Predicting the Configuration of Planetary System: KOI-152 Observed by Kepler

The recent Kepler discovery of KOI-152 reveals a system of three hot super-Earth candidates that are in or near a 4:2:1 mean motion resonance. It is unlikely that they formed in situ, the planets probably underwent orbital migration during the formation and evolution process. The small semimajor axes of the three planets suggest that migration stopped at the inner edge of the primordial gas disk. In this paper we focus on the influence of migration halting mechanisms, including migration "dead zones", and inner truncation by the stellar magnetic field. We show that the stellar accretion rate, stellar magnetic field and the speed of migration in the proto-planetary disk are the main factors affecting the final configuration of KOI-152. Our simulations suggest that three planets may be around a star with low star accretion rate or with high magnetic field. On the other hand, slow type I migration, which decreases to one tenth of the linear analysis results, favors forming the configuration of KOI-152. Under such formation scenario, the planets in the system are not massive enough to open gaps in the gas disk. The upper limit of the planetary masses are estimated to be about $15,~19$, and $24 M_\oplus$, respectively. Our results are also indicative of the near Laplacian configurations that are quite common in planetary systems.Comment: 11 pages, 8 figures, accepted for publication in Ap

Master Formula for Twist-3 Soft-Gluon-Pole Mechanism to Single Transverse-Spin Asymmetry

Perturbative QCD relates the single transverse-spin asymmetries (SSAs) for hard processes at large transverse-momentum of produced particle to partonic matrix elements that describe interference between scattering from a coherent quark-gluon pair and from a single quark, generated through twist-3 quark-gluon correlations inside a hadron. When the coherent gluon is soft at the gluonic poles, its coupling to partonic subprocess can be systematically disentangled, so that the relevant interfering amplitude can be derived entirely from the Born diagrams for the scattering from a single quark. We establish a new formula that represents the exact rules to derive the SSA due to soft-gluon poles from the knowledge of the twist-2 cross section formula for unpolarized processes. This single master formula is applicable to a range of processes like Drell-Yan and direct-photon production, and semi-inclusive deep inelastic scattering, and is also useful to manifest the gauge invariance of the results.Comment: 20 pages, 6 figures; [v2] a paragraph with new Eq. (30) added, minor modifications, typos corrected; [v3] Erratum added, and minor change

Spin densities in the transverse plane and generalized transversity distributions

We show how generalized quark distributions in the nucleon describe the density of polarized quarks in the impact parameter plane, both for longitudinal and transverse polarization of the quark and the nucleon. This density representation entails positivity bounds including chiral-odd distributions, which tighten the known bounds in the chiral-even sector. Using the quark equations of motion, we derive relations between the moments of chiral-odd generalized parton distributions of twist two and twist three. We exhibit the analogy between polarized quark distributions in impact parameter space and transverse momentum dependent distribution functions.Comment: 23 pages, 6 eps-figure

Single Transverse Spin Asymmetry for Large-p_T Pion Production in Semi-Inclusive Deep Inelastic Scattering

We study the single spin asymmetry (SSA) for the pion production with large transverse momentum p_T in semi-inclusive deep inelastic scattering $ep^\uparrow\to e\pi X$. We derive the twist-3 cross section formula for SSA, focussing on the soft-gluon-pole contributions associated with the twist-3 distribution for the nucleon and with the twist-3 fragmentation function for the pion. We present a simple estimate of the asymmetries due to each twist-3 effect from nucleon and pion, respectively, by fixing the overall strength of the relevant nonperturbative quantities by the data on the SSA A_N in $p^\uparrow p\to\pi X$ collision.Comment: 19 pages in LaTex. Some discussions added. To appear in Nucl. Phys.

Photosynthetic recovery of desiccated intertidal seaweeds after rehydration

Intertidal seaweeds experience periodical desiccation and rehydration to different extents due to the tidal cycles and their vertical distributions. Their photosynthetic recovery process during the rehydration may show different patterns among the seaweeds from different zonations or depths at intertidal zone. In this study 12 species of seaweeds collected from the upper, middle, lower and sublittoral zones were examined. The relationship of the photosynthetic recovery to vertical distribution was assessed by comparing their patterns of photosynthetic and respiratory performances after rehydration following desiccation. Both the photosynthesis and dark respiration declined during emersion, showing certain degrees of recovery after re-immersion into seawater for most species, but the extents were markedly different from one species to the other. The species from upper intertidal zone after being rehydrated for 1 hour, following 2 hours of desiccation, achieved 100 % recovery of their initial physiological activity, while most of the lower or sublittoral species did not achieve full recovery. It is the ability to withstand desiccation stress (fast recovery during rehydration), but not that to avoid desiccation (water retaining ability) that determines the distribution of intertidal seaweeds. Such physiological behavior during rehydration after desiccation reflects the adaptive strategy of intertidal seaweeds against desiccation and their capability of primary production in the process of rehydration

Twist-3 Formalism for Single Transverse Spin Asymmetry Reexamined: Semi-Inclusive Deep Inelastic Scattering

We study the single spin asymmetry (SSA) for the pion production in semi-inclusive deep inelastic scattering, $ep^\uparrow\to e\pi X$, in the framework of the collinear factorization. We derive the complete cross section formula associated with the twist-3 quark-gluon correlation functions for the transversely polarized nucleon, including all types of pole (hard-pole, soft-fermion-pole and soft-gluon-pole) contributions which produce the strong interaction phase necessary for SSA. We prove that the partonic hard part from each pole contribution satisfies certain constraints from Ward identities for color gauge invariance. We demonstrate that the use of these new constraints is crucial to reorganize the collinear expansion of the Feynman diagrams into manifestly gauge-invariant form so as to obtain the factorization formula for the cross section in terms of a complete set of the twist-3 distributions without any double counting. It also provides a simpler method for the actual calculation. We also present a simple estimate of SSA based on our cross section formula, using a model for the ``soft-gluon-pole function'' that represents the relevant twist-3 quark-gluon correlation, and compare the magnitude of the terms involving the derivative of the soft-gluon-pole function with that of the ``non-derivative'' terms.Comment: 38 pages, 11 figures. Final version, to appear in Nucl. Phys.

Forming Habitable Planets around Dwarf Stars: Application to OGLE-06-109L

Dwarf stars are believed to have small protostar disk where planets may grow up. During the planet formation stage, embryos undergoing type I migration are expected to be stalled at inner edge of magnetic inactive disk ($a_{\rm crit} \sim 0.2-0.3 ~$AU). This mechanism makes the location around $a_{\rm crit}$ a sweet spot of forming planets. Especially, $a_{\rm crit}$ of dwarf stars with masses $\sim 0.5 M_\odot$ is roughly inside the habitable zone of the system. In this paper we study the formation of habitable planets due to this mechanism with a model system OGLE-06-109L. It has a $0.51 M_\odot$ dwarf star with two giant planets in 2.3 and 4.6 AU observed by microlensing. We model the embryos undergoing type I migration in the gas disk with a constant disk accretion rate ($\dot M$). Giant planets in outside orbits affect the formation of habitable planets through secular perturbations at the early stage and secular resonance at the later stage. We find that the existence and the masses of the habitable planets in OGLE-06-10L system depend on both $\dot M$ and the speed of type I migration. If planets formed earlier so that $\dot M$ is larger ($\sim 10^{-7} M_\odot$ yr$^{-1}$), terrestrial planet can not be survived unless the type I migration rate is an order of magnitude less. If planets formed later so that $\dot M$ is smaller ($\sim 10^{-8} M_\odot$ yr$^{-1}$), single and high mass terrestrial planets with high water contents ($\sim 5$) will be formed by inward migration of outer planet cores. A slower speed migration will result in several planets by collisions of embryos, thus their water contents are low ($\sim 2$). Mean motion resonances or apsidal resonances among planets may be observed if multiple planets survived in the inner system.Comment: 10 pages, 9 figures, accepted by Ap

QCD Corrections to the nucleon's spin structure function G2(x,Q2)G_2(x,Q^2)

We investigate the renormalization of the twist-3 operators which are relevant for the spin-dependent structure function $g_{2}(x, Q^{2})$. We derive the anomalous dimension for the non-singlet part by calculating the off-shell Green's functions of the twist-3 operators including the operators which are proportional to the equation of motion.Comment: 10 pages, LaTeX, 1 Postscript figur