Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing, and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 while reducing the correlations and boosts up the efficiency by almost a factor of $D$ in a $D$-dimensional parameter space. Therefore shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation. Also we discuss possible ways of getting good estimates of the derivatives of (the log of) posterior which is needed for HMC.

We perform one-zone simulations of the infall epoch of a presupernova stellar core in the presence of neutrino flavor changing scattering interactions. Our calculations give a self-consistent assessment of the relationship between flavor changing rates and the reduction in electron fraction and redistribution of initial electron lepton number among the neutrino flavors. We discuss and include in our calculations subnuclear density medium corrections for flavor changing scattering coherence factors. We find that flavor changing couplings $ϵ>3\times {10}^{-4}$ in either the ${\nu }_e\leftrightarrow {\nu }_{\mu }$ or ${\nu }_e\leftrightarrow {\nu }_{\tau }$ channels result in a dynamically significant reduction in the core electron fraction relatively soon after neutrino trapping and well before the core reaches nuclear matter density.

We study the contributions of the nonstandard neutrino interactions to the rare meson decays of $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $D^{+}\to {\pi }^{+}\nu \overline{\nu }$. We show that both decays could provide strong constraints on the free parameters in the nonstandard neutrino interactions. We point out that the branching ratio of $D^{+}\to {\pi }^{+}\nu \overline{\nu }$ could be at the level of ${10}^{-8}$.

We investigate the possibility of measuring the $H^{\pm }{W}^{\mp }{Z}^0$ vertex from the single $H^{\pm }$ production process via $WZ$ fusion at the CERN Large Hadron Collider (LHC). This vertex strongly depends on the structure of the Higgs sector in various new physics scenarios, so that its measurement can be useful to distinguish the models. A signal and background simulation under the expected detector performance at the LHC is done for the processes of $pp\to W^{\pm }{Z}^{0}X\to H^{\pm }X\to tbX$ and $pp\to W^{\pm }{Z}^{0}X\to H^{\pm }X\to W^{\pm }{Z}^{0}X$, and the required magnitudes of the $H^{\pm }{W}^{\mp }{Z}^0$ vertex for observation are evaluated. It is found that although the loop-induced $H^{\pm }{W}^{\pm }{Z}^0$ vertex in multi-Higgs doublet models cannot be measurable, the latter process can be useful to test the model with a real and a complex triplets.

We investigate the spectroscopy and decays of the charmonium and upsilon systems in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which allows us to compare the results for both perturbative and nonperturbative treatments of the potential. As well as comparing the mass spectra, radiative widths and leptonic widths with the available data, we include a discussion of the errors on the parameters contained in the potential, the effect of mixing on the leptonic widths, the Lorentz nature of the confining potential, and the possible $c\overline{c}$ interpretation of recently discovered charmoniumlike states.

We propose a method of numerical modeling Bose-Einstein correlations by using the notion of the elementary emitting cell (EEC). They are intermediary objects containing identical bosons and are supposed to be produced independently during the hadronization process. Only bosons in the EEC, which represents a single quantum state here, are subjected to the effects of Bose-Einstein (BE) statistics, which forces them to follow a geometrical distribution. There are no such effects between particles from different EECs. We illustrate our proposition by calculating a representative number of typical distributions and discussing their sensitivity to EECs and their characteristics.

We study corrections to tribimaximal (TBM) neutrino mixing from renormalization group (RG) running and from Planck scale effects. We show that while the RG effects are negligible in the standard model (SM), for quasidegenerate neutrinos and large $\tan \beta$ in the minimal supersymmetric standard model (MSSM) all three mixing angles may change significantly. In both these cases, the direction of the modification of ${\theta }_{12}$ is fixed, while that of ${\theta }_{23}$ is determined by the neutrino mass ordering. The Planck scale effects can also change ${\theta }_{12}$ up to a few degrees in either direction for quasidegenerate neutrinos. These effects may dominate over the RG effects in the SM, and in the MSSM with small $\tan \beta$. The usual constraints on neutrino masses, Majorana phases or $\tan \beta$ stemming from RG running arguments can then be relaxed. We quantify the extent of Planck scale effects on the mixing angles in terms of “mismatch phases” which break the symmetries leading to TBM. In particular, we show that when the mismatch phases vanish, the mixing angles are not affected in spite of the Planck scale contribution. Similar statements may be made for $\mu –\tau$ symmetric mass matrices.

In previous papers, we studied ’t Hooft-Polyakov (TP) monopole configurations in $U(2)$ gauge theory on the fuzzy 2-sphere, and showed that they have nonzero topological charges in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provides meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that configuration space can be classified into topological sectors. We further calculate the spectrum of the GW Dirac operator in TP monopole backgrounds, and consider the index theorem in these cases.

We consider charge transport properties of $2+1$ dimensional conformal field theories at nonzero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For $\mathcal{N}=8$ supersymmetric, $\mathrm{SU}(N)$ Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large $N$ limit by applying the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to M theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in $3+1$ dimensional anti-de Sitter space. The electromagnetic self-duality of the $3+1$ dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in $2+1$ dimensional Abelian theories. Thus the $2+1$ dimensional, superconformal Yang Mills theory obeys a “holographic self-duality” in the large $N$ limit, and perhaps more generally.

The new exact formulas for the attractive Casimir force acting on each of the two identical perfectly conducting plates moving freely inside an infinite perfectly conducting cylinder with the same cross section are derived at zero and finite temperatures by making use of the zeta function technique. The long and short distance behavior of the plates’ free energy is investigated.

We study quasistatic perturbations in a cosmological background in the Dvali-Gabadadze-Porrati braneworld model. We identify the Vainshtein radius at which the nonlinear interactions of the brane bending mode become important in a cosmological background. The Vainshtein radius in the early universe is much smaller than the one in the Minkowski background, but in a self-accelerating universe it is the same as the Minkowski background. Our result shows that the perturbative approach is applicable beyond the Vainshtein radius for weak gravity by taking into account the second-order effects of the brane bending mode. The linearized cosmological perturbations are shown to be smoothly matched to the solutions inside the Vainshtein radius. We emphasize the importance of imposing a regularity condition in the bulk by solving the 5D perturbations and we highlight the problem of ad hoc assumptions on the bulk gravity that lead to different conclusions.

Bianchi ${\mathrm{VII}}_h$ models have been recently proposed to explain potential anomalies in the CMB anisotropy as observed by WMAP. We investigate the violation of statistical isotropy due to an embedded Bianchi ${\mathrm{VII}}_h$ template in the CMB anisotropy maps to determine whether the existence of a hidden Bianchi template in the WMAP data is consistent with the previous null detection of the bipolar power spectrum in the WMAP first-year maps. We argue that, although correcting the WMAP maps for the Bianchi template may explain some features in the WMAP data, it may cause other anomalies such as preferred directions leading to detectable levels of violation of statistical isotropy in the Bianchi corrected maps. We compute the bipolar power spectrum for the low density Bianchi ${\mathrm{VII}}_h$ models embedded in the background CMB anisotropy maps with the power spectrum that have been shown in recent literature to best fit the first-year WMAP data. By examining the statistical isotropy of these maps, we put a limit of $(\frac{\sigma }{H}{)}_0\le 2.77\times {10}^{-10}(99\%\mathrm{C}.\mathrm{L}.)$ on the shear parameter in Bianchi ${\mathrm{VII}}_h$ models.

A new generation of upcoming space-based experiments will soon start to probe the spectrum of cosmic-ray antiparticles with an unprecedented accuracy and, in particular, will open up a window to energies much higher than those accessible so far. It is thus timely to carefully investigate the expected antiparticle fluxes at high energies. Here, we perform such an analysis for the case of antiprotons. We consider both standard sources as the collision of other cosmic rays with interstellar matter, as well as exotic contributions from dark matter annihilations in the galactic halo. Up to energies well above 100 GeV, we find that the background flux in antiprotons is almost uniquely determined by the existing low-energy data on various cosmic-ray species; for even higher energies, however, the uncertainties in the parameters of the underlying propagation model eventually become significant. We also show that if the dark matter is composed of particles with masses at the TeV scale, which is naturally expected in extra-dimensional models as well as in certain parameter regions of supersymmetric models, the annihilation flux can become comparable to—or even dominate—the antiproton background at the high energies considered here.

We systematically calculate various flavor-changing neutral-current top-quark processes induced by supersymmetry at the Large Hadron Collider, which include five decay modes and six production channels. To reveal the characteristics of these processes, we first compare the dependence of the rates for these channels on the relevant supersymmetric parameters, then we scan the whole parameter space to find their maximal rates, including all the direct and indirect current experimental constraints on the scharm-stop flavor mixings. We find that, under all these constraints, only a few channels, through $cg\to t$ at parton level and $t\to ch$, may be observable at the Large Hadron Collider.

We examine the possible resolution of the recently observed polarization anomaly in $B^0({\overline{B}}^0)\to \varphi K^{*0}({\overline{K}}^{*0})$-decay within $R$-parity violating (${\mathrm{R̸}}_p$) SUSY. We show that a combination of the superpotential trilinear ${\mathrm{R̸}}_p$-interactions, with the couplings ${\lambda }^{\prime }$, and the soft SUSY breaking bilinear ${\mathrm{R̸}}_p$ sneutrino-Higgs mixing, proportional to ${\tilde{\mu }}^2$, can potentially generate the effective operators with the chirality structure necessary to account for this anomaly. However, we demonstrate that the existing experimental data on $B_s\to {\mu }^{+}{\mu }^{-}$-decay lead to stringent upper limits on the Wilson coefficients of these operators, which are about 2 orders of magnitude below the values required for the resolution of the $B$-decay polarization anomaly, and, therefore, it can hardly be explained within the ${\mathrm{R̸}}_p$ SUSY framework. As a byproduct result of our analysis we derive new limits on the products of the soft bilinear and the superpotential trilinear ${\mathrm{R̸}}_p$-parameters of the form ${\tilde{\mu }}^2{\lambda }^{\prime }$.

I address the question of what can be learned from the observation of the diffuse supernova neutrino flux in the precision phase, at next generation detectors of Megaton scale. An analytical study of the spectrum of the diffuse flux shows that, above realistic detection thresholds of 10 MeV or higher, the spectrum essentially reflects the exponential-times-polynomial structure of the original neutrino spectrum at the emission point. There is only a weak (tens of percent) dependence on the power $\beta$ describing the growth of the supernova rate with the redshift. Different original neutrino spectra correspond to large differences in the observed spectrum of events at a water Cherenkov detector: for typical supernova rates, the ratio of the numbers of events in the first and second energy bins (of 5 MeV width) varies in the interval 1.5–4.3 for pure water (energy threshold 18 MeV) and in the range 1–2.5 for water with gadolinium (10 MeV threshold). In the first case, discrimination would be difficult due to the large errors associated with background. With gadolinium, instead, the reduction of the total error down to the 10%–20% level would allow spectral sensitivity, with a dramatic improvement of precision with respect to the SN1987A data. Even in this latter case, for typical neutrino luminosity the dependence on $\beta$ is below sensitivity, so that it can be safely neglected in data analysis.

In models of thick wall electroweak baryogenesis a common assumption is that the plasma interacting with the expanding Higgs bubble wall during the electroweak phase transition is in kinetic equilibrium (or close to it). We point out that, in addition to the requirement of low wall velocity, kinetic equilibrium requires that the change in the momentum of the particles due to the force exerted by the wall should be much less than that due to scattering as the plasma passes through the wall. We investigate whether this condition is satisfied for charginos and neutralinos participating in thick wall supersymmetric electroweak baryogenesis.

We study the phase diagram as a function of the number of colors and flavors of asymptotically free nonsupersymmetric theories with matter in higher-dimensional representations of arbitrary $\mathrm{SU}(N)$ gauge groups. Since matter in higher-dimensional representations screens more than in the fundamental a general feature is that a lower number of flavors is needed to achieve a near-conformal theory.

We consider the possibility of having an MeV right-handed neutrino as a dark matter constituent. The initial reason for this study was the 511 keV spectral line observed by the satellite experiment INTEGRAL: could it be due to an interaction between dark matter and baryons? Independently of this, we find a number of constraints on the assumed right-handed interactions. They arise, in particular, from the measurements by solar neutrino experiments. We come to the conclusion that such particle interactions are possible, and could reproduce the peculiar angular distribution, but not the rate of the INTEGRAL signal. However, we stress that solar neutrino experiments are susceptible to provide further constraints in the future.

We extract the Weyl scalars in the quasi-Kinnersley tetrad by finding initially the (gauge-, tetrad-, and background-independent) transverse quasi-Kinnersley frame. This step still leaves two undetermined degrees of freedom: the ratio $|{\Psi }_0|/|{\Psi }_4|$, and one of the phases (the product $|{\Psi }_0|·|{\Psi }_4|$ and the sum of the phases are determined by the so-called Beetle-Burko radiation scalar). The residual symmetry (“spin/boost”) can be removed by gauge fixing of spin coefficients in two steps: First, we break the boost symmetry by requiring that $\rho$ corresponds to a global constant mass parameter that equals the ADM mass (or, equivalently in perturbation theory, that $\rho$ or $\mu$ equal their values in the no-radiation limits), thus determining the two moduli of the Weyl scalars $|{\Psi }_0|$, $|{\Psi }_4|$, while leaving their phases as yet undetermined. Second, we break the spin symmetry by requiring that the ratio $\pi /\tau$ gives the expected polarization state for the gravitational waves, thus determining the phases. Our method of gauge fixing—specifically its second step—is appropriate for cases for which the Weyl curvature is purely electric. Applying this method to Misner and Brill-Lindquist data, we explicitly find the Weyl scalars ${\Psi }_0$ and ${\Psi }_4$ in the quasi-Kinnersley tetrad.