Interior potential of a toroidal shell from pole values

We have investigated the toroidal analog of ellipsoidal shells of matter, which are of great significance in Astrophysics. The exact formula for the gravitational potential $\Psi(R,Z)$ of a shell with a circular section at the pole of toroidal coordinates is first established. It depends on the mass of the shell, its main radius and axis-ratio $e$ (i.e. core-to-main radius ratio), and involves the product of the complete elliptic integrals of the first and second kinds. Next, we show that successive partial derivatives $\partial^{n +m} \Psi/\partial_{R^n} \partial_{Z^m}$ are also accessible by analytical means at that singular point, thereby enabling the expansion of the interior potential as a bivariate series. Then, we have generated approximations at orders $0$, $1$, $2$ and $3$, corresponding to increasing accuracy. Numerical experiments confirm the great reliability of the approach, in particular for small-to-moderate axis ratios ($e^2 \lesssim 0.1$ typically). In contrast with the ellipsoidal case (Newton's theorem), the potential is not uniform inside the shell cavity as a consequence of the curvature. We explain how to construct the interior potential of toroidal shells with a thick edge (i.e. tubes), and how a core stratification can be accounted for. This is a new step towards the full description of the gravitating potential and forces of tori and rings. Applications also concern electrically-charged systems, and thus go beyond the context of gravitation.Comment: Accepted for publication in MNRA

Static and radiating p -form black holes in the higher dimensional Robinson-Trautman class

We study Robinson-Trautman spacetimes in the presence of an aligned p -form Maxwell field and an arbitrary cosmological constant in n ≥ 4 dimensions. As it turns out, the character of these exact solutions depends significantly on the (relative) value of n and p . In odd dimensions the solutions reduce to static black holes dressed with an electric and a magnetic field, with an Einstein space horizon (further constrained by the Einstein-Maxwell equations) — both the Weyl and Maxwell types are D. Even dimensions, however, open up more possibilities. In particular, when 2 p = n there exist non-static solutions describing black holes gaining (or losing) mass by receiving (or emitting) electromagnetic radiation. In this case the Weyl type is II (D) and the Maxwell type can be II (D) or N. Conditions under which the Maxwell field is self-dual (for odd p ) are also discussed, and a few explicit examples presented. Finally, the case p = 1 is special in all dimensions and leads to static metrics with a non-Einstein transverse space

Mirror Development for the Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) is a planned observatory for very-high energy gamma-ray astronomy. It will consist of several tens of telescopes of different sizes, with a total mirror area of up to 10,000 square meters. Most mirrors of current installations are either polished glass mirrors or diamond-turned aluminium mirrors, both labour intensive technologies. For CTA, several new technologies for a fast and cost-efficient production of light-weight and reliable mirror substrates have been developed and industrial pre-production has started for most of them. In addition, new or improved aluminium-based and dielectric surface coatings have been developed to increase the reflectance over the lifetime of the mirrors compared to those of current Cherenkov telescope instruments

Gauge independence in a higher-order Lagrangian formalism via change of variables in the path integral

In this paper we work out the explicit form of the change of variables that reproduces an arbitrary change of gauge in a higher-order Lagrangian formalism

Measurement of the forward charged particle pseudorapidity density in pp collisions at s=8 TeV using a displaced interaction point

The pseudorapidity density of charged particles dN ch /d η is measured by the TOTEM experiment in proton–proton collisions at s=8  TeV within the range 3.9<η<4.7 and -6.95<η<-6.9 . Data were collected in a low intensity LHC run with collisions occurring at a distance of 11.25 m from the nominal interaction point. The data sample is expected to include 96–97 % of the inelastic proton–proton interactions. The measurement reported here considers charged particles with pT>0 MeV/c, produced in inelastic interactions with at least one charged particle in -7<η<-6 or 3.7<η<4.8 . The dN ch /d η has been found to decrease with |η| , from 5.11 ± 0.73 at η=3.95 to 1.81 ± 0.56 at η=- 6.925. Several Monte Carlo generators are compared to the data and are found to be within the systematic uncertainty of the measurement

Evidence for non-exponential elastic proton–proton differential cross-section at low |t| and s=8TeV by TOTEM

The TOTEM experiment has made a precise measurement of the elastic proton–proton differential cross-section at the centre-of-mass energy s=8 TeV based on a high-statistics data sample obtained with the β⁎=90 m optics. Both the statistical and systematic uncertainties remain below 1%, except for the t -independent contribution from the overall normalisation. This unprecedented precision allows to exclude a purely exponential differential cross-section in the range of four-momentum transfer squared 0.027<|t|<0.2 GeV2 with a significance greater than 7 σ . Two extended parametrisations, with quadratic and cubic polynomials in the exponent, are shown to be well compatible with the data. Using them for the differential cross-section extrapolation to t=0 , and further applying the optical theorem, yields total cross-section estimates of (101.5±2.1) mb and (101.9±2.1) mb , respectively, in agreement with previous TOTEM measurements

Baryon resonance production and dielectron decays in proton-proton collisions at 3.5 GeV

We report on baryon resonance production and decay in proton-proton collisions at a kinetic energy of $3.5$ GeV based on data measured with HADES. The exclusive channels $pp \rightarrow np\pi^{+}$ and $pp \rightarrow pp\pi^{0}$ as well as $pp \rightarrow ppe^{+}e^{-}$ are studied simultaneously for the first time. The invariant masses and angular distributions of the pion-nucleon systems were studied and compared to simulations based on a resonance model ansatz assuming saturation of the pion production by an incoherent sum of baryonic resonances (R) with masses $<2~$ GeV/$c^2$. A very good description of the one-pion production is achieved allowing for an estimate of individual baryon-resonance production-cross-sections which are used as input to calculate the dielectron yields from $R\rightarrow pe^+e^-$ decays. Two models of the resonance decays into dielectrons are examined assuming a point-like $RN \gamma^*$ coupling and the dominance of the $\rho$ meson. The results of model calculations are compared to data from the exclusive $ppe^{+}e^{-}$ channel by means of the dielectron and $pe^+e^-$ invariant mass distributions

Searching a dark photon with HADES

We present a search for the <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> decay of a hypothetical dark photon, also named U vector boson, in inclusive dielectron spectra measured by HADES in the p(3.5 GeV) + p, Nb reactions, as well as the Ar ( <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.756</mn><mtext> GeV</mtext><mo stretchy="false">/</mo><mtext>u</mtext></math> ) + KCl reaction. An upper limit on the kinetic mixing parameter squared <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>2</mn></mrow></msup></math> at 90% CL has been obtained for the mass range <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>M</mi></mrow><mrow><mi>U</mi></mrow></msub><mo>=</mo><mn>0.02</mn><mtext>–</mtext><mn>0.55</mn><mtext> GeV</mtext><mo stretchy="false">/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></math> and is compared with the present world data set. For masses <math altimg="si5.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.03</mn><mtext>–</mtext><mn>0.1</mn><mtext> GeV</mtext><mo stretchy="false">/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></math> , the limit has been lowered with respect to previous results, allowing now to exclude a large part of the parameter region favored by the muon <math altimg="si6.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly. Furthermore, an improved upper limit on the branching ratio of <math altimg="si7.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.3</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> has been set on the helicity-suppressed direct decay of the eta meson, <math altimg="si8.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi><mo stretchy="false">→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> , at 90% CL

Diffractive dijet production with a leading proton in ep collisions at HERA

The cross section of the diffractive process e + p → e + Xp is measured at a centre-of-mass energy of 318 GeV, where the system X contains at least two jets and the leading final state proton p is detected in the H1 Very Forward Proton Spectrometer. The measurement is performed in photoproduction with photon virtualities Q 2 < 2 GeV 2 and in deep-inelastic scattering with 4 GeV 2 < Q 2 < 80 GeV 2 . The results are compared to next- to-leading order QCD calculations based on diffractive parton distribution functions as extracted from measurements of inclusive cross sections in diffractive deep-inelastic scattering

Measurement of dijet production in diffractive deep-inelastic ep scattering at HERA

A measurement is presented of single- and double-differential dijet cross sections in diffractive deep-inelastic ep scattering at HERA using data collected by the H1 experiment corresponding to an integrated luminosity of 290 pb −1 . The investigated phase space is spanned by the photon virtuality in the range of 4 < Q 2 < 100 GeV 2 and by the fractional proton longitudinal momentum loss x ℙ < 0 . 03. The resulting cross sections are compared with next-to-leading order QCD predictions based on diffractive parton distribution functions and the value of the strong coupling constant is extracted