The leading-order parton processes that produce a dilepton with large transverse momentum predict that the transverse polarization should increase with the transverse momentum for almost any choice of the quantization axis for the spin of the virtual photon. The rate of approach to complete transverse polarization depends on the choice of spin quantization axis. We propose axes that optimize that rate of approach. They are determined by the momentum of the dilepton and the direction of the jet that provides most of the balancing transverse momentum.

We deduce the mass of the pseudoscalar glueball $G$ from an $\eta$-${\eta }^{\prime }$-$G$ mixing formalism based on the anomalous Ward identity for transition matrix elements. With the inputs from the recent KLOE experiment, we find a solution for the pseudoscalar glueball mass around $(1.4\pm 0.1)\mathrm{GeV}$, which is fairly insensitive to a range of inputs with or without Okubo-Zweig-Iizuka-rule violating effects. This affirms that $\eta (1405)$, having a large production rate in the radiative $J/\Psi$ decay and not seen in $\gamma \gamma$ reactions, is indeed a leading candidate for the pseudoscalar glueball. Other relevant quantities including the anomaly and pseudoscalar density matrix elements are obtained. The decay widths for $G\to \gamma \gamma$, ${\ell }^{+}{\ell }^{-}$ are also predicted.

In the heavy quark limit of QCD, using the operator product expansion, the formalism of Falk for hadrons of arbitrary spin, and the nonforward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function ${\xi }_{\Lambda }(w)$ of the baryon transition ${\Lambda }_b\to {\Lambda }_c\ell {\overline{\nu }}_{\ell }$, where the light cloud has $j^P=0^{+}$ for both initial and final baryons. We recover the lower bound for the slope ${\rho }_{\Lambda }^2=-{\xi }_{\Lambda }^{\prime }(1)\ge 0$ obtained by Isgur et al., and we generalize it by demonstrating that the Isgur-Wise function ${\xi }_{\Lambda }(w)$ is an alternate series in powers of $(w-1)$, i.e. $(-1{)}^n{\xi }_{\Lambda }^{(n)}(1)\ge 0$. Moreover, exploiting systematically the sum rules, we get an improved lower bound for the curvature in terms of the slope, ${\sigma }_{\Lambda }^2={\xi }_{\Lambda }^{\prime \prime }(1)\ge \frac{3}{5}[{\rho }_{\Lambda }^2+({\rho }_{\Lambda }^2{)}^2]$. This bound constrains the shape of the Isgur-Wise function and it will be compelling in the analysis of future precise data on the differential rate of the baryon semileptonic decay ${\Lambda }_b\to {\Lambda }_c\ell {\overline{\nu }}_{\ell }$, that has a large measured branching ratio, of about 5%.

A nonlocal covariant extension of the two-flavor Nambu and Jona-Lasinio model is constructed, with built-in constraints from the running coupling of QCD at high-momentum and instanton physics at low-momentum scales. Chiral low-energy theorems and basic current algebra relations involving pion properties are shown to be reproduced. The momentum-dependent dynamical quark mass derived from this approach is in agreement with results from Dyson-Schwinger equations and lattice QCD. At finite temperature, inclusion of the Polyakov loop and its gauge invariant coupling to quarks reproduces the dynamical entanglement of the chiral and deconfinement crossover transitions as in the (local) Polyakov-loop-extended Nambu and Jona-Lasinio model, but now without the requirement of introducing an artificial momentum cutoff. Steps beyond the mean-field approximation are made including mesonic correlations through quark-antiquark ring summations. Various quantities of interest (pressure, energy density, speed of sound, etc.) are calculated and discussed in comparison with lattice QCD thermodynamics at zero chemical potential. The extension to finite quark chemical potential and the phase diagram in the $(T,\mu )$-plane are also discussed.

We describe the deconfining critical temperature dependence on the pion mass and on the isospin chemical potential in remarkably good agreement with lattice data. Our framework incorporates explicit dependence on quark masses, isospin and baryonic chemical potentials for the case of two flavors through ingredients from well-known high- and low-energy theories. In the low-energy sector, the system is described by a minimal chiral perturbation theory effective action, corresponding to a hot gas of pion quasiparticles and heavy nucleons. For the high-temperature sector we adopt a simple extension of the fuzzy bag model. We also briefly discuss the effects of mass asymmetry and baryon chemical potential.

We propose a new parametrization of the $B\to \pi$ vector form factor $f_{+}(q^2)$ as an expansion in powers of a conformal mapping variable, which satisfies unitarity, analyticity and perturbative QCD scaling. The unitarity constraint is used also for defining the systematic error of the expansion. We fit with the new parametrization the available experimental and theoretical information on exclusive $B\to \pi l\nu$ decays, making a conservative estimate of the effects of correlations in the systematic and statistical errors of the lattice results. With four parameters to describe $f_{+}(q^2)$, the systematic error is negligible in the whole semileptonic region. We also obtain $|V_{ub}|=(3.50\pm 0.24)\times {10}^{-3}$ where, in our approach, the uncertainty is predominantly statistical.

Theories beyond the standard model must necessarily respect its gauge symmetry. This implies strict constraints on the possible models of nonstandard neutrino interactions, which we analyze. The focus is set on the effective low-energy dimension six and eight operators involving four leptons, decomposing them according to all possible tree-level mediators, as a guide for model building. The new couplings are required to have sizable strength, while processes involving four charged leptons are required to be suppressed. For nonstandard interactions in matter, only diagonal tau-neutrino interactions can escape these requirements and can be allowed to result from dimension six operators. Large nonstandard neutrino interactions from dimension eight operators alone are phenomenologically allowed in all flavor channels and are shown to require at least two new mediator particles. The new couplings must obey general cancellation conditions both at the dimension six and dimension eight levels, which result from expressing the operators obtained from the mediator analysis in terms of a complete basis of operators. We illustrate with one example how to apply this information to model building.

The PHENIX experiment presents results from the RHIC 2006 run with polarized $p+p$ collisions at $\sqrt{s}=62.4\mathrm{GeV}$, for inclusive ${\pi }^0$ production at midrapidity. Unpolarized cross section results are measured for transverse momenta $p_T=0.5$ to $7\mathrm{GeV}/c$. Next-to-leading order perturbative quantum chromodynamics calculations are compared with the data, and while the calculations are consistent with the measurements, next-to-leading logarithmic corrections improve the agreement. Double helicity asymmetries $A_{LL}$ are presented for $p_T=1$ to $4\mathrm{GeV}/c$ and probe the higher range of Bjorken $x$ of the gluon ($x_g$) with better statistical precision than our previous measurements at $\sqrt{s}=200\mathrm{GeV}$. These measurements are sensitive to the gluon polarization in the proton for $0.06<x_g<0.4$.

We study the thermal part of the energy density spatial correlator in the quark-gluon plasma. We describe its qualitative form at high temperatures. We then calculate it out to distances $\approx 1.5/T$ in SU(3) gauge theory lattice simulations for the range of temperatures $0.9\le T/T_c\le 2.2$. The vacuum-subtracted correlator exhibits nonmonotonic behavior, and is almost conformal by $2T_c$. Its broad maximum at $r\approx 0.6/T$ suggests a dense medium with only weak short-range order, similar to a nonrelativistic fluid near the liquid-gas phase transition, where $\eta /s$ is minimal.

Starting from the temperature dependencies of the energy density and pressure from lattice QCD calculation, we extract the temperature dependencies of the electric and magnetic condensate near $T_c$. While the magnetic condensate hardly changes across $T_c$, we find that the electric condensate increases abruptly above $T_c$. This induces a small but equally abrupt decrease in the mass of $J/\psi$, which can be calculated through the second-order Stark effect. Combining the present result with the previously determined QCD sum rule constraint, we extract the thermal width of $J/\psi$ above $T_c$, which also increases fast. These changes can be identified as the critical behavior of $J/\psi$ across $T_c$ associated with the phase transition. We find that the mass shift and width broadening of $J/\psi$ at $1.05T_c$ will be around $-100\mathrm{MeV}$ and 100 MeV, respectively.

We search for $b\to s{\mu }^{+}{\mu }^{-}$ transitions in $B$ meson ($B^{+}$, $B^0$, or $B_s^0$) decays with $924{\mathrm{pb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected with the CDF II detector at the Fermilab Tevatron. We find excesses with significances of 4.5, 2.9, and 2.4 standard deviations in the $B^{+}\to {\mu }^{+}{\mu }^{-}{K}^{+}$, $B^0\to {\mu }^{+}{\mu }^{-}{K}^{*}(892{)}^0$, and $B_s^0\to {\mu }^{+}{\mu }^{-}\varphi$ decay modes, respectively. Using $B\to J/\psi h$ ($h=K^{+}$, $K^{*}(892{)}^0$, $\varphi$) decays as normalization channels, we report branching fractions for the previously observed $B^{+}$ and $B^0$ decays, $\mathcal{B}(B^{+}\to {\mu }^{+}{\mu }^{-}{K}^{+})=(0.59\pm 0.15\pm 0.04)\times {10}^{-6}$, and $\mathcal{B}(B^0\to {\mu }^{+}{\mu }^{-}{K}^{*}(892{)}^0)=(0.81\pm 0.30\pm 0.10)\times {10}^{-6}$, where the first uncertainty is statistical, and the second is systematic. We set an upper limit on the relative branching fraction $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-}\varphi )/\mathcal{B}(B_s^0\to J/\psi \varphi )<2.6(2.3)\times {10}^{-3}$ at the 95(90)% confidence level, which is the most stringent to date.

We study the production cross section of a highly excited string with fixed angular momentum from an ultrahigh energy collision of two light strings. We find that the cross section exhibits geometric behavior in a certain region of angular-momentum/impact-parameter space. This geometric behavior is common to the differential cross sections of a black hole production with fixed angular momentum and thus we see another correspondence between strings and black holes.

The flavor structure of the standard model may arise from random selection on a landscape. In a class of simple models, called “Gaussian landscapes,” Yukawa couplings derive from overlap integrals of Gaussian zero-mode wave functions on an extra-dimensional space. Statistics of vacua are generated by scanning the peak positions of these wave functions, giving probability distributions for all flavor observables. Gaussian landscapes can account for all of the major features of flavor, including both the small electroweak mixing in the quark sector and the large mixing observed in the lepton sector. We find that large lepton mixing stems directly from lepton doublets having broad wave functions on the internal manifold. Assuming the seesaw mechanism, we find the mass hierarchy among neutrinos is sensitive to the number of right-handed neutrinos and can provide a good fit to neutrino oscillation measurements.

We study the effect of a cosmological constant $\Lambda$ on the propagation and detection of gravitational waves. To this purpose we investigate the linearized Einstein’s equations with terms up to linear order in $\Lambda$ in a de Sitter and an anti-de Sitter background spacetime. In this framework the cosmological term does not induce changes in the polarization states of the waves, whereas the amplitude gets modified with terms depending on $\Lambda$. Moreover, if a source emits a periodic waveform, its periodicity as measured by a distant observer gets modified. These effects are, however, extremely tiny and thus well below the detectability by some 20 orders of magnitude within present gravitational wave detectors such as LIGO or future planned ones such as LISA.

We have derived whole-sky cosmic microwave background polarization maps from the WMAP 5 year polarization data, using the harmonic internal linear combination (HILC) method. Our HILC method incorporates spatial variability of linear weights in a natural way and yields continuous linear weights over the entire sky. To estimate the power spectrum of HILC maps, we have derived an unbiased quadratic estimator, which is similar to the WMAP team’s cross-power estimator, but in a more convenient form for HILC maps. From our cosmic microwave background polarization map, we have obtained $TE$ correlation and $E$ mode power spectra without applying any mask. They are similar to the WMAP team’s estimation and consistent with the WMAP best-fit $\Lambda \mathrm{CDM}$ model. Foreground reduction by the HILC method is more effective for high resolution and low noise data. Hence, our HILC method will enable effective foreground reduction in polarization data from the Planck surveyor.

The detection of primordial gravitational waves is one of the biggest challenges of the present time. The existing (Wilkinson Microwave Anisotropy Probe) observations are helpful in achieving this goal, and the forthcoming experiments (Planck) are likely to complete this mission. We show that the 5-year Wilkinson Microwave Anisotropy Probe $TE$ data contain a hint of the presence of the gravitational wave contribution. In terms of the parameter $R$, which gives the ratio of contributions from gravitational waves and density perturbations to the temperature quadrupole, the best-fit model produced $R=0.24$. Because of large residual noises, the uncertainty of this determination is still large, and it easily includes the $R=0$ hypothesis. However, the uncertainty will be strongly reduced in the forthcoming observations which are more sensitive. We numerically simulated the Planck data and concluded that the relic gravitational waves with $R=0.24$ will be present at a better than $3\sigma$ level in the $TE$ observational channel, and at a better than $2\sigma$ level in the “realistic” $BB$ channel. The balloon-borne and ground-based observations may provide healthy competition for Planck in some parts of the lower-$\ell$ spectrum.

The derivation of the response function of an interferometric gravitational wave detector is a paradigmatic calculation in the field of gravitational wave detection. Surprisingly, the standard derivation of the response wave detectors makes several unjustifiable assumptions, both conceptual and quantitative, regarding the coordinate trajectory and coordinate velocity of the null geodesic the light travels along. These errors, which appear to have remained unrecognized for at least 35 years, render the standard derivation inadequate and misleading as an archetype calculation. Here we identify the flaws in the existing derivation and provide, in full detail, a correct derivation of the response of a single-bounce Michelson interferometer to gravitational waves, following a procedure that will always yield correct results; compare it to the standard, but incorrect, derivation; show where the earlier mistakes were made; and identify the general conditions under which the standard derivation will yield correct results. By a fortuitous set of circumstances, not generally so, the final result is the same in the case of Minkowski background spacetime, synchronous coordinates, transverse-traceless gauge metric perturbations, and arm mirrors at coordinate rest.

We develop techniques to calculate the four $\Delta$ electromagnetic form factors using lattice QCD, with particular emphasis on the subdominant electric quadrupole form factor that probes deformation of the $\Delta$. Results are presented for pion masses down to approximately 350 MeV for three cases: quenched QCD, two flavors of dynamical Wilson quarks, and three flavors of quarks described by a mixed action combining domain-wall valence quarks and dynamical staggered sea quarks. The magnetic moment of the $\Delta$ is compared with chiral effective field theory calculations and the $\Delta$ charge density distributions are discussed.

We derive generalization of the Balitsky-Kovchegov (BK) equation for a dipole, which consists of a parton and an antiparton of arbitrary charge. At first, we develop one method of indexless transformation of color expressions. The method is based on an evaluation of the Casimir operator on a tensor product. From the Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov–Kovner equation, we derive the evolution equation for a single parton and prove gluon Reggeization in an arbitrary color channel. We show that there is a color duplication of such Regge poles. Higher $t$-channel color exchange has its own Regge pole, which residue is proportional to the quadratic Casimir. Taking a fundamental representation, we derive the usual BK equation and shed new light on the meaning of linear and nonlinear terms. Finally, we discuss a linearized version of the generalized BK equation.