We solve, analytically and numerically, a gap equation in parity invariant ${\mathrm{QED}}_3$ in the presence of an infrared cutoff $\mu$ and derive an expression for the critical fermion number $N_c$ as a function of $\mu .$ We argue that this dependence of $N_c$ on the infrared scale might solve the discrepancy between continuum Schwinger-Dyson equations studies and lattice simulations of ${\mathrm{QED}}_3.$

The satellite experiment, the Wilkinson Microwave Anisotropy Probe (WMAP), has produced for the first time a high-coverage, high-resolution survey of the microwave sky, releasing publicly available data that are likely to remain unrivaled for years to come. Here we compare the WMAP temperature power spectrum, along with an exhaustive compilation of previous experiments, to models of dark energy that allow for a tracking epoch at the present, deriving updated bounds on the dark energy equation of state and the other cosmological parameters. Moreover, we complement the analysis by including a coupling of the dark energy to dark matter. The main results are (a) the WMAP data alone constrain the equation of state of tracking dark energy to be $w_{\phi }<-0.67(-0.49)$ to 68%(95%) (confining the analysis to $w_{\phi }>-1),$ which implies for an inverse power-law potential an exponent $\alpha <0.99\mathrm{}\left(2.08\right),$ and (b) the dimensionless coupling to dark matter is $|\beta |<0.07\mathrm{}\left(0.13\right).$ Including the results from supernovae type Ia further constrains the dark energy equation of state.

We investigate the constraints on the Cardassian model using the recent results from the Wilkinson microwave anisotropy probe for the locations of the peaks of the cosmic microwave background (CMB) anisotropy spectrum. We find that the model is consistent with the recent observational data for a certain range of the model parameter n and the cosmological parameters. We find that the Cardassian model is favored compared to the ΛCDM model for a higher spectral index ${(n}_s\approx 1)$ together with a lower value of the Hubble parameter h $(h<~0.71).$ But for smaller values of $n_s,$ both ΛCDM and Cardassian models are equally favored. Also, irrespective of supernova constraints, CMB data alone predict the current acceleration of the Universe in this model. We have also studied the constraint on ${\sigma }_8,$ the rms density fluctuations at the ${8h}^{-1}\mathrm{Mpc}$ scale.

We propose a mechanism leading naturally to spontaneous symmetry breaking in a gauge theory. The Higgs field is assumed to have global and gauged internal symmetries. We associate a nonzero chemical potential with one of the globally conserved charges commuting with all the gauge transformations. This induces a negative mass squared for the Higgs field, triggering the spontaneous symmetry breaking of the global and local symmetries. The mechanism is general and we test the idea for the electroweak theory in which the Higgs sector is extended to possess an extra global Abelian symmetry. With this symmetry we associate a nonzero chemical potential. The Bose-Einstein condensation of the Higgs bosons leads, at the tree level, to modified dispersion relations for the Higgs field, while the dispersion relations of the gauge bosons and fermions remain undisturbed. The latter are modified through higher order corrections. We have computed some corrections to the vacuum polarizations of the gauge bosons and fermions. To quantify the corrections to the gauge boson vacuum polarizations with respect to the standard model we considered the effects on the T parameter. We finally derive the one loop modified fermion dispersion relations.

Charmed meson decays into a pseudoscalar meson P and a tensor meson T are studied. The charm to tensor meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise (ISGW) quark model. It is shown that the Cabibbo-allowed decay $D_s^{+}\to f_2\mathrm{}\left(1270\right)\mathrm{}{\pi }^{+}$ is dominated by the W-annihilation contribution and has the largest branching ratio in $\overrightarrow{D}\mathrm{TP}$ decays. We argue that the Cabibbo-suppressed mode $D^{+}\to f_2\mathrm{}\left(1270\right)\mathrm{}{\pi }^{+}$ should be suppressed by one order of magnitude relative to $D_s^{+}\to f_2\mathrm{}\left(1270\right)\mathrm{}{\pi }^{+}.$ When the finite width effect of the tensor resonances is taken into account, the decay rate of $\overrightarrow{D}\mathrm{TP}$ is generally enhanced by a factor of 2–3. Except for $D_s^{+}\to f_2\mathrm{}\left(1270\right)\mathrm{}{\pi }^{+},$ the predicted branching ratios of $\overrightarrow{D}\mathrm{TP}$ decays are in general too small by one to two orders of magnitude compared to experiment. However, it is very unlikely that the $\overrightarrow{D}T$ transition form factors can be enhanced by a factor of 3–5 within the ISGW quark model to account for the discrepancy between theory and experiment. As many of the current data are still preliminary and lack sufficient statistic significance, more accurate measurements are needed to pin down the issue.

Inclusive momentum distributions of charged particles in restricted cones around jet axes were measured in dijet events with invariant dijet masses in the range 80 to $600\mathrm{GeV}{/c}^2.$ Events were produced at the Fermilab Tevatron in $p\overline{p}$ collisions with a center of mass energy of 1.8 TeV and recorded by the Collider Detector at Fermilab. The results were compared to perturbative QCD calculations carried out in the framework of the modified leading log approximation (MLLA) and assuming local parton-hadron duality. It was shown that the data follow theoretical predictions quite well over the whole range of the jet energies included in this analysis. We extracted the MLLA cutoff scale $Q_{\mathrm{eff}}$ and found a value of $230\pm 40\mathrm{MeV}.$ The theoretical prediction of $E_{\mathrm{jet}}\sin {\theta }_c$ scaling, where ${\theta }_c$ is the cone opening angle, was experimentally observed for the first time. From the MLLA fits to the data, two more parameters were extracted: the ratio of parton multiplicities in gluon and quark jets, ${r=N}_{\mathrm{partons}}^{g-\mathrm{jet}}{/N}_{\mathrm{partons}}^{q-\mathrm{jet}}=1.9\mathrm{}\pm 0.5,$ and the ratio of the number of charged hadrons to the number of predicted partons in a jet, $K_{\mathrm{LPHD}}^{\mathrm{charged}}{=N}_{\mathrm{hadrons}}^{\mathrm{charged}}{/N}_{\mathrm{partons}}=0.56\mathrm{}\pm \mathrm{0.10.}$

The signal of a lighter top squark has been looked at for using Fermilab Tevatron data in the dielectron plus dijet channel. We find that the mass of the lighter top squark when it decays dominantly in the electron plus jet channel can be ruled out up to 220 GeV at 95% C.L. using dielectron data. In the framework of the R-parity breaking supersymmetry (SUSY) model we exclude relevant R-parity violating couplings for a range of top squark masses and other SUSY parameters. The bounds on R-parity violating couplings are very stringent for the parameter space where the lighter top squark turns out to be the next to lightest supersymmetric particle.

The chiral phase transition at finite temperature and density is discussed in the framework of the QCD-like gauge field theory. The thermodynamical potential is investigated using a variational approach. Latent heat generated in the first-order phase transition is calculated. It is found that the latent heat is enhanced near the tricritical point and is more than several hundred MeV per quark.

We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $\beta$ function in the so-called conformal scheme. The Wilson coefficients appearing in the nonforward kinematics are then entirely determined from those of the polarized deep inelastic scattering known to next-to-next-to-leading order accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $\beta$ function and discuss numerical predictions calculated in different kinematical regions. It is demonstrated that the photon-to-pion transition form factor can provide a fundamental testing ground for our QCD understanding of exclusive reactions.

We give an analytical calculation of solar neutrino masses and mixing at one-loop order within bilinear R-parity breaking supersymmetry, and compare our results to the exact numerical calculation. Our method is based on a systematic perturbative expansion of R-parity violating vertices to leading order. We find in general quite good agreement between the approximate and full numerical calculations, but the approximate expressions are much simpler to implement. Our formalism works especially well for the case of the large mixing angle Mikheyev-Smirnov-Wolfenstein solution, now strongly favored by the recent KamLAND reactor neutrino data.

We update the curves of the effective degrees of freedom for energy density $g_{*}\mathrm{}\left(T\right)\mathrm{}$ and for the entropy density $g_{*S}\mathrm{}\left(T\right)\mathrm{}$ during the era of radiation domination in the Universe. We find that a plain count of effective degrees of freedom sets an upper limit to the temperature of the quark-hadron transition at $T_c<235\mathrm{}\mathrm{MeV}$ for the energy density and $T_c<245\mathrm{}\mathrm{MeV}$ for the entropy density.

We consider Yang-Mills theories formulated on a noncommutative space-time described by a space-time dependent antisymmetric field ${\theta }^{\mu \nu }\mathrm{}\left(x\right).$ Using Seiberg-Witten map techniques, we derive the leading order operators for the effective field theories that take into account the effects of such a background field. These effective theories are valid for a weakly noncommutative space-time. It is remarkable to note that already simple models for ${\theta }^{\mu \nu }\mathrm{}\left(x\right)\mathrm{}$ can help to loosen the bounds on space-time noncommutativity coming from low energy physics. Noncommutative geometry formulated in our framework is a potential candidate for new physics beyond the standard model.

We present a study of the three-point angular correlation function $w_3=〈{\delta }_1{\delta }_2{\delta }_3〉$ of (adimensional) temperature anisotropies measured by the Wilkinson Microwave Anisotropy Probe. The results can be normalized to the two-point function $w_2=〈{\delta }_1{\delta }_2〉$ in terms of the hierarchical $q_3\sim w_3{/w}_2^2$ or dimensionless $d_3\sim w_3{/w}_2^{3/2}$ amplitudes. Strongly non-Gaussian models are generically expected to show $d_3>1\mathrm{}$ or $q_3>{10}^3{d}_3.$ Unfortunately, this is comparable to the cosmic variance on large angular scales. For Gaussian primordial models, $q_3$ gives a direct measure of the nonlinear corrections to temperature anisotropies in the sky: $\delta ={\delta }_L{+f}_{\mathrm{NLT}}\left({\delta }_L^2-〈{\delta }_L^2〉\right)$ with $f_{\mathrm{NLT}}{=q}_3/2\mathrm{}$ for the leading order term in $w_2^2.$ We find good agreement with the Gaussian hypothesis $d_3\sim 0$ within the cosmic variance of the simulations of the cold dark matter model with a cosmological constant $\left(\Lambda \mathrm{CDM}\right)$ (with or without a low quadrupole). The strongest constraints on $q_3$ come from scales smaller than $1°.$ We find $q_3=19\mathrm{}\pm 141$ for (pseudo) collapsed configurations and an average of $q_3=336\mathrm{}\pm 218$ for noncollapsed triangles. The corresponding nonlinear coupling parameter $f_{\mathrm{NL}}$ for curvature perturbations $\Phi ,$ in the Sachs-Wolfe regime is $f_{\mathrm{NL}}^{\mathrm{SW}}{=q}_3/6,$ while on degree scales, the extra power in acoustic oscillations produces $f_{\mathrm{NL}}\sim q_3/30\mathrm{}$ in the $\Lambda \mathrm{CDM}.$ Errors are dominated by cosmic variance, but for the first time they begin to be small enough to constrain the leading order nonlinear effects with a coupling of the order of unity.

We introduce a set of correlations between energy flow and event shapes that are sensitive to the flow of color at short distances in jet events. These correlations are formulated for a general set of event shapes, which includes jet broadening and thrust as special cases. We illustrate the method for $e^{+}{e}^{-}$ dijet events, and calculate the correlation at leading logarithm in the energy flow and at next-to-leading-logarithm in the event shape.

We investigate and solve in the context of general relativity the apparent paradox which appears when bodies floating in a background fluid are set in relativistic motion. Suppose some macroscopic body, say, a submarine designed to lie just in equilibrium when it rests (totally) immersed in a certain background fluid. The puzzle arises when different observers are asked to describe what is expected to happen when the submarine is given some high velocity parallel to the direction of the fluid surface. On the one hand, according to observers at rest with the fluid, the submarine would contract and, thus, sink as a consequence of the density increase. On the other hand, mariners at rest with the submarine using an analogous reasoning for the fluid elements would reach the opposite conclusion. The general relativistic extension of the Archimedes law for moving bodies shows that the submarine sinks. As an extra bonus, this problem suggests a new gedankenexperiment for the generalized second law of thermodynamics.

We study the dynamical evolution of a stationary, axisymmetric, and perfectly conducting cold accretion disk containing a large-scale magnetic field around a Kerr black hole, trying to understand the relation between accretion and the transportation of angular momentum and energy. A one-dimensional radial momentum equation is derived near the equatorial plane, which has one intrinsic singularity at the fast critical point. We solve the radial momentum equation for solutions corresponding to an accretion flow that starts from a subsonic state at infinity, smoothly passes the fast critical point, then supersonically falls into the horizon of the black hole. The solutions always have the following features: (1) The specific energy of fluid particles remains constant but the specific angular momentum is effectively removed by the magnetic field. (2) At large radii, where the disk motion is dominantly rotational, the energy density of the magnetic field is equipartitioned with the rotational energy density of the disk. (3) Inside the fast critical point, where radial motion becomes important, the ratio of the electromagnetic energy density to the kinetic energy density drops quickly. The results indicate that: (1) disk accretion does not necessarily imply energy dissipation since magnetic fields do not have to transport or dissipate a lot of energy as they effectively transport angular momentum and (2) when resistivity is small, the large-scale magnetic field is amplified by the shearing rotation of the disk until the magnetic energy density is equipartitioned with the rotational energy density, ending up with a geometrically thick disk. This is in contrast to the evolution of small-scale magnetic fields where if the resistivity is nonzero the magnetic energy density is likely to be equipartitioned with the kinetic energy density associated with local random motions (e.g., turbulence), making a thin Keplerian disk possible.

It is shown that the supersymmetric extension of the Stelle-West formalism permits the construction of an action for $\mathrm{}(3+1)\mathrm{}$-dimensional $N=1\mathrm{}$ supergravity with a cosmological constant genuinely invariant under the $\mathrm{OSp}(4/1).$ Since the action is invariant under the supersymmetric extension of the AdS group, the supersymmetry algebra closes off shell without the need for auxiliary fields. The limit case $\overrightarrow{m}0,$ i.e., $\mathrm{}(3+1)\mathrm{}$-dimensional $N=1\mathrm{}$ supergravity, invariant under the Poincaré supergroup is also discussed.

We address the physics implications of a precise determination of the weak charge of the proton, $Q_W\mathrm{}\left(p\right),$ from a parity violating elastic electron proton scattering experiment to be performed at the Jefferson Laboratory. We present the standard model (SM) expression for $Q_W\mathrm{}\left(p\right)\mathrm{}$ including one-loop radiative corrections, and discuss in detail the theoretical uncertainties and missing higher order QCD corrections. Owing to a fortuitous cancellation, the value of $Q_W\mathrm{}\left(p\right)\mathrm{}$ is suppressed in the SM, making it a unique place to look for physics beyond the SM. Examples include extra neutral gauge bosons, supersymmetry, and leptoquarks. We argue that a $Q_W\mathrm{}\left(p\right)\mathrm{}$ measurement will provide an important complement to both high energy collider experiments and other low energy electroweak measurements. The anticipated experimental precision requires the knowledge of the $O\left({\alpha }_s\right)$ corrections to the pure electroweak box contributions. We compute these contributions for $Q_W\mathrm{}\left(p\right),$ as well as for the weak charges of heavy elements as determined from atomic parity violation.

Based on a measurement of high momentum ${\eta }^{\prime }$ production in B decays, we determine the charmless inclusive $\overrightarrow{B}{\eta }^{\prime }{X}_{\mathrm{nc}}$ branching fraction in the lab-frame momentum interval $2.0<\mathrm{}{P}_{{\eta }^{\prime }}<2.7\mathrm{}\mathrm{GeV}/c.\mathrm{}$ Using $9.7\times {10}^{6}B\overline{B}$ pairs collected at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ center-of-mass energy with the CLEO II and II.V detector configurations, we find $\mathcal{B}\left(\overrightarrow{B}{\eta }^{\prime }{X}_{\mathrm{nc}}\right)=[4.6\pm 1.1\pm 0.4\pm 0.5]\times {10}^{-4}$ in the $2.0<\mathrm{}{P}_{{\eta }^{\prime }}<2.7\mathrm{}\mathrm{GeV}/c$ momentum range, where the uncertainties are statistical, systematic, and from subtraction of background from B decays to charm, respectively.

It has recently been proposed that the Universe might be accelerating as a consequence of extra dimensions with time-varying size. We show that, although these scenarios can lead to acceleration, they run into serious difficulty when taking into account the limits on the time variation of the four-dimensional Newton constant. On the other hand, models of “Cardassian” expansion based on extra dimensions which have been constructed so far violate the weak energy condition for the bulk stress energy, for parameters that give an accelerating Universe.