The renormalization of a gapless $\Phi$-derivable Hartree-Fock approximation to the $O(N)$-symmetric $\lambda {\varphi }^4$ theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper [Yu. B. Ivanov, F. Riek, and J. Knoll, Phys. Rev. D 71, 105016 (2005).] in order to preserve all the desirable features of $\Phi$-derivable Dyson-Schwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) while simultaneously restoring the Nambu-Goldstone theorem in the broken phase. It is shown that unlike for the conventional Hartree-Fock approximation this approach allows for a scale-independent renormalization in the vacuum. However, the scale dependence still persists at finite temperatures. Various branches of the solution are studied. The occurrence of a limiting temperature inherent in the renormalized Hartree-Fock approximation at fixed renormalization scale $\mu$ is discussed.

Multiple parton collisions will represent a rather common feature in $pp$ collisions at the LHC, where regimes with very large momentum transfer may be studied and events rare in lower energy accelerators might occur with a significant rate. A reason of interest in large $p_t$ regimes is that, differently from low $p_t$, evolution will induce correlations in $x$ in the multiparton structure functions. We have estimated the cross section of multiple production of $W$ bosons with equal sign, where the correlations in $x$ induced by evolution are particularly relevant, and the cross section of $b\overline{b}b\overline{b}$ production, where the effects of evolution are much smaller. Our result is that, in the case of multiple production of $W$ bosons, the terms with correlations may represent a correction of the order of 40% of the cross sections, for $pp$ collisions at 1 TeV c.m. energy, and a correction of the order of 20% at 14 TeV. In the case of $b\overline{b}$ pairs the correction terms are of the order of 10–15% at 1 TeV and of the order of 5% at 14 TeV.

By analogy with potential nonrelativistic QCD, we construct effective field theories suitable to describe the heavy-quark sector of baryons made of two and three heavy quarks. A long-standing discrepancy between the hyperfine splitting of doubly heavy baryons obtained in the heavy-quark effective theory and potential models is solved. The one-loop matching of the 4-quark operators of dimension 6 is provided.

In this paper, we study the chiral symmetry restoration in the hadronic spectrum in the framework of generalized Nambu–Jona-Lasinio quark models with instantaneous confining quark kernels. We investigate a heavy-light quarkonium and derive its bound-state equation in the form of a Schrödinger-like equation and, after the exact inverse Foldy-Wouthuysen transformation, in the form of a Diraclike equation. We discuss the Lorentz nature of confinement for such a system and demonstrate explicitly the effective chiral symmetry restoration for highly excited states in the mesonic spectrum. We give an estimate for the scale of this restoration.

We compute the tree level cross section for gluon-gluon elastic scattering taking into account a dynamical gluon mass, and show that this mass scale is a natural regulator for this subprocess cross section. Using an eikonal approach in order to examine the relationship between this gluon-gluon scattering and the elastic $pp$ and $\overline{p}p$ channels, we found that the dynamical gluon mass is of the same order of magnitude as the ad hoc infrared mass scale $m_0$ underlying eikonalized QCD-inspired models. We argue that this correspondence is not an accidental result, and that this dynamical scale indeed represents the onset of nonperturbative contributions to the elastic hadron-hadron scattering. We apply the eikonal model with a dynamical infrared mass scale to obtain predictions for ${\sigma }_{tot}^{pp,\overline{p}p}$, ${\rho }^{pp,\overline{p}p}$, slope $B^{pp,\overline{p}p}$, and differential elastic scattering cross section $d{\sigma }^{\overline{p}p}/dt$ at Tevatron and CERN-LHC energies.

We present two- and three-dimensional simulations of the growth of quantum fluctuations of the scalar fields in supersymmetric hybrid inflation models. For a natural range of couplings, subhorizon quantum fluctuations undergo rapid growth due to scalar field dynamics, resulting in the formation of quasistable nontopological solitons (inflaton condensate lumps) which dominate the postinflation era.

Two new one-parameter tracking behavior dark energy representations $\omega ={\omega }_0/(1+z)$ and $\omega ={\omega }_0{e}^{z/(1+z)}/(1+z)$ are used to probe the geometry of the Universe and the property of dark energy. The combined type Ia supernova, Sloan Digital Sky Survey, and Wilkinson Microwave Anisotropy Probe data indicate that the Universe is almost spatially flat and that dark energy contributes about 72% of the matter content of the present universe. The observational data also tell us that $\omega (0)\sim -1$. It is argued that the current observational data can hardly distinguish different dark energy models to the zeroth order. The transition redshift when the expansion of the Universe changed from deceleration phase to acceleration phase is around $z_{\mathrm{T}}\sim 0.6$ by using our one-parameter dark energy models.

The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low-frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50 000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analysis, and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we supercool the chains to extract maximum likelihood estimates, and estimates of the Bayes factors for competing models. We find that the MCMC approach is able to correctly identify the number of signals present, extract the source parameters, and return error estimates consistent with Fisher information matrix predictions.

Top quark and Higgs boson decays induced by flavor-changing neutral currents (FCNC) are very much suppressed in the standard model. Their detection in colliders such as the Large Hadron Collider, Next Linear Collider, or Tevatron would be a signal of new physics. We evaluate the FCNC decays $t\to H^0+c$, $t\to Z+c$, and $H^0\to t+\overline{c}$ in the context of alternative left-right symmetric models with extra isosinglet heavy fermions; in this case, FCNC decays occur at tree level, and they are suppressed only by the mixing between ordinary top and charm quarks, which is poorly constrained by current experimental values. This provides the possibility for future colliders either to detect new physics or to improve present bounds on the parameters of the model.

Cosmic superstrings are produced at the end of brane inflation. Their properties are similar to cosmic strings arising in grand unified theories. Like cosmic strings they can give rise to a primordial magnetic field, as a result of vortical motions stirred in the ionized plasma by the gravitational pull of moving string segments. The resulting magnetic field is both strong enough and coherent enough to seed the galactic dynamo and explain the observed magnetic fields of the galaxies.

We consider the existence of bound states of two mesons in an imaginary-time formulation of lattice QCD. We analyze an SU(3) theory with two flavors in $2+1$ dimensions and two-dimensional spin matrices. For a small hopping parameter and a sufficiently large glueball mass, as a preliminary, we show the existence of isoscalar and isovector mesonlike particles that have isolated dispersion curves (upper gap up to near the two-particle threshold $\sim -4\ln \kappa$). The corresponding meson masses are equal up to and including $\mathcal{O}({\kappa }^3)$ and are asymptotically of order $-2\ln \kappa -{\kappa }^2$. Considering the zero total isospin sector, we show that there is a meson-meson bound state solution to the Bethe-Salpeter equation in a ladder approximation, below the two-meson threshold, and with binding energy of order $\overline{b}{\kappa }^2\simeq 0.02359{\kappa }^2$. In the context of the strong coupling expansion in $\kappa$, we show that there are two sources of meson-meson attraction. One comes from a quark-antiquark exchange. This is not a meson exchange, as the spin indices are not those of the meson particle, and we refer to this as a quasimeson exchange. The other arises from gauge field correlations of four overlapping bonds, two positively oriented and two of opposite orientation. Although the exchange part gives rise to a space range-one attractive potential, the main mechanism for the formation of the bound state comes from the gauge contribution. In our lattice Bethe-Salpeter equation approach, this mechanism is manifested by an attractive distance-zero energy-dependent potential. We recall that no bound state appeared in the one-flavor case, where the repulsive effect of Pauli exclusion is stronger.

We calculate the mass shift for the pion in a finite volume with renormalization group methods in the framework of the quark-meson model. In particular, we investigate the importance of the quark effects on the pion mass. As in lattice gauge theory, the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes, in addition to the shift due to pion interactions. We compare our results to chiral perturbation theory calculations and find differences due to the fact that chiral perturbation theory only considers pion effects in the finite volume.

The flavor-changing electromagnetic dipole operator $O_7$ gives the dominant contribution to the $\overline{B}\to X_s\gamma$ decay rate. We calculate two-loop QCD corrections to its matrix element together with the corresponding bremsstrahlung contributions. The optical theorem is applied, and the relevant imaginary parts of three-loop diagrams are computed following the lines of our recent $t\to X_{b}W$ calculation. The complete result allows us to test the validity of the naive non-Abelianization (NNA) approximation that has been previously applied to estimate the next-to-next-to-leading order QCD correction to $\Gamma (\overline{B}\to X_s\gamma )/\Gamma (\overline{B}\to X_{u}e\overline{\nu })$. When both decay widths are normalized to $m_{b,R}^5$ in the same renormalization scheme $R$, the calculated $\mathcal{O}({\alpha }_s^2)$ correction is sizable ($\sim 6\%$), and the NNA estimate is about $1/3$ too large. On the other hand, when the ratio of the decay widths is written as $S\times m_{b,\overline{\mathrm{MS}}}^2(m_b)/m_{b,\mathrm{pole}}^2$, the calculated $\mathcal{O}({\alpha }_s^2)$ correction to $S$ is at the level of $1\%$ for both the complete and the NNA results.

We extend the “analogue spacetime” program by investigating a condensed-matter system that is in principle capable of simulating the massive Klein-Gordon equation in curved spacetime. Since many elementary particles have mass, this is an essential step in building realistic analogue models, and a first step towards simulating quantum gravity phenomenology. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components. This system exhibits a complicated spectrum of normal mode excitations, which can be viewed as two interacting phonon modes that exhibit the phenomenon of refringence. We study the conditions required to make these two phonon modes decouple. Once decoupled, the two distinct phonons generically couple to distinct effective spacetimes, representing a bi-metric model, with one of the modes acquiring a mass. In the eikonal limit the massive mode exhibits the dispersion relation of a massive relativistic particle $\omega =\sqrt{{\omega }_0^2+c^2{k}^2}$, plus curved-space modifications. Furthermore, it is possible to tune the system so that both modes can be arranged to travel at the same speed, in which case the two phonon excitations couple to the same effective metric. From the analogue spacetime perspective this situation corresponds to the Einstein equivalence principle being satisfied.

We consider the evolution of linear perturbations in models with a nonminimal coupling between dark matter and scalar field dark energy. Growth of matter inhomogeneities in two examples of such models proposed in the literature are investigated in detail. Both of these models are based on a low-energy limit of effective string theory action, and have been previously shown to naturally lead to late acceleration of the Universe. However, we find that these models can be ruled out by taking properly into account the impact of the scalar field coupling on the formation of structure in the dark matter density. In particular, when the transition to acceleration in these models begins, the interaction with dark energy enhances the small scale clustering in dark matter much too strongly. We discuss also the role of an effective small scale sound speed squared and the issue of adiabatic initial conditions in models with a coupled dark sector.

The polarization of the cosmic microwave background radiation will have a distribution of singularities and antisingularities, points where the polarization vanishes for topological reasons. The statistics of polarization singularities provides a nontrivial scheme to analyze the polarization maps that is distinct from the usual two-point correlation functions. Here we characterize the statistics of the singularity distribution in simulated polarization maps, and make predictions that can be compared with ongoing and upcoming observations. We use four different characterizations: the number density of singularities, the nearest-neighbor distance between singularities, the critical exponent $\nu$ that describes the scaling of total topological charge $q$ within a closed curve of length $L$ ($q\propto L^{\nu }$), and the angular two-point angular correlation functions for singularities of equal and opposite charge. In general, we find that the number density of singularities is sensitive to the underlying cosmology but the distribution is uniform random except on small scales where singularities of the same charge repel and those of opposite charge attract. These conclusions appear to be extremely robust with respect to variations in the underlying cosmological model and the presence of non-Gaussianity; the only exception we found are cases where statistical isotropy is grossly violated. This suggests that, within the assumption of statistical isotropy, the distribution is a robust feature of the last scattering surface and potentially may be used as a tool to discriminate effects that occur during photon propagation from the last scattering surface to the present epoch.

Current searches for doubly charged Higgs bosons ($H^{\pm \pm }$) at the Fermilab Tevatron are sensitive to single production of $H^{\pm \pm }$, although the pair production mechanism $q\overline{q}\to H^{++}{H}^{--}$ is assumed to be dominant. In the context of a Higgs Triplet Model we study the mechanism $q^{\prime }\overline{q}\to H^{\pm \pm }{H}^{\mp }$ at the Tevatron and CERN Large Hadron Collider, and show that its inclusion can significantly improve the search potential for $H^{\pm \pm }$. Moreover, assuming that the neutrino mass is generated solely by the triplet field Yukawa coupling to leptons, we compare the branching ratios of $H^{\pm \pm }\to l^{\pm }{l}^{\pm }$ and $H^{\pm \pm }\to H^{\pm }{W}^{*}$ for the cases of a normal hierarchical, inverted hierarchical, and degenerate neutrino mass spectrum.

Using experimental results at the $Z$-pole and atomic parity violation, we perform a ${\chi }^2$ fit at 95% C.L. to obtain family-dependent bounds to $Z_2$ mass and $Z_{\mu }-Z_{\mu }^{\prime }$ mixing angle $\theta$ in the framework of $\mathrm{SU}(3{)}_c\otimes \mathrm{SU}(3{)}_L\otimes \mathrm{U}(1{)}_X$ models. The allowed regions depend on the assignment of the quark families in mass eigenstates into the three different families in weak eigenstates that cancel anomalies.

Assuming that supersymmetry is realized with parameters in the hyperbolic branch/focus point region of the minimal supergravity model, we show that by searching for $\mathrm{\text{multijet}}+E_T^{\mathrm{miss}}$ events with tagged $b$ jets the reach of experiments at the LHC may be extended by as much as 20% from current projections. The reason for this is that gluino decays to third generation quarks are enhanced because the lightest neutralino has substantial Higgsino components. Although we were motivated to perform this analysis because the hyperbolic branch/focus point region is compatible with the recent determination of the relic density of cold dark matter, our considerations may well have a wider applicability since decays of gluinos to third generation quarks are favored in a wide variety of models.