We define the nonperturbative part of a quantity as the difference between its numerical value and the perturbative series truncated by dropping the order of minimal contribution and the higher orders. For the anharmonic oscillator, the double-well potential, and the single plaquette gauge theory, the nonperturbative part can be parametrized as $A{\lambda }^B{\mathrm{e}}^{-C/\lambda }$ and the coefficients can be calculated analytically. For lattice QCD in the quenched approximation, the perturbative series for the average plaquette is dominated at low order by a singularity in the complex coupling plane and the asymptotic behavior can only be reached by using extrapolations of the existing series. We discuss two extrapolations that provide a consistent description of the series up to order 20–25. These extrapolations favor the idea that the nonperturbative part scales like $(a/r_0{)}^4$ with $a/r_0$ defined with the force method. We discuss the large uncertainties associated with this statement. We propose a parametrization of $\ln (a/r_0)$ as the two-loop universal terms plus a constant and exponential corrections. These corrections are consistent with $a_{1\mathrm{\text{−}}\mathrm{loop}}^2$ and play an important role when $\beta <6$. We briefly discuss the possibility of calculating them semiclassically at large $\beta$.

We study the sensitivity of $e\gamma$ colliders to physics beyond the standard model, when such interactions are natural and their scale lies below the collider energy. Using the reaction $e\gamma \to bt\nu$ as a specific example, we show that the deviations from the standard model can be parameterized in a model-independent way by only 3 numbers. We investigate the sensitivity of several observables to these 3 quantities, using the various collider polarization modes to increase the signal to noise ratio. These results are then translated into the expected sensitivity derived from this reaction to the new-physics effects present in several specific models.

We identify a “$\Lambda$ selection rule” for $N^{*}$ resonances in the presence of QCD mixing effects. We quantify these mixing effects from existing data and predict amplitudes for exciting $\mathbf{20}$ representations in SU(6), which are forbidden in strict diquark models. By classifying Particle-Data-Group (PDG) states at $N=2$, we show that $\gamma N\to K\Lambda$, $K^{*}\Lambda$, $K\Sigma$, $K^{*}\Sigma$, and $J/\psi \to \overline{p}{N}^{*}$ are ideal probes of baryon dynamics and for establishing whether strongly correlated diquarks survive for $L>0$.

Using heavy baryon chiral perturbation theory we study the leading chiral corrections to the complete set of nucleon generalized parton distributions (GPDs). We compute the leading quark mass and momentum transfer dependence of the moments of nucleon GPDs through the nucleon off-forward twist-2 matrix elements. These results are then applied to get insight on the GPDs and their impact parameter space distributions.

In this paper we tackle the issue of causality in quantum gravity, in the context of 3d spin foam models. We identify the correct procedure for implementing the causality/orientation dependence restriction that reduces the path integral for BF theory to that of quantum gravity in first order form. We construct explicitly the resulting causal spin foam model. We then add matter degrees of freedom to it and construct a causal spin foam model for 3d quantum gravity coupled to matter fields. Finally, we show that the corresponding spin foam amplitudes admit a natural approximation as the Feynman amplitudes of a noncommutative quantum field theory, with the appropriate Feynman propagators weighting the lines of propagation, and that this effective field theory reduces to the usual quantum field theory in flat space in the no-gravity limit.

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted as a discrete set of complex quasinormal frequencies, whose values depend only on the black hole’s mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna (LISA). If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial data). A universal, initial data-independent measure of the relative mode excitation is encoded in the poles of the Green’s function that propagates small perturbations of the geometry (“excitation factors”). We compute the excitation factors for general-spin perturbations of Kerr black holes. We find that for corotating modes with $l=m$ the excitation factors tend to zero in the extremal limit, and that the contribution of the overtones should be more significant when the black hole is fast rotating. We also present the first analytical calculation of the large-damping asymptotics of the excitation factors for static black holes, including the Schwarzschild and Reissner-Nordström metrics. This is an important step to determine the convergence properties of the quasinormal mode expansion.

Using $232{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data recorded by the BABAR experiment, we measure the rates of three-body Cabibbo-suppressed decays of the $D^0$ meson relative to the Cabibbo-favored decay, $D^0\to K^{-}{\pi }^{+}{\pi }^0$. We find: $\frac{B(D^0\to {\pi }^{-}{\pi }^{+}{\pi }^0)}{B(D^0\to K^{-}{\pi }^{+}{\pi }^0)}=(10.59\pm 0.06\pm 0.13)\times {10}^{-2}$ and $\frac{B(D^0\to K^{-}{K}^{+}{\pi }^0)}{B(D^0\to K^{-}{\pi }^{+}{\pi }^0)}=(2.37\pm 0.03\pm 0.04)\times {10}^{-2}$, where the errors are statistical and systematic, respectively. These measurements are significantly more precise than the current world average measurements.

We review and extend evidence for the validity of a generalized Verlinde formula, in particular, nonrational conformal field theories. We identify a subset of representations of the chiral algebra in nonrational conformal field theories that give rise to an analogue of the relation between modular $S$-matrices and fusion coefficients in rational conformal field theories. To that end we review and extend the Cardy-type brane calculations in bosonic and supersymmetric Liouville theory (and its duals) as well as in $H_3^{+}$. We analyze the three-point functions of Liouville theory and of $H_3^{+}$ in detail to directly identify the fusion coefficients from the operator product expansion. Moreover, we check the validity of a proposed generic formula for localized brane one-point functions in nonrational conformal field theories.

In theories with anomalous fermion number nonconservation, the level-crossing picture is considered a faithful representation of the fermionic quantum number variation. It represents each created fermion by an energy level that crosses the zero-energy line from below. If several fermions of various masses are created, the level-crossing picture contains several levels that cross the zero-energy line and cross each other. However, we know from quantum mechanics that the corresponding levels cannot cross if the different fermions are mixed via some interaction potential. The simultaneous application of these two requirements on the level behavior leads to paradoxes. For instance, a naive interpretation of the resulting level-crossing picture gives rise to charge nonconservation. In this paper, we resolve this paradox by a precise calculation of the transition probability, and discuss what are the implications for the electroweak theory. In particular, the nonperturbative transition probability is higher if top quarks are present in the initial state.

We give a direct path-integral calculation of the partition function for pure $3+1$ dimensional $U(N)$ Yang-Mills theory at large $N$ on a small $S^3$, up to two loop order in perturbation theory. From this, we calculate the one loop shift in the Hagedorn/deconfinement temperature for the theory at small volume, finding that it increases (in units of the inverse sphere radius) as we go to larger coupling (larger volume). Our results also allow us to read off the sum of one loop anomalous dimensions for all operators with a given engineering dimension in planar Yang-Mills theory on ${\mathbb{R}}^4$. As checks on our calculation, we reproduce both the Hagedorn shift and some of the anomalous dimension sums by independent methods using the results of Beisert et al. [Nucl. Phys. B 717, 137 (2005)] and Spradlin and Volovich [Nucl. Phys. B 711, 199 (2005)]. The success of our calculation provides a significant check of methods used by Aharony et al. [Phys. Rev. D 71, 125018 (2005)] to establish a first-order deconfinement transition for pure Yang-Mills theory on a small $S^3$.

Noncommutativity in an open bosonic string moving in the presence of a background Neveu-Schwarz two-form field $B_{\mu \nu }$ is investigated in a conformal field theory approach, leading to noncommutativity at the boundaries. In contrast to several discussions, in which boundary conditions are taken as Dirac constraints, we first obtain the mode algebra by using the newly proposed normal ordering, which satisfies both equations of motion and boundary conditions. Using these the commutator among the string coordinates is obtained. Interestingly, this new normal ordering yields the same algebra between the modes as the one satisfying only the equations of motion. In this approach, we find that noncommutativity originates more transparently, and our results match with the existing results in the literature.

Neutrino-neutrino interactions can lead to collective flavor conversion effects in supernovae and in the early universe. We demonstrate that the case of bipolar oscillations, where a dense gas of neutrinos and antineutrinos in equal numbers completely converts from one flavor to another even if the mixing angle is small, is equivalent to a pendulum in flavor space. Bipolar flavor conversion corresponds to the swinging of the pendulum, which begins in an unstable upright position (the initial flavor), and passes through momentarily the vertically downward position (the other flavor) in the course of its motion. The time scale to complete one cycle of oscillation depends logarithmically on the vacuum mixing angle. Likewise, the presence of an ordinary medium can be shown analytically to contribute to a logarithmic increase in the bipolar conversion period. We further find that a more complex (and realistic) system of unequal numbers of neutrinos and antineutrinos is analogous to a spinning top subject to a torque. This analogy easily explains how such a system can oscillate in both the bipolar and the synchronized mode, depending on the neutrino density and the size of the neutrino-antineutrino asymmetry. Our simple model applies strictly only to isotropic neutrino gasses. In more general cases, and especially for neutrinos streaming from a supernova core, different modes couple to each other with unequal strength, an effect that can lead to kinematical decoherence in flavor space rather than collective oscillations. The exact circumstances under which collective oscillations occur in nonisotropic media remain to be understood.

The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the equation of state $P=\alpha \rho$, we study spherically symmetric non-self-similar perturbations in homogeneous self-similar collapse described by the flat Friedmann solution. In the low pressure approximation $\alpha \ll 1$, we analytically derive an infinite set of the normal modes and their growth (or decay) rate. The existence of one unstable normal mode is found to conclude that the self-similar behavior in homogeneous collapse of a sufficiently low pressure perfect fluid must terminate and a certain inhomogeneous density profile can develop with the lapse of time.

We present the first simulations in full general relativity of the head-on collision between a neutron star and a black hole of comparable mass. These simulations are performed through the solution of the Einstein equations combined with an accurate solution of the relativistic hydrodynamics equations via high-resolution shock-capturing techniques. The initial data is obtained by following the York-Lichnerowicz conformal decomposition with the assumption of time symmetry. Unlike other relativistic studies of such systems, no limitation is set for the mass ratio between the black hole and the neutron star, nor on the position of the black hole, whose apparent horizon is entirely contained within the computational domain. The latter extends over $\sim 400M$ and is covered with six levels of fixed mesh refinement. Concentrating on a prototypical binary system with mass ratio $\sim 6$, we find that although a tidal deformation is evident the neutron star is accreted promptly and entirely into the black hole. While the collision is completed before $\sim 300M$, the evolution is carried over up to $\sim 1700M$, thus providing time for the extraction of the gravitational-wave signal produced and allowing for a first estimate of the radiative efficiency of processes of this type.

The Dolgov-Kawasaki instability discovered in the matter sector of the modified gravity scenario incorporating a $-{\mu }^4/R$ correction to Einstein gravity is studied in general $f(R)$ theories. A stability condition is found in the metric version of these theories to help ruling out models that are unviable from the theoretical point of view. For example, the theories $f(R)=R+\alpha {\mu }^{2(n+1)}/R^n$, where $\alpha$ and $n$ are real constants and $n>0$, are ruled out for any negative value of $\alpha$.

We consider the phenomenological consequences of a hidden Higgs sector extending the standard model (SM), in which the “shadow Higgs” are uncharged under the SM gauge groups. We consider a simple $U(1)$ model with one Higgs singlet. One mechanism which sheds light on the shadow sector is the mixing between the neutral gauge boson of the SM and the additional $U(1)$ gauge group. The mixing happens through the usual mass mixing and also kinetic mixing, and is the only way the “shadow $Z$” couples to the SM. We study in detail modifications that the presence of such shadow sector would bring to the electroweak precision tests, which in turn provide constraints on the kinetic-mixing parameter, $s_{ϵ}$, left free in our model. The shadow $Z$ production rate at the CERN LHC and the International Linear Collider depends on $s_{ϵ}$. We find that the observable event rate at both facilities is possible for a reasonable range of $s_{ϵ}$ allowed by electroweak precision tests.

The electromagnetic properties of the baryon octet are calculated in quenched QCD on a ${20}^3\times 40$ lattice with a lattice spacing of 0.128 fm using the fat-link irrelevant clover (FLIC) fermion action. FLIC fermions enable simulations to be performed efficiently at pion masses as low as 300 MeV. By combining FLIC fermions with an improved-conserved vector current, we ensure that discretization errors occur only at $\mathcal{O}(a^2)$ while maintaining current conservation. Magnetic moments and electric and magnetic radii are extracted from the electric and magnetic form factors for each individual quark sector. From these, the corresponding baryon properties are constructed. Our results are compared with the predictions of quenched chiral perturbation theory. We detect substantial curvature and environment sensitivity of the quark contributions to electric charge radii and magnetic moments in the low quark-mass region.