The Euclidean fermionic determinant in four-dimensional quantum electrodynamics is considered as a function of the fermionic mass for a class of $O(2)\times O(3)$ symmetric background gauge fields. These fields result in a determinant free of all cutoffs. Consider the one-loop effective action, the logarithm of the determinant, and subtract off the renormalization dependent second-order term. Suppose the small-mass behavior of this remainder is fully determined by the chiral anomaly. Then either the remainder vanishes at least once as the fermionic mass is varied in the interval $0<m<\infty$ or it reduces to its fourth-order value in which case the new remainder, obtained after subtracting the fourth-order term, vanishes at least once. Which possibility is chosen depends on the sign of simple integrnals involving the field strength tensor and its dual.

We consider the minimal supersymmetric standard model (MSSM) extended by introducing three right-handed (s)neutrinos to account for neutrino masses in the oscillation experiments. Assuming that the neutrino masses are purely Dirac type, the lightest right-handed sneutrino ${\tilde{\nu }}_R$ can be the lightest superparticle (LSP), which is a good candidate of cold dark matter (CDM) of the Universe. We study the possibility of realizing ${\tilde{\nu }}_R$-CDM, paying special attention to the production of ${\tilde{\nu }}_R$ via decay of the next-to-lightest superparticle after its freeze-out time. It is shown that the late decay of the MSSM-LSP (the LSP among superparticles in the MSSM) can produce a sufficient amount of ${\tilde{\nu }}_R$ to explain the observed dark matter density, and that the ${\tilde{\nu }}_R$-CDM scenario can be realized in a wide range of parameter space. We also consider the constraint on the decay of MSSM-LSP from the big bang nucleosynthesis; we found that the case with stau being the MSSM-LSP is severely constrained.

The self-accelerating braneworld model (DGP) can be tested from measurements of the expansion history of the Universe and the formation of structure. Current constraints on the expansion history from supernova luminosity distances, the cosmic microwave background (CMB), and the Hubble constant exclude the simplest flat DGP model at about $3\sigma$. Even including spatial curvature, the best-fit open DGP model is a marginally poorer fit to the data than flat $\Lambda \mathrm{CDM}$. Moreover, its substantially different expansion history raises serious challenges for the model from structure formation. A dark energy model with the same expansion history would predict a highly significant discrepancy with the baryon oscillation measurement due the high Hubble constant required. For the DGP model to satisfy this constraint new nonlinear phenomena must correct this discrepancy. Likewise the large enhancement of CMB anisotropies at the lowest multipoles due to the ISW effect would require either a cutoff in the initial power or new phenomena at the cross-over scale. A prediction that is robust to both possibilities is that high-redshift galaxies should be substantially correlated with the CMB through the ISW effect. This correlation should provide a sharp test of the DGP model in the future.

We develop a scaling ansatz for the master equation in Dvali, Gabadadze, Porrati cosmologies, which allows us to solve the equations of motion for perturbations off the brane during periods when the on-brane evolution is scale free. This allows us to understand the behavior of the gravitational potentials outside the horizon at high redshifts and close to the horizon today. We confirm that the results of Koyama and Maartens are valid at scales relevant for observations such as galaxy-ISW correlations. At larger scales, there is an additional suppression of the potential which reduces the growth rate even further and would strengthen the integrated Sachs-Wolf effect.

We consider the problem of gravitational forces between point particles on the branes in a five-dimensional (5D) Randall-Sundrum model with two branes (at $y_1$ and $y_2$) and $S^1/Z_2$ symmetry of the fifth dimension. The matter on the branes is viewed as a perturbation on the vacuum metric and treated to linear order. In a previous work [R. Arnowitt and J. Dent, Phys. Rev. D 71, 124024 (2005).] it was seen that the trace of the transverse part of the 4D metric on the TeV brane, $f^T(y_2)$, contributed a Newtonian potential enhanced by $e^{2\beta y_2}\cong {10}^{32}$ and thus produced gross disagreement with the experiment. In this work we include a scalar stabilizing field $\varphi$ and solve the coupled Einstein and scalar equations to leading order for the case where ${\varphi }_0^2/M_5^3$ is small and the vacuum field ${\varphi }_0(y)$ is a decreasing function of $y$. $f^T$ then grows a mass factor $e^{-\mu r}$ where, however, $\mu$ is suppressed from its natural value, $\mathcal{O}(M_{Pl})$, by an exponential factor $e^{-(1+{\lambda }_b)\beta y_2}$, ${\lambda }_b>0$. Thus agreement with the experiment depends on the interplay between the enhancing and decaying exponentials. Current data eliminates a significant part of the parameter space, and the Randall-Sundrum model will be sensitive to any improvements on the tests of the Newtonian force law at smaller distances. An example of coupling of the $\varphi$ field to the Higgs field is examined and found to generally produce very small effects.

Sum rules are derived relating Dirac mean square radii and anomalous magnetic moments of various couples of the ground state $1/2^{+}$ octet baryons with the convergent integral of the difference of hadron photoproduction total cross-sections on the baryons. The chain of inequalities for corresponding total cross-sections has been found from those sum rules.

Considering the $\mu \mathrm{\text{−}}\tau$ symmetry, we discuss a direct linkage between phases of flavor neutrino masses and leptonic $CP$ violation by determining three eigenvectors associated with $\mathbf{M}=M_{\nu }^{†}{M}_{\nu }$ for a complex flavor neutrino mass matrix $M_{\nu }$ in the flavor basis. Since the Dirac $CP$ violation is absent in the $\mu \mathrm{\text{−}}\tau$ symmetric limit, leptonic $CP$ violation is sensitive to the $\mu \mathrm{\text{−}}\tau$ symmetry breaking, whose effect can be evaluated by perturbation. It is found that the Dirac phase ($\delta$) arises from the $\mu \mathrm{\text{−}}\tau$ symmetry breaking part of ${\mathbf{M}}_{e\mu ,e\tau }$ and an additional phase ($\rho$) is associated with the $\mu \mathrm{\text{−}}\tau$ symmetric part of ${\mathbf{M}}_{e\mu ,e\tau }$, where ${\mathbf{M}}_{ij}$ stands for an $ij$ matrix element ($i,j=e,\mu ,\tau$). The phase $\rho$ is redundant and can be removed but leaves its effect in the Dirac $CP$ violation characterized by $\sin (\delta +\rho )$. The perturbative results suggest the exact formula of mixing parameters including that of $\delta$ and $\rho$, which turns out to be free from the effects of the redundant phases. As a result, it is generally shown that the maximal atmospheric neutrino mixing necessarily accompanies either $\sin {\theta }_{13}=0$ or $\cos (\delta +\rho )=0$, the latter of which indicates maximal $CP$ violation, where ${\theta }_{13}$ is the ${\nu }_e\mathrm{\text{−}}{\nu }_{\tau }$ mixing angle.

Unphysical effects associated with finite lattice spacing and partial quenching may lead to the presence of unphysical terms in chiral extrapolation formulas. These unphysical terms must then be removed during data analysis before physical predictions can be made. In this work, we show that through next-to-leading order, there are no unphysical counterterms in the extrapolation formulas, expressed in lattice-physical parameters, for meson scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work applies to most sea quark discretizations, provided that chiral perturbation theory is a valid approximation. We demonstrate our results with explicit computations and show that, in favorable circumstances, the extrapolation formulas do not depend on the unknown constant $C_{\mathrm{Mix}}$ appearing at lowest order in the mixed action chiral Lagrangian. We show that the $I=1$ $KK$ scattering length does not depend on $C_{\mathrm{Mix}}$ in contrast to the $I=3/2$ $K\pi$ scattering length. In addition, we show that these observables combined with $f_K/f_{\pi }$ and the $I=2$ $\pi \pi$ scattering length share only two linearly independent sets of counterterms, providing a means to test the mixed action theory at one lattice spacing. We therefore make a prediction for the $I=1$ $KK$ scattering length.

In the quark-flavor mixing scheme, $\eta$ and ${\eta }^{\prime }$ are linear combinations of flavor states ${\eta }_q=(u\overline{u}+d\overline{d})/\sqrt{2}$ and ${\eta }_s=s\overline{s}$ with the masses of $m_{qq}$ and $m_{ss}$, respectively. Phenomenologically, $m_{ss}$ is strictly fixed to be around 0.69, which is close to $\sqrt{2m_K^2-m_{\pi }^2}$ by the approximate flavor symmetry, while $m_{qq}$ is found to be $0.18\pm 0.08\mathrm{GeV}$. For a large allowed value of $m_{qq}$, we show that the branching ratios (BRs) for $B\to {\eta }^{(\prime )}X$ decays with $X=({\ell }^{-}{\overline{\nu }}_{\ell },{\ell }^{+}{\ell }^{-})$ are enhanced. We also illustrate that $\mathrm{BR}(B\to \eta X)>\mathrm{BR}(B\to {\eta }^{\prime }X)$ in the mechanism without the flavor-singlet contribution. Moreover, we demonstrate that the decay branching ratios for $B\to {\eta }^{(\prime )}{K}^{[*]}$ are consistent with the data. In particular, the puzzle of the large $\mathrm{BR}(B\to {\eta }^{\prime }K)$ can be solved. In addition, we find that the $CP$ asymmetry for $B^{\pm }\to \eta K^{\pm }$ can be as large as $-30\%$, which agrees well with the data. However, we cannot accommodate the $CP$ asymmetries of $B\to \eta K^{*}$ in our analysis, which could indicate the existence of some new $CP$ violating sources.

We have recently studied the QCD pomeron loop evolution equations in zero transverse dimensions [Phys. Rev. D 73, 094014 (2006)]. Using the techniques developed in [Phys. Rev. D 73, 094014 (2006)] together with the AGK cutting rules, we present a calculation of single, double and central diffractive cross sections (for large diffractive masses and large rapidity gaps) in zero transverse dimensions in which all dominant pomeron loop graphs are consistently summed. We find that the diffractive cross sections unitarise at large energies and that they are suppressed by powers of ${\alpha }_s$. Our calculation is expected to expose some of the diffractive physics in hadron-hadron collisions at high energy.

We extend the analysis of the deeply virtual Compton scattering process to the weak interaction sector in the generalized Bjorken limit. The virtual Compton scattering amplitudes for the weak neutral and charged currents are calculated at the leading twist within the framework of the nonlocal light-cone expansion via coordinate space QCD string operators. Using a simple model, we estimate cross sections for neutrino scattering off the nucleon, relevant for future high-intensity neutrino beam facilities.

We discuss the neutrino oscillation physics of a very long neutrino factory baseline over a broad range of lengths (between 6000 km and 9000 km), centered on the “magic baseline” ($\sim 7500\mathrm{km}$) where correlations with the leptonic $CP$ phase are suppressed by matter effects. Since the magic baseline depends only on the density, we study the impact of matter density profile effects and density uncertainties over this range, and the impact of detector locations off the optimal baseline. We find that the optimal constant density describing the physics over this entire baseline range is about 5% higher than the average matter density. This implies that the magic baseline is significantly shorter than previously inferred. However, while a single detector optimization requires fine-tuning of the (very long) baseline length, its combination with a near detector at a shorter baseline is much less sensitive to the far detector location and to uncertainties in the matter density. In addition, we point out different applications of this baseline which go beyond its excellent correlation and degeneracy resolution potential. We demonstrate that such a long baseline assists in the improvement of the ${\theta }_{13}$ precision and in the resolution of the octant degeneracy. Moreover, we show that the neutrino data from such a baseline could be used to extract the matter density along the profile up to 0.24% at $1\sigma$ for large ${sin}^{2}2{\theta }_{13}$, providing a useful discriminator between different geophysical models.

In the light of recent neutrino oscillation and nonoscillation data, we revisit the phenomenological constraints applicable to three observables sensitive to absolute neutrino masses: The effective neutrino mass in single beta decay $(m_{\beta })$; the effective Majorana neutrino mass in neutrinoless double beta decay $(m_{\beta \beta })$; and the sum of neutrino masses in cosmology $(\Sigma )$. In particular, we include the constraints coming from the first Main Injector Neutrino Oscillation Search (MINOS) data and from the Wilkinson Microwave Anisotropy Probe (WMAP) three-year (3y) data, as well as other relevant cosmological data and priors. We find that the largest neutrino squared mass difference is determined with a 15% accuracy (at $2\sigma$) after adding MINOS to world data. We also find upper bounds on the sum of neutrino masses $\Sigma$ ranging from $\sim 2\mathrm{eV}$ (WMAP-3y data only) to $\sim 0.2\mathrm{eV}$ (all cosmological data) at $2\sigma$, in agreement with previous studies. In addition, we discuss the connection of such bounds with those placed on the matter power spectrum normalization parameter ${\sigma }_8$. We show how the partial degeneracy between $\Sigma$ and ${\sigma }_8$ in WMAP-3y data is broken by adding further cosmological data, and how the overall preference of such data for relatively high values of ${\sigma }_8$ pushes the upper bound of $\Sigma$ in the sub-eV range. Finally, for various combination of data sets, we revisit the (in)compatibility between current $\Sigma$ and $m_{\beta \beta }$ constraints (and claims), and derive quantitative predictions for future single and double beta decay experiments.

I show that an application of renormalization group arguments may lead to significant corrections to the vacuum decay rate for phase transitions in flat and curved space-time. It can also give some information regarding its dependence on the parameters of the theory, including the cosmological constant in the case of decay in curved space-time.

The supersymmetric $\mathrm{SU}(N_C)$ Yang-Mills theory coupled to $N_F$ matter fields in the fundamental representation has metastable vacua with broken supersymmetry when $N_C<N_F<\frac{3}{2}{N}_C$. By gauging the flavor symmetry, this model can be coupled directly to the standard model. We show that it is possible to make a slight deformation to the model so that gaugino masses are generated and the Landau pole problem can be avoided. The deformed model has simple realizations on intersecting branes in string theory, where various features of the metastable vacua are encoded geometrically as brane configurations.

We study the behavior of Lagrangian perturbative solutions. For a spherical void model, the higher order the Lagrangian perturbation we consider, the worse the approximation becomes in late-time evolution. In particular, if we stop to improve until an even order is reached, the perturbative solution describes the contraction of the void. To solve this problem, we consider improving the perturbative solution using Shanks transformation, which accelerates the convergence of the sequence. After the transformation, we find that the accuracy of higher-order perturbation is recovered and the perturbative solution is refined well. Then we show that this improvement method can apply for a $\Lambda \mathrm{CDM}$ model and improved the power spectrum of the density field.

The tunneling effect near a weakly isolated horizon (WIH) has been studied. By applying the null geodesic method of Parikh and Wilczek and the Hamilton-Jacibi method of Angheben et al. to a WIH, we recover the semiclassical emission rate in the tunneling process. We show that the tunneling effect exists in a wide class of space-times admitting weakly isolated horizons. The general thermodynamic nature of WIH is then confirmed.

A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Green’s function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Green’s functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field, are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix A.

We analyze various theoretical aspects of $CP$ violation in singly Cabibbo suppressed (SCS) $D$ meson decays, such as $D\to KK,\pi \pi$. In particular, we explore the possibility that $CP$ asymmetries will be measured close to the present level of experimental sensitivity of $\mathcal{O}({10}^{-2})$. Such measurements would signal new physics. We make the following points: (i) The mechanism at work in neutral $D$ decays could be indirect or direct $CP$ violation (or both). (ii) One can experimentally distinguish between these possibilities. (iii) If the dominant $CP$ violation is indirect, then there are clear predictions for other modes. (iv) Tree-level direct $CP$ violation in various known models is constrained to be much smaller than ${10}^{-2}$. (v) SCS decays, unlike Cabibbo favored or doubly Cabibbo suppressed decays, are sensitive to new contributions from QCD penguin operators and especially from chromomagnetic dipole operators. This point is illustrated with supersymmetric gluino-squark loops, which can yield direct $CP$ violating effects of $\mathcal{O}({10}^{-2})$.

Recently the PVLAS Collaboration reported the observation of a rotation of linearly polarized laser light induced by a transverse magnetic field—a signal being unexpected within standard QED. Two mechanisms have been proposed to explain this result: production of a single (pseudo-)scalar particle coupled to two photons or pair production of light millicharged particles. In this work, we study how the different scenarios can be distinguished. We summarize the expected signals for vacuum magnetic dichroism (rotation) and birefringence (ellipticity) for the different types of particles—including new results for the case of millicharged scalars. The sign of the rotation and ellipticity signals as well as their dependencies on experimental parameters, such as the strength of the magnetic field and the wavelength of the laser, can be used to obtain information about the quantum numbers of the particle candidates and to discriminate between the different scenarios. We perform a statistical analysis of all available data, resulting in strongly restricted regions in the parameter space of all scenarios. These domains suggest clear target regions for upcoming experimental tests. As an illustration, we use preliminary PVLAS data to demonstrate that near-future data may already rule out some of these scenarios.