flow equations, we can obtain an infinite hierarchical equations for the $1$PI vertices. We also point out that a Callan-Symanzik type equation holds among the vertices when partition function is invariant under some changes of the parameters. After discussing general aspects of parameter response, we apply our formalism to several examples and reproduce the well-known functional flow equations. Our response theory provides us a systematic and general way to obtain various functional flow equations in equilibrium systems.Comment: 24 page

Multiple Point Principle of the Standard Model with Scalar Singlet Dark Matter and Right Handed Neutrinos

We consider the multiple point principle (MPP) of the Standard Model (SM) with the scalar singlet Dark Matter (DM) and three heavy right-handed neutrinos at the scale where the beta function $\beta_{\lambda}$ of the effective Higgs self coupling $\lambda_{\text{eff}}$ becomes zero. We make the two-loop analysis and find that the top quark mass $M_{t}$ and the Higgs portal coupling $\kappa$ are strongly related each other. One of the good points in this model is that the larger $M_{t}{1mm}(\gtrsim 171\text{GeV})$ is allowed. This fact is consistent with the recent experimental value \cite{ATLAS:2014wva} $M_{t}=173.34\pm0.76$ GeV, which corresponds to the DM mass $769{1mm}\text{GeV}\leq m_{\text{DM}}\leq 1053 {1mm}\text{GeV}$.Comment: 16 pages, 4 figures; references added, Version to appear in PTEP(v2