A spherically symmetric monopole solution is found in $SO(5)$ gauge theory with Higgs scalar fields in the vector representation in six-dimensional Minkowski spacetime. The action of the Yang-Mills fields is quartic in field strengths. The solution saturates the Bogomolny bound and is stable.

A high precision numerical analysis of the static, spherically symmetric SU(2) magnetic monopole equations is carried out. Using multishooting and multidomain spectral methods, the mass of the monopole is obtained rather precisely as a function of $\beta =M_H/M_W$ for a large $\beta$-interval ($M_H$ and $M_W$ denote the mass of the Higgs and gauge field, respectively). The numerical results necessitated the reexamination and subsequent correction of a previous asymptotic analysis of the monopole mass in the literature for $\beta \ll 1$.

In the minimal left-right symmetric model, there are only two intrinsic $CP$ violating phases to account for all $CP$ violation in both the quark and lepton sectors, if $CP$ is broken spontaneously by the complex phases in the VEV’s of the scalar fields. In addition, the left- and right-handed Majorana mass terms for the neutrinos are proportional to each other due to the parity in the model. This is thus a very constrained framework, making the existence of correlations among the $CP$ violation in leptogenesis, neutrino oscillation and neutrinoless double beta decay possible. In these models, $CP$ violation in the leptonic sector and $CP$ violation in the quark sector are also related. We find, however, that such connection is rather weak due to the large hierarchy in the bi-doublet VEV required by a realistic quark sector.

We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature $T$ and the strange quark mass $M_s$. At $T=0$, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where $M_s^2/\mu <2\Delta$, and the metallic gapless CFL phase, which occurs at larger $M_s^2/\mu$. Here, $\mu$ is the chemical potential for quark number and $\Delta$ is the gap in the CFL phase. We find this distinction blurred at $T\ne 0$, as the CFL phase undergoes an insulator to metal crossover when it is heated. We present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters ${\Delta }_1$, ${\Delta }_2$, and ${\Delta }_3$ describing $ds$ pairing, $us$ pairing and $ud$ pairing, respectively, go to zero in an Nambu–Jona-Lasinio (NJL) model. For small values of $M_s^2/\mu$, we find that ${\Delta }_2$ vanishes first, then ${\Delta }_1$, then ${\Delta }_3$. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger $M_s^2/\mu$, we find that ${\Delta }_1$ vanishes first, then ${\Delta }_2$, then ${\Delta }_3$. Hence, we find a “doubly critical” point in the $(M_s^2/\mu ,T)$ plane at which two lines of second order phase transitions (${\Delta }_1\to 0$ and ${\Delta }_2\to 0$) cross. Because we do not make any small-$M_s$ approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of $M_s$ that there are no strange quarks present.

The pentaquark (5Q) baryon is studied in anisotropic quenched lattice QCD with renormalized anisotropy $a_s/a_t=4$ for a high-precision mass measurement. The standard Wilson action at $\beta =5.75$ and the $O(a)$ improved Wilson quark action with $\kappa =0.1210(0.0010)0.1240$ are employed on a ${12}^3\times 96$ lattice. Contribution of excited states is suppressed by using a smeared source. We investigate both the positive- and negative-parity 5Q baryons with $I=0$ and spin $J=1/2$ using a non-NK-type interpolating field. After chiral extrapolation, the lowest positive-parity state is found to have a mass, $m_{5\mathrm{Q}}=2.25\mathrm{G}\mathrm{e}\mathrm{V}$, which is much heavier than the experimentally observed ${\Theta }^{+}(1540)$. The lowest negative-parity 5Q state appears at $m_{5\mathrm{Q}}=1.75\mathrm{G}\mathrm{e}\mathrm{V}$, which is near the s-wave NK threshold. To distinguish spatially-localized 5Q resonances from NK-scattering states, we propose a new general method imposing a “Hybrid Boundary Condition (HBC),” where the NK threshold is artificially raised without affecting compact five-quark states. The study using the HBC method shows that the negative-parity state observed on the lattice is not a compact 5Q state but an s-wave NK-scattering state.

We consider the possible modification of the Friedmann equation due to the operator ordering parameter entering the Wheeler-DeWitt equation.

The $1+1$ dimensional Dirac field in a finite volume is quantized canonically by using two different methods in this paper. First, we take the boundary conditions (BCs) as primary Dirac constraints, and prove that those BCs as well as the intrinsic constraints are entangled and they form the second class constraints. The quantization is performed canonically by using Dirac’s procedure. And then, we study this model in the reduced phase space. It shows that the Poisson brackets in the reduced phase space are equivalent to the Dirac brackets in the original phase space.

We give a definition of admissible counterterms appropriate for massive quantum field theories on the noncommutative Minkowski space, based on a suitable notion of locality. We then define products of fields of arbitrary order, the so-called quasiplanar Wick products, by subtracting only such admissible counterterms. We derive the analogue of Wick's theorem and comment on the consequences of using quasiplanar Wick products in the perturbative expansion.

We propose a systematic way to carry out the method introduced in F. Cachazo, hep-th/0410077 for computing certain unitarity cuts of one-loop $\mathcal{N}=4$ amplitudes of gluons. We observe that the class of cuts for which the method works involves all next-to-MHV $n$-gluon one-loop amplitudes of any helicity configurations. As an application of our systematic procedure, we obtain the complete seven-gluon one-loop leading-color amplitude $A_{7;1}(1^{-},2^{-},3^{-},4^{+},5^{+},6^{+},7^{+})$.

We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely, the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum, and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser, and Misner-type coordinates. Our parametric solution is applicable in the following two distinct cases: (i) the binary consists of equal-mass compact objects, having two arbitrary spins, and (ii) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. As an application of our parametrization, we present gravitational-wave polarizations, whose amplitudes are restricted to the leading quadrupolar order, suitable to describe gravitational radiation from spinning compact binaries moving in eccentric orbits. The present parametrization will be required to construct “ready to use” reference templates for gravitational waves from spinning compact binaries in inspiralling eccentric orbits. Our parametric solution for the post-Newtonian accurate conservative dynamics of spinning compact binaries clearly indicates, for the cases considered, the absence of chaos in these systems. Finally, we note that our parametrization provides the first step in deriving a fully second post-Newtonian accurate “timing formula” that may be useful for the radio observations of relativistic binary pulsars such as J0737–3039.

The $D$-dimensional string generated gravity models lead to Einstein-Maxwell equations with a quadratic order correction term called the Gauss-Bonnet (GB) term. We calculate the quasinormal modes for the $D$-dimensional charged black hole in the framework of this model. The quasinormal spectrum essentially depends upon the Gauss-Bonnet coupling parameter $\alpha$ which is related to the string scale, and is totally different from that for black holes derived from Einstein action. In particular, at large $\alpha$ the quasinormal modes are proportional to $\alpha$ and, thus, have greater oscillation frequency and damping rate, while as $\alpha$ goes to zero the quasinormal modes approach their Schwarzschild values. In contrary to Einstein theory black hole behavior, the damping rate of the charged GB black hole as a function of charge does not contain a characteristic maximum, but instead the monotonic falling down is observed. In addition, there has been obtained an asymptotic formula for large multipole numbers.

The gravitational self-force on a point particle moving in a vacuum background space-time can be expressed as an integral over the past world line of the particle, the so-called tail term. In this paper, we consider that piece of the self-force obtained by integrating over a portion of the past world line that extends a proper time $\Delta \tau$ into the past, provided that $\Delta \tau$ does not extend beyond the normal neighborhood of the particle. We express this quasilocal piece as a power series in the proper time interval $\Delta \tau$. We argue from symmetries and dimensional considerations that the $O(\Delta {\tau }^0)$ and $O(\Delta \tau )$ terms in this power series must vanish, and compute the first two nonvanishing terms which occur at $O(\Delta {\tau }^2)$ and $O(\Delta {\tau }^3)$. The coefficients in the expansion depend only on the particle’s four velocity and on the Weyl tensor and its derivatives at the particle’s location. The result may be useful as a foundation for a practical computational method for gravitational self-forces in the Kerr space-time, in which the portion of the tail integral in the distant past is computed numerically from a mode-sum decomposition.

We report in this paper the results of a measurement of the gravitational constant $G$ obtained in a laboratory at distances of about 1 m, using a superconducting gravimeter. The instrument measured the gravitational effect due to an annular mass of about 280 kg moving up and down around the gravimeter. The experiment yielded for the gravitational constant the value $G=(6.675\pm 0.007){10}^{-11}\mathrm{N}{\mathrm{m}}^2/\mathrm{k}{\mathrm{g}}^2$ which agrees, within its uncertainty, with the last CODATA value.

We have calculated the width of the rare decay $H\to \gamma \gamma Z$ at one-loop level in the standard model for Higgs boson masses in the range $115\mathrm{G}\mathrm{e}\mathrm{V}\le m_H\le 160\mathrm{G}\mathrm{e}\mathrm{V}$ . For this range of Higgs boson masses we find that $Z$ boson is predominantly longitudinally polarized, and the photons have the same helicity. A comparison of the decay width $\Gamma (H\to \gamma \gamma Z)$ to those of $H\to \gamma \gamma$ and $H\to \gamma Z$ shows that, for the Higgs boson mass of $m_H\sim 135\mathrm{G}\mathrm{e}\mathrm{V}$, the ratios of the decay widths are $\Gamma (H\to \gamma \gamma Z)/\Gamma (H\to \gamma \gamma )\sim \Gamma (H\to \gamma \gamma Z)/\Gamma (H\to \gamma Z)\sim {10}^{-5}-{10}^{-6}$.

Motivated by recent works on “Higgsless theories,” I discuss an $SU(2{)}_0\times SU(2{)}^N\times U(1)$ gauge theory with arbitrary bifundamental (or custodial $SU(2)$ preserving) symmetry breaking between the gauge subgroups and with ordinary matter transforming only under the $U(1)$ and $SU(2{)}_0$. When the couplings, $g_j$, of the other $SU(2)$s are very large, this reproduces the standard model at the tree level. I calculate the $W$ and $Z$ masses and other electroweak parameters in a perturbative expansion in $1/g_j^2$, and give physical interpretations of the results in a mechanical analog built out of masses and springs. In the mechanical analog, it is clear that even for arbitrary patterns of symmetry breaking, it is not possible (in the perturbative regime) to raise the Higgs mass by a large factor while keeping the $S$ parameter small.

It is shown that gluonic corrections to the tadpole diagrams vanish in the two-flavor color superconducting and in the color-flavor locked phase at the order where one might have expected next-to-leading order corrections. This implies that the gluonic part of the color charge density is negligible at the order of my computation. This statement remains true after inclusion of the gluon vertex correction and contributions from Nambu-Goldstone bosons.

Heavy-light diquarks can be the building blocks of a rich spectrum of states which can accommodate some of the newly observed charmoniumlike resonances not fitting a pure $c\overline{c}$ assignment. We examine this possibility for hidden and open charm diquark-antidiquark states deducing spectra from constituent quark masses and spin-spin interactions. Taking the $X(3872)$ as input we predict the existence of a $2^{++}$ state that can be associated to the $X(3940)$ observed by Belle and reexamine the state claimed by SELEX, $X(2632)$. The possible assignment of the previously discovered states $D_s(2317)$ and $D_s(2457)$ is discussed. We predict $X(3872)$ to be made of two components with a mass difference related to $m_u-m_d$ and discuss the production of $X(3872)$ and of its charged partner $X^{\pm }$ in the weak decays of $B^{+,0}$.

The equation of motion for the expectation value of a scalar quantum field does not have the local form that is commonly assumed in studies of inflationary cosmology. We have recently argued that the true, temporally nonlocal equation of motion does not possess a time-derivative expansion and that the conversion of inflaton energy into particles is not, in principle, described by the friction term estimated from linear response theory. Here, we use numerical methods to investigate whether this obstacle to deriving a local equation of motion is purely formal, or of some quantitative importance. Using a simple scalar-field model, we find that, although the nonequilibrium evolution can exhibit significant damping, this damping is not well described by the local equation of motion obtained from linear response theory. It is possible that linear response theory does not apply to the situation we study only because thermalization turns out to be slow, but we argue that the large discrepancies we observe indicate a failure of the local approximation at a more fundamental level.

Newtonian theory predicts that the velocity $\mathcal{V}$ of free test particles on circular orbits around a spherical gravity center is a decreasing function of the orbital radius $r$, $\mathrm{d}\mathcal{V}/\mathrm{d}r<0$. Only very recently, Aschenbach [B. Aschenbach, Astronomy and Astrophysics, 425, 1075 (2004)] has shown that, unexpectedly, the same is not true for particles orbiting black holes: for Kerr black holes with the spin parameter $a>0.9953$, the velocity has a positive radial gradient for geodesic, stable, circular orbits in a small radial range close to the black-hole horizon. We show here that the Aschenbach effect occurs also for nongeodesic circular orbits with constant specific angular momentum $\ell ={\ell }_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$. In Newtonian theory it is $\mathcal{V}={\ell }_0/\mathcal{R}$, with $\mathcal{R}$ being the cylindrical radius. The equivelocity surfaces coincide with the $\mathcal{R}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ surfaces which, of course, are just coaxial cylinders. It was previously known that in the black-hole case this simple topology changes because one of the “cylinders” self-crosses. The results indicate that the Aschenbach effect is connected to a second topology change that for the $\ell =\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ tori occurs only for very highly spinning black holes, $a>0.99979$.

I consider a scenario proposed by Fardon, Nelson, and Weiner where dark energy and neutrinos are connected. As a result, neutrino masses are not constant but depend on the neutrino number density. By examining the full equation of state for the dark sector, I show that in this scenario the dark energy is equivalent to having a cosmological constant, but one that “runs” as the neutrino mass changes with temperature. Two examples are examined that illustrate the principal features of the dark sector of this scenario. In particular, the cosmological constant is seen to be negligible for most of the evolution of the Universe, becoming important only when neutrinos become nonrelativistic. Some speculations on features of this scenario which might be present in a more realistic theory are also presented.