We combine the D0 measurement of the width difference between the light and heavy $B_s^0$ mass eigenstates and of the $CP$-violating mixing phase determined from the time-dependent angular distributions in the $B_s^0\to J/\psi \varphi$ decays along with the charge asymmetry in semileptonic decays also measured with the D0 detector. With the additional constraint from the world average of the flavor-specific $B_s^0$ lifetime, we obtain $\Delta {\Gamma }_s\equiv ({\Gamma }_L-{\Gamma }_H)=0.13\pm 0.09{\mathrm{ps}}^{-1}$ and $|{\varphi }_s|={0.70}_{-0.47}^{+0.39}$ or $\Delta {\Gamma }_s=-0.13\pm 0.09{\mathrm{ps}}^{-1}$ and $|{\varphi }_s|={2.44}_{-0.39}^{+0.47}$. The data sample corresponds to an integrated luminosity of $1.1{\mathrm{fb}}^{-1}$ accumulated with the D0 detector at the Fermilab Tevatron Collider.

We study the possible bound states of the $K\overline{K}$ system in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. We find that the bound states exist. However, these bound states have very small decay widths. Therefore, besides the possible $K\overline{K}$ component, there may be some other structures in the observed $f_0(980)$ and $a_0(980)$.

Different theoretical and phenomenological aspects of the minimal and nonminimal walking technicolor theories have recently been studied. The goal here is to make the models ready for collider phenomenology. We do this by constructing the low energy effective theory containing scalars, pseudoscalars, vector mesons, and other fields predicted by the minimal walking theory. We construct their self-interactions and interactions with standard model fields. Using the Weinberg sum rules, opportunely modified to take into account the walking behavior of the underlying gauge theory, we find interesting relations for the spin-one spectrum. We derive the electroweak parameters using the newly constructed effective theory and compare the results with the underlying gauge theory. Our analysis is sufficiently general such that the resulting model can be used to represent a generic walking technicolor theory not at odds with precision data.

A disorder parameter detecting dual superconductivity of the vacuum is used as a probe to characterize the confining properties of the phase diagram of two-color QCD at finite temperature and density. We obtain evidence for the disappearing of dual superconductivity (deconfinement) induced by a finite density of baryonic matter, as well as for a coincidence of this phenomenon with the restoration of chiral symmetry both at zero and finite density. The saturation transition induced by Pauli blocking is studied as well, and a general warning is given about the possible effects that this unphysical transition could have on the study of the QCD phase diagram at strong values of the gauge coupling.

The neutrino mass hierarchy can be determined, in principle, by measuring a phase in the disappearance oscillation probability in vacuum, without relying on the matter effect, using a single channel. This phase is not the same for the normal and inverted neutrino mass spectra. In this paper, we give a complete description and physics understanding of the method. The key feature of the method is to detect advancement (normal) or retardation (inverted) of the phase of the atmospheric-scale oscillation relative to the solar-scale oscillation. We then show that this method can be realized with the recently proposed resonant ${\overline{\nu }}_e$ absorption reaction enhanced by the Mössbauer effect. The unique feature of this setup is the ultramonochromaticity of the observed ${\overline{\nu }}_e$’s. Because of this feature, the phase advancement or retardation of atmospheric-scale neutrino oscillation is detectable after 20 or more oscillations if the source and the target are made sufficiently compact in size. A quantitative estimate of the sensitivity to mass hierarchy resolution is given. We have also examined how a possible continuation of such an experiment can be carried out in order also to achieve high precision (few percent) determination of the solar-scale oscillation parameters $\Delta m_{21}^2$ and ${\theta }_{12}$.

Field quantization in 5D flat and warped space-times with $Z_2$ parity is comparatively examined. We carefully and closely derive 5D position/momentum propagators. Their characteristic behaviors depend on the 4D (real world) momentum in relation to the boundary parameter ($l$) and the bulk curvature ($\omega$). They also depend on whether the 4D momentum is spacelike or timelike. Their behaviors are graphically presented, and the $Z_2$ symmetry, the brane formation, and the singularities are examined. It is shown that the use of absolute functions is important for properly treating the singular behavior. The extra coordinate appears as a directed one like the temperature. The $\delta (0)$ problem, which is an important consistency check of the bulk-boundary system, is solved without the use of Kaluza-Klein (KK) expansion. The relation between the position/momentum propagator (a closed expression which takes into account all KK modes) and the KK-expansion-series propagator is clarified. In this process of comparison, two views on the extra space naturally come up: the orbifold picture and the interval (boundary) picture. Sturm-Liouville expansion (a generalized Fourier expansion) is essential there. Both 5D flat and warped quantum systems are formulated by Dirac’s bra and ket vector formalism, which shows that the warped model can be regarded as a deformation of the flat one with the deformation parameter $\omega$. We examine the meaning of the position-dependent cutoff proposed by Randall and Schwartz.

The first order perturbations of the energy levels of a stationary hydrogen atom in a static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic $1S$, $2S$, $2P$, $3S$, $3P$, $3D$, $4S$, $4P$, $4D$, and $4F$ levels. The results show that the energy-level shifts of the states with total angular momentum quantum number $1/2$ are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number $5/2$ is $1:4:5$. This feature can be used to help us to distinguish the gravitational effect from other effects.

It is investigated whether a massive Abelian vector field, whose gauge kinetic function is growing during inflation, can be responsible for the generation of the curvature perturbation in the Universe. Particle production is studied and it is shown that the vector field can obtain a scale-invariant superhorizon spectrum of perturbations with a reasonable choice of kinetic function. After inflation the vector field begins coherent oscillations, during which it corresponds to pressureless isotropic matter. When the vector field dominates the Universe, its perturbations give rise to the observed curvature perturbation following the curvaton scenario. It is found that this is possible if, after the end of inflation, the mass of the vector field increases at a phase transition at temperature of order 1 TeV or lower. Inhomogeneous reheating, whereby the vector field modulates the decay rate of the inflaton, is also studied.

Best-fit values of recent global analyses of neutrino data imply large solar neutrino mixing, vanishing $U_{e3}$, and a nonmaximal atmospheric neutrino mixing angle ${\theta }_{23}$. We show that these values emerge naturally by the hypothesis of scaling in the Majorana neutrino mass matrix, which states that the ratios of its elements are equal. It also predicts an inverted hierarchy for the neutrino masses. We point out several advantages and distinguishing tests of the scaling hypothesis compared to the $L_e-L_{\mu }-L_{\tau }$ flavor symmetry, which is usually assumed to provide an understanding of the inverted hierarchy. Scenarios which have initially vanishing $U_{e3}$ and maximal atmospheric neutrino mixing are shown to be unlikely to lead to nonmaximal ${\theta }_{23}$ while simultaneously keeping $U_{e3}$ zero. We find a peculiar ratio of the branching ratios $\mu \to e\gamma$ and $\tau \to e\gamma$ in supersymmetric seesaw frameworks, which only depends on atmospheric neutrino mixing and results in $\tau \to e\gamma$ being unobservable. The consequences of the scaling hypothesis for high energy astrophysical neutrinos at neutrino telescopes are also investigated. Then we analyze a seesaw model based on the discrete symmetry $D_4\times Z_2$ leading to scaling in the low energy mass matrix and being capable of generating the baryon asymmetry of the Universe via leptogenesis. The relevant $CP$ phase is identical to the low energy Majorana phase, and successful leptogenesis requires an effective mass for neutrinoless double beta decay larger than 0.045 eV.

We provide a careful analysis of the generating functional in the path-integral formulation of pseudo-Hermitian and in particular $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics and show how the metric operator enters the expression for the generating functional.

This is an extended version of the previous paper [S. Iso, T. Morita, and H. Umetsu, Phys. Rev. D 75, 124004 (2007).]. Quantum fields near horizons can be described in terms of an infinite set of two-dimensional conformal fields. We first generalize the method of Christensen and Fulling to charged black holes to derive fluxes of energy and charge. These fluxes can be obtained by employing a conformal field theory technique. We then apply this technique to obtain the fluxes of higher-spin currents and show that the thermal distribution of Hawking radiation from a charged black hole can be completely reproduced by investigating transformation properties of the higher-spin currents under conformal and gauge transformations.

We have studied the wave dynamics and the energy absorption problem for the scalar field as well as the brane-localized gravitational field in the background of a brane-world black hole. Comparing our results with the four-dimensional Schwarzschild black hole, we have observed the signature of the extra dimension in the energy absorption spectrum.

Some models are presented in which the strength of the gravitational coupling of the potential energy relative to the same coupling for the kinetic energy is, in a precise sense, adjustable. The gauge symmetry of these models consists of those coordinate changes with unit Jacobian.

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a “Helfer state.” This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already encoded in the fluctuations of the vacuum.

We search for viable $f(R)$ theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass or by exploiting the so-called chameleon effect. However, in both cases, it appears likely that any late-time cosmic acceleration will be observationally indistinguishable from acceleration caused by a cosmological constant. We also explore further observational constraints from, e.g., big bang nucleosynthesis and inflation.

We consider $f(R)$ modified gravity theories in the metric variation formalism and attempt to reconstruct the function $f(R)$ by demanding a background $\Lambda \mathrm{CDM}$ cosmology. In particular we impose the following requirements: (a) A background cosmic history $H(z)$ provided by the usual flat $\Lambda \mathrm{CDM}$ parametrization though the radiation ($w_{\mathrm{eff}}=1/3$), matter ($w_{\mathrm{eff}}=0$), and de Sitter ($w_{\mathrm{eff}}=-1$) eras. (b) Matter and radiation dominate during the “matter” and “radiation” eras, respectively, i.e. ${\Omega }_m=1$ when $w_{\mathrm{eff}}=0$ and ${\Omega }_r=1$ when $w_{\mathrm{eff}}=1/3$. We have found that the cosmological dynamical system constrained to obey the $\Lambda \mathrm{CDM}$ cosmic history has four critical points in each era which correspondingly lead to four forms of $f(R)$. One of them is the usual general relativistic form $f(R)=R-2\Lambda$. The other three forms in each era, reproduce the $\Lambda \mathrm{CDM}$ cosmic history but they do not satisfy requirement (b) stated above.

Black-hole (BH) oscillations known as quasinormal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs, are detectable and worth searching for in observations and simulations of binary BH mergers. We calculate the metric perturbations to second order and explicitly regularize the master equation at the horizon and spatial infinity. We find that the second-order QNMs have frequencies twice the first-order ones and the GW amplitude is up to $\sim 10\%$ of that of the first-order one. The QNM frequency would also shift blueward up to $\sim 1\%$. This provides a new test of general relativity as well as a possible distance indicator.

The first limit on the branching ratio of the electric charge-nonconserving invisible muon decay $\mathrm{Br}({\mu }^{+}\to \mathrm{invisible})<5.2\times {10}^{-3}$ is obtained from the recently reported results on new determination of the Fermi constant from muon decays. The results of a feasibility study of a new proposed experiment for a sensitive search for this decay mode at the level of a few parts in ${10}^{11}$ are presented. Constrains on the $\tau \to \mathrm{invisible}$ decay rate are discussed. These leptonic charge-nonconserving processes may hold in four-dimensional world in models with infinite extra dimensions, thus making their searches complementary to collider experiments probing new physics.

The low-lying eigenvalue spectrum of the QCD Dirac operator in the $ϵ$ regime is expected to match with that of chiral random matrix theory (ChRMT). We study this correspondence for the case including sea quarks by performing two-flavor QCD simulations on the lattice. Using the overlap fermion formulation, which preserves exact chiral symmetry at finite lattice spacings, we push the sea quark mass down to $\sim 3\mathrm{MeV}$ on a ${16}^3\times 32$ lattice at a lattice spacing $a\simeq 0.11\mathrm{fm}$. We compare the low-lying eigenvalue distributions and find a good agreement with the analytical predictions of ChRMT. By matching the lowest-lying eigenvalue we extract the chiral condensate, ${\Sigma }^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=(251\pm 7\pm 11\mathrm{MeV}{)}^3$, where errors represent statistical and higher order effects in the $ϵ$ expansion. We also calculate the eigenvalue distributions on the lattices with heavier sea quarks at two lattice spacings. Although the $ϵ$ expansion is not applied for those sea quarks, we find a reasonable agreement of the Dirac operator spectrum with ChRMT. The value of $\Sigma$, after extrapolating to the chiral limit, is consistent with the estimate in the $ϵ$ regime.

In the framework of the impact picture we compute the analyzing power $A_N$ for $pp$ elastic scattering at high energy and in the very forward direction. We consider the full set of Coulomb amplitudes and show that the interference between the hadronic nonflip amplitude and the single-flip Coulomb amplitude is sufficient to obtain a good agreement with the present experimental data. This leads us to conclude that the single-flip hadronic amplitude is small in this low momentum transfer region and it strongly suggests that this process can be used as an absolute polarimeter at the Relativistic Heavy Ions Collider, at Brookhaven National Laboratory, working as a polarized $pp$ collider.