Cosmological magnetic fields induce temperature and polarization fluctuations in the cosmic microwave background (CMB) radiation. A cosmological magnetic field with current amplitude of order ${10}^{-9}\mathrm{G}$ is detectable via observations of CMB anisotropies. This magnetic field (with or without helicity) generates vector perturbations through vortical motions of the primordial plasma. This paper shows that magnetic field helicity induces parity-odd cross correlations between CMB temperature and $B$-polarization fluctuations and between $E$- and $B$-polarization fluctuations, correlations which are zero for fields with no helicity (or for any parity-invariant source). Helical fields also contribute to parity-even temperature and polarization anisotropies, canceling part of the contribution from the symmetric component of the magnetic field. We give analytic approximations for all CMB temperature and polarization anisotropy vector power spectra due to helical magnetic fields. These power spectra offer a method for detecting cosmological helical magnetic fields, particularly when combined with Faraday rotation measurements which are insensitive to helicity.

Gravitational radiation from a slightly distorted black hole with ringdown waveform is well understood in general relativity. It provides a probe for direct observation of black holes and determination of their physical parameters, masses and angular momenta (Kerr parameters). For ringdown searches using data of gravitational wave detectors, matched filtering technique is useful. In this paper, we describe studies on problems in matched filtering analysis in realistic gravitational wave searches using observational data. Above all, we focus on template constructions, matches or signal-to-noise ratios (SNRs), detection probabilities for Galactic events, and accuracies in evaluation of waveform parameters or black hole hairs. In template design for matched filtering, search parameter ranges and template separations are determined by requirements from acceptable maximum loss of SNRs, detection efficiencies, and computational costs. In realistic searches using observational data, however, effects of nonstationary noises cause decreases of SNRs, and increases of errors in waveform parameter determinations. These problems will potentially arise in any matched filtering searches for any kind of waveforms. To investigate them, we have performed matched filtering analysis for artificial ringdown signals which are generated with Monte-Carlo technique and injected into the TAMA300 observational data. We employed an efficient method to construct a bank of ringdown filters recently proposed by Nakano et al., and use a template bank generated from a criterion such that losses of SNRs of any signals do not exceed $2\%$. We found that this criterion is fulfilled in ringdown searches using TAMA300 data, by examining distribution of SNRs of simulated signals. It is also shown that with TAMA300 sensitivity, the detection probability for Galactic ringdown events is about $50\%$ for black holes of masses greater than $20M_{\odot }$ with $\mathrm{SNR}>10$. The accuracies in waveform parameter estimations are found to be consistent with the template spacings, and resolutions for black hole masses and the Kerr parameters are evaluated as a few $\%$ and $\sim 40\%$, respectively. They can be improved up to $<0.9\%$ and $<24\%$ for events of $\mathrm{SNR}\ge 10$ by using fine-meshed template bank in the hierarchical search strategy.

We show that the fermionic zero mode in nontrivial SU(2) gauge field backgrounds must have a zero. We demonstrate this explicitly for calorons where its location is related to a constituent monopole. Furthermore a topological reasoning for the existence of the zero is given which therefore will be present for any nontrivial configuration. We propose the use of this property, in particular, for lattice simulations in order to uncover the topological content of a configuration.

We systematically study the possibility for realizing realistic values of lepton mass ratios and mixing angles by using only renormalizable Yukawa couplings derived from the heterotic $Z_6\mathrm{\text{−}}\mathrm{I}$ orbifold. We assume one pair of up and down sector Higgs fields. We consider both the Dirac neutrino mass scenario and the seesaw scenario with degenerate right-handed majorana neutrino masses. It is found that realistic values of the charged lepton mass ratios, $m_e/m_{\tau }$ and $m_{\mu }/m_{\tau }$, the neutrino mass squared difference ratio, $\Delta m_{31}^2/\Delta m_{21}^2$, and the lepton mixing angles can be obtained in certain cases.

We study properties of spacelike monopole trajectories in the Maximal Abelian gauge of quenched SU(2) QCD at finite temperature. We concentrate on infrared monopole clusters which are responsible for the confinement properties of the theory. We determine numerically the effective action of the monopoles projected onto the three-dimensional time-slice. Then we derive the length distributions of the monopole loops and fix their entropy.

We report results on the Dalitz analysis of three-body charmless $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ and $B^{+}\to K^{+}{K}^{+}{K}^{-}$ decays based on a $140{\mathrm{fb}}^{-1}$ data sample collected with the Belle detector. Measurements of branching fractions for quasi-two-body decays to scalar-pseudoscalar states: $B^{+}\to f_0(980)K^{+}$, $B^{+}\to K_0^{*}(1430{)}^0{\pi }^{+}$, and to vector-pseudoscalar states: $B^{+}\to K^{*}(892{)}^0{\pi }^{+}$, $B^{+}\to {\rho }^0{K}^{+}$, $B^{+}\to \varphi K^{+}$ are presented. Upper limits on decays to some pseudoscalar-tensor final states are reported. We also report the measurement of the $B^{+}\to {\chi }_{c0}{K}^{+}$ branching fraction in two ${\chi }_{c0}$ decays channels: ${\chi }_{c0}\to {\pi }^{+}{\pi }^{-}$ and ${\chi }_{c0}\to K^{+}{K}^{-}$.

We consider the equation of state of QCD at high density and zero temperature in perturbation theory to first order in the coupling constant ${\alpha }_s$. We compute the thermodynamic potential including the effect of a nonvanishing mass for the strange quark and show that corrections are sizable. Renormalization group running of the coupling and the strange quark mass plays a crucial role. The structure of quark stars is dramatically modified.

In this paper we prove that the Hamilton-Jacobi equation for a particle in the five dimensional Kerr-(A)dS black hole is separable, for arbitrary rotation parameters. As a result we find an irreducible Killing tensor. We also consider the Klein-Gordon equation in this background and show that this is also separable. Finally, we comment on extensions and implications of these results.

Radiative weak decays of antitriplet bottom baryons are studied under the assumption of penguin diagram dominance and flavor-SU(3) (or SU(2)) symmetry. Relations among decay rates of various decay modes are derived.

The infrared freezing of observables is known to hold at fixed orders of perturbative QCD if the Minkowskian quantities are defined through the analytic continuation from the Euclidean region. In a recent paper [D. M. Howe and C. J. Maxwell, Phys. Rev. D 70, 014002 (2004)] it is claimed that infrared freezing can be proved also for Borel-resummed all-orders quantities in perturbative QCD. In the present paper we obtain the Minkowskian quantities by the analytic continuation of the all-orders Euclidean amplitudes expressed in terms of the inverse Mellin transform of the corresponding Borel functions [I. Caprini and M. Neubert, J. High Energy Phys. 03 (1999) 007]. Our result shows that if the principle of analytic continuation is preserved in Borel-type resummations, the Minkowskian quantities exhibit a divergent increase in the infrared regime, which contradicts the claim made in [D. M. Howe and C. J. Maxwell, Phys. Rev. D 70, 014002 (2004)]. We discuss the arguments given in this paper and show that the special redefinition of Borel summation at low energies adopted there does not reproduce the lowest order result obtained by analytic continuation.

The string theory in the Penrose limit of ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$ is investigated. The specific Penrose limit is the background known as the Nappi-Witten spacetime, which is a plane-wave background with an axion field. The string theory on it is given as the Wess-Zumino-Novikov-Witten (WZNW) model on nonsemi-simple group $H_4$. It is found that, in the past literature, an important type of irreducible representations of the corresponding algebra, $h_4$, were missed. We present these “new” representations, which have the type of continuous series representations. All three types of representations of the previous literature can be obtained from the new representations by setting the momenta in the theory to special values. Then we realized the affine currents of the WZNW model in terms of four bosonic free fields and constructed the spectrum of the theory by acting the negative frequency modes of free fields on the ground level states in the $h_4$ continuous series representation. The spectrum is shown to be free of ghosts, after the Virasoro constraints are satisfied. In particular we argued that there is no need for constraining one of the longitudinal momenta to have unitarity. The tachyon vertex operator, that correspond to a particular state in the ground level of the string spectrum, is constructed. The operator products of the vertex operator with the currents and the energy-momentum tensor are shown to have the correct forms, with the correct conformal weight of the vertex operator.

We present examples of on-shell recurrence relations for determining rational functions appearing in one-loop QCD amplitudes. In particular, we give relations for one-loop QCD amplitudes with all legs of positive helicity, or with one leg of negative helicity and the rest of positive helicity. Our recurrence relations are similar to the tree-level ones described by Britto, Cachazo, Feng, and Witten. A number of new features arise for loop amplitudes in nonsupersymmetric theories like QCD, including boundary terms and double poles. We show how to eliminate the boundary terms, which would interfere with obtaining useful relations. Using the relations we give compact explicit expressions for the $n$-gluon amplitudes with one negative-helicity gluon, up through $n=7$.

The free energy of $U(N)$ gauge theory is expanded about a center-symmetric topological background configuration with vanishing action and vanishing Polyakov loops. We construct this background for $SU(N)$ lattice gauge theory and show that it uniquely describes center-symmetric minimal action orbits in the limit of infinite lattice volume. The leading contribution to the free energy in the $1/N$ expansion about this background is of $\mathcal{O}(N^0)$ rather than $\mathcal{O}(N^2)$ as one finds when the center symmetry is spontaneously broken. The contribution of planar ’t Hooft diagrams to the free energy is $\mathcal{O}(1/N^2)$ and subleading in this case. The change in behavior of the diagrammatic expansion is traced to Linde’s observation that the usual perturbation series of non-Abelian gauge theories suffers from severe infrared divergences [A. Linde, Phys. Lett. B 96, 289 (1980).]. This infrared problem does not arise in a center-symmetric expansion. The ’t Hooft coupling $\lambda =g^{2}N$ is found to decrease $\propto 1/\ln (N)$ for large $N$. There is evidence of a vector-ghost in the planar truncation of the model.

The trinification grand unified theory (GUT) has gauge group $SU(3{)}^3$ and a discrete symmetry permuting the $SU(3)$ factors. In common with other GUTs, the attractive nature of the fermionic multiplet assignments is obviated by the complicated multiparameter Higgs potential apparently needed for phenomenological reasons, and also by vacuum expectation value (VEV) hierarchies within a given multiplet. This motivates the rigorous consideration of Higgs potentials, symmetry breaking patterns, and alternative symmetry breaking mechanisms in models with this gauge group. Specifically, we study the recently proposed “clash of symmetries” brane-world mechanism to see if it can help with the symmetry breaking conundrum. This requires a detailed analysis of Higgs potential global minima and kink or domain wall solutions interpolating between the disconnected global minima created through spontaneous discrete symmetry breaking. Sufficiently long-lived metastable kinks can also be considered. We develop what we think is an interesting, albeit speculative, brane-world scheme whereby the hierarchical symmetry breaking cascade, trinification to left-right symmetry to the standard model to color cross electromagnetism, may be induced without an initial hierarchy in vacuum expectation values. Another motivation for this paper is simply to continue the exploration of the rich class of kinks arising in models that are invariant under both discrete and continuous symmetries.

We compute the angular pattern and the overlap reduction functions for the geodesic and nongeodesic response of the common mode of two interferometers interacting with a stochastic, massive scalar background. We also discuss the possible overlap between common and differential modes. We find that the cross-correlated response of two common modes to a nonrelativistic background may be higher than the response of two differential modes to the same background.

We investigate how the ghost condensate reacts to black holes immersed in it. A ghost condensate defines a hypersurface-orthogonal congruence of timelike curves, each of which has the tangent vector $u^{\mu }=-g^{\mu \nu }{\partial }_{\nu }\varphi$. It is argued that the ghost condensate in this picture approximately corresponds to a congruence of geodesics. In other words, the ghost condensate accretes into a black hole just like a pressureless dust. Correspondingly, if the energy density of the ghost condensate at large distance is set to an extremely small value by cosmic expansion then the late-time accretion rate of the ghost condensate should be negligible. The accretion rate remains very small even if effects of higher derivative terms are taken into account, provided that the black hole is sufficiently large. It is also discussed how to reconcile the black-hole accretion with the possibility that the ghost condensate might behave like dark matter.

We study a six-dimensional braneworld model with infinite warped extra dimensions in the case where the four-dimensional brane is described by a topological vortex of a U(1) symmetry-breaking Abelian Higgs model in the presence of a negative cosmological constant. A detailed analysis of the microscopic parameters leading to a finite-volume space-time in the extra dimensions is numerically performed. As previously shown, we find that a fine-tuning is required to avoid any kind of singularity on the brane. We then discuss the stability of the vortex by investigating the scalar part of the gauge-invariant perturbations around this fine-tuned configuration. It is found that the hyperstring forming Higgs and gauge fields, as well as the background metric warp factors, cannot be perturbed at all, whereas transverse modes can be considered stable. The warped space-time structure that is imposed around the vortex thus appears severely constrained and cannot generically support nonempty universe models. The genericness of our conclusions is discussed; this will shed some light on the possibility of describing our space-time as a general six-dimensional warped braneworld.

The next generation of CMB experiments should get a better handle on cosmological parameters by mapping the weak lensing deflection field, which is separable from primary anisotropies thanks to the non-Gaussianity induced by lensing. However, the generation of perturbations in the Early Universe also produces a level of non-Gaussianity which is known to be small, but can contribute to the anisotropy trispectrum at the same level as lensing. In this work, we study whether the primordial non-Gaussianity can mask the lensing statistics. We concentrate only on the “temperature quadratic estimator” of lensing, which will be nearly optimal for the Planck satellite, and work in the flat-sky approximation. We find that primordial non-Gaussianity contaminates the deflection field estimator by roughly $(0.1f_{NL})\%$ at large angular scales, which represents at most a $10\%$ contribution, not sufficient to threaten lensing extraction, but enough to be taken into account.

Hadron masses are computed from quenched twisted mass lattice QCD for a degenerate doublet of up and down quarks with the twist angle set to $\pi /2$, since this maximally-twisted theory is expected to be free of linear discretization errors. Two separate definitions of the twist angle are used, and the hadron masses for these two cases are compared. The flavor breaking, that can arise due to twisting, is discussed in the context of mass splittings within the $\Delta (1232)$ multiplet.