Analytical radiative corrections of order $(\alpha /\pi )(q/M_1)$ are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the ${\widehat{\mathbf{s}}}_1·{\widehat{\mathbf{p}}}_2$ correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter. We cover two cases, a charged and a neutral polarized decaying baryon.

Standard model gauge bosons propagating in two universal extra dimensions give rise to heavy spin-1 and spin-0 particles. The lightest of these, carrying Kaluza-Klein numbers (1,0), may be produced only in pairs at colliders, whereas the (1,1) modes, which are heavier by a factor of $\sqrt{2}$, may be singly produced. We show that the cascade decays of (1,1) particles generate a series of closely-spaced narrow resonances in the $t\overline{t}$ invariant mass distribution. At the Tevatron, $s$-channel production of (1,1) gluons and electroweak bosons will be sensitive to $t\overline{t}$ resonances up to masses in the 0.5–0.7 TeV range. Searches at the LHC for resonances originating from several higher-level modes will further test the existence of two universal extra dimensions.

The problem of estimating the 10th order QED corrections to the muon anomalous magnetic moment is reconsidered. The incorporation of the recently improved contributions to the ${\alpha }^4$ and ${\alpha }^5$-corrections to $a_{\mu }$ within the renormalization group inspired scheme-invariant approach leads to the estimate $a_{\mu }^{(10)}\approx 643(\alpha /\pi {)}^5$. It is in good agreement with the estimate $a_{\mu }^{(10)}=663(20)(\alpha /\pi {)}^5$, obtained by Kinoshita and Nio from the numerical calculations of 2958 10th order diagrams, which are considered to be more important than the still uncalculated 6122 10th-order ${\mathrm{m}}_{\mu }/{\mathrm{m}}_e$-dependent vertex graphs, and 12 672 5-loop diagrams, responsible for the mass-independent constant contribution both to $a_{\mu }$ and $a_e$. This confirms Kinoshita and Nio guess about dominance of the 10th order diagrams calculated by them. Comparisons with other estimates of the ${\alpha }^5$- contributions to $a_{\mu }$, which exist in the literature, are presented.

We have studied the possibility of extracting the $W^{+}{W}^{-}\to W^{+}{W}^{-}$ signal using the process $us\to cd{W}^{+}{W}^{-}$ as a test case. We have investigated numerically the strong gauge cancellations between signal and irreducible background, critically analyzing the reliability of the equivalent vector boson approximation which is commonly used to define the signal. Complete matrix elements are necessary to study electroweak symmetry breaking effects at high $WW$ invariant mass.

We develop the general scheme for modified $f(R)$ gravity reconstruction from any realistic Friedmann-Robertson-Walker (FRW) cosmology. We formulate several versions of modified gravity compatible with solar system tests where the following sequence of cosmological epochs occurs: (a) matter dominated phase (with or without usual matter), transition from deceleration to acceleration, accelerating epoch consistent with recent WMAP data, (b) $\Lambda \mathrm{CDM}$ cosmology without cosmological constant. As a rule, such modified gravities are expressed implicitly (in terms of special functions) with late-time asymptotics of known type (for instance, the model with negative and positive powers of curvature). In the alternative approach, it is demonstrated that even simple versions of modified gravity may lead to the unification of matter dominated and accelerated phases at the price of the introduction of compensating dark energy.

We explore the numerical stability properties of an evolution system suggested by Alekseenko and Arnold. We examine its behavior on a set of standardized testbeds, and we evolve a single black hole with different gauges. Based on a comparison with two other evolution systems with well-known properties, we discuss some of the strengths and limitations of such simple tests in predicting numerical stability in general.

Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd number of dimensions (greater than five), allowing for a cosmological constant. We find a class of perturbations for which the equations of motion reduce to a single radial equation. In the asymptotically flat case, we find no evidence of any instability. In the asymptotically anti-de Sitter case, we demonstrate the existence of a superradiant instability that sets in precisely when the angular velocity of the black hole exceeds the speed of light from the point of view of the conformal boundary. We suggest that the end point of the instability may be a stationary, nonaxisymmetric black hole.

We discuss how an extended foreground of the cosmic microwave background (CMB) can account for the anomalies in the low multipoles of the CMB anisotropies. The distortion needed to account for the anomalies is consistent with a cold spot with the spatial geometry of the local supercluster (LSC) and a temperature quadrupole of order $\Delta T_2^2\approx 50\mu K^2$. If this hypothetic foreground is subtracted from the CMB data, the amplitude of the quadrupole ($\ell =2$) is substantially increased, and the statistically improbable alignment of the quadrupole with the octopole ($\ell =3$) is substantially weakened, increasing dramatically the likelihood of the cleaned maps. By placing the foreground on random locations and then computing the likelihood of the cleaned maps we can estimate the most likely place for this foreground. Although the 1-year WMAP data clearly points the location of this hypothetical foreground to the LSC or its specular image (i.e., the vicinity of the poles of the cosmic dipole axis), the three-year data seems to point to these locations as well as the north ecliptic pole. We show that this is consistent with the symmetries of the cosmic quadrupole. We also discuss a possible mechanism that could have generated this foreground: the thermal Sunyaev-Zeldovich effect caused by hot electrons in the LSC. We argue that the temperature and density of the hot gas which are necessary to generate such an effect, though in the upper end of the expected range of values, are marginally consistent with present observations of the X-ray background of spectral distortions of the CMB.

We study D-brane inspired models with $U(3)\times U(2)\times U(1{)}^N$ gauge symmetry in the context of split supersymmetry. We consider configurations with one, two and three $(N=1,2,3)$ Abelian branes and derive all hypercharge embeddings which imply a realistic particle content. Then, we analyze the implications of split supersymmetry on the magnitude of the string scale, the gauge coupling evolution, the third family fermion mass relations and the gaugino masses. We consider gauge coupling relations which may arise in parallel as well as intersecting brane scenarios and classify the various models according to their predictions for the magnitude of the string scale and the low energy implications. In the parallel brane scenario where the $U(1)$ branes are superposed to $U(2)$ or $U(3)$ brane stacks, varying the split-SUSY scale in a wide range, we find three distinct cases of models predicting a high, intermediate and low string scale, $M_S\sim {10}^{16}\mathrm{GeV}$, $M_S\sim {10}^7\mathrm{GeV}$ and $M_S\sim {10}^4\mathrm{GeV}$, respectively. We further find that in the intermediate string scale model the low energy ratio $m_b/m_{\tau }$ is compatible with $b–\tau$ Yukawa unification at the string scale. Furthermore, we perform a similar analysis for arbitrary Abelian gauge coupling relations at $M_S$ corresponding to possible intersecting brane models. We find cases which predict a string scale of the order $M_S\ge {10}^{14}\mathrm{GeV}$ that accommodate a right-handed neutrino mass of the same order so that a seesaw type, light, left-handed neutrino component is obtained in the sub-eV range as required by experimental and cosmological data. Finally, a short discussion is devoted to the gaugino masses and the lifetime of the gluino.

We calculate the electric dipole moments (EDM) of the neutral ${}^{199}\mathrm{Hg}$ atom, deuteron, nucleons and neutral hyperons $\Lambda$, ${\Sigma }^0$ and ${\Xi }^0$ in the framework of a generic SUSY model without $R$-parity conservation (${\mathrm{R̸}}_p\mathrm{SUSY}$) on the basis of the SU(3) version of chiral perturbation theory (ChPT). We consider $CP$-violation in the hadronic sector induced by the chromoelectric quark dipole moments and $CP$-violating 4-quark effective interactions. From the null experimental results on the neutron and ${}^{199}\mathrm{Hg}$ atom EDMs we derive limits on the imaginary parts of certain products $\mathrm{Im}({\lambda }^{\prime }{\lambda }^{\prime *})$ of the trilinear ${\mathrm{R̸}}_p$-couplings and demonstrate that they are more stringent than those existing in the literature. Using these limits we give predictions for the EDMs of neutral hyperons. We also estimate the prospects of future storage ring experiments on the deuteron EDM and show that the expected improvement of the above limits in these experiments may reach several orders of magnitude.

We have performed numerical simulations of the single-polarized $e^{+}{e}^{-}\to \overrightarrow{p}\overline{p}$ process in kinematic conditions under discussion for a possible upgrade of the existing DAFNE facility. By fitting the cross section and spin asymmetry angular distributions with typical Born expressions, we can study the conditions for extracting information on moduli and phases of the proton electromagnetic form factors in the timelike region, which are poorly known and whose preliminary data show puzzling features. We have explored also non-Born contributions by introducing a further component in the angular fit, which is related to two-photon exchange diagrams. Using a dipole parametrization, we show that these corrections can be identified if larger than 5% of the Born contribution; we also explore the conditions for extracting information on the phase and, consequently, on the relative weight between their real and imaginary parts, which are presently unknown.

We investigate the ${\overline{B}}_s\to {\mu }^{+}{\mu }^{-}$ decay in the presence of a light stabilized radion in Randall-Sundrum model. The branching ratio $\mathrm{BR}({\overline{B}}_s\to {\mu }^{+}{\mu }^{-})$ in the standard model is found to be $3.17\times {10}^{-9}$ (two order smaller than the experimental upper bound) and raises the question whether some new physics can play a crucial role or not. We found that for a reasonable range of parameters (i.e. radion mass $m_{\varphi }$ and radion vev $⟨\varphi ⟩$), the above deficit between the experimental bound and the standard model result can well be accomodated. Using this upper bound on $\mathrm{BR}({\overline{B}}_s\to {\mu }^{+}{\mu }^{-})$, we obtain the lower bound on $⟨\varphi ⟩$.

We present results for the $\Delta S=2$ matrix elements which are required to study neutral kaon mixing in the standard model (SM) and beyond . We also provide leading chiral order results for the matrix elements of the electroweak penguin operators which give the dominant $\Delta I=3/2$ contribution to direct $CP$ violation in $K\to \pi \pi$ decays. Our calculations were performed with Neuberger fermions on two sets of quenched Wilson gauge configurations at inverse lattice spacings of approximately 2.2 GeV and 1.5 GeV. All renormalizations were implemented nonperturbatively in the regularization-independent/momentum (RI/MOM) scheme, where we accounted for subleading operator product expansion corrections and discretization errors. We find ratios of non-SM to SM matrix elements which are roughly twice as large as in the only other dedicated lattice study of these amplitudes. On the other hand, our results for the electroweak penguin matrix elements are in good agreement with two recent domain-wall fermion calculations. As a by-product of our study, we determine the strange quark mass. Our main results are summarized and discussed in Sec. VII. Within our statistics, we find no evidence for scaling violations.

The quantity $P_{\mu }^{\pi }\xi$, where $\xi$ is one of the muon decay parameters and $P_{\mu }^{\pi }$ is the degree of muon polarization in pion decay, has been measured. The value $P_{\mu }^{\pi }\xi =1.0003\pm 0.0006(\mathrm{stat}.)\pm 0.0038(\mathrm{syst}.)$ was obtained. This result agrees with previous measurements but is over a factor of 2 more precise. It also agrees with the Standard Model prediction for $P_{\mu }^{\pi }\xi$ and thus leads to restrictions on left-right symmetric models.

Three-body interactions are expected to be common in globular clusters and in galactic cores hosting supermassive black holes. We consider an equal-mass binary black hole system in the presence of a third black hole. Using numerically generated binary black hole initial data sets, and first and second-order post-Newtonian (1PN and 2PN) techniques, we find that the presence of the third black hole has non-negligible relativistic effects on the location of the binary’s innermost stable circular orbit (ISCO), and that these effects arise at 2PN order. For a stellar-mass black hole binary in orbit about a supermassive black hole, the massive black hole has stabilizing effects on the orbiting binary, leading to an increase in merger time and a decrease of the terminal orbital frequency, and an amplification of the gravitational radiation emitted from the binary system by up to 6%.

It was recently proposed that deformations of the relativistic symmetry, as those considered in deformed special relativity (DSR), can be seen as the outcome of a measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations [S. Liberati, S. Sonego, and M. Visser, Phys. Rev. D 71, 045001 (2005).][R. Aloisio, A. Galante, A. Grillo, S. Liberati, E. Luzio, and F. Mendez, Phys. Rev. D 73, 045020 (2006).]. In this paper we explicitly consider the case of a spacetime described by a flat metric endowed with stochastic fluctuations and, for a free particle, we show that DSR-like nonlinear relations between the spaces of the measured and classical momenta, can result from the average of the stochastic fluctuations over a scale set to be the de Broglie wavelength of the particle. As illustrative examples we consider explicitly the averaging procedure for some simple stochastic processes and discuss the physical implications of our results.

In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the exact doubly special relativity (DSR) dispersion relation in the Magueijo-Smolin framework. Next we demonstrate how a noncommutative phase space is needed to maintain Lorentz invariance for the DSR dispersion relation. Lastly we address the very important issue of velocity of this DSR particle. Exploiting the above noncommutative phase space algebra in a Hamiltonian framework, we show that the speed of massless particles is $c$ and for massive particles the speed saturates at $c$ when the particle energy reaches the maximum value $\kappa$, the Planck mass.