We analyze observational constraints from TeV astrophysics on Lorentz violating nonlinear dispersion for photons and electrons without assuming any a priori equality between the photon and electron parameters. The constraints arise from thresholds for vacuum Čerenkov radiation, photon decay and photo-production of electron-positron pairs. We show that the parameter plane for cubic momentum terms in the dispersion relations is constrained to an order unity region in Planck units. We find that the threshold configuration can occur with an asymmetric distribution of momentum for pair creation, and with a hard photon for vacuum Čerenkov radiation.

Cosmological observations suggest the existence of two different kinds of energy densities dominating at small $(\lesssim 500\mathrm{Mpc})$ and large $\left(\gtrsim 1000\mathrm{Mpc}\right)$ scales. The dark matter component, which dominates at small scales, contributes ${\Omega }_m\approx 0.35$ and has an equation of state $p=0,$ while the dark energy component, which dominates at large scales, contributes ${\Omega }_V\approx 0.65$ and has an equation of state $p\simeq -\rho .$ It is usual to postulate weakly interacting massive particles (WIMPs) for the first component and some form of scalar field or cosmological constant for the second component. We explore the possibility of a scalar field with a Lagrangian $L=-V\left(\phi \right)\sqrt{1-{\partial }^i\phi {\partial }_i\phi }$ acting as both clustered dark matter and smoother dark energy and having a scale-dependent equation of state. This model predicts a relation between the ratio $r={\rho }_V/{\rho }_{\mathrm{DM}}$ of the energy densities of the two dark components and an expansion rate n of the universe [with $a\left(t\right)\mathrm{}\propto t^n]$ in the form $n=(2/3)\mathrm{}(1+r).$ For $r\approx 2,$ we get $n\approx 2$ which is consistent with observations.

The energy dependence of “secondary” neutrinos from the process $({\nu }_{\tau }\to \overrightarrow{\tau }{\overline{\nu }}_{\mu }\to \overline{\mu })$ for two input tau neutrino fluxes ${(F}_{\nu }^0\sim E_{\nu }^{-1}$ and $E_{\nu }^{-2}),$ assumed to have been produced via neutrino oscillations from extragalactic sources, is evaluated to assess the impact of secondary neutrinos on upward muon rates in a ${\mathrm{km}}^3$ detector. We show that the secondary fluxes are considerably suppressed for the steeper flux, and even for fluxes $\sim E_{\nu }^{-1}$ the secondary flux will be difficult to observe experimentally.

The extrapolation of the decay amplitudes of the pseudoscalar mesons into two photons from the soft meson limit where it is obtained from the axial anomaly to the mass shell involves the contribution of the $0^{-}$ continuum. These chiral symmetry breaking corrections turn out to be large. The effects of these corrections on the calculated ${\pi }^0$ decay rate, on the values of the singlet-octet mixing angle, and on the ratios $f_8{/f}_{\pi }$ and $f_0{/f}_{\pi }$ are discussed. The implications for the transition form factors $\gamma {\gamma }^{*}\to {\pi }^0,$ η, ${\eta }^{\prime }$ are also evaluated and confronted with the available experimental data.

We argue that in QCD near the chiral limit, at all temperatures below the chiral phase transition, the dispersion relation of soft pions can be expressed entirely in terms of three temperature-dependent quantities: the pion screening mass, a pion decay constant, and the axial isospin susceptibility. The definitions of these quantities are given in terms of equal-time (static) correlation functions. Thus, all three quantities can be determined directly by lattice methods. The precise meaning of the Gell-Mann–Oakes–Renner relation at finite temperature is given.

The generalization of the two-loop pinch technique to the electroweak sector of the standard model is presented. We restrict ourselves to the case of conserved external currents, and provide a detailed analysis of both the charged and neutral sectors. The crucial ingredient for this construction is the identification of the parts discarded during the pinching procedure with well-defined contributions to the Slavnov-Taylor identity satisfied by the off-shell one-loop gauge-boson vertices; the latter are nested inside the conventional two-loop self-energies. It is shown by resorting to a set of powerful identities that the two-loop effective pinch technique self-energies coincide with the corresponding ones computed in the background Feynman gauge. The aforementioned identities are derived in the context of the Batalin-Vilkovisky formalism, a fact which enables the individual treatment of the self-energies of the photon and the Z boson. Some possible phenomenological applications are briefly discussed.

Starting with the most general effective Hamiltonian comprising scalar and vector operators beyond the standard model, we discuss the impact of various operators on the zero of the forward-backward asymmetry in the dileptonic B decay $\overrightarrow{B}{K}^{*}{\mu }^{+}{\mu }^{-}.$ We find that the zero of the asymmetry is highly sensitive to the sign and size of the vector-vector operators and opposite chirality counterparts of the usual operators. The scalar-scalar four-fermion operators, on the other hand, have a mild effect on the zero of the asymmetry. Our results are expected to be checked in near future experiments.

We examine the $N=2\mathrm{}$ Wess-Zumino model defined on the $d=2\mathrm{}$ Euclidean lattice in connection with a restoration of the Leibniz rule in the limit $\overrightarrow{a}0$ in perturbatively finite theory. We are interested in the difference between the Wilson and Ginsparg-Wilson fermions and in the effects of extra interactions introduced by an analysis of Nicolai mapping. As for the Wilson fermion, it induces a linear divergence to individual tadpole diagrams in the limit $\overrightarrow{a}0,$ which is absent in the Ginsparg-Wilson fermion. This divergence suggests that a careful choice of lattice regularization is required in a reliable numerical simulation. As for the effects of the extra couplings introduced by an analysis of Nicolai mapping, the extra couplings do not completely remedy the supersymmetry breaking in correlation functions induced by the failure of the Leibniz rule in perturbation theory, though those couplings ensure the vanishing of vacuum energy arising from disconnected diagrams. Supersymmetry in correlation functions is recovered in the limit $\overrightarrow{a}0$ with or without those extra couplings. In the context of lattice theory, it may be properly said that supersymmetry does not improve ultraviolet properties but rather it is well accommodated in theories with good ultraviolet properties.

In current lattice simulations of nucleon properties, the up and down quark masses are significantly larger than their physical values, while the strange quark can be included in simulations with its physical mass. When the up and down quark masses are much smaller than the strange-quark mass the chiral extrapolation of strange-quark matrix elements in the nucleon from the lattice up and down quark masses to their physical values can be performed with two-flavor chiral perturbation theory, thereby avoiding the slow convergence problem of the three-flavor chiral expansion. We explore the chiral expansion of several matrix elements of strange operators in the nucleon in two-flavor chiral perturbation theory and two-flavor partial-quenched chiral perturbation theory.

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of continuum loop integrals in analytic regularization and a few genuine lattice integrals (“master integrals”). These lattice master integrals are independent of external momenta and masses and can be computed numerically. At the one-loop level, there are four master integrals in a theory with only bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions.

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $\mu .$ Derivatives of quark and gluonic observables with respect to $\mu$ are computed at $\mu =0\mathrm{}$ for two flavors of $p4\mathrm{}$ improved staggered fermions with $ma=0.1,0.2\mathrm{}$ on a ${16}^3\times 4$ lattice, and used to calculate the leading order Taylor expansion in $\mu$ of the location of the pseudocritical point about $\mu =0.\mathrm{}$ This expansion should be well behaved for the small values of ${\mu }_{\mathrm{q}}{/T}_c\sim 0.1$ relevant for BNL RHIC phenomenology, and predicts a critical curve $T_c\left(\mu \right)$ in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of $\mu \ne 0$ on the equation of state, and comment on the complex phase of the fermion determinant in QCD with $\mu \ne 0.$

A model for the QCD vacuum based on a domainlike structured background gluon field with a definite duality attributed to the domains has been shown elsewhere to give confinement of static quarks, a reasonable value for the topological susceptibility, and indications that chiral symmetry is spontaneously broken. In this paper, we study in detail the eigenvalue problem for the Dirac operator in such a gluon mean field. A study of the local chirality parameter shows that the lowest nonzero eigenmodes possess a definite mean chirality correlated with the duality of a given domain. A probability distribution of the local chirality qualitatively reproduces histograms seen in lattice simulations.

The effect of lepton transverse polarization in $B^0\to D^{-}{l}^{+}{\nu }_l,$ $B^{+}\to D^0{l}^{+}{\nu }_l$ decays $(l=\tau ,\mu )$ is analyzed within the framework of the standard model in the leading order of heavy quark effective theory. It is shown that a nonzero transverse polarization appears due to the electromagnetic final state interaction. The diagrams with intermediate ${D,D}^{*}$ mesons contributing to the nonvanishing $P_T$ are considered. Regarding only the contribution of these mesons, the values of the $\tau$-lepton transverse polarization averaged over the physical region in the $B^0\to D^{-}{\tau }^{+}{\nu }_l$ and $B^{+}\to D^0{\tau }^{+}{\nu }_l$ decays are equal to $2.60\times {10}^{-3}$ and $-1.59\times {10}^{-3},$ respectively. In the case of muon decay modes the values of $〈P_T〉$ are equal to $2.97\times {10}^{-4}$ and $-6.79\times {10}^{-4}.$

We compute the QCD corrections to the gluon fusion subprocess $g\overrightarrow{g}\gamma \gamma ,$ which forms an important component of the background to the search for a light Higgs boson at the CERN LHC. We study the dependence of the improved $p\overrightarrow{p}\gamma \gamma X$ background calculation on the factorization and renormalization scales, on various choices for photon isolation cuts, and on the rapidities of the photons. We also investigate ways to enhance the statistical significance of the Higgs signal in the $\gamma \gamma$ channel.

We investigate neutrino oscillations in constant matter within the context of the standard three neutrino scenario. We derive an exact and simple formula for the oscillation probability applicable to all channels. In the standard parametrization, the probability for the ${\nu }_e\to {\nu }_{\mu }$ transition can be written in the form $P({\nu }_e\to {\nu }_{\mu }{)=A}_{e\mu }\cos \delta {+B}_{e\mu }\sin \delta {+C}_{e\mu }$ without any approximation using the $\mathrm{CP}$ phase $\delta .$ For the ${\nu }_{\mu }\to {\nu }_{\tau }$ transition, the linear term of $\cos 2\delta$ is added and the probability can be written in the form $P({\nu }_{\mu }\to {\nu }_{\tau }{)=A}_{\mu \tau }\cos \delta {+B}_{\mu \tau }\sin \delta {+C}_{\mu \tau }{+D}_{\mu \tau }\cos 2\delta .$ We give the $\mathrm{CP}$ dependences of the probability for other channels. We show that the probability for each channel in matter has the same form with respect to $\delta$ as in vacuum. It means that matter effects just modify the coefficients A, B, C, and D. We also give the exact expression of the coefficients for each channel. Furthermore, we show that our results with respect to $\mathrm{CP}$ dependences are reproduced from the effective mixing angles and the effective $\mathrm{CP}$ phase calculated by Zaglauer and Schwarzer. Through the calculation, a new identity is obtained by dividing the Naumov-Harrison-Scott identity by the Toshev identity.

We calculate the pressure for pure-glue QCD at high temperature to two-loop order using hard-thermal-loop (HTL) perturbation theory. At this order, all the ultraviolet divergences can be absorbed into renormalizations of the vacuum energy density and the HTL mass parameter. We determine the HTL mass parameter by a variational prescription. The resulting predictions for the pressure fail to agree with results from lattice gauge theory at temperatures for which they are available.

The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic formulations of the equations, an exact expression for the growth rate is derived using an energy norm. This expression agrees with the growth rate determined by numerical solution of the equations. An approximate method for estimating the growth rate is also derived. This estimate can be evaluated algebraically from the initial data, and is shown to exhibit qualitatively the same dependence as the numerically determined rate on the parameters that specify the formulation of the equations. This simple rate estimate therefore provides a useful tool for finding the most well-behaved forms of the evolution equations.

We recently studied the formation and evaporation of primordial black holes in a simple braneworld cosmology, namely the Randall-Sundrum type II cosmology. Here we study the effect of accretion from the cosmological background onto the black holes after formation. While it is generally believed that in the standard cosmology such accretion is of negligible importance, we find that during the high-energy regime of braneworld cosmology accretion can be the dominant effect and lead to a mass increase of potentially orders of magnitude. However, unfortunately the growth is exponentially sensitive to the accretion efficiency, which cannot be determined accurately. Since accretion becomes unimportant once the high-energy regime is over, it does not affect any constraints expressed at the time of black hole evaporation, but it can change the interpretation of those constraints in terms of early Universe formation rates.

A suite of three evolution systems is presented in the framework of the 3+1 formalism. The first one is of second order in space derivatives and has the same causal structure as the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system for a suitable choice of parameters. The second one is the standard first order version of the first one and has the same causal structure as the Bona-Massó system for a given parameter choice. The third one is obtained from the second one by reducing the space of variables in such a way that the only modes that propagate with zero characteristic speed are the trivial ones. This last system has the same structure as the ones recently presented by Kidder, Scheel, and Teukolsky: the correspondence between the two sets of parameters is explicitly given. The fact that the suite started with a system in which all the dynamical variables behave as tensors (contrary to what happens with the BSSN system) allows one to keep the same parametrization when passing from one system to the next in the suite. The direct relationship between each parameter and a particular characteristic speed, which is quite evident in the second and third systems, is a direct consequence of the manifest 3+1 covariance of the approach.

The slow-rotation approximation of Hartle is developed to a setting where a charged rotating fluid is present. The linearized Einstein-Maxwell equations are solved on the background of the Reissner-Nordström space-time in the exterior electrovacuum region. The theory is put to action for the charged generalization of the Wahlquist solution found by García. The García solution is transformed to coordinates suitable for the matching and expanded in powers of the angular velocity. The two domains are then matched along the zero pressure surface using the Darmois-Israel procedure. We prove a theorem to the effect that the exterior region is asymptotically flat if and only if the parameter $C_2,$ characterizing the magnitude of an external magnetic field, vanishes. We obtain the form of the constant $C_2$ for the García solution. We conjecture that the García metric cannot be matched to an asymptotically flat exterior electrovacuum region even to first order in the angular velocity. This conjecture is supported by a high precision numerical analysis.