New methods in conformal partial wave analysis

We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.Comment: 16 page

Refined physical properties and g',r',i',z',J,H,K transmission spectrum of WASP-23b from the ground

Multi-band observations of planetary transits using the telescope defocus technique may yield high-quality light curves suitable for refining the physical properties of exoplanets even with small or medium size telescopes. Such observations can be used to construct a broad-band transmission spectrum of transiting planets and search for the presence of strong absorbers. We have thoroughly characterised the orbital ephemeris and physical properties of the transiting planet and host star in the WASP-23b system, constructed a broad-band transmission spectrum of WASP-23b and performed a comparative analysis with theoretical models of hot Jupiters. We observed a complete transit of WASP-23b in seven bands simultaneously, using the GROND instrument on the MPG/ESO 2.2m telescope at La Silla Observatory and telescope defocussing. The optical data were taken in the Sloan g',r',i' and z' bands. The resulting light curves are of high quality, with a root-mean-square scatter of the residual as low as 330ppm in the z'-band, with a cadence of 90s. Near-infrared data were obtained in the JHK bands. We performed MCMC analysis of our photometry plus existing radial velocity data to refine measurements of the ephemeris and physical properties of the WASP-23. We constructed a broad-band transmission spectrum of WASP-23b and compared it with a theoretical transmission spectrum of a Hot Jupiter. We measured the central transit time with a precision about 8s. From this and earlier observations we obtain an orbital period of P=2.9444300+/-0.0000011d. Our analysis also yielded a larger radius and mass for the planet (Rp=1.067+0.045-0.038 RJup and, Mp=0.917+0.040-0.039MJup). The transmission spectrum is marginally flat, given the limited precision of the measurements for the planet radius and poor spectral resolution of the data.Comment: 8 pages, 5 figures, accepted for publication in Astronomy & Astrophysic

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Simultaneous follow-up of planetary transits: revised physical properties for the planetary systems HAT-P-16 and WASP-21

Context. By now more than 300 planets transiting their host star have been found, and much effort is being put into measuring the properties of each system. Light curves of planetary transits often contain deviations from a simple transit shape, and it is generally difficult to differentiate between anomalies of astrophysical nature (e.g. starspots) and correlated noise due to instrumental or atmospheric effects. Our solution is to observe transit events simultaneously with two telescopes located at different observatories. Aims. Using this observational strategy, we look for anomalies in the light curves of two transiting planetary systems and accurately estimate their physical parameters. Methods. We present the first photometric follow-up of the transiting planet HAT-P-16 b, and new photometric observations of WASP-21 b, obtained simultaneously with two medium-class telescopes located in different countries, using the telescope defocussing technique. We modeled these and other published data in order to estimate the physical parameters of the two planetary systems. Results. The simultaneous observations did not highlight particular features in the light curves, which is consistent with the low activity levels of the two stars. For HAT-P-16, we calculated a new ephemeris and found that the planet is 1.3 \sigma colder and smaller (Rb = 1.190 \pm 0.037 RJup) than the initial estimates, suggesting the presence of a massive core. Our physical parameters for this system point towards a younger age than previously thought. The results obtained for WASP-21 reveal lower values for the mass and the density of the planet (by 1.0 \sigma and 1.4 \sigma respectively) with respect to those found in the discovery paper, in agreement with a subsequent study. We found no evidence of any transit timing variations in either system.Comment: 8 pages, 6 figures, accepted for publication in A&

Physical properties of the WASP-44 planetary system from simultaneous multi-colour photometry

We present ground-based broad-band photometry of two transits in the WASP-44 planetary system obtained simultaneously through four optical (Sloan g', r', i', z') and three near-infrared (NIR; J, H, K) filters. We achieved low scatters of 1-2 mmag per observation in the optical bands with a cadence of 48 s, but the NIR-band light curves present much greater scatter. We also observed another transit of WASP-44 b by using a Gunn-r filter and telescope defocussing, with a scatter of 0.37 mmag per point and an observing cadence around 135 s. We used these data to improve measurements of the time of mid-transit and the physical properties of the system. In particular, we improved the radius measurements of the star and planet by factors of 3 and 4, respectively. We find that the radius of WASP-44 b is 1.002 R_Jup, which is slightly smaller than previously thought and differs from that expected for a core-free planet. In addition, with the help of a synthetic spectrum, we investigated the theoretically-predicted variation of the planetary radius as a function of wavelength, covering the range 370-2440 nm. We can rule out extreme variations at optical wavelengths, but unfortunately our data are not precise enough (especially in the NIR bands) to differentiate between the theoretical spectrum and a radius which does not change with wavelength.Comment: 13 pages, 6 figures, to appear in Monthly Notices of the Royal Astronomical Societ

WASP-4b Transit Observations With GROND

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this recordGround-based simultaneous multiband transit observations allow an accurate system parameters determination and may lead to the detection and characterization of additional bodies via the transit timing variations (TTVs) method. We aimed to (i) characterize the heavily bloated WASP-4b hot Jupiter and its star by measuring system parameters and the dependence of the planetary radius as a function of four (Sloan g', r', i', z') wavelengths and (ii) search for TTVs. We recorded 987 images during three complete transits with the GROND instrument, mounted on the MPG/ESO-2.2m telescope at La Silla Observatory. Assuming a quadratic law for the stellar limb darkening we derive system parameters by fitting a composite transit light curve over all bandpasses simultaneously. To compute uncertainties of the fitted parameters, we employ the Bootstrap Monte Carlo Method. The three central transit times are measured with precision down to 6 s. We find a planetary radius Rp = 1.413+/-0.020 RJup, an orbital inclination i = 88deg57'+/-0.45deg and calculate a new ephemeris, a period P = 1.33823144+/-0.00000032days and a reference transit epoch T0 = 2454697.798311+/-0.000046 (BJD). Analysis of the new transit mid-times in combination with previous measurements shows no sign of a TTV signal greater than 20s. We perform simplified numerical simulations to place upper-mass limits of a hypothetical perturber in the WASP-4b system.Part of the funding for GROND (both hardware as well as personnel) was generously granted from the Leibniz-Prize to Prof. G. Hasinger (DFG grant HA 1850/28-1). N.N. acknowledges the Klaus Tschira Stiftung (KTS) and the Heidelberg Graduate School of Fundamental Physics (HGSFP) for the financial support of his Ph.D. research. G.M. acknowledges the financial support from the Polish Ministry of Science and Higher Education through the Iuventus Plus grant IP2010 023070

Proper holomorphic mappings between symmetrized ellipsoids

We characterize the existence of proper holomorphic mappings in the special class of bounded $(1,2,...,n)$-balanced domains in $\mathbb{C}^n$, called the symmetrized ellipsoids. Using this result we conclude that there are no non-trivial proper holomorphic self-mappings in the class of symmetrized ellipsoids. We also describe the automorphism groupof these domains.Comment: 10 pages, some modification

Refined physical properties and g',r',i',z',J,H,K transmission spectrum of WASP-23b from the ground

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this recordMulti-band observations of planetary transits using the telescope defocus technique may yield high-quality light curves suitable for refining the physical properties of exoplanets even with small or medium size telescopes. Such observations can be used to construct a broad-band transmission spectrum of transiting planets and search for the presence of strong absorbers. We have thoroughly characterised the orbital ephemeris and physical properties of the transiting planet and host star in the WASP-23b system, constructed a broad-band transmission spectrum of WASP-23b and performed a comparative analysis with theoretical models of hot Jupiters. We observed a complete transit of WASP-23b in seven bands simultaneously, using the GROND instrument on the MPG/ESO 2.2m telescope at La Silla Observatory and telescope defocussing. The optical data were taken in the Sloan g',r',i' and z' bands. The resulting light curves are of high quality, with a root-mean-square scatter of the residual as low as 330ppm in the z'-band, with a cadence of 90s. Near-infrared data were obtained in the JHK bands. We performed MCMC analysis of our photometry plus existing radial velocity data to refine measurements of the ephemeris and physical properties of the WASP-23. We constructed a broad-band transmission spectrum of WASP-23b and compared it with a theoretical transmission spectrum of a Hot Jupiter. We measured the central transit time with a precision about 8s. From this and earlier observations we obtain an orbital period of P=2.9444300+/-0.0000011d. Our analysis also yielded a larger radius and mass for the planet (Rp=1.067+0.045-0.038 RJup and, Mp=0.917+0.040-0.039MJup). The transmission spectrum is marginally flat, given the limited precision of the measurements for the planet radius and poor spectral resolution of the data.N.N. acknowledges support from an STFC consolidated grant. J.S. acknowledges STFC for the award of an Advanced Fellowship

Two regularizations - two different models of Nambu-Jona-Lasinio

Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional cutoff and the model with dimensionally-analytical regularization -- are systematically compared. It is shown that they are, in essence, two different models of light-quark interaction. In the mean-field approximation the distinction becomes apparent in a behavior of scalar amplitude near the threshold. For 4-dimensional cutoff the pole term can be extracted, which corresponds to sigma-meson. For dimensionally-analytical regularization the singularity of the scalar amplitude is not pole, and this singularity is quite disappeared at some value of the regularization parameter. Still more essential distinction of these models exists in the next-to-leading order of mean-field expansion. The calculations of meson contributions in the quark chiral condensate and in the dynamical quark mass demonstrate, that these contributions though their relatively smallness can destabilize the Nambu--Jona-Lasinio model with 4-dimensional cutoff. On the contrary, the Nambu--Jona-Lasinio model with dimensionally-analytical regularization is stabilized with the next-to-leading order, i.e. the value of the regularization parameter shifts to the stability region, where these contributions decrease.Comment: 14 pages; Journal version; parameter fixing procedure is modifie