High-precision mass measurements of a pentaquark (5Q) ${\Theta }^{+}$ in the $J^P=3/2^{\pm }$ channels are performed in anisotropic quenched lattice QCD. A large number of gauge configurations ($N_{\mathrm{conf}}=1000$) are prepared for the standard Wilson gauge action at $\beta =5.75$ and the $O(a)$ improved Wilson (clover) quark action is employed for $\kappa =0.1210(0.0010)0.1240$ on a ${12}^3\times 96$ lattice with the renormalized anisotropy as $a_s/a_t=4$. The Rarita-Schwinger formalism is adopted for interpolating fields. We examine several interpolating fields with isospin $I=0$, such as (a) the $N{K}^{*}$-type, (b) the color-twisted $N{K}^{*}$-type, and (c) the diquark-type operators. After chiral extrapolation, we obtain massive states, $m_{5\mathrm{Q}}\simeq 2.1–2.2\mathrm{GeV}$ in $J^P=3/2^{-}$, and $m_{5\mathrm{Q}}=2.4–2.6\mathrm{GeV}$ in $J^P=3/2^{+}$. Analyses using the hybrid boundary condition method are performed to determine whether these states are compact 5Q resonances or two-hadron scattering states. No compact 5Q resonance state is found below 2.1 GeV.

In the relativistic mean field approximation three quarks in baryons from the lowest octet and the decuplet are bound by the self-consistent chiral field, and there are additional quark-antiquark pairs whose wave function also follows from the mean field. We present a generating functional for the 3-quark, 5-quark, 7-quark . . . wave functions inside the octet, decuplet and antidecuplet baryons treated in a universal and compact way. The 3-quark components have the $SU(6)$-symmetric wave functions but with specific relativistic corrections which are generally not small. In particular, the normalization of the 5-quark component in the nucleon is about 50% of the 3-quark component. We give explicitly the 5-quark wave functions of the nucleon and of the exotic ${\Theta }^{+}$. We develop a formalism how to compute observables related to the 3- and 5-quark Fock components of baryons, and apply it to estimate the ${\Theta }^{+}$ width which turns out to be very small, 2–4 MeV, although with a large uncertainty.

We consider the problem of the physical process version of the first law of black ring thermodynamics in $n$-dimensional Einstein gravity with additional $(p+1)$-form field strength and dilaton fields. The first order variations of mass, angular momentum and local charge for black ring are derived. From them we prove the physical process version of the first law of thermodynamic for stationary black rings.

Motivated by the recent experimental data, we have revisited the $B\to \pi K,\pi \pi$ decays in the framework of QCD factorization, with inclusion of the important strong penguin corrections of order ${\alpha }_s^2$ induced by $b\to D{g}^{*}{g}^{*}$ ($D=d$ or $s$ and $g^{*}$ denotes an off-shell gluon) transitions. We find that these higher order strong penguin contributions can provide $\sim 30\%$ enhancement to the penguin-dominated $B\to \pi K$ decay rates, and such an enhancement can improve the consistency between the theoretical predictions and the experimental data significantly, while for the tree-dominated $B\to \pi \pi$ decays, these higher order contributions play only a minor role. When these strong penguin contributions are summed, only a small strong phase remains and the direct $CP$ asymmetries get small corrections. We also find that patterns of the ratios between the $CP$-averaged branching fractions remain nearly unaffected even after including these higher order corrections and the $\pi K$ puzzle still persists. Our results may indicate that to resolve the puzzle one would have to resort to new physics contributions in the electroweak penguin sector as found by Buras et al.

It is shown that, based only upon empirically and semiempirically known facts together with some reasonable theoretical postulates, we are inevitably led to a novel conclusion that the quark orbital angular momentum carries nearly half of the total nucleon spin at the low energy scale around $Q^2\simeq (600\mathrm{MeV}{)}^2$. We also perform an explicit model analysis to find that the quark spin fraction $\Delta \Sigma$ is extremely sensitive to the pion mass, which may resolve the discrepancy between the observation and the prediction of the recent lattice QCD simulation carried out in the heavy pion region.

We present a study of rates and kinematical properties of lepton pairs contained in central jets with transverse energy $E_T\ge 15\mathrm{GeV}$ that are produced at the Fermilab Tevatron collider. We compare the data to a QCD prediction based on the herwig and qq Monte Carlo generator programs. We find that the data are poorly described by the simulation, in which sequential semileptonic decays of single $b$ quarks ($b\to lcX$ with $c\to lsX$) are the major source of such lepton pairs.

We propose to measure the Cabibbo-Kobayashi-Maskawa parameter $2\beta +\gamma$ using $B^0$ decays involving several intermediate states, and describe a general formalism that applies to a broad class of decays. The main advantage of this method is that the ratios between the interfering amplitudes can be measured without requiring external input. In addition, discrete ambiguities are resolved.

We find $pp$ wave solutions in string theory with null-like linear dilatons. These provide toy models of big bang cosmologies. We formulate matrix string theory in these backgrounds. Near the big bang “singularity,” the string theory becomes strongly coupled but the Yang-Mills description of the matrix string is weakly coupled. The presence of a second length scale allows us to focus on a specific class of non-Abelian configurations, viz. fuzzy cylinders, for a suitable regime of parameters. We show that, for a class of $pp$ waves, fuzzy cylinders which start out big at early times dynamically shrink into usual strings at sufficiently late times.

For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the extensions of this machinery to the logarithmic case are studied and used. More precisely, from Möbius symmetry constraints, the generic three- and four-point functions of logarithmic quasiprimary fields are calculated in closed form for arbitrary Jordan rank. As an example, $c=0$ disordered systems with nondegenerate vacua are studied. With the aid of two-, three-, and four-point functions, the operator algebra is obtained and associativity of the algebra studied.

We study flavor structure and the coupling selection rule in intersecting $D$-brane configurations on $T^2\times T^2\times T^2$ as well as its orbifold/orientifold compactifications. We formulate the selection rule for Yukawa couplings and its extensions to generic $n$-point couplings. We investigate the possible flavor structure, which can appear from intersecting $D$-brane configuration. Then, we show there is a certain rule among intersecting numbers for states corresponding to allowed Yukawa couplings, and also it is found that their couplings are determined by discrete Abelian symmetries. Our studies on the flavor structure and the coupling selection rule in this class of models show that there is no solution to derive realistic Yukawa matrices only from stringy 3-point couplings at the tree-level within the framework of the minimal matter content of the supersymmetric standard model.

We study an integrable conformal $\mathrm{OSp}(2m+2|2m)$ supercoset model as an analog to the $\mathrm{Ad}{\mathrm{S}}_5\times {\mathrm{S}}^5$ superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle number in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the well-studied classical limit, the ${\lambda }^{-1/2}$ effects and the $1/J$ effects. Our approach captures the first type, but not the second.

We study the open B-model representing D-branes on 2-cycles of local Calabi-Yau geometries. To this end we work out a reduction technique linking D-brane partition functions and multimatrix models in the case of conifold geometries so that the matrix potential is related to the complex moduli of the conifold. We study the geometric engineering of the multimatrix models and focus on two-matrix models with bilinear couplings. We show how to solve this models in an exact way, without resorting to the customary saddle point/large $N$ approximation. The method consists of solving the quantum equations of motion and using the flow equations of the underlying integrable hierarchy to derive explicit expressions for correlators. Finally, we show how to incorporate in this formalism the description of several group of D-branes wrapped around different cycles.

It is presented a thorough analysis of scalar perturbations in the background of Gauss-Bonnet, Gauss-Bonnet-de Sitter and Gauss-Bonnet-anti-de Sitter black hole spacetimes. The perturbations are considered both in frequency and time domain. The dependence of the scalar field evolution on the values of the cosmological constant $\Lambda$ and the Gauss-Bonnet coupling $\alpha$ is investigated. For Gauss-Bonnet and Gauss-Bonnet-de Sitter black holes, at asymptotically late times either power-law or exponential tails dominate, while for Gauss-Bonnet-anti-de Sitter black hole, the quasinormal modes govern the scalar field decay at all times. The power-law tails at asymptotically late times for odd-dimensional Gauss-Bonnet black holes does not depend on $\alpha$, even though the black hole metric contains $\alpha$ as a new parameter. The corrections to quasinormal spectrum due to Gauss-Bonnet coupling is not small and should not be neglected. For the limit of near extremal value of the (positive) cosmological constant and pure de Sitter and anti-de Sitter modes in Gauss-Bonnet gravity we have found analytical expressions.

We introduce a new phenomenological one-scale model for the evolution of domain wall networks, and test it against high-resolution field theory numerical simulations. We argue that previous numerical estimates of wall velocities are inaccurate, and suggest a more accurate method of measurement. We show that the model provides an adequate approximation to the evolution of key parameters characterizing the evolution of the network. We use the model to study possible scaling solutions for domain wall networks, and discuss some of their cosmological consequences.

We compute the complete post-Newtonian limit of both the metric and Palatini formulations of $f(R)$ gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian $f(R)$ must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that in both formalisms the lagrangian $f(R)$ must be almost linear in $R$ and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.

It has been suggested that secondary CMB anisotropies generated by neutral lithium could open a new observational window into the universe around the redshift $z\sim 400$, and permit a determination of the primordial lithium abundance. The effect is due to resonant scattering in the allowed Li i doublet ($2s^2{S}_{1/2}-2p^2{P}_{1/2,3/2}$), so its observability depends on the formation history of neutral lithium. Here we show that the ultraviolet photons produced during hydrogen recombination are sufficient to keep lithium in the Li ii ionization stage in the relevant redshift range and suppress the neutral fraction by $\sim 3$ orders of magnitude from previous calculations, making the lithium signature unobservable.

We analyze the effects of finite chemical potential on spontaneous breaking of internal symmetries within the class of relativistic field theories described by the linear sigma model. Special attention is paid to the emergence of “abnormal” Goldstone bosons with a quadratic dispersion relation. We show that their presence is tightly connected to nonzero density of the Noether charges, and formulate a general counting rule. The general results are demonstrated on an $\mathrm{SU}(3)\times \mathrm{U}(1)$ invariant model with an SU(3)-sextet scalar field, which describes one of the color-superconducting phases of QCD.

An impact parameter representation for soft gluon radiation is applied to obtain both the initial decrease of the total cross section (${\sigma }_{\mathrm{tot}}$) for proton-proton collisions as well as the later rise of ${\sigma }_{\mathrm{tot}}$ with energy for both $pp$ and $p\overline{p}$. The nonperturbative soft part of the eikonal includes only limited low energy gluon emission and leads to the initial decrease in the proton-proton cross section. On the other hand, the rapid rise in the hard, perturbative jet part of the eikonal is tamed into the experimentally observed mild increase by soft gluon radiation whose maximum energy rises slowly with energy.

In the light of new experimental results on $B\to K\pi$ decays, we critically study the decay processes $B\to K\pi$ in a phenomenological way. Using the quark diagram approach and the currently available data, we determine the allowed values of the relevant theoretical parameters, corresponding to the electroweak (EW) penguin, the color-suppressed tree contribution, etc. In order to find the most likely values of the parameters in a statistically reliable way, we use the ${\chi }^2$ minimization technique. Our result shows that the current data for $B\to K\pi$ decays strongly indicate (large) enhancements of both the EW penguin and the color-suppressed tree contributions. In particular, the color-suppressed tree effect needs to be enhanced by about an order of magnitude to fit the present data.

We study radiative decays of $D_{sJ}^{*}(2317)$ and $D_{sJ}(2460)$ using light-cone QCD sum rules. In particular, we consider the decay modes $D_{sJ}^{*}(2317)\to D_s^{*}\gamma$ and $D_{sJ}(2460)\to D_s^{(*)}\gamma ,D_{sJ}^{*}(2317)\gamma$ and evaluate the hadronic parameters in the transition amplitudes analyzing correlation functions of scalar, pseudoscalar, vector, and axial-vector $\overline{c}s$ currents. In the case of $D_{sJ}^{*}(2317)\to D_s^{*}\gamma$ we also consider determinations based on two different correlation functions in heavy quark effective theory (HQET), in order to estimate the finite charm-quark mass effects. The mode $D_{sJ}(2460)\to D_s\gamma$ turns out to have the largest decay rate among the radiative $D_{sJ}(2460)$ channels, as experimentally observed, a result thus favoring the interpretation of $D_{sJ}$ states as ordinary $\overline{c}s$ mesons.