• #### Integral points on elliptic curves and explicit valuations of division polynomialsver. 4

Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant C such that for any elliptic curve E/Q and non-torsion point P in E(Q), there is at most one integral multiple [n]P such that n > C. The proof is a modification of a proof of Ingram giving an unconditional but not uniform bound. The new ingredient is a collection of explicit formulae for the sequence of valuations of the division polynomials. For P of non-singular reduction, such sequences are already well described in most cases, but for P of singular reduction, we are led to define a new class of sequences called elliptic troublemaker sequences, which measure the failure of the Neron local height to be quadratic. As a corollary in the spirit of a conjecture of Lang and Hall, we obtain a uniform upper bound on h(P)/h(E) for integer points having two large integral multiples.
Elliptic divisibility sequenceIsomorphismRamificationResidue fieldTorsion tensorElliptic curveMultiplicative groupPrincipal valueHomogenizationCoprime...
• #### Cross-correlation of CFHTLenS galaxy catalogue and Planck CMB lensing using the halo model prescription

I cross-correlate the galaxy counts from the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) galaxy catalogue and Cosmic Microwave Background (CMB) convergence from the Planck data release 1 (2013) and 2 (2015), following the work of Omori & Holder (2015). I improve their study by computing an analytic covariance from the Halo Model, implementing simulations to validate the theoretically estimated error bars and the reconstruction method, fitting both a galaxy bias and a cross-correlation amplitude using the joint cross and galaxy auto-correlation, and performing a series of null tests. Using a bayesian analysis, I find a galaxy bias $b=0.92_{-0.02}^{+0.02}$ and a cross-correlation amplitude $A=0.85_{-0.16}^{+0.15}$ for the 2015 release, whereas for the 2013 release I find $b=0.93_{-0.02}^{+0.02}$ and $A=1.05_{-0.15}^{+0.15}$. I thus confirm the difference between the two releases found by Omori & Holder (2015), although both values of the amplitude now appear to be compatible with the fiducial value $A=1$.
Cross-correlationAutocorrelationHalo modelCovarianceCFHTLenS surveyPlanck missionGalaxy biasTrispectrumCosmic microwave backgroundCMB lensing...
• #### The EAGLE simulation of galaxy formation: public release of halo and galaxy catalogues

We present the public data release of halo and galaxy catalogues extracted from the EAGLE suite of cosmological hydrodynamical simulations of galaxy formation. These simulations were performed with an enhanced version of the GADGET code that includes a modified hydrodynamics solver, time-step limiter and subgrid treatments of baryonic physics, such as stellar mass loss, element-by-element radiative cooling, star formation and feedback from star formation and black hole accretion. The simulation suite includes runs performed in volumes ranging from 25 to 100 comoving megaparsecs per side, with numerical resolution chosen to marginally resolve the Jeans mass of the gas at the star formation threshold. The free parameters of the subgrid models for feedback are calibrated to the redshift z=0 galaxy stellar mass function, galaxy sizes and black hole mass - stellar mass relation. The simulations have been shown to match a wide range of observations for present-day and higher-redshift galaxies. The raw particle data have been used to link galaxies across redshifts by creating merger trees. The indexing of the tree produces a simple way to connect a galaxy at one redshift to its progenitors at higher redshift and to identify its descendants at lower redshift. In this paper we present a relational database which we are making available for general use. A large number of properties of haloes and galaxies and their merger trees are stored in the database, including stellar masses, star formation rates, metallicities, photometric measurements and mock gri images. Complex queries can be created to explore the evolution of more than 10^5 galaxies, examples of which are provided in appendix. (abridged)
Stellar massDark matter subhaloStar formationStar formation rateMerger treeStarGalaxy FormationBlack holeCalibrationDark matter...
• #### Electron interferometry in integer quantum Hall edge channels

We consider the electronic analog of the Hong-Ou-Mandel interferometer from quantum optics. In this realistic condensed matter device, single electrons are injected and travel along opposite chiral edge states of the integer quantum Hall effect, colliding at a quantum point contact (QPC). We monitor the fate of the colliding excitations by calculating zero-frequency current correlations at the output of the QPC. In the simpler case of filling factor $\nu=1$, we recover the standard result of a dip in the current noise as a function of the time delay between electron injections. For simultaneous injection, the current correlations exactly vanish, as dictated by the Pauli principle. This picture is however dramatically modified when interactions are present, as we show in the case of a filling factor $\nu=2$. There, each edge state is made out of two co-propagating channels, leading to charge fractionalization, and ultimately to decoherence. The latter phenomenon reduces the degree of indistinguishability between the two electron wavepackets, yielding a reduced contrast in the HOM signal. This naturally brings about the question of stronger interaction, offering a natural extension of the present work to the case of fractional quantum Hall effect where many open and fascinating questions remain.
Quantum point contactWave packetInterferometryInterferenceEdge excitationsFilling fractionQuantum opticsTime delayInterferometersHamiltonian...
• #### Edge mode velocities in the quantum Hall effect from a dc measurement

Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. We propose a way to extract edge velocities from dc transport in a point contact geometry defined by narrow gates. The width of the gates assumes two different sizes at small and large distances from the point contact. The Coulomb interaction across the gates depends on the gate width and affects the conductance of the contact. The conductance exhibits two different temperature dependencies at high and low temperatures. The transition between the two regimes is determined by the edge velocity. An interesting feature of the low-temperature I-V curve is current oscillations as a function of the voltage. The oscillations emerge due to charge reflection from the interface of the regions defined by the narrow and wide sections of the gates.
Quantum point contactQuantum Hall EffectBumpingEdge reconstructionChiralityFilling fractionTwo-point correlation functionTunneling amplitudesInterferometryTopological order...
• #### Coherent state path integral and super-symmetry for condensates composed of bosonic and fermionic atomsver. 4

A super-symmetric coherent state path integral on the Keldysh time contour is considered for bosonic and fermionic atoms which interact among each other with a common short-ranged two-body potential. We investigate the symmetries of Bose-Einstein condensation for the equivalent bosonic and fermionic constituents and specialize on the examination of super-symmetries for pair condensate terms. A Hubbard-Stratonovich transformation from 'Nambu'-doubled super-fields leads to a generating function with super-matrices for the self-energy whose manifold is given by the ortho-symplectic super-group Osp(S,S|2L). Effective equations are derived for anomalous terms which are related to the molecular- and BCS- condensate pairs. A change of integration measure for the coset decomposition Osp(S,S|2L)/U(L|S)xU(L|S) is performed, including a separation of density and anomalous parts of the self-energy with a gradient expansion for the Goldstone modes. The independent anomalous fields in the actions can be transformed by the inverse square root of the metric tensor of Osp(S,S|2L)/U(L|S) so that the coset integration measure with the super-Jacobi-determinant can be removed from the coherent state path integral and Gaussian-like integrations remain. The variations of the independent coset fields in the effective actions result in classical field equations for a nonlinear sigma model with the anomalous terms.
• #### Universal far-from-equilibrium Dynamics of a Holographic Superconductorver. 2

Symmetry breaking phase transitions are an example of non-equilibrium processes that require real time treatment, a major challenge in strongly coupled systems without long-lived quasiparticles. Holographic duality provides such an approach by mapping strongly coupled field theories in D dimensions into weakly coupled quantum gravity in D+1 anti-de Sitter spacetime. Here, we use holographic duality to study formation of topological defects -- winding numbers -- in the course of a superconducting transition in a strongly coupled theory in a 1D ring. When the system undergoes the transition on a given quench time, the condensate builds up with a delay that can be deduced using the Kibble-Zurek mechanism from the quench time and the universality class of the theory, as determined from the quasinormal mode spectrum of the dual model. Typical winding numbers deposited in the ring exhibit a universal fractional power law dependence on the quench time, also predicted by the Kibble-Zurek Mechanism.
QuenchingWinding numberField theorySuperconductorQuasinormal modesKibble-Zurek mechanismDualityCritical pointTwo-point correlation functionBlack hole...
• #### The X-ray/SZ view of the virial region. II. Gas mass fractionver. 2

Several recent studies used the hot gas fraction of galaxy clusters as a standard ruler to constrain dark energy, which provides competitive results compared to other techniques. This method, however, relies on the assumption that the baryon fraction in clusters agrees with the cosmic value Omega_b/Omega_m, and does not differ from one system to another. We test this hypothesis by measuring the gas mass fraction over the entire cluster volume in a sample of local clusters. Combining the SZ thermal pressure from Planck and the X-ray gas density from ROSAT, we measured for the first time the average gas fraction (fgas) out to the virial radius and beyond in a large sample of clusters. We also obtained azimuthally-averaged measurements of the gas fraction for 18 individual systems, which we used to compute the scatter of fgas around the mean value at different radii and its dependence on the cluster's temperature. The gas mass fraction increases with radius and reaches the cosmic baryon fraction close to R200. At R200, we measure fgas,200=0.176+/-0.009. We find significant differences between the baryon fraction of relaxed, cool-core (CC) systems and unrelaxed, non-cool core (NCC) clusters in the outer regions. In average, the gas fraction in NCC clusters slightly exceeds the cosmic baryon fraction, while in CC systems the gas fraction converges to the expected value when accounting for the stellar content, without any evidence for variations from one system to another. We find that fgas estimates in NCC systems slightly disagree with the cosmic value approaching R200. This result could be explained either by a violation of the assumption of hydrostatic equilibrium or by an inhomogeneous distribution of the gas mass. Conversely, cool-core clusters are found to provide reliable constraints on fgas at overdensities >200, which makes them suitable for cosmological studies.
Hydrostatic equilibriumVirial radiusNon cool-core galaxy clusterCluster of galaxiesCosmologyRelaxationOutskirt of a galaxy clusterStandard rulerHot gasIntrinsic scatter...
• #### The X-ray/SZ view of the virial region. I. Thermodynamic propertiesver. 2

We measure the thermodynamic properties of cluster outer regions to provide constraints on the processes that rule the formation of large scale structures. We derived the thermodynamic properties of the intracluster gas (temperature, entropy) by combining the SZ thermal pressure from Planck and the X-ray gas density from ROSAT. This method allowed us to reconstruct for the first time temperature and entropy profiles out to the virial radius and beyond in a large sample of objects. At variance with several recent Suzaku studies, we find that the entropy rises steadily with radius, albeit at at a somewhat lower rate than predicted by self-similar expectations. We note significant differences between relaxed, cool-core systems and unrelaxed clusters in the outer regions. Relaxed systems appear to follow the self-similar expectations more closely than perturbed objects. Our results indicate that the well-known entropy excess observed in cluster cores extends well beyond the central regions. When correcting for the gas depletion, the observed entropy profiles agree with the prediction from gravitational collapse only, especially for cool-core clusters.
EntropyEntropy profileSelf-similarityTemperature profileRelaxationCool core galaxy clusterPressure profileGravitational collapseMonte Carlo Markov chainAccretion...
• #### An adaptively refined phase-space element method for cosmological simulations and collisionless dynamicsver. 2

N-body simulations are essential for understanding the formation and evolution of structure in the Universe. However, the discrete nature of these simulations affects their accuracy when modelling collisionless systems. We introduce a new approach to simulate the gravitational evolution of cold collisionless fluids by solving the Vlasov-Poisson equations in terms of adaptively refineable "Lagrangian phase space elements". These geometrical elements are piecewise smooth maps between Lagrangian space and Eulerian phase space and approximate the continuum structure of the distribution function. They allow for dynamical adaptive splitting to accurately follow the evolution even in regions of very strong mixing. We discuss in detail various one-, two- and three-dimensional test problems to demonstrate the performance of our method. Its advantages compared to N-body algorithms are: i) explicit tracking of the fine-grained distribution function, ii) natural representation of caustics, iii) intrinsically smooth gravitational potential fields, thus iv) eliminating the need for any type of ad-hoc force softening. We show the potential of our method by simulating structure formation in a warm dark matter scenario. We discuss how spurious collisionality and large-scale discreteness noise of N-body methods are both strongly suppressed, which eliminates the artificial fragmentation of filaments. Therefore, we argue that our new approach improves on the N-body method when simulating self-gravitating cold and collisionless fluids, and is the first method that allows to explicitly follow the fine-grained evolution in six-dimensional phase space.
Phase spacePhase space causticDark matterCosmologyGalaxy filamentVlasov-Poisson equationRegularizationSimulations of structure formationManifoldVlasov equation...
• #### The Galaxy Cluster Concentration-Mass Scaling Relation

Scaling relations of clusters have made them particularly important cosmological probes of structure formation. In this work, we present a comprehensive study of the relation between two profile observables, concentration ($\mathrm{c_{vir}}$) and mass ($\mathrm{M_{vir}}$). We have collected the largest known sample of measurements from the literature which make use of one or more of the following reconstruction techniques: Weak gravitational lensing (WL), strong gravitational lensing (SL), Weak+Strong Lensing (WL+SL), the Caustic Method (CM), Line-of-sight Velocity Dispersion (LOSVD), and X-ray. We find that the concentration-mass (c-M) relation is highly variable depending upon the reconstruction technique used. We also find concentrations derived from dark matter only simulations (at approximately $\mathrm{M_{vir} \sim 10^{14} M_{\odot}}$) to be inconsistent with the WL and WL+SL relations at the $\mathrm{1\sigma}$ level, even after the projection of triaxial halos is taken into account. However, to fully determine consistency between simulations and observations, a volume-limited sample of clusters is required, as selection effects become increasingly more important in answering this. Interestingly, we also find evidence for a steeper WL+SL relation as compared to WL alone, a result which could perhaps be caused by the varying shape of cluster isodensities, though most likely reflects differences in selection effects caused by these two techniques. Lastly, we compare concentration and mass measurements of individual clusters made using more than one technique, highlighting the magnitude of the potential bias which could exist in such observational samples.
Weak lensingStrong gravitational lensingConcentration-mass relationCosmologyLine of sightPhase space causticScaling lawCluster of galaxiesNavarro-Frenk-White profileN-body simulation...
• #### The role of self-interacting right-handed neutrinos in galactic structurever. 2

It has been shown previously that the dark matter in galactic halos can be explained by a self-gravitating system of massive keV fermions (inos') in thermodynamic equilibrium, and predicted the existence of a denser quantum core of inos towards the center of galaxies. In this article we show that the inclusion of self-interactions among the inos, modeled within a relativistic mean-field-theory approach, allows the quantum core to become massive and compact enough to explain the dynamics of the S-cluster stars closest to the Milky Way's galactic center. We identify these inos with sterile right-handed neutrinos. The coincidence of an ino mass range of few tens of keV derived here only from the galactic structure, with the range obtained independently from other astrophysical and cosmological constraints, points towards an important role of the right-handed neutrinos in the cosmic structure.
Sterile neutrinoStandard ModelDark matterMilky WayGalactic structureWarm dark matterVector mesonRotation CurveDark matter haloCore radius...
• #### Higgs production in bottom-quark fusion in a matched scheme

We compute the total cross-section for Higgs boson production in bottom-quark fusion using the so-called FONLL method for the matching of a scheme in which the $b$-quark is treated as a massless parton to that in which it is treated as a massive final-state particle. We discuss the general framework for the application of the FONLL method to this process, and then we present explicit expressions for the case in which the next-to-next-to-leading-log five-flavor scheme result is combined with the leading-order $\cal O(\alpha_s^2)$ four-flavor scheme computation. We compare our results in this case to the four-and five-flavor scheme computations, and to the so-called Santander matching.
Bottom quarkParton distribution functionPartonNext-to-next-to-leading order computationRenormalizationHiggs bosonMassless limitYukawa couplingLight quarkPerturbative expansion...
• #### Lectures on knot homology

We provide various formulations of knot homology that are predicted by string dualities. In addition, we also explain the rich algebraic structure of knot homology which can be understood in terms of geometric representation theory in these formulations. These notes are based on lectures in the workshop "Physics and Mathematics of Link Homology" at Centre de Recherches Math\'ematiques, Universit\'e de Montr\'eal.
Torus knotBPS stateConifoldHilbert schemeRepresentation theoryM5 braneKnot invariantM2-braneChern-Simons theoryCodimension...
• #### Decomposing Nekrasov Decomposition

AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions - this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition - into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair "interaction" is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.
Macdonald polynomialTopological stringsGauge theorySchur polynomialPartition functionDualityQuiverConformal field theoryInstantonRandom matrix theory...
• #### Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers

We introduce brane brick models, a novel type of Type IIA brane configurations consisting of D4-branes ending on an NS5-brane. Brane brick models are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. They fully encode the infinite class of 2d (generically) N=(0,2) gauge theories on the worldvolume of the D1-branes and streamline their connection to the probed geometries. For this purpose, we also introduce new combinatorial procedures for deriving the Calabi-Yau associated to a given gauge theory and vice versa.
ChiralityQuiverGauge theoryOrientationOrbifoldD1 braneNS5-braneDimensional ReductionVacuum expectation valueSupersymmetry...
• #### Leptoproduction of Heavy Quarks II -- A Unified QCD Formulation of Charged and Neutral Current Processes from Fixed-target to Collider Energiesver. 2

A unified QCD formulation of leptoproduction of massive quarks in charged current and neutral current processes is described. This involves adopting consistent factorization and renormalization schemes which encompass both vector-boson-gluon-fusion (flavor creation) and vector-boson-massive-quark-scattering (flavor excitation) production mechanisms. It provides a framework which is valid from the threshold for producing the massive quark (where gluon-fusion is dominant) to the very high energy regime when the typical energy scale \mu is much larger than the quark mass m_Q (where the quark-scattering should be prevalent). This approach effectively resums all large logarithms of the type (alpha_s(mu) log(mu^2/m_Q^2)^n which limit the validity of existing fixed-order calculations to the region mu ~ O(m_Q). We show that the (massive) quark-scattering contribution (after subtraction of overlaps) is important in most parts of the (x, Q) plane except near the threshold region. We demonstrate that the factorization scale dependence of the structure functions calculated in this approach is substantially less than those obtained in the fixed-order calculations, as one would expect from a more consistent formulation.
• #### Leptoproduction of Heavy Quarks I-- General Formalism and Kinematics of Charged Current and Neutral Current Production Processesver. 2

Existing calculations of heavy quark production in charged-current and neutral current lepton-hadron scattering are formulated differently because of the artificial distinction of light'' and heavy'' quarks made in the traditional approach. A proper QCD formalism valid for a wide kinematic range from near threshold to energies much higher then the quark mass should treat these processes in a uniform way. We formulate a unified approach to both types of leptoproduction processes based on the conventional factorization theorem. In this paper, we present the general framework with complete kinematics appropriate for arbitrary masses, emphasizing the simplifications provided by the helicity formalism. We illustrate this approach with an explicit calculation of the leading order contribution to the quark structure functions with general masses. This provides the basis for a complete QCD analysis of charged current and neutral current leptoproduction of charm and bottom quarks to be presented in subsequent papers.
• #### What's in a ball? Constructing and characterizing uncertainty sets

In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that previous methods for measuring this radius, e.g. relative entropy or polynomial divergences, are inadequate for reference models which are moderately heavy-tailed such as lognormal models. Worst cases are either infinitely pessimistic, or they rule out the possibility of fat-tailed "power law" models as plausible alternatives. We introduce a new family of divergence measures which captures intermediate levels of pessimism.
Expectation ValueEntropyRegularizationGaussian distributionOptimizationCalibrationDecay rateConvex setClassificationSolar flare...
• #### Automata, reduced words, and Garside shadows in Coxeter groups

In this article, we introduce and investigate a class of finite deterministic automata that all recognize the language of reduced words of a finitely generated Coxeter system (W,S). The definition of these automata is straightforward as it only requires the notion of weak order on (W,S) and the related notion of Garside shadows in (W,S), an analog of the notion of a Garside family. Then we discuss the relations between this class of automata and the canonical automaton built from Brink and Howlett's small roots. We end this article by providing partial positive answers to two conjectures: (1) the automata associated to the smallest Garside shadow is minimal; (2) the canonical automaton is minimal if and only if the support of all small roots is spherical, i.e., the corresponding root system is finite.
Root systemMorphismSubgroupRankWeyl groupGraphDihedralNonnegativeOrientationConvex set...
• #### Sheaves and D-modules on Lorentzian manifolds

We introduce a class of causal manifolds which contains the globally hyperbolic spacetimes and we prove global propagation theorems for sheaves on such manifolds. As an application, we solve globally the Cauchy problem for hyperfunction solutions of hyperbolic systems.
ManifoldD-moduleCauchy problemHyperfunctionCausality...
• #### Heavy Quark Hadroproduction in Perturbative QCD

Existing calculations of heavy quark hadroproduction in perturbative QCD are either based on the approximate conventional zero-mass perturbative QCD theory or on next-to-leading order (NLO) fixed-flavor-number (FFN) scheme which is inadequate at high energies. We formulate this problem in the general mass variable-flavor-number scheme which incorporates initial/final state heavy quark parton distribution/fragmentation functions as well as exact mass dependence in the hard cross-section. This formalism has the built-in feature of reducing to the FFN scheme near threshold, and to the conventional zero-mass parton picture in the very high energy limit. Making use of existing calculations in NLO FFN scheme, we obtain more complete results on bottom production in the general scheme to order \alpha_s^3 both for current accelerator energies and for LHC. The scale dependence of the cross-section is reduced, and the magnitude is increased with respect to the NLO FFN results. It is shown that the bulk of the large NLO FFN contribution to the single heavy-quark inclusive cross-section is already contained in the (resummed) order \alpha_s^2 `heavy flavor excitation'' term in the general scheme.
• #### Updating neutrino magnetic moment constraints

In this paper we provide an updated analysis of the neutrino magnetic moments (NMMs), discussing both the constraints on the magnitudes of the three transition moments Lambda_i as well as the role of the CP violating phases present both in the mixing matrix and in the NMM matrix. The scattering of solar neutrinos off electrons in Borexino provides the most stringent restrictions, due to its robust statistics and the low energies observed, below 1 MeV. Our new limit on the effective neutrino magnetic moment which follows from the most recent Borexino data is 3.1 x 10^-11 mu_B at 90% C.L. This corresponds to the individual transition magnetic moment constraints: |Lambda_1| < 5.6 x10^-11 mu_B, |Lambda_2| < 4.0 x 10^-11 mu_B, and |Lambda_3| < 3.1 x 10^-11 mu_B (90% C.L.), irrespective of any complex phase. Indeed, the incoherent admixture of neutrino mass eigenstates present in the solar flux makes Borexino insensitive to the Majorana phases present in the NMM matrix. For this reason we also provide a global analysis including the case of reactor and accelerator neutrino sources, and presenting the resulting constraints for different values of the relevant CP phases. Improved reactor and accelerator neutrino experiments will be needed in order to underpin the full profile of the neutrino electromagnetic properties.
Neutrino magnetic dipole momentNeutrinoBorexinoSolar neutrinoStatisticsAntineutrinoReactor neutrino experimentsElectron neutrinoNeutrino fluxCP violating phase...
• #### Gapped Excitations of unconventional FQHE states in the Second Landau Levelver. 2

We report the observation of low-lying collective charge and spin excitations in the second Landau level at {\nu} = 2 + 1/3 and also for the very fragile states at {\nu} = 2 + 2/5, 2 + 3/8 in inelastic light scattering experiments. These modes exhibit a clear dependence on filling factor and temperature substantiating the unique access to the characteristic neutral excitation spectra of the incompressible FQHE states. A detailed mode analysis reveals low energy modes at around 70 {\mu}eV and a sharp mode slightly below the Zeeman energy interpreted as gap and spin wave excitation, respectively. The lowest energy collective charge excitation spectrum at {\nu} = 2 + 1/3 exhibits significant similarities and a universal scaling of the energies with its cousin state in the lowest Landau level at {\nu} = 1/3 suggesting similar underlying physics. The observed excitation spectra facilitate to distinguish between theoretical descriptions of the nature of those FQHE states. A striking polarization dependence in light scattering is discussed in the framework of anisotropic electron phases that allow for the stabilization of nematic FQHE states.
Fractional Quantum Hall EffectFilling fractionResonant Rayleigh scatteringIntensitySecond Landau levelLowest Landau LevelFragilityWave vectorSpin waveZeeman Energy...
• #### What determines large scale clustering: halo mass or environment?

We study the large scale halo bias b as a function of the environment (defined here as the background dark matter density fluctuation, d) and show that environment, and not halo mass m, is the main cause of large scale clustering. More massive haloes have a higher clustering because they live in denser regions, while low mass haloes can be found in a wide range of environments, and hence they have a lower clustering. Using a Halo Occupation Distribution (HOD) test, we can predict b(m) from b(d), but we cannot predict b(d) from b(m), which shows that environment is more fundamental for bias than mass. This has implications for the HOD model interpretation of the galaxy clustering, since when a galaxy selection is affected by environment, the standard HOD implementation fails. We show that the effects of environment are very important for colour selected samples in semi-analytic models of galaxy formation. In these cases, bias can be better recovered if we use environmental density instead of mass as the HOD variable. This can be readily applied to observations as the background density of galaxies is shown to be a very good proxy of environment.
Halo Occupation DistributionVirial massGalaxy clusteringSemi-analytical model of galaxy formationDark matterHalo assembly biasGalaxy biasDark matter haloMillennium RunHigh mass...
• #### Is Draco II one of the faintest dwarf galaxies? First evidence from Keck/DEIMOS spectroscopy

We present the first spectroscopic analysis of the faint and compact stellar system Draco II (Dra II, M_V=-2.9 +/- 0.8, r_h=19^{+8}_{-6} pc), recently discovered in the Pan-STARRS1 3\pi survey. The observations, conducted with DEIMOS on the Keck II telescope, reveal a cold velocity peak with 9 member stars at a systemic heliocentric velocity < v_r>=-347.6^{+1.7}_{-1.8} km/s, thereby confirming Dra II is a satellite of the Milky Way. We infer a marginally resolved velocity dispersion with \sigma_{vr}=2.9 +/- 2.1 km/s, which hints that this system is kinematically hotter than implied from its baryonic mass alone and potentially dark-matter-dominated (\log_{10}(M_{1/2})=5.5^{+0.4}_{-0.6} and log_{10}((M/L)_{1/2})=2.7^{+0.5}_{-0.8}, in Solar units). Furthermore, very weak Calcium triplet lines in the spectra of the high signal-to-noise member stars indicate that its metallicity is likely lower than that of the globular cluster NGC 2419 ([Fe/H]<-2.1). Finally, variations in the line strengths of two stars with similar colors and magnitudes suggest the presence of a metallicity spread in Dra II. Taken together, these three pieces of evidence lead us to conclude that Dra II is likely to be among the faintest, most compact, and closest dwarf galaxies. However, we emphasize that this conclusion needs to be strengthened through a more systematic spectroscopic campaign.
Dwarf galaxyStar systemsNGC 2419Globular clusterVelocity dispersionDraco Dwarf Spheroidal galaxyMilky WayEquivalent widthStarHertzsprung-Russell diagram...
• #### Neutrino Magnetic Moment

Current experimental and observational limits on the neutrino magnetic moment are reviewed. Implications of the recent results from the solar and reactor neutrino experiments for the value of the neutrino magnetic moment are discussed. It is shown that spin-flavor precession in the Sun is suppressed.
NeutrinoNeutrino magnetic dipole momentSunDirac neutrinoAntineutrinoNeutrino massReactor neutrino experimentsElectron neutrinoMajorana neutrinoSolar neutrino...
• #### Perturbative type II amplitudes for BPS interactions

We consider the perturbative contributions to the R^4, D^4 R^4 and D^6 R^4 interactions in toroidally compactified type II string theory. These BPS interactions do not receive perturbative contributions beyond genus three. We derive Poisson equations satisfied by these moduli dependent string amplitudes. These T--duality invariant equations have eigenvalues that are completely determined by the structure of the integrands of the multi--loop amplitudes. The source terms are given by boundary terms of the moduli space of Riemann surfaces corresponding to both separating and non--separating nodes. These are determined directly from the string amplitudes, as well as from the logarithmic divergences of maximal supergravity. We explicitly solve these Poisson equations in nine and eight dimensions.
SupergravityU-dualityEffective actionEinstein frameField theoryRiemann surfaceDilatonWorldsheetUltraviolet divergenceCompactification...
• #### Top-Quark Initiated Processes at High-Energy Hadron Collidersver. 2

In hadronic collisions at high energies, the top-quark may be treated as a parton inside a hadron. Top-quark initiated processes become increasingly important since the top-quark luminosity can reach a few percent of the bottom-quark luminosity. In the production of a heavy particle $H$ with mass $m_H > m_t$, treating the top-quark as a parton allows us to resum large logarithms $\log(m_{H}^{2}/m_{t}^{2}$) arising from collinear splitting in the initial state. We quantify the effect of collinear resummation at the 14-TeV LHC and a future 100-TeV hadron collider, focusing on the top-quark open-flavor process $gg\to t\bar t H$ in comparison with $t\bar t \to H$ and $tg\rightarrow tH$ at the leading order (LO) in QCD. We employ top-quark parton distribution functions with appropriate collinear subtraction and power counting. We find that (1) Collinear resummation enhances the inclusive production of a heavy particle with $m_H\approx$ 5 TeV (0.5 TeV) by more than a factor of two compared to the open-flavor process at a 100-TeV (14-TeV) collider; (2) Top-quark mass effects are important for scales $m_H$ near the top-quark threshold, where the cross section is largest. We advocate a modification of the ACOT factorization scheme, dubbed m-ACOT, to consistently treat heavy-quark masses in hadronic collisions; (3) The scale uncertainty of the total cross section in m-ACOT is of about 20 percent at the LO. While a higher-order calculation is indispensable for a precise prediction, the LO cross section is well described by the process $t\bar t\to H$ using an effective factorization scale significantly lower than $m_H$. We illustrate our results by the example of a heavy spin-0 particle. Our main results also apply to the production of particles with spin-1 and 2.
Top quarkHeavy quarkPartonLuminosityTop quark massResummationBottom quarkParton distribution functionHiggs bosonMassless limit...
• #### Morphology of blazar-induced gamma ray halos due to a helical intergalactic magnetic fieldver. 3

We study the characteristic size and shape of idealized blazar-induced cascade halos in the $1-100 \, {\rm GeV}$ energy range assuming various non-helical and helical configurations for the intergalactic magnetic field (IGMF). While the magnetic field creates an extended halo, the helicity provides the halo with a twist. Under simplifying assumptions, we assess the parameter regimes for which it is possible to measure the size and shape of the halo from a single source and then to deduce properties of the IGMF. We find that blazar halo measurements with an experiment similar to Fermi-LAT are best suited to probe a helical magnetic field with strength and coherence length today in the ranges $10^{-17} \lesssim B_{0} / {\rm Gauss} \lesssim 10^{-13}$ and $10 \, {\rm Mpc} \lesssim \lambda \lesssim 10 \, {\rm Gpc}$ where $\mathcal{H} \sim B_0^2 / \lambda$ is the magnetic helicity density. Stronger magnetic fields or smaller coherence scales can still potentially be investigated, but the connection between the halo morphology and the magnetic field properties is more involved. Weaker magnetic fields or longer coherence scales require high photon statistics or superior angular resolution.
Intergalactic magnetic fieldBlazarCoherence lengthHelicityLine of sightOrientationEarthTeV gamma raysMagnetic helicityStatistics...
• #### Majorana Neutrino Magnetic Moment and Neutrino Decoupling in Big Bang Nucleosynthesis

We examine the physics of the early universe when neutrinos (electron neutrino, muon neutrino, tau neutrino) possess transition magnetic moments. These extra couplings beyond the usual weak interaction couplings alter the way neutrinos decouple from the plasma of electrons/positrons and photons. We calculate how transition magnetic moment couplings modify neutrino decoupling temperatures, and then use a full weak, strong, and electromagnetic reaction network to compute corresponding changes in Big Bang Nucleosynthesis abundance yields. We find that light element observational constraints and other cosmological constraints may allow probes of neutrino transition magnetic moments which are not directly available in the laboratory.
NeutrinoBig bang nucleosynthesisNeutrino decouplingMajorana neutrinoDecoupling temperatureThe early UniverseThermalisationNeutrino magnetic dipole momentAbundanceActive neutrino...
• #### The Evolution of Dark Matter Halo Properties in Clusters, Filaments, Sheets and Voidsver. 2

We use a series of N-body simulations of the LCDM cosmology to investigate the redshift evolution since z=1 of the properties and alignment with the large-scale structure of haloes in clusters, filaments, sheets and voids. We find that: (i) Once a rescaling of the halo mass with M*, the mass scale collapsing at redshift z, is performed, there is no further significant redshift dependence in the halo properties; (ii) The environment influences halo shape and formation time at all investigated redshifts for haloes with masses M<M*; and (iii) There is a significant alignment of both spin and shape of haloes with filaments and sheets. In detail, at all redshifts up to z=1: a) Haloes with M<M* tend to be more oblate when located in clusters than in the other environments; this trend is reversed at higher masses: above about M*, halos in clusters are typically more prolate than similar massive haloes in sheets, filaments and voids. b) Haloes with M>M* in filaments spin more rapidly than similar mass haloes in clusters; haloes in voids have the lowest median spin parameters; c) Haloes with M<M* tend to be younger in voids and older in clusters; d) In sheets, halo spin vectors tend to lie within the sheet plane independent of mass; in filaments, instead, haloes with M<M* tend to spin parallel to the filament and haloes with M>M* perpendicular to it. For masses M>M*, the major axis of haloes in filaments and sheets is strongly aligned with the filament or the sheet. Such halo-LSS alignments may be of importance in weak lensing analyses of cosmic shear. A question that is opened by our study is why, in the 0 < z < 1 redshift regime that we have investigated, the mass scale M* sets roughly the threshold below which the LSS-environment either begins to affect, or reverses, the properties of dark matter haloes.
Galaxy filamentCluster of galaxiesVoidVirial massDark matter haloLarge scale structureCosmologyEllipticityMajor axisN-body simulation...
• #### Decaying dark matter and the tension in $\sigma_8$ver. 2

We consider decaying dark matter (DDM) as a resolution to the possible tension between cosmic microwave background (CMB) and weak lensing (WL) based determinations of the amplitude of matter fluctuations, $\sigma_8$. We perform N-body simulations in a model where dark matter decays into dark radiation and develop an accurate fitting formula for the non-linear matter power spectrum, which enables us to test the DDM model by the combined measurements of CMB, WL and the baryon acoustic oscillation (BAO). We employ a Markov chain Monte Carlo analysis to examine the overlap of posterior distributions of the cosmological parameters, comparing CMB alone with WL+BAO. We find an overlap that is significantly larger in the DDM model than in the standard CDM model. This may be hinting at DDM, although current data is not constraining enough to unambiguously favour a non-zero dark matter decay rate $\Gamma$. From the combined CMB+WL data, we obtain a lower bound $\Gamma^{-1}\ge 97$ Gyr at 95 % C.L, which is less tight than the constraint from CMB alone.
Decaying dark matterCosmic microwave backgroundWeak lensingBaryon acoustic oscillationsDark RadiationDark matterLambda-CDM modelN-body simulationNonlinear matter power spectrumDecay product...
• #### The Proton Radius from Electron Scattering Data

In an attempt to understand the discrepancy between the proton radius determined the muonic hydrogen Lamb shift and elastic electron-proton scattering measurements, we carefully review two classic, high precision electron scattering charge form factor, ${G_E}$, results. Upon examination, it was noted that the covariance matrices of common three parameter fits show large parameter correlations. Thus, we reanalyzed the classic data guided by statistical constraints and found low $q^2$, two-parameter fits were actually consistent with muonic hydrogen results. By subsequently including the highest measured values of ${G_E}(q^2)$ in the fits, we found that a dipole function, $G_E(q^2) = ( 1 + q^2/0.66[\rm{GeV}^2])^{-2}$, with the muonic hydrogen radius, 0.84087(39) fm, not only describes the low $q^2$ electron scattering data, but also describes the highest measured $q^2$ $G_E$ values.
Muonic hydrogenProton radiusElectron scatteringForm factorLamb shiftStatisticsMagnetic monopoleElasticityCovarianceProton charge...
• #### Dispersion approach to the renormalization group equations

Field theoryDispersion approachRenormalisation group equationsUnitarityRenormalizationS-matrixDispersionDispersion relation...
• #### Mathematical Analysis of the Historical Economic Growth

Historical economic growth is analysed using the method of reciprocal values. Included in the analysis is the world and regional economic growth. The analysis demonstrates that the natural tendency for the historical economic growth was to increase hyperbolically.
ReciprocityMathematical analysis
• #### Demographic Transition Theory Contradicted Repeatedly by Data

In the absence of convincing evidence, data for Sweden and Mauritius are used in academic publications to illustrate the Demographic Transition Theory. These data are closely examined and found to be in clear contradiction of this theory. Demographic Transition Theory is also contradicted by the best available data for England. Other examples of contradicting evidence are also discussed. This article is for demographers but even more importantly it is for teachers, lecturers and university professors who might not be aware of the long-lasting and serious problems with the Demographic Transition Theory, making it obsolete.
ContradictionUniverse
• #### Hyperbolic Growth of the World Population in the Past 12,000 Years

Data describing the growth of the world population in the past 12,000 years are analysed. It is shown that, if unchecked, population does not increase exponentially but hyperbolically. This analysis reveals three approximately-determined episodes of hyperbolic growth: 10,000-500 BC, AD 500-1200 and AD 1400-1950, representing a total of about 89% of the past 12,000 years. It also reveals three demographic transitions: 500 BC to AD 500, AD 1200 to AD 1400 and AD 1950 to present, representing the remaining 11% of the past 12,000 years. The first two transitions were between sustained hyperbolic trajectories. The current transition is to an unknown trajectory. There was never a transition from stagnation because there was no stagnation in the growth of the world population.
Hyperbolic growthTrajectory
• #### Rhapsody-G simulations I: the cool cores, hot gas and stellar content of massive galaxy clusters

We present the Rhapsody-G suite of cosmological hydrodynamic AMR zoom simulations of ten massive galaxy clusters at the $M_{\rm vir}\sim10^{15}\,{\rm M}_\odot$ scale. These simulations include cooling and sub-resolution models for star formation and stellar and supermassive black hole feedback. The sample is selected to capture the whole gamut of assembly histories that produce clusters of similar final mass. We present an overview of the successes and shortcomings of such simulations in reproducing both the stellar properties of galaxies as well as properties of the hot plasma in clusters. In our simulations, a long-lived cool-core/non-cool core dichotomy arises naturally, and the emergence of non-cool cores is related to low angular momentum major mergers. Nevertheless, the cool-core clusters exhibit a low central entropy compared to observations, which cannot be alleviated by thermal AGN feedback. For cluster scaling relations we find that the simulations match well the $M_{500}-Y_{500}$ scaling of Planck SZ clusters but deviate somewhat from the observed X-ray luminosity and temperature scaling relations in the sense of being slightly too bright and too cool at fixed mass, respectively. Stars are produced at an efficiency consistent with abundance matching constraints and central galaxies have star formation rates consistent with recent observations. While our simulations thus match various key properties remarkably well, we conclude that the shortcomings strongly suggest an important role for non-thermal processes (through feedback or otherwise) or thermal conduction in shaping the intra-cluster medium.
Cool core galaxy clusterCoolingAGN feedbackThermalisationScaling lawEntropyX-ray luminosityIntra-cluster mediumStellar massMassive cluster...
• #### Second-Order Fermions

It has been proposed several times in the past that one can obtain an equivalent, but in many aspects simpler description of fermions by first reformulating their first-order (Dirac) Lagrangian in terms of two-component spinors, and then integrating out the spinors of one chirality ($e.g.$ primed or dotted). The resulting new Lagrangian is second-order in derivatives, and contains two-component spinors of only one chirality. The new second-order formulation simplifies the fermion Feynman rules of the theory considerably, $e.g.$ the propagator becomes a multiple of an identity matrix in the field space. The aim of this thesis is to work out the details of this formulation for theories such as Quantum Electrodynamics, and the Standard Model of elementary particles. After having developed the tools necessary to establish the second-order formalism as an equivalent approach to spinor field theories, we proceed with some important consistency checks that the new formulation is required to pass, namely the presence or absence of anomalies in their perturbative and non-perturbative description, and the unitarity of the S-Matrix derived from their Lagrangian. Another aspect which is studied is unification, where we seek novel gauge-groups that can be used to embed all of the Standard Model content: forces and fermionic representations. Finally, we will explore the possibility to unify gravity and the Standard Model when the former is seen as a diffeomorphism invariant gauge-theory.
HamiltonianStandard ModelQuantum anomalyGauge fieldCovariant derivativeFeynman rulesLadder operatorFermionic fieldTwo-point correlation functionQuantum electrodynamics...
• #### Renormalization without infinities

Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only contain dressed irreducible vertices. The diagrams and equations that one ends up with do not contain any ultraviolet divergences. The original bare Lagrangian of the theory only enters in terms of freely adjustable integration constants. It is explained how the procedure proposed here is related to the renormalization group equations. The procedure requires the identification of unambiguous "paths" in a Feynman diagrams, and it is shown how to define such paths in most of the quantum field theories that are in use today. We do not claim to have a more convenient calculational scheme here, but rather a scheme that allows for a better conceptual understanding of ultraviolet infinities. Dedicated to Paul Frampton's 60th birthday
Feynman diagramsUltraviolet divergenceQuantum field theoryRenormalizationRenormalisation group equationsInfinitesimalOne particle irreducibleField theoryPerturbative expansionBosonic field...
• #### Partons in Quantum Chromodynamics

HadronizationForm factorQuarkoniumDeep inelastic scatteringQCD jetPositronDecay modePartonQuantum chromodynamicsTwo-photon exchange...
• #### Properties of hot and dense matter from relativistic heavy ion collisionsver. 2

We review the progress achieved in extracting the properties of hot and dense matter from relativistic heavy ion collisions at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory and the large hadron collider (LHC) at CERN. We focus on bulk properties of the medium, in particular the evidence for thermalization, aspects of the equation of state, transport properties, as well as fluctuations and correlations. We also discuss the in-medium properties of hadrons with light and heavy quarks, and measurements of dileptons and quarkonia. This review is dedicated to the memory of Gerald E. Brown.
ThermalisationLarge Hadron ColliderFluid dynamicsRelativistic Heavy Ion ColliderQuark-gluon plasmaHeavy ion collisionBaryon numberStrangenessFreeze-outEquation of state...
• #### The 2-8 keV cosmic X-ray background spectrum as observed with XMM-Newton

We have measured the spectrum of the Cosmic X-ray Background (CXB) in the 2-8 keV range with the high throughput EPIC/MOS instrument onboard XMM-Newton. A large sample of high galactic latitude observations was used, covering a total solid angle of 5.5 square degrees. Our study is based on a very careful characterization and subtraction of the instrumental background, which is crucial for a robust measurement of the faintest diffuse source of the X-ray sky. The CXB spectrum is consistent with a power law having a photon index Gamma=1.41+/-0.06 and a normalization of 2.46+/-0.09 photons/(cm^2 s sr keV) at 3 keV (~11.6 photons/(cm^2 s sr keV) at 1 keV), corresponding to a 2-10 keV flux of (2.24+/-0.16)x10^(-11) erg/(cm^2 s deg) (90% confidence level, including the absolute flux calibration uncertainty). Our results are in excellent agreement with two of the most recent CXB measurements, performed with BeppoSAX LECS/MECS data (Vecchi et al. 1999) and with an independent analysis of XMM-Newton EPIC/MOS data (Lumb et al. 2002), providing a very strong constrain to the absolute sky surface brightness in this energy range, so far affected by a ~40% uncertainty. Our measurement immediately implies that the fraction of CXB resolved by the recent deep X-ray observations in the 2-10 keV band is of 80+/-7% (1sigma), suggesting the existence of a new population of faint sources, largely undetected within the current sensitivity limits of the deepest X-ray surveys.
Cosmic X-ray backgroundIntensitySurface brightnessXMM-NewtonField of viewFluorescenceCharge coupled deviceCalibrationDiffuse sourceLight curve...
• #### Towards physics responsible for large-scale Lyman-$\alpha$ forest bias parameters

Using a series of carefully constructed numerical experiments based on hydrodynamic cosmological SPH simulations, we attempt to build an intuition for the relevant physics behind the large scale density ($b_\delta$) and velocity gradient ($b_\eta$) biases of the Lyman-$\alpha$ forest. Starting with the fluctuating Gunn-Peterson approximation applied to the smoothed total density field in real-space, and progressing through redshift-space with no thermal broadening, redshift-space with thermal broadening and hydrodynamicaly simulated baryon fields, we investigate how approximations found in the literature fare. We find that Seljak's 2012 analytical formulae for these bias parameters work surprisingly well in the limit of no thermal broadening and linear redshift-space distortions. We also show that his $b_\eta$ formula is exact in the limit of no thermal broadening. Since introduction of thermal broadening significantly affects its value, we speculate that a combination of large-scale measurements of $b_\eta$ and the small scale flux PDF might be a sensitive probe of the thermal state of the IGM. We find that large-scale biases derived from the smoothed total matter field are within 10-20\% to those based on hydrodynamical quantities, in line with other measurements in the literature.
ThermalisationFluctuating Gunn-Peterson ApproximationReal spaceRedshift-space distortionRedshift spaceFluid dynamicsCosmologyPerturbation theoryNeutral hydrogen gasAbsorbance...
• #### A Redux on "When is the Top Quark a Parton?"ver. 2

If a new heavy particle phi is produced in association with the top quark in a hadron collider, the production cross section exhibits a collinear singularity of the form log(m_phi/m_t), which can be resummed by introducing a top quark parton distribution function (PDF). We reassess the necessity of such resummation in the context of a high energy pp collider. We find that the introduction of a top PDF typically has a small effect at sqrt(S) ~ 100 TeV due to three factors: 1) alpha_s at the scale mu = m_phi is quite small when log(m_phi/m_t) is large, 2) the Bjorken x << 1 for m_phi < ~10 TeV, and 3) the kinematic region where log(m_phi/m_t) >> 1 is suppressed by phase space. We show that the effect of a top PDF is generically smaller than that of a bottom PDF in the associated production of b phi and consider the example of pp -> t H+ at next-to-leading logarithm order.
Parton distribution functionTop quarkHeavy quarkPartonKinematicsResummationHadronizationPhase spaceBottom quarkPerturbative expansion...
• #### Scattering Cross-Sections in Quantum Gravity - the Case of Matter-Matter Scatteringver. 2

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of a four-dimensional in- ner space. To analyse scattering in this theory the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity
Quantum gravityGauge theoryDiffeomorphismGauge fieldLSZ reduction formulaQuantum electrodynamicsQuantum mechanicsConserved quantitiesDirac fieldPerturbation theory...