Solving Einstein’s constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from the numerical grid, or with the puncture method, in which the singular part of the conformal factor is expressed in terms of an analytical background solution, and the Hamiltonian constraint is then solved for a correction to the background solution that, usually, is assumed to be regular everywhere. We discuss an alternative approach in which the Hamiltonian constraint is solved for an inverse power of the conformal factor. This new function remains finite everywhere, so that this approach requires neither excision nor a split into background and correction. In particular, this method can be used without modification even when the correction to the conformal factor is singular itself. We demonstrate this feature for rotating black holes in the trumpet topology.

Once the temperature of a bosonic gas is smaller than the critical, density dependent, transition temperature, a Bose-Einstein condensation process can take place during the cosmological evolution of the Universe. Bose-Einstein condensates are very strong candidates for dark matter, since they can solve some major issues in observational astrophysics, like, for example, the galactic core/cusp problem. The presence of the dark matter condensates also drastically affects the cosmic history of the Universe. In the present paper we analyze the effects of the finite dark matter temperature on the cosmological evolution of the Bose-Einstein condensate dark matter systems. We formulate the basic equations describing the finite temperature condensate, representing a generalized Gross-Pitaevskii equation that takes into account the presence of the thermal cloud in thermodynamic equilibrium with the condensate. The temperature dependent equations of state of the thermal cloud and of the condensate are explicitly obtained in an analytical form. By assuming a flat Friedmann-Robertson-Walker geometry, the cosmological evolution of the finite temperature dark matter filled Universe is considered in detail in the framework of a two interacting fluid dark matter model, describing the transition from the initial thermal cloud to the low temperature condensate state. The dynamics of the cosmological parameters during the finite temperature dominated phase of the dark matter evolution are investigated in detail, and it is shown that the presence of the thermal excitations leads to an overall increase in the expansion rate of the Universe.

In the next decade gravitational waves might be detected using a pulsar timing array. In an effort to develop optimal detection strategies for stochastic backgrounds of gravitational waves in generic metric theories of gravity, we investigate the overlap reduction functions for these theories and discuss their features. We show that the sensitivity to nontransverse gravitational waves is greater than the sensitivity to transverse gravitational waves and discuss the physical origin of this effect. We calculate the overlap reduction functions for the current NANOGrav pulsar timing array and show that the sensitivity to the vector and scalar-longitudinal modes can increase dramatically for pulsar pairs with small angular separations. For example, the $\mathrm{J}1853+1303-\mathrm{J}1857+0943$ pulsar pair, with an angular separation of about 3°, is about ${10}^4$ times more sensitive to the longitudinal component of the stochastic background, if it is present, than the transverse components.

The CMS Collaboration has released the results of its search for supersymmetry, by applying an ${\alpha }_T$ method to $1.1/\mathrm{fb}$ of data at 7 TeV. The null result excludes (at 95% C.L.) a low-mass region of the Constrained MSSM’s parameter space that was previously favored by other experiments. Additionally, the negative result of the XENON100 dark matter search has excluded (at 90% C.L.) values of the spin-independent scattering cross sections ${\sigma }_p^{\mathrm{SI}}$ as low as ${10}^{-8}\mathrm{pb}$. We incorporate these improved experimental constraints into a global Bayesian fit of the Constrained MSSM by constructing approximate likelihood functions. In the case of the ${\alpha }_T$ limit, we simulate detector efficiency for the CMS ${\alpha }_{T}1.1/\mathrm{fb}$ analysis and validate our method against the official 95% C.L. contour. We identify the 68% and 95% credible posterior regions of the CMSSM parameters, and also find the best-fit point. We find that the credible regions change considerably once a likelihood from ${\alpha }_T$ is included, in particular, the narrow light Higgs resonance region becomes excluded, but the focus point/horizontal branch region remains allowed at the $1\sigma$ level. Adding the limit from XENON100 has a weaker additional effect, in part due to large uncertainties in evaluating ${\sigma }_p^{\mathrm{SI}}$, which we include in a conservative way, although we find that it reduces the posterior probability of the focus point region to the $2\sigma$ level. The new regions of high posterior favor squarks lighter than the gluino and all but one Higgs bosons heavy. The dark matter neutralino mass is found in the range $250\mathrm{GeV}\lesssim m_{\chi }\lesssim 343\mathrm{GeV}$ (at $1\sigma$) while, as the result of improved limits from the LHC, the favored range of ${\sigma }_p^{\mathrm{SI}}$ is pushed down to values below ${10}^{-9}\mathrm{pb}$. We highlight tension between $\delta (g-2{)}_{\mu }^{\mathrm{SUSY}}$ and $\mathcal{B}\mathcal{R}(\overline{B}\to X_s\gamma )$, which is exacerbated by including the ${\alpha }_T$ limit; each constraint favors a different region of the CMSSM’s mass parameters.

New physics at the TeV scale is highly anticipated at the LHC. New particles with color, if within the LHC energy reach, will be copiously produced. One such particle is a diquark, having the quantum numbers of two quarks, and can be either a scalar or a vector. It will decay to two light quarks, or two top quarks, or a top and a light quark, (up-type or down-type depending on the quantum number of the produced diquark). If singly produced, it can be looked for as a dijet resonance, or as giving extra contribution to the single top production or $tt$ production. In this work, we consider a color-sextet vector diquark having the quantum number of $(ud)$-type, its resonance production, and the subsequent decay to $tb$, giving rise to excess contribution to the single top production. Even though the diquark mass is large, its strong resonance production dominates the weak production of $tb$ for a wide range of the diquark mass. Also, its subsequent decay to $tb$ produces a very hard $b$ jet compared to the usual electroweak production. In addition, the missing energy in the final state event is much larger from the massive diquark decays. Thus, with suitable cuts, the final state with $b$, $\overline{b}$ and a charged lepton together with large missing energy stands out compared to the standard model background. We perform a detailed study of both the signal and the background. We find that such a diquark is accessible at the 7 TeV LHC up to a mass of about 3.3 TeV with the luminosity $1{\mathrm{fb}}^{-1}$, while the reach goes up to about 4.3 TeV with a luminosity of $10{\mathrm{fb}}^{-1}$.

The ATLAS and CMS collaborations have reported an excess of events in the $\gamma \gamma$, $Z{Z}^{*}\to 4\ell$ and $W{W}^{*}$ search channels at an invariant mass $m\simeq 125\mathrm{GeV}$, which could be the first evidence for the long-awaited Higgs boson. We investigate the consequences of requiring $m_h\simeq 125\mathrm{GeV}$ in both the minimal supergravity and 2-parameter nonuniversal Higgs supersymmetric models. In minimal supergravity, large values of trilinear soft breaking parameter $|A_0|$ are required, and universal scalar $m_0\gtrsim 0.8\mathrm{TeV}$ is favored so that we expect squark and slepton masses typically in the multi-TeV range. This typically gives rise to an “effective supersymmetric” type of sparticle mass spectrum. In this case, we expect gluino pair production as the dominant sparticle creation reaction at LHC. For $m_0\lesssim 5\mathrm{TeV}$, the superpotential parameter $\mu \gtrsim 2\mathrm{TeV}$ and $m_A\gtrsim 0.8\mathrm{TeV}$, greatly restricting neutralino annihilation mechanisms. These latter conclusions are softened if $m_0\sim 10–20\mathrm{TeV}$ or if one proceeds to the 2-parameter nonuniversal Higgs model. The standard neutralino abundance tends to be far above WMAP-measured values unless the neutralino is Higgsino-like. We remark upon possible nonstandard (but perhaps more attractive) cosmological scenarios which can bring the predicted dark matter abundance into accord with the measured value, and discuss the implications for direct and indirect detection of neutralino cold dark matter.

We consider an electroweak scale model for dark matter (DM) and radiative neutrino mass generation. Despite the leptophilic nature of DM with no direct couplings to quarks and gluons, scattering with nuclei is induced at the 1-loop level through photon exchange. Effectively, there are charge-charge, dipole-charge, and dipole-dipole interactions. We investigate the parameter space consistent with constraints from neutrino masses and mixing, charged lepton-flavor violation, perturbativity, and the thermal production of the correct DM abundance, and calculate the expected event rate in DM direct detection experiments. We show that current data from XENON100 start to constrain certain regions of the allowed parameter space, whereas future data from XENON1T has the potential to significantly probe the model.

We recalculate the color-Coulomb potential to one-loop order, under the assumption that the effect of the Gribov horizon is to make (i) the transverse gluon propagator less singular and (ii) the color-Coulomb potential more singular than their perturbative behavior in the low-momentum limit. As a first guess, the effect of the Gribov horizon is mimicked by introducing a transverse momentum-dependent gluon mass term, leading to a propagator of the Gribov form, with the prescription that the mass parameter should be adjusted to the unique value where the infrared behavior of the Coulomb potential is enhanced. We find that this procedure leads to a Coulomb potential rising asymptotically as a linear term modified by a logarithm.

We use methods of quantum field theory in toroidal topologies to study the $N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-$N$ coupling constant ($g$), investigating its dependence on the compactification length ($L$) and the temperature ($T$). For all values of the fixed coupling constant ($\lambda$), we find an asymptotic-freedom type of behavior, with $g\to 0$ as $L\to 0$ and/or $T\to \infty$. At $T=0$, and for $\lambda \ge {\lambda }_c^{(D)}$ (the strong-coupling regime), we show that, starting in the region of asymptotic freedom and increasing $L$, a divergence of $g$ appears at a finite value of $L$, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, $L_c^{(D)}$, and the deconfining temperature, $T_d^{(D)}$, are determined as functions of $\lambda$ and the mass ($m$) of the fermions, in the case of $D=2,3,4$. Taking $m$ as the constituent quark mass ($\approx 350\mathrm{MeV}$), the results obtained are of the same order of magnitude as the diameter ($\approx 1.7\mathrm{fm}$) and the estimated deconfining temperature ($\approx 200\mathrm{MeV}$) of hadrons.

A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\le \mathcal{N}\le 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge-invariant variables is also presented.

Recently, a local true (completely gauge fixed) Hamiltonian for spherically symmetric collapse was derived in terms of Ashtekar variables. We show that such a local Hamiltonian follows directly from the geometrodynamics of gravity theories that obey a Birkhoff theorem and possess a mass function that is constant on the constraint surface in vacuum. In addition to clarifying the geometrical content, our approach has the advantage that it can be directly applied to a large class of spherically symmetric and two-dimensional gravity theories, including $p$th order Lovelock gravity in $D$ dimensions. The resulting expression for the true local Hamiltonian is universal and remarkably simple in form.

The neutrino-driven wind, which occurs after the onset of a core-collapse supernova explosion, has long been considered as the possible site for the synthesis of heavy $r$-process elements in the Universe. Only recently, it has been possible to simulate supernova explosions up to $\sim 10\mathrm{seconds}$, based on three-flavor Boltzmann neutrino transport. These simulations show that the neutrino luminosities and spectra of all flavors are very similar and their difference even decreases during the deleptonization of the proto-neutron star. As a consequence, the ejecta are always proton rich which rules out the possible production of heavy $r$-process elements ($Z>56$). We perform a detailed analysis of the different weak processes that determine the neutrino spectra. Nonelectron flavor (anti)neutrinos are produced and interact only via neutral-current processes, while electron (anti)neutrinos have additional contributions from charge-current processes. The latter are dominated by ${\nu }_e$-absorption on neutrons and ${\overline{\nu }}_e$-absorption on protons. At early times, charge-current processes are responsible for spectral differences between ${\nu }_e$, ${\overline{\nu }}_e$ and ${\nu }_{\mu /\tau }$. However, as the region of neutrino decoupling moves to higher densities during deleptonization, charge-current reactions are suppressed by final state Pauli blocking. ${\overline{\nu }}_e$ absorption on protons is suppressed due to the continuously increasing chemical potential of the neutrons. ${\nu }_e$ absorption on neutrons is blocked by the increasing degeneracy of the electrons. These effects result in negligible contributions from charge-current reactions on time scales on the order of tens of seconds, depending on the progenitor star. Hence, the neutrino spectra are mainly determined from neutral-current processes which do not distinguish between the different flavors and result in the convergence of the spectra. These findings are independent of the charge-current reaction rates used. It rules out the possibility of neutron-rich ejecta at late times and the production of heavy $r$-process elements from nonrotating and not magnetized proto-neutron stars.

We study the implications of phenomenological processes on a two-singlet extension of the standard model that we introduced in a previous work to describe light cold dark matter. We look into the rare decays of ${\rm Y}$ and $B$ mesons, in particular, the invisible channels, and study the decay channels of the Higgs particle. Preferred regions of the parameter space are indicated, together with others that are excluded. We also comment on the recent Higgs search and findings at the LHC.

A detailed analysis of the open charm effects on the decays of $J/\psi ({\psi }^{\prime })\to VP$ is presented, where $V$ stands for light vector meson and $P$ for light pseudoscalar meson. These are the channels that the so-called “12% rule” of perturbative QCD (pQCD) is obviously violated. Nevertheless, they are also the channels that violate the pQCD helicity selection rule at leading order. In this work, we put constraints on the electromagnetic contribution, short-distance contribution from the $c\overline{c}$ annihilation at the wave function origin, and long-distance contribution from the open charm threshold effects on these two decays. We show that interferences among these amplitudes, in particular, the destructive interferences between the short-distance and long-distance strong amplitudes, play a key role to evade the helicity selection rule and cause the significant deviations from the pQCD expected 12% rule.

The recently observed narrow resonance $Z_b(10610)$ is examined with the assumptions both as a $B^{*}\overline{B}$ molecular state and a $[bd][\overline{b}\overline{u}]$ tetraquark state with quantum numbers $I^G{J}^P=1^{+}{1}^{+}$. Possible interpolating currents are constructed to describe the $Z_b(10650)$ as an axial-vector $B^{*}{\overline{B}}^{*}$ molecular state or a $[bd][\overline{b}\overline{u}]$ tetraquark state. Using QCD sum rules, we consider contributions up to dimension-6 in the operator product expansion at leading order in ${\alpha }_s$. The mass is obtained as $(10.44\pm 0.23)\mathrm{GeV}$ for the molecular state and $(10.50\pm 0.19)\mathrm{GeV}$ for the tetraquark state, both of which coincide with the $Z_b(10610)$. The results $m_{B^{*}{\overline{B}}^{*}}=(10.45\pm 0.31)\mathrm{GeV}$ and $m_{[bd][\overline{b}\overline{u}]}=(10.48\pm 0.33)\mathrm{GeV}$ are consistent with the $Z_b(10650)$.

Multijet cross sections at the LHC and Tevatron are sensitive to several distinct kinematic energy scales. When measuring the dijet invariant mass $m_{jj}$ between two signal jets produced in association with other jets or weak bosons, $m_{jj}$ will typically be much smaller than the total partonic center-of-mass energy $Q$, but larger than the individual jet masses $m$, such that there can be a hierarchy of scales $m\ll m_{jj}\ll Q$. This situation arises in many new-physics analyses at the LHC, where the invariant mass between jets is used to gain access to the masses of new-physics particles in a decay chain. At present, the logarithms arising from such a hierarchy of kinematic scales can only be summed at the leading-logarithmic level provided by parton-shower programs. We construct an effective field theory, ${\mathrm{SCET}}_{+}$, which is an extension of soft-collinear effective theory that applies to this situation of hierarchical jets. It allows for a rigorous separation of different scales in a multiscale soft function and for a systematic resummation of logarithms of both $m_{jj}/Q$ and $m/Q$. As an explicit example, we consider the invariant mass spectrum of the two closest jets in $e^{+}{e}^{-}\to 3$ jets. We also give the generalization to $pp\to N$ jets plus leptons relevant for the LHC.

We consider an extension of the radiative neutrino mass model at TeV regions so as to give the origin for inflation of the Universe. This extension also gives a consistent explanation for both the origin of baryon number asymmetry and dark matter. A small scalar coupling which plays a crucial role in the neutrino mass generation in the original model may be related to parameters which control inflation.

We study the initial properties and positron annihilation within a small electron-positron plasma drop formed by intense laser pulse energy. Such QED cascade generated plasma is, in general, far below the chemical (particle yield) equilibrium. We find that the available electrons and positrons equilibrate kinetically, yet despite relatively high particle density, the electron-positron annihilation is very slow, suggesting a rather long life span of the plasma drop.

We investigate and revisit certain aspects of relativistic baryons in the Skyrme model. Starting from static baryons in the helicity eigenstates, we generalize their wave functions to the nonstatic and relativistic regime. A new representation for gamma matrices in the $SU(2)$ collective space is constructed and the corresponding Dirac equation is obtained. Furthermore, we extend the analysis of Adkins et al. concerning vector current vacuum expectation values for baryon states to arbitrary momenta and calculate baryon elastic form factors in a general framework exhibiting vector meson dominance.