General structure of the graviton self-energy

The graviton self-energy at finite temperature depends on fourteen structure functions. We show that, in the absence of tadpoles, the gauge invariance of the effective action imposes three non-linear relations among these functions. The consequences of such constraints, which must be satisfied by the thermal graviton self-energy to all orders, are explicitly verified in general linear gauges to one loop order.Comment: 4 pages, minor corrections of typo

Thermal one- and two-graviton Green's functions in the temporal gauge

The thermal one- and two-graviton Green's function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the 't Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.Comment: 17 pages, 5 figures. Revised version to be published in Phys. Rev.

Schubert calculus of Richardson varieties stable under spherical Levi subgroups

We observe that the expansion in the basis of Schubert cycles for $H^*(G/B)$ of the class of a Richardson variety stable under a spherical Levi subgroup is described by a theorem of Brion. Using this observation, along with a combinatorial model of the poset of certain symmetric subgroup orbit closures, we give positive combinatorial descriptions of certain Schubert structure constants on the full flag variety in type $A$. Namely, we describe $c_{u,v}^w$ when $u$ and $v$ are inverse to Grassmannian permutations with unique descents at $p$ and $q$, respectively. We offer some conjectures for similar rules in types $B$ and $D$, associated to Richardson varieties stable under spherical Levi subgroups of SO(2n+1,\C) and SO(2n,\C), respectively.Comment: Section 4 significantly shortened, and other minor changes made as suggested by referees. Final version, to appear in Journal of Algebraic Combinatoric

String compactification, QCD axion and axion-photon-photon coupling

It is pointed out that there exist a few problems to be overcome toward an observable sub-eV QCD axion in superstring compactification. We give a general expression for the axion decay constant. For a large domain wall number $N_{DW}$, the axion decay constant can be substantially lowered from a generic value of a scalar singlet VEV. The Yukawa coupling structure in the recent $Z_{12-I}$ model is studied completely, including the needed nonrenormalizable terms toward realistic quark and lepton masses. In this model we find an approximate global symmetry and vacuum so that a QCD axion results but its decay constant is at the GUT scale. The axion-photon-photon coupling is calculated for a realistic vacuum satisfying the quark and lepton mass matrix conditions. It is the first time calculation of $c_{a\gamma\gamma}$ in realistic string compactifications: $c_{a\gamma\gamma}={5/3}-1.93\simeq -0.26$.Comment: 33 pages, 2 figures, JHEP format, some errors in the superpotential couplings are corrected and the following discussions are changed correspondingl

Effects of S-wave thresholds

The opening of a new S-wave threshold is frequently accompanied by an abrupt dip in the magnitude of an amplitude for an already-open channel. One familiar example is the behavior of the I=0 S-wave $\pi \pi$ scattering amplitude at $K \bar K$ threshold. Numerous other examples of this phenomenon in recent data are noted, and a unified description of the underlying dynamics is sought.Comment: 17 pages, 2 figures. Two additional references; typographic correction. To be published in Phys. Rev.

Heavy Flavor Hadrons in Statistical Hadronization of Strangeness-rich QGP

We study b, c quark hadronization from QGP. We obtain the yields of charm and bottom flavored hadrons within the statistical hadronization model. The important novel feature of this study is that we take into account the high strangeness and entropy content of QGP, conserving strangeness and entropy yields at hadronization.Comment: v2 expended: 20 pages, 23 figures, 5 tables, in press EPJ-

Spectroscopy of Heavy Mesons Expanded in 1/m_Q

Operating just once with the naive Foldy-Wouthuysen-Tani transformation on the relativistic Fermi-Yang equation for $Q\bar q$ bound states described by the semi-relativistic Hamiltonian which includes Coulomb-like as well as confining scalar potentials, we have calculated heavy meson mass spectra of D and B together with higher spin states. Based on the formulation recently proposed, their masses and wave functions are expanded up to the second order in $1/m_Q$ with a heavy quark mass $m_Q$ and the lowest order equation is examined carefully to obtain a complete set of eigenfunctions for the Schr\"odinger equation. Heavy quark effective theory parameters, $\bar\Lambda$, $\lambda_1$, and $\lambda_2$, are also determined at the first and second order in $1/m_Q$.Comment: 49 pages, 5 epsf figure

Two charged strangeonium-like structures observable in the Y(2175)→ϕ(1020)π+π−Y(2175) \to \phi(1020)\pi^{+} \pi^{-} process

Via the Initial Single Pion Emission (ISPE) mechanism, we study the $\phi(1020)\pi^{+}$ invariant mass spectrum distribution of $Y(2175) \to \phi(1020)\pi^{+} \pi^{-}$. Our calculation indicates there exist a sharp peak structure ($Z_{s1}^+$) close to the $K\bar{K}^\ast$ threshold and a broad structure ($Z_{s2}^+$) near the $K^\ast\bar{K}^\ast$ threshold. In addition, we also investigate the $\phi(1680) \to \phi(1020)\pi^{+} \pi^{-}$ process due to the ISPE mechanism, where a sharp peak around the $K\bar{K}^\ast$ threshold appears in the $\phi(1020)\pi^{+}$ invariant mass spectrum distribution. We suggest to carry out the search for these charged strangeonium-like structures in future experiment, especially Belle II, Super-B and BESIII.Comment: 7 pages, 5 figures. Accepted by Eur. Phys. J.

Spontaneous Chiral-Symmetry Breaking in Three-Dimensional QED with a Chern--Simons Term

In three-dimensional QED with a Chern--Simons term we study the phase structure associated with chiral-symmetry breaking in the framework of the Schwinger--Dyson equation. We give detailed analyses on the analytical and numerical solutions for the Schwinger--Dyson equation of the fermion propagator, where the nonlocal gauge-fixing procedure is adopted to avoid wave-function renormalization for the fermion. In the absence of the Chern--Simons term, there exists a finite critical number of four-component fermion flavors, at which a continuous (infinite-order) chiral phase transition takes place and below which the chiral symmetry is spontaneously broken. In the presence of the Chern--Simons term, we find that the spontaneous chiral-symmetry-breaking transition continues to exist, but the type of phase transition turns into a discontinuous first-order transition. A simple stability argument is given based on the effective potential, whose stationary point gives the solution of the Schwinger-Dyson equation.Comment: 34 pages, revtex, with 9 postscriptfigures appended (uuencoded

Стоимость энергетической безопасности как внешняя переменная — устойчивость экономики Украины при растущей цене на импортированный газ

Досліджено стійкість економіки України при зростаючій ціні на імпортований газ. Запропоновано методологію моделювання і прогнозування фінансово-економічних процесів, яка ґрунтується на ієрархічній процедурі пошуку структури і оптимізації параметрів моделей. Виконано аналіз залежності економічного зростання та ціни на імпортований газ. Цей аналіз виявив, що споживання газу для виробництва продуктів харчування та в інших, більш дрібних галузях виробництва, зростає при загальному зростанні ціни на імпортований газ. Тоді як крупніші галузі, такі як хімічна та виробнича, зменшували споживання газу під час зростання його ціни. Також виявлено можливість знижувати ціну на імпортований газ для України до рівня порівняного з поточною ціною.In this research, the tolerability of the economy of Ukraine for the increase of the gas import price is investigated. The relationship between the economic growth and imported gas price is analyzed, and it was found that the gas consumption of the food and other smaller industries was growing while the gas price was increasing; although, the larger industries such as chemical and manufacturing industries reduced the gas consumption. It was also found that Ukraine may hold a capability to lower the gas import price to the degree comparable to the current price. For the analysis, the national statistics of every month from 2002 through 2008 was used with the least squares model and the ARMA model for time-series forecasting. The data contains the GDP, the imported gas price and volume, the PPIs for the food industry, the chemical industry, the manufacturers and the energy industry, as well as the gas volumes consumed by the industries of low price hand, other than the manufacturers and the chemical industries.Исследована устойчивость экономики Украины при растущей цене на импортированный газ. Предложена методология моделирования и прогнозирования финансово-экономических процессов, которая базируется на иерархической процедуре поиска структуры и оптимизации параметров моделей. Выполнен анализ зависимости экономического роста и цены на импортированный газ. Этот анализ выявил, что потребление газа при производстве продуктов питания и в других, более мелких отраслях производства растет при общем росте цен на импортированный газ. Тогда как более крупные отрасли, такие как химическая и производственная, снижали потребление газа при росте его цены. Также выявлена возможность снижать цену на импортированный газ для Украины до уровня, сопоставимого с текущей ценой