The semileptonic $B\to \pi l^{+}{\nu }_l$ decay is studied starting from a simple quark model which includes the influence of the $B^{*}$ pole. To extend the predictions of a nonrelativistic constituent quark model from its region of applicability near $q_{\max }^2=(m_B-m_{\pi }{)}^2$ to all $q^2$ values accessible in the physical decay, we use a novel multiply subtracted Omnès dispersion relation, which considerably diminishes the form-factor dependence on the elastic $\pi B\to \pi B$ scattering amplitudes at high energies. By comparison to the experimental branching fraction we extract $|V_{ub}|=0.0034\pm 0.0003(\exp )\pm 0.0007(\mathrm{theory})$. To further test our framework, we also study $D\to \pi$ and $D\to K$ decays and find excellent results $f_{\pi }^{+}(0)/f_K^{+}(0)=0.80\pm 0.03$, $\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e)/\mathcal{B}(D^0\to K^{-}{e}^{+}{\nu }_e)=0.079\pm 0.008$. In particular for the $D\to \pi$ case, we reproduce, with high accuracy, the three-flavor lattice QCD results recently obtained by the Fermilab-MILC-HPQCD Collaboration. While for the $D\to K$ case, we successfully describe the data for $f^{+}(q^2)/f^{+}(0)$ recently measured by the FOCUS Collaboration.

The stress tensor for the quantized electromagnetic field is calculated in the region between a pair of dispersive, dielectric half-spaces. This generalizes the stress tensor for the Casimir energy to the case where the boundaries have finite reflectivity. We also include the effects of finite temperature. This allows us to discuss the circumstances under which the weak energy condition and the null energy condition can be violated in the presence of finite reflectivity and finite temperature.

$D-\overline{D}$ mixing is the source of the largest theoretical uncertainty in the extraction of $\gamma$ from $B\to DK$ decays. In the standard model, the mixing can have a rate close to its current experimental upper bound and is $CP$ conserving to an excellent approximation. We show that neglecting $CP$-conserving $D-\overline{D}$ mixing leads to an error in the determination of $\gamma$ only at second order in the small parameters $\Delta m_D/{\Gamma }_D$ and $\Delta {\Gamma }_D/{\Gamma }_D$ and is therefore very small and can be safely neglected.

In the context of AdS/CFT with flavor, we consider the type IIB supergravity solution corresponding to a fully localized D3/D7 intersection. We complete the standard metric ansatz by providing an analytic expression for the warp factor, under the assumption of a logarithmically running axion-dilaton. From the gauge dual perspective, this behavior is related to the positive beta function of the $\mathcal{N}=4$, $d=4$ $\mathrm{SU}(N_c)$ super Yang-Mills gauge theory, coupled to $N_f$ fundamental $\mathcal{N}=2$ hypermultiplets. We comment on the existence of tadpoles and relate them to the same gauge theory beta function. Next we consider a classical spinning string configuration in the decoupling limit of the D3/D7 geometry and extract the flavor ($N_f$) dependence of the associated meson Regge trajectory. Including the backreaction of the D7-branes in the supergravity dual allows for going beyond the quenched approximation on the dual gauge theory side.

Exact solutions to static and nonstatic Einstein-Maxwell equations in the presence of extremely charged dust embedded on thin shells are constructed. Singularities of multi-black-hole Majumdar- Papapetrou and Kastor-Traschen solutions are removed by placing the matter on thin shells. Double spherical thin shell solution is given as an illustration and the matter densities on the shells are derived.

We apply the consistent discretization scheme to general relativity particularized to the Gowdy spacetimes. This is the first time the framework has been applied in detail in a nonlinear generally covariant gravitational situation with local degrees of freedom. We show that the scheme can be correctly used to numerically evolve the spacetimes. We show that the resulting numerical schemes are convergent and preserve approximately the constraints as expected. Given the numerical complexity of the method, further work will be needed to make it competitive with the usual free evolution methods currently in use in numerical relativity.

The rates of ${\nu }_e+n\rightleftharpoons e^{-}+p$ and ${\overline{\nu }}_e+p\rightleftharpoons e^{+}+n$ are important for understanding the dynamics of supernova explosion and the production of heavy elements in the supernova environment above the protoneutron star. Observations and theoretical considerations suggest that some protoneutron stars may be born with strong magnetic fields. In a previous paper we calculated the above rates in supernova environments with magnetic fields up to $\sim {10}^{16}\mathrm{G}$ assuming that the nucleon mass $m_N$ is infinite. We also applied these rates to discuss the implications of such strong fields for supernova dynamics. In the present paper we take into account the effects of a finite $m_N$ and develop a numerical method to recalculate the above rates in similar environments. This method is accurate to $\mathcal{O}(1/m_N)$ and such an accuracy is required for application to supernova nucleosynthesis. We show that our results have the correct behavior in the limit of high neutrino energy or small magnetic field. Based on comparison of our results with various approximations, we recommend efficient estimates of the above rates for use in models of supernova nucleosynthesis in the presence of strong magnetic fields.

We study the behavior of the gluon and ghost dressing functions in $SU(3)$ Landau gauge at low momenta available on lattice sizes ${12}^4–{32}^4$ at $\beta =5.8$, $6.0$ and $6.2$. We demonstrate the ghost dressing function to be systematically dependent on the choice of Gribov copies, while the influence on the gluon dressing function is not resolvable. The running coupling given in terms of these functions is found to be decreasing for momenta $q<0.6\mathrm{GeV}$. We study also effects of the finite volume and of the lattice discretization.

Details of the calculation of the nonforward Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel at next-to-leading order (NLO) are offered. Specifically we show the calculation of the two-gluon production contribution. This contribution was the last missing part of the kernel. Together with the NLO gluon Regge trajectory, the NLO contribution of one-gluon production and the contribution of quark-antiquark production which were found before it defines the kernel completely for any color state in the $t$-channel, in particular, the Pomeron kernel presented recently.

We show that by combining high precision measurements of the atmospheric $\delta m^2$ in both the electron and muon neutrino (or antineutrino) disappearance channels one can determine the neutrino mass hierarchy. The required precision is a very challenging fraction of one per cent for both measurements. At even higher precision, sensitivity to the cosine of the $CP$ violating phase is also possible. This method for determining the mass hierarchy of the neutrino sector does not depend on matter effects.

We present a measurement of the fraction $f_{+}$ of right-handed $W$ bosons produced in top quark decays, based on a candidate sample of $t\overline{t}$ events in the lepton+jets decay mode. These data correspond to an integrated luminosity of $230{\mathrm{pb}}^{-1}$, collected by the D0 detector at the Fermilab Tevatron $p\overline{p}$ Collider at $\sqrt{s}=1.96\mathrm{TeV}$. We use a constrained fit to reconstruct the kinematics of the $t\overline{t}$ and decay products, which allows for the measurement of the leptonic decay angle ${\theta }^{*}$ for each event. By comparing the $\cos {\theta }^{*}$ distribution from the data with those for the expected background and signal for various values of $f_{+}$, we find $f_{+}=0.00\pm 0.13(\mathrm{\text{stat}})\pm 0.07(\mathrm{\text{syst}})$. This measurement is consistent with the standard model prediction of $f_{+}=3.6\times {10}^{-4}$.

Supersymmetric extensions of the Standard Model contain nontopological solitons, Q-balls, which can be stable and can be a form of cosmological dark matter. Understanding the interaction of SUSY Q-balls with matter fermions is important for both astrophysical limits and laboratory searches for these dark-matter candidates. We show that a baryon scattering off a baryonic SUSY Q-ball can convert into its antiparticle with a high probability, while the baryon number of the Q-ball is increased by two units. For a SUSY Q-ball interacting with matter, this process dominates over those previously discussed in the literature.

The process of equilibration in ${\phi }^4$ theory is investigated for a homogeneous system in $3+1$ dimensions and a variety of out-of-equilibrium initial conditions, both in the symmetric and broken phase, by means of the 2PI effective action. Two $\Phi$-derivable approximations including scattering effects are used: the two-loop and the basketball, the latter corresponding to the truncation of the 2PI effective action at $\mathcal{O}({\lambda }^2)$. The approach to equilibrium, as well as the kinetic and chemical equilibration is investigated.

We present an observation about the proposal that four-dimensional modification of general relativity may explain the observed cosmic acceleration today. Assuming that the thermodynamical nature of gravity theory continues to hold in modified gravity theories, we derive the modified horizon entropy formula from the modified Friedmann equation. We argue that our results imply that there are conceptual problems in some models of four-dimensional modification of general relativity.

We consider a gravitational wave oscillating in an initially homogeneous, magnetized fluid. The fluid is perfectly conducting and isentropic, and the magnetic field is initially uniform. We find analytic solutions for the case in which the gravitational wave is linear and unaffected by the background fluid and field. Our solutions show how gravitational waves can excite three magnetohydrodynamic (MHD) modes in the fluid: Alfvén waves, and both fast and slow magnetosonic waves. Our analytic solutions are particularly useful for testing numerical codes designed to treat general relativistic MHD in dynamical spacetimes, as we demonstrate in a companion paper.

Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation in nascent neutron stars arising from stellar core collapse or binary neutron star merger, the formation of jets and magnetized disks around newborn black holes, etc. To model these phenomena, all of which involve both general relativity (GR) and magnetohydrodynamics (MHD), we have developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes. Our code solves the Einstein-Maxwell-MHD system of coupled equations in axisymmetry and in full $3+1$ dimensions. We evolve the metric by integrating the Baumgarte-Shapiro-Shibata-Nakamura equations, and use a conservative, shock-capturing scheme to evolve the MHD equations. Our code gives accurate results in standard MHD code-test problems, including magnetized shocks and magnetized Bondi flow. To test our code’s ability to evolve the MHD equations in a dynamical spacetime, we study the perturbations of a homogeneous, magnetized fluid excited by a gravitational plane wave, and we find good agreement between the analytic and numerical solutions.

Primordial tangled cosmological Magnetic Fields source rotational velocity perturbations of the baryon fluid, even in the post-recombination universe. These vortical modes inturn leave a characteristic imprint on the temperature anisotropy of the Cosmic Microwave Background (CMB), if the CMB photons can be rescattered after recombination. Observations from WMAP indicate that the Universe underwent a relatively early reionization ($z_{ri}\sim 15$), which does indeed lead to a significant optical depth for rescattering of CMB photons after the reionization epoch. We compute the resulting additional temperature anisotropies, induced by primordial magnetic fields in the post-recombination universe. We show that in models with early reionization, a nearly scale-invariant spectrum of tangled magnetic fields which redshift to a present value of $B_0\sim 3\times {10}^{-9}$ Gauss, produce vector mode perturbations which in turn induce additional temperature anisotropy of about $0.3$ to $0.4$ $\mu$K over very small angular scales, with $l$ upto $\sim 10000$ or so.

Recently, Iancu and Triantafyllopoulos have proposed a hierarchy of evolution equations in QCD at high energy which generalizes previous approaches by including the effects on gluon number fluctuations and thus the pomeron loops. In this paper, we present the first numerical simulations of the Langevin equation which reproduces that hierarchy. This equation is formally the Balitsky-Kovchegov equation supplemented with a noise term accounting for the relevant fluctuations. In agreement with theoretical predictions, we find that the effect of the fluctuations is to reduce the saturation exponent and to induce geometric scaling violations at high energy.

The theory of supersymmetric quantum electrodynamics is extended by interactions with external vector and tensor backgrounds, that are assumed to be generated by some Lorentz-violating (LV) dynamics at an ultraviolet scale perhaps related to the Planck scale. Exact supersymmetry requires that such interactions correspond to LV operators of dimension five or higher, providing a solution to the naturalness problem in the LV sector. We classify all dimension five and six LV operators, analyze their properties at the quantum level and describe observational consequences of LV in this theory. We show that LV operators do not induce destabilizing $D$-terms, gauge anomaly, and the Chern-Simons term for photons. We calculate the renormalization group evolution of dimension five LV operators and their mixing with dimension three LV operators, controlled by the scale of the soft-breaking masses. Dimension five LV operators are constrained by low-energy precision measurements at ${10}^{-10}–{10}^{-5}$ level in units of the inverse Planck scale, while the Planck-scale suppressed dimension six LV operators are allowed by observational data.

We estimate the two-photon exchange contribution to elastic electron-proton scattering at large momentum transfer by using a quark-parton representation of virtual Compton scattering. We thus can relate the two-photon exchange amplitude to the generalized parton distributions which also enter in other wide-angle scattering processes. We find that the interference of one- and two-photon exchange contribution is able to substantially resolve the difference between electric form factor measurements from Rosenbluth and polarization transfer experiments. Two-photon exchange has additional consequences which could be experimentally observed, including nonzero polarization effects and a positron-proton/electron-proton scattering asymmetry. The predicted Rosenbluth plot is no longer precisely linear; it acquires a measurable curvature, particularly at large laboratory angle.