We consider the pion matrix elements of the isoscalar and isovector combinations of the vector and tensor twist-two operators that determine the moments of the various pion generalized parton distributions. Our analysis is performed using partially-quenched chiral perturbation theory. We work in the SU(2) and $\mathrm{SU}(4|2)$ theories and present our results at infinite volume and also at finite volume where some subtleties arise. These results are useful for extrapolations of lattice calculations of these matrix elements at small momentum transfer to the physical regime.

We show that in the framework of the economical 3-3-1 model, the suitable pattern of neutrino masses arises from three quite different sources—the lepton-number conserving, the spontaneous lepton-number breaking, and the explicit lepton-number violating, widely ranging over mass scales including the GUT one: $u\sim O(1)\mathrm{GeV}$, $v\approx 246\mathrm{GeV}$, $\omega \sim O(1)\mathrm{TeV}$, and $\mathcal{M}\sim \mathcal{O}({10}^{16})\mathrm{GeV}$. At the tree level, the model contains three Dirac neutrinos: one massless, and two large with degenerate masses in the range of the electron mass. At the one-loop level, the left-handed and right-handed neutrinos obtain Majorana masses $M_{L,R}$ in orders of ${10}^{-2}–{10}^{-3}\mathrm{eV}$ and degenerate in $M_R=-M_L$, while the Dirac masses get a large reduction down to eV scale through a finite mass renormalization. In this model, the contributions of new physics are strongly signified, the degenerations in the masses and the last hierarchy between the Majorana and Dirac masses can be completely removed by heavy particles. All the neutrinos get mass and can fit the data. The acceptable set of the input data does not induce the large lepton flavor violating branching ratios such as $\mathrm{Br}(\mu \to e\gamma )$.

The spectrum of $(p,q)$ bound states of $F$- and $D$-strings has a distinctive square-root tension formula that is hoped to be a hallmark of fundamental cosmic strings. We point out that the Bogomol’nyi-Prasad-Sommerfield (BPS) bound for vortices in $\mathcal{N}=2$ supersymmetric Abelian-Higgs models also takes the square-root form. In contrast to string theory, the most general supersymmetric field theoretic model allows for $(p,q,r)$ strings, with three classes of strings rather than two. Unfortunately, we find that there do not exist BPS solutions except in the trivial case. The issue of whether there exist non-BPS solutions which may closely resemble the square-root form is left as an open question.

We perform two-dimensional, magneto-hydrodynamical core-collapse simulations of massive stars accompanying the QCD phase transition. We study how the phase-transition affects the gravitational waveforms near the epoch of core-bounce. As for initial models, we change the strength of rotation and magnetic fields. Particularly, the degree of differential rotation in the iron core (Fe-core) is changed parametrically. As for the microphysics, we adopt a phenomenological equation of state above the saturation density, including two parameters to change the hardness before the transition. We assume the first order phase transition, where the conversion of bulk nuclear matter to a chirally symmetric quark-gluon phase is described by the MIT bag model. Based on these computations, we find that the phase transition can make the maximum amplitudes larger up to $\sim 10$ percents than the ones without the phase transition. On the other hand, when the degree of the differential rotation becomes larger, the maximum amplitudes become smaller up to $\sim 10$ percents owing to the phase transition. We find that even extremely strong magnetic fields $\sim {10}^{17}\mathrm{G}$ in the protoneutron star do not affect these results.

New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where the waves have not reached and wave amplitudes fall off more rapidly than they do in Einstein-Rosen solutions, permitting a more regular null inifinity.

We consider the cosmologies that arise in a subclass of $f(R)$ gravity with $f(R)=R+{\mu }^{2n+2}/(-R{)}^n$ and $n\in (-1,0)$ in the metric (as opposed to the Palatini) variational approach to deriving the gravitational field equations. The calculations of the isotropic and homogeneous cosmological models are undertaken in the Jordan frame and at both the background and the perturbation levels. For the former, we also discuss the connection to the Einstein frame in which the extra degree of freedom in the theory is associated with a scalar field sharing some of the properties of a “chameleon” field. For the latter, we derive the cosmological perturbation equations in general theories of $f(R)$ gravity in covariant form and implement them numerically to calculate the cosmic microwave background (CMB) temperature and matter power spectra of the cosmological model. The CMB power is shown to reduce at low $l$’s, and the matter power spectrum is almost scale independent at small scales, thus having a similar shape to that in standard general relativity. These are in stark contrast with what was found in the Palatini $f(R)$ gravity, where the CMB power is largely amplified at low $l$’s and the matter spectrum is strongly scale dependent at small scales. These features make the present model more adaptable than that arising from the Palatini $f(R)$ field equations, and none of the data on background evolution, CMB power spectrum, or matter power spectrum currently rule it out.

Time-dependent backreaction corrections of the renormalized expectation value of the stress-energy tensor operator of a massless quantum scalar field, minimally coupled, in the two-dimensional spherically symmetric nondilatonic Schwarzschild-de Sitter dynamical black hole metric, is applied to determine the final state of its thermal radiation. Renormalization theory in the two-dimensional analog of a generally curved space-time reduces to a trace anomaly defined in terms of the Ricci scalar. So the regularized stress-energy tensor, in close relation to the work by Christensen and Fulling, may be obtained by the nonlocal contribution of the trace anomaly and some suitable parameters. Linear-order, time-dependent solutions of the metric backreaction equations, in close relation to the work by Bousso et al., show that the spherically symmetric nondilatonic evaporating Schwarzschild-de Sitter dynamical black hole final state, reduces to a set of remnant, stable, mini black holes where their metric should be described in terms of some permissible discrete Eddington-Finkelstein advance times. Also the results of this article are confirmed by the consequences of time-independent backreaction solutions which were derived recently by the author and may propose a new approach for quantization of gravity, in which the cosmological constant and a distinguished observer have a key role.

We investigate the stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound. The boundary conditions in these “designer gravity” theories are defined in terms of an arbitrary function $W$. Previous work had suggested that the energy in designer gravity is bounded below if (i) $W$ has a global minimum and (ii) the scalar potential admits a superpotential $P$. More recently, however, certain solutions were found (numerically) to violate the proposed energy bound. We resolve the discrepancy by observing that a given scalar potential can admit two possible branches of the corresponding superpotential, $P_{\pm }$. When there is a $P_{-}$ branch, we rigorously prove a lower bound on the energy; the $P_{+}$ branch alone is not sufficient. Our numerical investigations (i) confirm this picture, (ii) confirm other critical aspects of the (complicated) proofs, and (iii) suggest that the existence of $P_{-}$ may in fact be necessary (as well as sufficient) for the energy of a designer gravity theory to be bounded below.

The Parametrized Post-Newtonian expansion of gravitational theories with a scalar field coupled to the Gauss-Bonnet invariant is performed and confrontation of such theories with solar system experiments is discussed.

We extend the recent microscopic analysis of extremal dyonic Kaluza-Klein (D0-D6) black holes to cover the regime of fast rotation in addition to slow rotation. Fastly rotating black holes, in contrast to slow ones, have nonzero angular velocity and possess ergospheres, so they are more similar to the Kerr black hole. The D-brane model reproduces their entropy exactly, but the mass gets renormalized from weak to strong coupling, in agreement with recent macroscopic analyses of rotating attractors. We discuss how the existence of the ergosphere and superradiance manifest themselves within the microscopic model. In addition, we show in full generality how Myers-Perry black holes are obtained as a limit of Kaluza-Klein black holes, and discuss the slow and fast rotation regimes and superradiance in this context.

We perform a comprehensive study of a class of dark energy models—scalar field models where the effective potential can be described by a polynomial series—exploring their dynamical behavior using the method of flow equations that has previously been applied to inflationary models. Using supernova, baryon oscillation, cosmic microwave background (CMB) and Hubble constant data, and an implicit theoretical prior imposed by the scalar field dynamics, we find that the $\Lambda \mathrm{CDM}$ model provides an excellent fit to the data. Constraints on the generic scalar field potential parameters are presented, along with the reconstructed $w(z)$ histories consistent with the data and the theoretical prior. We propose and pursue computationally feasible algorithms to obtain estimates of the principal components of the equation of state, as well as parameters $w_0$ and $w_a$. Further, we use the Monte Carlo Markov chain machinery to simulate future data based on the Joint Dark Energy Mission, Planck, and baryon acoustic oscillation surveys and find that the inverse area figure of merit improves nearly by an order of magnitude. Therefore, most scalar field models that are currently consistent with data can be potentially ruled out by future experiments. We also comment on the classification of dark energy models into thawing and freezing in light of the more diverse evolution histories allowed by this general class of potentials.

Rotational invariance is a well-established feature of low-energy physics. Violations of this symmetry must be extremely small today, but could have been larger in earlier epochs. In this paper we examine the consequences of a small breaking of rotational invariance during the inflationary era when the primordial density fluctuations were generated. Assuming that a fixed-norm vector picked out a preferred-direction during the inflationary era, we explore the imprint it would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $⟨a_{lm}{a}_{l^{\prime }{m}^{\prime }}^{*}⟩$ of the spherical-harmonic coefficients. We suggest that it is natural to expect that the imprint on the primordial power spectrum of a preferred spatial direction is approximately scale-invariant, and examine a simple model in which this is true.

The $B$-mode polarization lensing signal is a useful probe of the neutrino mass and to a lesser extent the dark energy equation of state as the signal depends on the integrated mass power spectrum between us and the last scattering surface. This lensing $B$-mode signal, however, is non-Gaussian and the resulting non-Gaussian covariance to the power spectrum could impact cosmological parameter measurements, as correlations between $B$-mode bins are at a level of 0.1. On the other hand, for temperature and $E$-mode polarization power spectra, the non-Gaussian covariance is not significant, where we find correlations at the ${10}^{-5}$ level even for adjacent bins. When the power spectrum is estimated with roughly 5 uniformly spaced bins from $l=5$ to $l=100$ and 13 logarithmic uniformly spaced bins from $l=100$ to $l=2000$, the resulting degradation on neutrino mass and dark energy equation of state is about a factor of 2 to 3 when compared to the case where statistics are simply considered to be Gaussian. If we increase the total number of bins between $l=5$ and $l=2000$ to be about 100, we find that the non-Gaussianities only make a minor difference with less than a few percent correction to uncertainties of most cosmological parameters determined from the data. For Planck, the resulting constraints on the sum of the neutrino masses is ${\sigma }_{\Sigma m_{\nu }}\sim 0.2\mathrm{eV}$ and on the dark energy equation of state parameter we find that ${\sigma }_w\sim 0.5$. A post-Planck experiment can improve the neutrino mass measurement by a factor of 3 to 4.

Recent Milagro observations of the Cygnus region have revealed both diffuse TeV gamma-ray emission and a bright and extended TeV source, MGRO $\mathrm{J}2019+37$, which seems to lack an obvious counterpart at other wavelengths. Additional study of this curious object also promises to provide important clues concerning one of the Milky Way’s most active environments. We point out some of the principal facts involved by following three modes of attack. First, to gain insight into this mysterious source, we consider its relation to known objects in both the Cygnus region and the rest of the Galaxy. Second, we find that a simple hadronic model can easily accommodate Milagro’s flux measurement (which is at a single energy), as well as other existing observations spanning nearly 7 orders of magnitude in gamma-ray energy. Third, since a hadronic gamma-ray spectrum necessitates an accompanying TeV neutrino flux, we show that IceCube observations may provide the first direct evidence of a Galactic cosmic-ray accelerator.

We calculate the perifocus precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the effectiveness of our formula for the case of the Yukawa potential. We obtain analytic results for potentials of the form $V(r)=\alpha r^n$ and $V(r)=\alpha \ln (r/\lambda )$ in terms of the hypergeometric function ${}_{2}F_1(\frac{1}{2}-\frac{n}{2},1-\frac{n}{2};2;e^2)$, where $e$ is the eccentricity. Our results reproduce the known general relativistic ($n=-3$), constant force ($n=1$), and cosmological constant ($n=2$) precession formulas. Planetary perihelion precessions are often used to constrain the sizes of hypothetical new weak forces—our results allow for more precise, and often stronger, constraints on such proposed new forces.

Supersymmetric models with an additional singlet field offer the Higgs boson the possibility to decay to two pseudoscalars, $a$. If the mass of these pseudoscalars is above the $b\overline{b}$ threshold, $a\to b\overline{b}$ is generically the dominant decay mode. The decay $h\to aa\to b\overline{b}b\overline{b}$ may be seen above backgrounds at the Tevatron if the Higgs production cross section is enhanced relative to that of the standard model.

A low intermediate scale within minimal supersymmetric $SO(10)$ GUTs is a desirable feature to accommodate leptogenesis. We explore this possibility in models where the intermediate gauge symmetry breaks spontaneously by (a) doublet Higgs scalars and also (b) by triplets. In both scenarios, gauge coupling unification requires the scale of left-right symmetry breaking ($M_R$) to be close to the unification scale. This will entail unnaturally small neutrino Yukawa couplings to avoid the gravitino problem and allow successful leptogenesis. We point out that any one of three options—threshold corrections due to the mass spectrum near the unification scale, gravity induced nonrenormalizable operators near the Planck scale, or presence of additional light Higgs multiplets—can permit unification along with much lower values of $M_R$ as required for leptogenesis. In the triplet model, independent of these corrections, we find a lower bound on the intermediate scale, $M_R>{10}^9\mathrm{GeV}$, arising from the requirement that the theory must remain perturbative at least up to the GUT scale. We show that in the doublet model $M_R$ can even be in the TeV region which, apart from permitting resonant leptogenesis, can be tested at LHC and ILC.

The mass spectrum and magnetic moments of $\Xi$ and $\Omega$ baryon resonances are investigated in the bound-state approach of the Skyrme model. The empirical hyperon spectrum shows that several hyperon resonances share a pattern of (approximately) equal mass spacings between the states of same spin but of opposite parity. It is found that this pattern can be explained mostly by the energy difference between the $P$-wave and $S$-wave kaons bound to the soliton. Although one cannot exclude the possibility that these states can be described as pion-hyperon resonances, the present approach predicts that $\Xi (1620)$ and $\Xi (1690)$ have $J^P={\frac{1}{2}}^{-}$, while $\Xi (1950)$ has $J^P={\frac{1}{2}}^{+}$. The differences with the quark model predictions for the $\Xi$ and $\Omega$ baryon spectrum are pointed out. Several relations for the masses and magnetic moments of those resonances are also obtained.

We analyze the structure of a recently proposed effective field theory (EFT) for the generation of quark and lepton mass ratios and mixing angles, based on the spontaneous breaking of an $SU(3)$ family gauge symmetry at a high scale $F$. We classify the Yukawa operators necessary to seed the masses, making use of the continuous global symmetries that they preserve. One global $U(1)$, in addition to baryon number and electroweak hypercharge, remains unbroken after the inclusion of all operators required by standard model fermion phenomenology. An associated vacuum symmetry insures the vanishing of the first-family quark and charged-lepton masses in the absence of the family gauge interaction. If this $U(1)$ symmetry is taken to be exact in the EFT, broken explicitly by only the QCD-induced anomaly, and if the breaking scale $F$ is taken to lie in the range ${10}^9–{10}^{12}\mathrm{GeV}$, then the associated Nambu-Goldstone boson is a potential QCD axion.

We present the calculation of the next-to-leading-order QCD corrections to electroweak $pp\to e^{+}{\nu }_e{\mu }^{+}{\mu }^{-}jj$ and $pp\to e^{-}{\overline{\nu }}_e{\mu }^{+}{\mu }^{-}jj$ production at the CERN LHC in the form of a fully flexible parton-level Monte Carlo program. The QCD corrections to the total cross sections are modest, changing the leading-order results by less than 10%. At the Born level, the shape of kinematic distributions can depend significantly on the choice of factorization scale. This theoretical uncertainty is strongly reduced by the inclusion of the next-to-leading-order QCD corrections.