We consider a class of theories involving an extension of the standard model gauge group to an a priori arbitrary number of colors, $N_c$, and derive constraints on $N_c$. One motivation for this is the string theory landscape. For two natural classes of embeddings of this $N_c$-extended standard model in a supersymmetric grand unified theory, we show that requiring unbroken electromagnetic gauge invariance, asymptotic freedom of color, and three generations of quarks and leptons forces one to choose $N_c=3$. Similarly, we show that for a theory combining the $N_c$-extended standard model with a one-family $\mathrm{SU}(2{)}_{\mathrm{TC}}$ technicolor theory, only the value $N_c=3$ is allowed.

TeV-scale extra dimensions may play an important role in electroweak or supersymmetry breaking. We examine the phenomenology of such dimensions, compactified on a sphere $S^n$, $n\ge 2$, and show that they possess distinct features and signatures. For example, unlike flat toroidal manifolds, spheres do not trivially allow fermion massless modes. Acceptable phenomenology then generically leads to “nonuniversal” extra dimensions with “pole-localized” 4D fermions; the bosonic fields can be in the bulk. Because of spherical symmetry, some Kaluza-Klein (KK) modes of bulk gauge fields are either stable or extremely long-lived, depending on the graviton KK spectrum. Using precision electroweak data, we constrain the lightest gauge field KK modes to lie above $\simeq 4\mathrm{TeV}$. We show that some of these KK resonances are within the reach of the LHC in several different production channels. The models we study can be uniquely identified by their collider signatures.

Phenomenologically viable and interesting regions of parameter space in the minimal supergravity (mSUGRA) model with small $m_0$ and small $m_{1/2}$ consistent with the WMAP data on dark matter relic density and the bound on the mass of the lightest Higgs scalar $m_h>114\mathrm{GeV}$ from the Linear Electron Positron Collider open up if the rather ad hoc assumption $A_0=0$, where $A_0$ is the common trilinear soft breaking parameter, employed in most of the existing analyses is relaxed. Since this region corresponds to relatively light squarks and gluinos which are likely to be probed extensively in the very early stages of the LHC experiments, the consequences of moderate or large negative values of $A_0$ are examined in detail. We find that in this region several processes including lightest supersymmetric particle (LSP) pair annihilation, LSP—lighter tau slepton (${\tilde{\tau }}_1$) coannihilation and LSP—lighter top squark (${\tilde{t}}_1$) coannihilation contribute to the observed dark matter relic density. The possibility that a ${\tilde{t}}_1$ that can participate in coannihilation with the lightest neutralino to satisfy the WMAP bound on relic density and at the same time be observed at the current experiments at the Tevatron is wide open. At the LHC a large number of squark-gluino events lead to a very distinctive semi-inclusive signature ${\tau }^{\pm }+X_{\tau }$ (anything without a tau lepton) with a characteristic size much larger than $e^{\pm }+X_e$ or ${\mu }^{\pm }+X_{\mu }$ events.

The color diagonal and color antisymmetric ghost propagators slightly above $T_c$ of $N_f=2$ MILC ${24}^3\times 12$ lattices are measured and compared with zero-temperature unquenched $N_f=2+1$ ${\mathrm{MILC}}_c$ ${20}^3\times 64$ and ${\mathrm{MILC}}_f$ ${28}^3\times 96$ lattices and zero-temperature quenched ${56}^4$ $\beta =6.4$ and 6.45 lattices. The expectation value of the color antisymmetric ghost propagator ${\varphi }^c(q)$ is zero, but its Binder cumulant, which is consistent with that of $N_c^2-1$ dimensional Gaussian distribution below $T_c$, decreases above $T_c$. Although the color diagonal ghost propagator is temperature independent, the $l^1$ norm of the color antisymmetric ghost propagator is temperature dependent. The expectation value of the ghost condensate observed at zero-temperature unquenched configuration is consistent with 0 in $T>T_c$. We also measure transverse, magnetic, and electric gluon propagator and extract gluon screening masses. The running coupling measured from the product of the gluon dressing function and the ghost dressing function are almost temperature independent, but the effect of $A^2$ condensate observed at zero temperature is consistent with 0 in $T>T_c$. The transverse gluon dressing function at low temperature has a peak in the infrared at low temperature, but it becomes flatter at high temperature. The magnetic gluon propagator at high momentum depends on the temperature. These data imply that the magnetic gluon propagator and the color antisymmetric ghost propagator are affected by the presence of dynamical quarks, and there are strong nonperturbative effects through the temperature-dependent color antisymmetric ghost propagator.

We explore the phase structure of two-color and two-flavor QCD in the space of the quark chemical potential ${\mu }_{\mathrm{q}}$ and the isospin chemical potential ${\mu }_{\mathrm{I}}$. Using a mean-field model we calculate the chiral and diquark condensates, $\sigma$ and $\Delta$, self-consistently. In weak coupling and in the chiral limit, we confirm the interval of the isospin chemical potential, $0.71{\Delta }_0<{\mu }_{\mathrm{I}}<0.75{\Delta }_0$, in which a single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase is favored over isotropic superfluidity and normal quark matter. The LOFF window becomes slightly wider at high density. For stronger coupling with nonzero quark mass, which is relevant to currently available numerical simulations in lattice two-color QCD, the single plane-wave LOFF phase appears only at sufficiently high density. The prediction obtained for the LOFF region could be tested with lattice since we can prove that the present system is free from the fermion sign problem. We draw the energy landscape on which local minima corresponding to the isotropic superfluid phase and the LOFF phase and a local maximum corresponding to the gapless phase are manifest. Our results clearly illustrate the path from the unstable gapless phase down to the LOFF phase.

We investigate the process $\gamma \gamma \to e^{+}{e}^{-}{G}_n$ at the future International Linear Collider (ILC), where $G_n$ is the Kaluza-Klein graviton in the large extra dimension model. When the fundamental energy scale is of a few TeV, the cross section of this process can reach several hundred fb at a photon-photon collider with $\sqrt{s}=500–1000\mathrm{GeV}$, and the cross section in the $J=2$ polarized photon collision mode is much larger than that in the $J=0$ polarized photon collision mode. We present strategies to distinguish the graviton signal from numerous SM backgrounds, and find that the graviton signal with extra dimensions $\delta =3$ can be detected when $M_S\le 2.67(1.40)\mathrm{TeV}$ and $\gamma \gamma$ center of mass system energy $\sqrt{s}=1000(500)\mathrm{GeV}$ in unpolarized photon collision mode, while the detecting upper limit can be increased to $2.79(1.44)\mathrm{TeV}$ in $+-$ (${\lambda }_1=1$, ${\lambda }_2=-1$) polarized photon collision mode (with photon polarization efficiency $P_{\gamma }=0.9$).

The shape of the hadronic form factor $f_{+}(q^2)$ in the decay $D^0\to K^{-}{e}^{+}{\nu }_e$ has been measured in a model independent analysis and compared with theoretical calculations. We use $75{\mathrm{fb}}^{-1}$ of data recorded by the BABAR detector at the PEP-II electron-positron collider. The corresponding decay branching fraction, relative to the decay $D^0\to K^{-}{\pi }^{+}$, has also been measured to be $R_D=\mathcal{B}(D^0\to K^{-}{e}^{+}{\nu }_e(\gamma ))/\mathcal{B}(D^0\to K^{-}{\pi }^{+}(\gamma ))=0.927\pm 0.007\pm 0.012$. From these results, and using the present world average value for $\mathcal{B}(D^0\to K^{-}{\pi }^{+})$, the normalization of the form factor at $q^2=0$ is determined to be $f_{+}(0)=0.727\pm 0.007\pm 0.005\pm 0.007$ where the uncertainties are statistical, systematic, and from external inputs, respectively.

We explore the observability of extra dimensions through five-dimensional squashed Kaluza-Klein black holes residing in the Kaluza-Klein spacetime. With the expectation that the Hawking radiation reflects the five-dimensional nature of the squashed horizon, we study the Hawking radiation of a scalar field in the squashed black hole background. As a result, we show that the luminosity of Hawking radiation tells us the size of the extra dimension, namely, the squashed Kaluza-Klein black holes open a window to extra dimensions.

Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ i.e. given a matter distribution and an equation state, one cannot determine the functional form of $f(R)$. However, we also show that matching the outside Schwarzschild–de Sitter metric to the metric inside the mass distribution leads to additional constraints that severely limit the allowed fluid configurations.

High power detuned signal-recycling interferometers currently planned for second-generation interferometric gravitational-wave detectors (for example Advanced LIGO) are characterized by two resonances in the detection band, an optical resonance and an optomechanical resonance which is upshifted from the suspension pendulum frequency due to the so-called optical-spring effect. The detector’s sensitivity is enhanced around these two resonances. However, at frequencies below the optomechanical resonance frequency, the sensitivity of such interferometers is significantly lower than non-optical-spring configurations with comparable circulating power; such a drawback can also compromise high-frequency sensitivity, when an optimization is performed on the overall sensitivity of the interferometer to a class of sources. In this paper, we clarify the reason for such a low sensitivity, and propose a way to fix this problem. Motivated by the optical-bar scheme of Braginsky, Gorodetsky, and Khalili, we propose to add a local readout scheme which measures the motion of the arm-cavity front mirror, which at low frequencies moves together with the arm-cavity end mirror, under the influence of gravitational waves. This scheme improves the low-frequency quantum-noise-limited sensitivity of optical-spring interferometers significantly and can be considered as an incorporation of the optical-bar scheme into currently planned second-generation interferometers. On the other hand it can be regarded as an extension of the optical-bar scheme. Taking compact binary inspiral signals as an example, we illustrate how this scheme can be used to improve the sensitivity of the planned Advanced LIGO interferometer, in various scenarios, using a realistic classical-noise budget. We also discuss how this scheme can be implemented in Advanced LIGO with relative ease.

Long-lived gluinos are the trademark of split supersymmetry. They form $R$-hadrons that, when charged, efficiently lose energy in matter via ionization. Independent of $R$-spectroscopy and initial hadronization, a fraction of $R$-hadrons become charged while traversing a detector. This results in a large number of stopped gluinos at present and future detectors. For a 300 GeV gluino, ${10}^6$ will stop each year in LHC detectors, while several hundred stop in detectors during Run II at the Tevatron. The subsequent decays of stopped gluinos produce distinctive depositions of energy in calorimeters with no activity in either the tracker or the muon chamber. The gluino lifetime can be determined by looking for events where both gluinos stop and subsequently decay.

We study the following charmless baryonic three-body decays of $B$ mesons: $B^{+}\to p\overline{\Lambda }\gamma$, $B^{+}\to p\overline{\Lambda }{\pi }^0$, and $B^0\to p\overline{\Lambda }{\pi }^{-}$. The partial branching fractions as a function of the baryon-antibaryon mass and the polar angle distributions of the proton in the baryon-antibaryon system are presented. This study includes the first observation of $B^{+}\to p\overline{\Lambda }{\pi }^0$, which is measured to have a branching fraction of $({3.00}_{-0.53}^{+0.61}\pm 0.33)\times {10}^{-6}$. We also set upper limits on branching fractions of the two-body decays $B^0\to p{\overline{\Sigma }}^{*-}$, $B^0\to {\Delta }^0\overline{\Lambda }$, $B^{+}\to p{\overline{\Sigma }}^{*0}$, and $B^{+}\to {\Delta }^{+}\overline{\Lambda }$ at the 90% confidence level. These results are obtained from a $414{\mathrm{fb}}^{-1}$ data sample collected near the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Completely natural electroweak symmetry breaking is easily achieved in supersymmetric models if there is a SM-like Higgs boson, $h$, with $m_h\lesssim 100\mathrm{GeV}$. In the minimal supersymmetric model, such an $h$ decays mainly to $b\overline{b}$ and is ruled out by LEP constraints. However, if the MSSM Higgs sector is expanded so that $h$ decays mainly to still lighter Higgs bosons, e.g. $h\to aa$, with $\mathrm{Br}(h\to aa)>0.7$, and if $m_a<2m_b$, then the LEP constraints are satisfied even if $m_h\lesssim 100$ GeV. In this paper, we show that in the next-to-minimal supersymmetric model the above $h$ and $a$ properties (for the lightest $CP$-even and $CP$-odd Higgs bosons, respectively) imply a lower bound on $\mathrm{Br}({\rm Y}\to \gamma a)$ that dedicated runs at present (and future) $B$ factories can explore.

Anomalies of discrete $R$ symmetries appearing in heterotic orbifold models are studied. We find that the mixed anomalies for different gauge groups satisfy the universal Green-Schwarz condition, indicating that these anomalies are canceled by the Green-Schwarz mechanism. An exact relation between the anomaly coefficients of the discrete $R$ symmetries and one-loop beta-function coefficients is obtained. We also find that the discrete $R$ symmetries have a good chance to be unbroken down to the supersymmetry breaking scale. Even below this scale a $Z_2$ subgroup is unbroken, and it may be an origin of the $R$ parity of the minimal supersymmetric standard model. Relations between the $R$-symmetry anomalies and $T$-duality anomalies are also investigated.

We describe $D=4$ twistorial membrane in terms of two twistorial three-dimensional world volume fields. We start with the $D$-dimensional $p$-brane generalizations of two phase space string formulations: one with $p+1$ vectorial momenta, and the second with tensorial momenta of $(p+1)$-th rank. Further, we consider the tensionful membrane case in $D=4$. By using the membrane generalization of the Cartan-Penrose formula, we express the four-momenta by spinorial fields and obtain the intermediate spinor-space-time formulation. By expressing the world volume dreibein and the membrane space-time coordinate fields in terms of two twistor fields one obtains the purely twistorial formulation. It appears that the action is generated by a geometric three-form on two-twistor space. Finally, we comment on higher-dimensional ($D>4$) twistorial $p$-brane models and their superextensions.

The interaction of the electromagnetic field with a two-dimensional plasma sheet intended to describe the pi-electrons of a carbon nanotube or a ${\mathrm{C}}_{60}$ molecule is investigated. By first integrating out the displacement field of the plasma or the electromagnetic field, different representations for quantities like the Casimir energy are derived which are shown to be consistent with one another. Starting from the covariant gauge for the electromagnetic field, it is shown that the matching conditions to which the presence of the plasma sheet can be reduced are different from the commonly used ones. The difference in the treatments does not show up in the Casimir force between two parallel sheets, but it is present in the Casimir-Polder force between a charge or a neutral atom and a sheet. At once, since the plasma sheet is a regularization of the conductor boundary conditions, this sheds light on the difference in physics found earlier in the realization of conductor boundary conditions as “thin” or “thick” boundary conditions in Phys. Rev. D 70, 085010 (2004).

We give an extensive study of the tunnelling between arbitrary (anti-)de Sitter spacetimes separated by an infinitesimally thin relativistic shell in arbitrary spacetime dimensions. In particular, we find analytically an exact expression for the tunnelling amplitude. The detailed spacetime structures that can arise are discussed, together with an effective regularization scheme for before tunnelling configurations.

The nonlinear saturation of the $r$-mode instability and its effects on the spin evolution of low mass x-ray binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three modes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasistationary states that change slowly as the temperature and spin of the star evolve. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. The evolution of the neutron star angular velocity and temperature follow easily calculated trajectories along these sequences of quasistationary states. The outcome depends on whether or not the star will reach thermal equilibrium, where the viscous heating by the three modes is equal to the neutrino cooling ($H=C$ curve). If, when the $r$-mode becomes unstable, the star spins at a frequency below the maximum of the $H=C$ curve, then it will reach a state of thermal equilibrium. It can then either (1) undergo a cyclic evolution with a small cycle size with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long time scale of $\approx {10}^6\mathrm{years}$. If the star does not reach a state of thermal equilibrium, then a faster thermal runaway (time scale of $\approx 100\mathrm{years}$) occurs and the $r$-mode amplitude increases above the second parametric instability threshold. Following this evolution requires more inertial modes to be included. The sources of damping considered are shear viscosity, hyperon bulk viscosity, and viscosity within the core-crust boundary layer. We vary proprieties of the star such as the hyperon superfluid transition temperature $T_c$, the fraction of the star that is above the threshold for direct URCA reactions, and slippage factor, and map the different scenarios we obtain to ranges of these parameters. We focus on $T_c\gtrsim 5\times {10}^9\mathrm{K}$ where nonlinear effects are important. Wagoner [R. Wagoner, Astrophys. J. 578, L63 (2002).] has shown that a very low $r$-mode amplitude arises at smaller $T_c$. For all our bounded evolutions the $r$-mode amplitude remains small $\sim {10}^{-5}$. The spin frequency of accreting neutron stars is limited by boundary layer viscosity to ${\nu }_{\max }\approx 800\mathrm{Hz}[S_{\mathrm{ns}}/(M_{1.4}{R}_6){]}^{4/11}{T}_8^{-2/11}$. Fast rotators are allowed for $[S_{\mathrm{ns}}/(M_{1.4}{R}_6){]}^{4/11}{T}_8^{-2/11}\sim 1$ and we find that in this case the $r$-mode instability would be active for about 1 in 1000 LMXBs and that only the gravitational waves from LMXBs in the local group of galaxies could be detected by advanced LIGO interferometers.

We evaluate the possibility of observable effects arising from collisions between vacuum bubbles in a universe undergoing false-vacuum eternal inflation. Contrary to conventional wisdom, we find that under certain assumptions most positions inside a bubble should have access to a large number of collision events. We calculate the expected number and angular size distribution of such collisions on an observer’s “sky,” finding that for typical observers the distribution is anisotropic and includes many bubbles, each of which will affect the majority of the observer’s sky. After a qualitative discussion of the physics involved in collisions between arbitrary bubbles, we evaluate the implications of our results, and outline possible detectable effects. In an optimistic sense, then, the present paper constitutes a first step in an assessment of the possible effects of other bubble universes on the cosmic microwave background and other observables.

We study baryons in a holographic model of QCD by Sakai and Sugimoto, realized as small instantons with fundamental string hairs. We introduce an effective field theory of the baryons in the five-dimensional setting, and show that the instanton interpretation implies a particular magnetic coupling. Dimensional reduction to four dimensions reproduces the usual chiral effective action, and, in particular, we estimate the axial coupling $g_A$ between baryons and pions and the magnetic dipole moments, both of which are proportional to $N_c$. We extrapolate to finite $N_c$ and discuss subleading corrections.