• #### Radiative decay of keV-mass sterile neutrinos in a strongly magnetized plasma

The radiative decay of sterile neutrinos with typical masses of 10 keV is investigated in the presence of a strong magnetic field and degenerate plasma. Full account is taken of the strongly modified photon dispersion relation relative to vacuum. The limiting cases of relativistic and non-relativistic plasma are analyzed. The decay rate in a strongly magnetized plasma as a function of the electron number density is compared with the un-magnetized case. We find that a strong magnetic field suppresses the catalyzing influence of the plasma on the decay rate.
NeutrinoPlasma frequencyKinematicsPolarization vectorEigenvalueLowest Landau LevelActive neutrinoPlasmonEffective massMassive neutrino...
• #### Faint dwarfs as a test of DM models: WDM vs. CDM

We use high resolution Hydro$+$N-Body cosmological simulations to compare the assembly and evolution of a small field dwarf (stellar mass ~ 10$^{6-7}$ M$\odot$, total mass 10$^{10}$ M$\odot$ in $\Lambda$ dominated CDM and 2keV WDM cosmologies. We find that star formation (SF) in the WDM model is reduced and delayed by 1-2 Gyr relative to the CDM model, independently of the details of SF and feedback. Independent of the DM model, but proportionally to the SF efficiency, gas outflows lower the central mass density through dynamical heating', such that all realizations have circular velocities $<$ 20kms at 500$~$pc, in agreement with local kinematic constraints. As a result of dynamical heating, older stars are less centrally concentrated than younger stars, similar to stellar population gradients observed in nearby dwarf galaxies. We translate our simulations into artificial color-magnitude diagrams and star formation histories in order to directly compare to available observations. The simulated galaxies formed most of their stars in many $\sim$10 Myr long bursts. The CDM galaxy has a global SFH, HI abundance and Fe/H and alpha-elements distribution well matched to current observations of dwarf galaxies. These results highlight the importance of directly including baryon physics' in simulations when 1) comparing predictions of galaxy formation models with the kinematics and number density of local dwarf galaxies and 2) differentiating between CDM and non-standard models with different DM or power spectra.
Star formationWarm dark matterGalaxyCold dark matterDark matterStarCosmologyA dwarfsDwarf galaxyStellar populations...
• #### Beyond the Bulge: a Fundamental Relation Between Supermassive Black Holes and Dark Matter Halosver. 2

The possibility that the masses of supermassive black holes (SBHs) correlate with the total gravitational mass of their host galaxy, or the mass of the dark matter halo in which they presumably formed, is investigated using a sample of 16 spiral and 20 elliptical galaxies. The bulge velocity dispersion, typically defined within an aperture of size less than 0.5 kpc, is found to correlate tightly with the galaxy's circular velocity, the latter measured at distances from the galactic center at which the rotation curve is flat, 20 to 80kpc. By using the well known M-sigma relation for SBHs, and a prescription to relate the circular velocity to the mass of the dark matter halo in a standard CDM cosmology, the correlation between velocity dispersion and circular velocity is equivalent to one between SBH and halo masses. Such a correlation is found to be nonlinear, with the ratio between the two masses decreasing from 2X10^-4 for halos of 10^14 solar masses, to 10^-5 for halos of 10^12 solar masses. Preliminary evidence suggests that halos smaller than ~5X10^11 solar masses are increasingly less efficient -- perhaps unable -- at forming SBHs.
Rotation CurveGalaxyDark matter haloEllipticityHost galaxyTriangulum GalaxySpiral galaxyDark Matter Density ProfileDark matterHubble sequence...
• #### Gauge invariance at work in FDR: H -> gamma gamma

We present the first complete calculation performed within the Four Dimensional Regularization scheme (FDR), namely the loop-induced on-shell amplitude for the Higgs boson decay into two photons in an arbitrary R_csi gauge. FDR is a new technique -free of infinities- for addressing multi-loop calculus, which automatically preserves gauge invariance, allowing for a 4-dimensional computation at the same time. We obtained the same result as that assessed in dimensional regularization, thereby explicitly verifying, in a realistic case, that FDR respects gauge invariance.
Gauge invarianceBosonizationRenormalizationLoop integralQuantum field theoryStandard ModelFeynman rulesKinematicsRegularizationDimensional regularization...
• #### A four-dimensional approach to quantum field theoriesver. 2

I present a novel Four-Dimensional Regularization/Renormalization approach (FDR) to ultraviolet divergences in field theories which can be interpreted as a natural separation between physical and non physical degrees of freedom. Based on the observation that, in some cases, infinities can be reabsorbed into the vacuum expectation value of the fields, a new type of four-dimensional, gauge invariant and cutoff independent loop integral is introduced, which reproduces the correct ABJ anomaly and does not require changes in the definition of gamma_5. Finally, I comment on a possible interpretation of non-renormalizable theories in the context of the proposed procedure, and show how FDR can also be used to regularize infrared and collinear divergences.
RenormalizationGauge invarianceGreen's functionDegree of freedomTadpolePropagatorLoop integralQuantum field theoryABJ anomalyPhase space...
• #### Studying the dwarf galaxies in nearby groups of galaxies: spectroscopic and photometric data

Galaxy evolution by interaction driven transformation is probably highly efficient in groups of galaxies. Dwarf galaxies with their shallow potential are expected to reflect the interaction most prominently in their observable structure. The major aim of this series of papers is to establish a data base which allows to study the impact of group interaction onto the morphology and star-forming properties of dwarf galaxies. Firstly, we present our selection rules for target groups and the morphological selection method of target dwarf member candidates. Secondly, the spectroscopic follow-up observations with the HET are present. Thirdly, we applied own reduction methods based on adaptive filtering to derive surface photometry of the candidates. The spectroscopic follow-up indicate a dwarf identification success rate of roughly 55%, and a group member success rate of about 33%. A total of 17 new low surface brightness members is presented. For all candidates, total magnitudes, colours, and light distribution parameters are derived and discussed in the context of scaling relations. We point out short comings of the SDSS standard pipeline for surface photometry for these dim objects. We conclude that our selection strategy is rather efficient to obtain a sample of dim, low surface brightness members of groups of galaxies within the Virgo super-cluster. The photometric scaling relation in these X-ray dim, rather isolated groups does not significantly differ from those of the galaxies within the Local Volume.
GalaxySloan Digital Sky SurveyDwarf galaxyNGC catalogA dwarfsLow surface brightness galaxyStar formationLuminosityGroup of galaxiesStar formation rate...
• #### Wavelet Approach to Search for Sterile Neutrinos in Tritium $\beta$-Decay Spectra

Sterile neutrinos in the mass range of a few keV are candidates for both cold and warm dark matter. An ad-mixture of a heavy neutrino mass eigenstate to the electron neutrino would result in a minuscule distortion - a 'kink' - in a $\beta$-decay spectrum. In this paper we show that a wavelet transform is a very powerful shape analysis method to detect this signature. For a tritium source strength, similar to what is expected from the KATRIN experiment, a statistical sensitivity to active-to-sterile neutrino mixing down to $\sin^2 \theta= 10^{-6}$ ($90\%$ CL) can be obtained after 3 years of measurement time. It is demonstrated that the wavelet approach is largely insensitive to systematic effects that result in smooth spectral modifications. To make full use of this analysis technique a high resolution measurement (FWHM of $\sim100$~eV) of the tritium $\beta$-decay spectrum is required.
SpectrometersKATRIN experimentMixing angleSterile neutrino massNeutrino mass eigenstatesNeutrino massWarm dark matterStandard ModelSterile neutrinoCold dark matter...
• #### Baryogenesis from Strong CP Violation and the QCD Axionver. 3

The strong CP-violating parameter is small today as indicated by constraints on the neutron electric dipole moment. In the early universe, the QCD axion has not yet relaxed to its QCD-cancelling minimum and it is natural to wonder whether this large CP violation could be responsible for baryogenesis. We show that strong CP violation from the QCD axion can be responsible for the matter antimatter asymmetry of the universe in the context of cold EW baryogenesis if the EW phase transition is delayed below the GeV scale. This can occur naturally if the Higgs couples to a O(100) GeV dilaton, as expected in some models where the Higgs is a pseudo-Nambu Goldstone boson of a new strongly interacting sector at the TeV scale. The only new relevant ingredients beyond the Standard Model in our framework are the QCD axion and an EW scale dilaton-like scalar field. The existence of such a second scalar resonance with a mass and properties similar to the Higgs boson will soon be tested at the LHC. Our conclusions are independent of the Peccei-Quinn scale, apart from the usual constraints on the QCD axion, and apply on general grounds, whether the axion accounts for all of dark matter or not. In this context, the QCD axion would not only solve the strong CP problem, but also the matter anti-matter asymmetry and possibly dark matter.
Electroweak phase transitionQuenchingSupercoolingStandard ModelReheating temperatureHiggs boson massSphaleronAxion massReheatingChern-Simons number...
• #### Cold and Fuzzy Dark Matterver. 2

Cold dark matter (CDM) models predict small-scale structure in excess of observations of the cores and abundance of dwarf galaxies. These problems might be solved, and the virtues of CDM models retained, even without postulating {\it ad hoc} dark matter particle or field interactions, if the dark matter is composed of ultra-light scalar particles (m ~ 10^{-22}eV), initially in a (cold) Bose-Einstein condensate, similar to axion dark matter models. The wave properties of the dark matter stabilize gravitational collapse providing halo cores and sharply suppressing small-scale linear power.
Cold dark matterDark matterDwarf galaxyDark matter haloLambda-CDM modelMatter power spectrumReionizationScalar fieldDark matter particleDynamical time...
• #### Cosmic Structure as the Quantum Interference of a Coherent Dark Wave

The conventional cold, particle interpretation of dark matter (CDM) still lacks laboratory support and struggles with the basic properties of common dwarf galaxies, which have surprisingly uniform central masses and shallow density profiles. In contrast, galaxies predicted by CDM extend to much lower masses, with steeper, singular profiles. This tension motivates cold, wavelike dark matter ($\psi$DM) composed of a non-relativistic Bose-Einstein condensate, so the uncertainty principle counters gravity below a Jeans scale. Here we achieve the first cosmological simulations of this quantum state at unprecedentedly high resolution capable of resolving dwarf galaxies, with only one free parameter, $\bf{m_B}$, the boson mass. We demonstrate the large scale structure of this $\psi$DM simulation is indistinguishable from CDM, as desired, but differs radically inside galaxies. Connected filaments and collapsed haloes form a large interference network, with gravitationally self-bound solitonic cores inside every galaxy surrounded by extended haloes of fluctuating density granules. These results allow us to determine $\bf{m_B=(8.1^{+1.6}_{-1.7})\times 10^{-23}~eV}$ using stellar phase-space distributions in dwarf spheroidal galaxies. Denser, more massive solitons are predicted for Milky Way sized galaxies, providing a substantial seed to help explain early spheroid formation. Suppression of small structures means the onset of galaxy formation for $\psi$DM is substantially delayed relative to CDM, appearing at $\bf{z\lesssim 13}$ in our simulations.
Dark matterGalaxyCold dark matterInterferenceDwarf galaxySolitonGranuleLarge scale structureSimulations of structure formationGalaxy Formation...
• #### Re-examining the Too-Big-To-Fail Problem for Dark Matter Haloes with Central Density Coresver. 2

Recent studies found the densities of dark matter (DM) subhaloes which surround nearby dwarf spheroidal galaxies (dSphs) to be significantly lower than those of the most massive subhaloes expected around Milky Way sized galaxies in cosmological simulations, the so called "too-big-to-fail" (TBTF) problem. A caveat of previous work has been that dark substructures were assumed to contain steep density cusps in the center of DM haloes even though the central density structure of DM haloes is still under debate. In this study, we re-examine the TBTF problem for models of DM density structure with cores or shallowed cusps. Our analysis demonstrates that the TBTF problem is alleviated as the logarithmic slope of the central cusp becomes shallower. We find that the TBTF problem is avoided if the central cusps of DM haloes surrounding dSphs are shallower than $r^{-0.6}$.
Milky WayDark matter haloNavarro-Frenk-White profileVirial massCosmologySupernovaCold dark matterToo big to fail problemMilky Way haloMass profile...
• #### Magnetars and the Chiral Plasma Instabilities

We propose a possible new mechanism for a strong and stable magnetic field of compact stars due to an instability in the presence of a chirality imbalance of electrons---the chiral plasma instability. A large chirality imbalance of electrons inevitably occurs associated with the parity-violating weak process during core collapse of supernovae. We estimate the maximal magnetic field due to this instability to be of order 10^{18} G at the core. This mechanism naturally generates a large magnetic helicity from the chiral asymmetry, which ensures the stability of the large magnetic field.
ChiralityDissipationHelicityChiral chemical potentialElectron massStrong magnetic fieldElectron captureStarWeak interactionMagnetohydrodynamics...
• #### Time-dependent Diffusive Shock Acceleration in Slow Supernova Remnant Shocks

Recent gamma ray observations show that middle aged supernova remnants interacting with molecular clouds can be sources of both GeV and TeV emission. Models involving re-acceleration of pre-existing cosmic rays in the ambient medium and direct interaction between supernova remnant and molecular clouds have been proposed to explain the observed gamma ray emission. For the re-acceleration process, standard DSA theory in the test particle limit produces a steady state particle spectrum that is too flat compared to observations, which suggests that the high energy part of the observed spectrum has not yet reached a steady state. We derive a time dependent DSA solution in the test particle limit for situations involving re-acceleration of pre-existing cosmic rays in the preshock medium. Simple estimates with our time dependent DSA solution plus a molecular cloud interaction model can reproduce the overall shape of the spectra of IC 443 and W44 from GeV to TeV energies through pure $\pi^0$-decay emission. We allow for a power law momentum dependence of the diffusion coefficient, finding that a power law index of 0.5 is favored.
Cosmic raySupernova remnantCosmic ray spectrumForward shockCompressibilityBohm diffusionPulsarFilling fractionDiffusive shock accelerationDynamical evolution...
• #### Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts

Magnetized neutron starGamma ray burstFormate
• #### Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect

We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain correct gravitational linear response functions. In the lowest order in gradients the linear response generating functional includes Chern-Simons, Wen-Zee and gravitational Chern- Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
Central chargeChiralitySpin connectionManifoldPartonGauge fieldPartition functionFluid dynamicsRead-Rezayi parafermionic wavefunctionGravitational anomaly...
• #### Magnetic field instability in a neutron star driven by electroweak electron-nucleon interaction versus chiral magnetic effect

We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons ($eN$ interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to $\gtrsim 10^{15}\thinspace\text{G}$ during a time comparable with the ages of young magnetars $\sim 10^4\thinspace\text{yr}$. The magnetic field instability originates from the parity violation in the $eN$ interaction entering the generalized Dirac equation for right and left massless electrons in an external uniform magnetic field. The averaged electric current given by the solution of the modified Dirac equation contains an extra current for right and left electrons (positrons). Such current includes both a changing chiral imbalance of electrons and the $eN$ potential given by a constant neutron density in NS. Then we derive the system of the kinetic equations for the chiral imbalance and the magnetic helicity which accounts for the $eN$ interaction. By solving this system, we show that a sizable chiral imbalance arising in a neutron protostar due to the Urca-process $e^-_\mathrm{L} + p\to N + \nu_\mathrm{eL}$ diminishes very rapidly because of a huge chirality flip rate. Thus the $eN$ term prevails the chiral effect providing a huge growth of the magnetic helicity and the helical magnetic field.
Neutron starChern-Simons termHelicityStandard ModelCoolingNeutrinoChiralityPseudovectorHelicity density spectrumStrong magnetic field...
• #### QCD at Low Energiesver. 2

The modern status of basic low energy QCD parameters is reviewed. It is demonstrated, that the recent data allows one to determine the light quark mass ratios with an accuracy 10-15%. The general analysis of vacuum condensates in QCD is presented, including those induced by external fields. The QCD coupling constant alpha_s is found from the tau-lepton hadronic decay rate. V-A spectral functions of tau-decay are used for construction of the V-A polarization operator Pi_{V-A}(s) in the complex s-plane. The operator product expansion (OPE) is used up to dimension D=10 and the sum rules along the rays in the complex s-plane are constructed. The best values of quark condensate and alpha_s<0|qq|0>^2 are found. The value of quark condensate is confirmed by considering the sum rules for baryon masses. Gluon condensate is found in four ways: by considering of V+A polarization operator based on the tau-decay data, by studying the sum rules for polarization operators momenta in charmonia in vector, pseudoscalar and axial channels. All of these determinations are in agreement and result in <(alpha_s/pi)G^2 > =0.005 \pm 0.004 GeV^4. Valence quark distributions in proton are calculated in QCD using the OPE in proton current virtuality. The quark distributions agree with those found from the deep inelastic scattering data. The same value of gluon condensate is favoured.
Quantum chromodynamicsQuarkCondensationGluon condensateMass ratioLight quarkCoupling constantDeep inelastic scatteringOperator product expansionPseudoscalar...
• #### Calculation of Baryon Masses in Quantum Chromodynamics

Gauge fieldFeynman diagramQuarkStrange quarkCurrent quarkVacuum stateVacuum polarizationChiralityChiral symmetryOperator product expansion...
• #### Nucleon Magnetic Moments and Magnetic Properties of Vacuum in QCD

Quantum chromodynamicsCondensationQuarkVacuum stateFieldElectromagnetic fieldTransformationsPolarizationPhotonMagnetic susceptibility...
• #### On the multi-frequency inverse source problem in heterogeneous media

The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is shown that data obtained from finitely many frequencies is not sufficient. On the other hand, if the frequency varies within a set with an accumulation point, then the source is determined uniquely, even in the presence of highly heterogeneous media. In addition, an algorithm for the reconstruction of the source using multi-frequency data is proposed. The algorithm, based on a subspace projection method, approximates the minimum-norm solution given the available multi-frequency measurements. A few numerical examples are presented.
Helmholtz equationHomogenizationWeak solutionRegularizationPlane waveSesquilinear formFundamental solutionWeak formulationEigenvalueSommerfeld radiation condition...
• #### Scalar Simplified Models for Dark Matter

We introduce a set of minimal simplified models for dark matter interactions with the Standard Model, connecting the two sectors via either a scalar or pseudoscalar particle. These models have a wider regime of validity for dark matter searches at the LHC than the effective field theory approach, while still allowing straightforward comparison to results from non-collider dark matter detection experiments. Such models also motivate dark matter searches in multiple correlated channels. In this paper, we constrain scalar and pseudoscalar simplified models with direct and indirect detection experiments, as well as from existing LHC searches with missing energy plus tops, bottoms, or jets, using the exact loop-induced coupling with gluons. This calculation significantly affects key differential cross sections at the LHC, and must be properly included. We make connections with the Higgs sector, and conclude with a discussion of future searches at the LHC.
Effective field theoryThermalisationDM massCMS experimentBranching ratioKinematicsDark sectorTop quark massRelic abundanceParton...
• #### Nonlinear electromagnetic response in quark-gluon plasma

We perform the first systematic study of the nonlinear electromagnetic currents induced by external electromagnetic field in quark-gluon plasma, both in the two cases that the inhomogeneity of electromagnetic field is small (large) so that the collision effect is important (negligible). In the former case, we list and classify possible components of the currents in a systematic way, and make an order estimate of each component by using the Boltzmann equation in the relaxation time approximation. In the latter case, we explicitly calculate the quadratic current by using the Vlasov equation, and find that the current generated by the chiral magnetic effect and the quadratic current can have the same order of magnitude by using the Kadanoff-Baym equation. We also demonstrate this property by using a possible configuration of electromagnetic field realized in heavy ion collision.
Chiral magnetic effectHeavy ion collisionVlasov equationKadanoff-Baym equationQuarkBoltzmann transport equationRelaxation Time ApproximationQuark-gluon plasmaHard thermal loopInstability...
• #### Stochastic Star Formation & Feedback: Mapping Low-Mass Galaxies to Dark Matter Haloes

Comparison of observed satellite galaxies of the Milky Way (hereafter MW) with dark matter subhaloes in cosmological $N$-body simulations of MW-mass haloes suggest that such subhaloes, if they exist, are occupied by satellites in a stochastic fashion. We examine how inefficient massive star formation and associated supernova feedback in high-redshift progenitors of present-day low-mass subhaloes might contribute to this stochasticity. Using a Monte Carlo approach to follow the assembly histories of present-day low-mass haloes with $10^7 \lesssim M \leq 10^{10}$ ${\rm M}_{\odot}$, we identify when cooling and star formation is likely to proceed, and observe that haloes with present-day masses $\lesssim 10^9 {\rm M}_{\odot}$ never grow sufficiently massive to support atomic hydrogen line cooling. Noting that the star formation timescale decreases sharply with stellar mass as $t_{\rm PMS} \propto m_{\ast}^{-2.5}$, we argue that, should the conditions for high mass star formation arise in low-mass haloes, the ensuing supernovae are likely to disrupt ongoing lower-mass star formation and unbind gas within the halo. This potentially star-forming gas is unlikely to be replenished in lower mass haloes because of, e.g. cosmological reionization, and so we expect galaxy formation to be stymied in a manner that depends on host halo assembly history and the efficiency and timing of star formation in proto-galaxies, which we illustrate using a Monte Carlo model. Based on these simple physical arguments, we assert that stochasticity of star formation and feedback is an essential but overlooked ingredient in modelling galaxy formation on the smallest scales.
StarVirial massGalaxyZero-age main sequence starsCosmologyStar formationInitial mass functionReionizationAbundanceCircumgalactic medium...
• #### Planck 2013 results. XVI. Cosmological parametersver. 3

We present the first results based on Planck measurements of the CMB temperature and lensing-potential power spectra. The Planck spectra at high multipoles are extremely well described by the standard spatially-flat six-parameter LCDM cosmology. In this model Planck data determine the cosmological parameters to high precision. We find a low value of the Hubble constant, H0=67.3+/-1.2 km/s/Mpc and a high value of the matter density parameter, Omega_m=0.315+/-0.017 (+/-1 sigma errors) in excellent agreement with constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent-level precision using Planck CMB data alone. We present results from an analysis of extensions to the standard cosmology, using astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured significantly over standard LCDM. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find a 95% upper limit of r<0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles. Using BAO and CMB data, we find N_eff=3.30+/-0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the summed neutrino mass. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N_eff=3.046. We find no evidence for dynamical dark energy. Despite the success of the standard LCDM model, this cosmology does not provide a good fit to the CMB power spectrum at low multipoles, as noted previously by the WMAP team. While not of decisive significance, this is an anomaly in an otherwise self-consistent analysis of the Planck temperature data. [Abridged]
Matter power spectrumAtacama Cosmology TelescopeSouth Pole TelescopeReionizationRecombinationPoint sourceCosmic infrared backgroundCosmic microwave background experimentSound horizonCMB acoustic peak...
• #### Characteristic Length and Clustering

We explore relations between various variational problems for graphs like Euler characteristic chi(G), characteristic length mu(G), mean clustering nu(G), inductive dimension iota(G), edge density epsilon(G), scale measure sigma(G), Hilbert action eta(G) and spectral complexity xi(G). A new insight in this note is that the local cluster coefficient C(x) in a finite simple graph can be written as a relative characteristic length L(x) of the unit sphere S(x) within the unit ball B(x) of a vertex. This relation L(x) = 2-C(x) will allow to study clustering in more general metric spaces like Riemannian manifolds or fractals. If eta is the average of scalar curvature s(x), a formula mu ~ 1+log(epsilon)/log(eta) of Newman, Watts and Strogatz relates mu with the edge density epsilon and average scalar curvature eta telling that large curvature correlates with small characteristic length. Experiments show that the statistical relation mu ~ log(1/nu) holds for random or deterministic constructed networks, indicating that small clustering is often associated to large characteristic lengths and lambda=mu/log(nu) can converge in some graph limits of networks. Mean clustering nu, edge density epsilon and curvature average eta therefore can relate with characteristic length mu on a statistical level. We also discovered experimentally that inductive dimension iota and cluster-length ratio lambda correlate strongly on Erdos-Renyi probability spaces.
GeodesicClustering coefficientArboricityLine graphTorusManifoldGraph theoryEigenvalueCohomologyGeneral relativity...
• #### Experimental Realization of Quantum Artificial Intelligence

Machines are possible to have some artificial intelligence like human beings owing to particular algorithms or software. Such machines could learn knowledge from what people taught them and do works according to the knowledge. In practical learning cases, the data is often extremely complicated and large, thus classical learning machines often need huge computational resources. Quantum machine learning algorithm, on the other hand, could be exponentially faster than classical machines using quantum parallelism. Here, we demonstrate a quantum machine learning algorithm on a four-qubit NMR test bench to solve an optical character recognition problem, also known as the handwriting recognition. The quantum machine learns standard character fonts and then recognize handwritten characters from a set with two candidates. To our best knowledge, this is the first artificial intelligence realized on a quantum processor. Due to the widespreading importance of artificial intelligence and its tremendous consuming of computational resources, quantum speedup would be extremely attractive against the challenges from the Big Data.
Support vector machineClassificationQubitOptical Character RecognitionQuantum algorithmSegmentationExpectation ValueLeast squaresSubgroupTraining set...
• #### Chiral asymmetry in cold QED plasma in a strong magnetic fieldver. 2

The interaction induced chiral asymmetry is calculated in cold QED plasma beyond the weak-field approximation. By making use of the recently developed Landau-level representation for the fermion self-energy, the chiral shift and the parity-even chiral chemical potential function are obtained with the help of numerical methods. The results are used to quantify the chiral asymmetry of the Fermi surface in dense QED matter. Because of the weakness of the QED interactions, the value of the asymmetry appears to be rather small even in the strongest magnetic fields and at the highest stellar densities. However, the analogous asymmetry can be substantial in the case of dense quark matter.
Lowest Landau LevelChiral separation effectChiral magnetic effectFermion propagatorCoupling constantMonte Carlo methodTranslational invarianceRadiative correctionGamma distributionMagnetic field strength...
• #### Helical cosmological magnetic fields from extra-dimensionsver. 2

We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The evolution of extra-dimensional scale factor allows the breaking of conformal invariance of the effective electromagnetic action in $1+3$ dimensions required for such generation. Analytical solutions for the vector potential can be obtained in terms of Coulomb wave-functions for some special cases. We also present numerical solutions for the vector potential evolution in more general cases. In the presence of a higher-dimensional cosmological constant there exist solutions for the scale factors in which both normal and extra dimensional space either inflate or deflate simultaneously with the same rate. In such a scenario, with the number of extra dimensions $D=4$, a scale invariant spectrum of helical magnetic field is obtained. The net helicity arises, as one helical mode comes to dominate over the other at the superhorizon scales. A magnetic field strength of the order of $10^{-9}$ $G$ can be obtained for the inflationary scale $H\simeq 10^{-3}$ $M_{pl}$. Weaker fields will be generated for lower scales of inflation. Magnetic fields generated in this model respects the bounds on magnetic fields by Planck and $\gamma$-ray observations (i.e. $10^{-16}$ $G$ $<$ $B_{obs}<3.4\times 10^{-9}$ $G$).
HorizonHelical magnetic fieldCosmological magnetic fieldIntergalactic mediumDimensional ReductionHomogenizationGauge conditionGalaxyCosmological constantThe early Universe...
• #### Reionization constraints on primordial magnetic fields

We study the impact of the extra density fluctuations induced by primordial magnetic fields on the reionization history in the redshift range: $6 < z < 10$. We perform a comprehensive MCMC physical analysis allowing the variation of parameters related to primordial magnetic fields (strength, $B_0$, and power-spectrum index $n_{\scriptscriptstyle \rm B}$), reionization, and $\Lambda$CDM cosmological model. We find that magnetic field strengths in the range: $B_0 \simeq 0.05{-}0.3$ nG (for nearly scale-free power spectra) can significantly alter the reionization history in the above redshift range and can relieve the tension between the WMAP and quasar absorption spectra data. Our analysis puts upper-limits on the magnetic field strength $B_0 < 0.362, 0.116, 0.057$ nG (95 % c.l.) for $n_{\scriptscriptstyle \rm B} = -2.95, -2.9, -2.85$, respectively. These represent the strongest magnetic field constraints among those available from other cosmological observables.
IonizationIntergalactic mediumStarMatter power spectrumGalaxyLambda-CDM modelPhotoionization ratePrimordial density perturbationStructure formationCosmology...
• #### Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes

The polarized thermal emission from Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100GHz. We exploit the Planck HFI polarization data from 100 to 353GHz to measure the dust angular power spectra $C_\ell^{EE,BB}$ over the range $40<\ell<600$. These will bring new insights into interstellar dust physics and a precise determination of the level of contamination for CMB polarization experiments. We show that statistical properties of the emission can be characterized over large fractions of the sky using $C_\ell$. For the dust, they are well described by power laws in $\ell$ with exponents $\alpha^{EE,BB}=-2.42\pm0.02$. The amplitudes of the polarization $C_\ell$ vary with the average brightness in a way similar to the intensity ones. The dust polarization frequency dependence is consistent with modified blackbody emission with $\beta_d=1.59$ and $T_d=19.6$K. We find a systematic ratio between the amplitudes of the Galactic $B$- and $E$-modes of 0.5. We show that even in the faintest dust-emitting regions there are no "clean" windows where primordial CMB $B$-mode polarization could be measured without subtraction of dust emission. Finally, we investigate the level of dust polarization in the BICEP2 experiment field. Extrapolation of the Planck 353GHz data to 150GHz gives a dust power $\ell(\ell+1)C_\ell^{BB}/(2\pi)$ of $1.32\times10^{-2}\mu$K$_{CMB}^2$ over the $40<\ell<120$ range; the statistical uncertainty is $\pm0.29$ and there is an additional uncertainty (+0.28,-0.24) from the extrapolation, both in the same units. This is the same magnitude as reported by BICEP2 over this $\ell$ range, which highlights the need for assessment of the polarized dust signal. The present uncertainties will be reduced through an ongoing, joint analysis of the Planck and BICEP2 data sets.
Spectral energy distributionStatistical errorCosmic microwave background polarizationCosmic microwave background experimentSynchrotronGalactic latitudeScaling lawRecombinationPoint sourceMonte Carlo method...
• #### Extragalactic magnetic fields rule out electroweak phase transition magnetogenesis

In this letter we show that magnetic fields generated at the electroweak phase transition must have helicity in order to explain the void magnetic fields apparently observed today. In the most optimistic case, the helicity fraction must be at least of order $10^{-11}$. We show that the helicity naturally produced in conjunction with the baryon asymmetry is too small to explain observations, and therefore new mechanisms to generate primordial helicity are required.
Electroweak phase transitionVoid magnetic fieldsMagnetic energyMagnetic helicityCoherence lengthRecombinationHorizonMagnetic field strengthElectroweak baryogenesisBubble wall...
• #### Magnetohydrodynamics and Solar Physicsver. 2

In this short review, I present some of the recent progresses on the pending questions of solar physics. These questions let us revisit the solar wind, the solar dynamo problem, the dynamics of the photosphere and finally have a glimpse at other solar type stars. Discussing the use of direct numerical simulations in solar physics, I show that the full numerical calculation of the flow in a single supergranule would require more electric power than the luminosity of the sun itself with present computer technology.
StarMagnetic helicityCoronaGranuleNumerical simulationEarthMagnetohydrodynamicsTurbulence modelingIntensityChromosphere...
• #### Hydrodynamics with gauge anomaly: Variational principle and Hamiltonian formulation

We present a variational principle for relativistic hydrodynamics with gauge-anomaly terms for a fluid coupled to an Abelian background gauge field. For this we utilize the Clebsch parametrization of the velocity field. We also set up the Hamiltonian formulation and the canonical framework for the theory. While the equations of motion only involve the density and velocity fields, i.e., the Clebsch potentials only appear in the combination which is the velocity field, the generators of symmetry transformations (including the Hamiltonian) depend explicitly on one of the Clebsch potentials, if the background field is time-dependent. For the special case of time-independent background fields, this feature is absent.
Quantum anomalyGauge transformationPoisson bracketConstitutive relationGauge invarianceQuantum field theoryPerfect fluidPoisson algebraHamiltonian reductionDiffeomorphism...
• #### Sterile neutrino oscillations in core-collapse supernovaever. 3

We have made core-collapse supernova simulations that allow oscillations between electron neutrinos (or their anti particles) with right-handed sterile neutrinos. We have considered a range of mixing angles and sterile neutrino masses including those consistent with sterile neutrinos as a dark matter candidate. We examine whether such oscillations can impact the core bounce and shock reheating in supernovae. We identify the optimum ranges of mixing angles and masses that can dramatically enhance the supernova explosion by efficiently transporting electron anti-neutrinos from the core to behind the shock where they provide additional heating leading to much larger explosion kinetic energies. We show that this effect can cause stars to explode that otherwise would have collapsed. We find that an interesting periodicity in the neutrino luminosity develops due to a cycle of depletion of the neutrino density by conversion to sterile neutrinos that shuts off the conversion, followed by a replenished neutrino density as neutrinos transport through the core.
NeutrinosphereProto-neutron starAntineutrinoForward scatteringNeutrino flavorMikheev-Smirnov-Wolfenstein effectThermalisationCoolingActive neutrinoFree streaming...
• #### $H\rightarrow γγ$ as a Triangle Anomaly: Possible Implications for the Hierarchy Problem

The Standard Model calculation of $H\rightarrow\gamma\gamma$ has the curious feature of being finite but regulator-dependent. While dimensional regularization yields a result which respects the electromagnetic Ward identities, additional terms which violate gauge invariance arise if the calculation is done setting $d=4$. This discrepancy between the $d=4-\epsilon$ and $d=4$ results is recognized as a true ambiguity which must be resolved using physics input; as dimensional regularization respects gauge invariance, the $d=4-\epsilon$ calculation is accepted as the correct SM result. However, here we point out another possibility; working in analogy with the gauge chiral anomaly, we note that it is possible that the individual diagrams do violate the electromagnetic Ward identities, but that the gauge-invariance-violating terms cancel when all contributions to $H\rightarrow\gamma\gamma$, both from the SM and from new physics, are included. We thus examine the consequences of the hypothesis that the $d=4$ calculation is valid, but that such a cancellation occurs. We work in general renormalizable gauge, thus avoiding issues with momentum routing ambiguities. We point out that the gauge-invariance-violating terms in $d=4$ arise not just for the diagram containing a SM $W^{\pm}$ boson, but also for general fermion and scalar loops, and relate these terms to a lack of shift invariance in Higgs tadpole diagrams. We then derive the analogue of "anomaly cancellation conditions", and find consequences for solutions to the hierarchy problem. In particular, we find that supersymmetry obeys these conditions, even if it is softly broken at an arbitrarily high scale.
• #### The C IV forest as a probe of baryon acoustic oscillationsver. 2

In light of recent successes in measuring baryon acoustic oscillations in quasar absorption using the Lyman $\alpha$ (Ly$\alpha$) transition, I explore the possibility of using the 1548\AA\ transition of triply ionized carbon (C IV) as a tracer. While the Ly-alpha forest is a more sensitive tracer of intergalactic gas, it is limited by the fact that it can only be measured in the optical window at redshifts $z > 2$. Quasars are challenging to identify and observe at these high-redshifts, but the C IV forest can be probed down to redshifts $z \approx 1.3$, taking full advantage of the peak in the redshift distribution of quasars that can be targeted with high efficiency. I explore the strength of the C IV absorption signal and show that the absorbing population on the red side of the Ly-alpha emission line is dominated by C IV (and so will dominate over the potential BAO signal of other metals). As a consequence, I argue that forthcoming surveys may have a sufficient increase in quasar number density to offset the lower sensitivity of the C IV forest and provide competitive precision using both the C IV autocorrelation and the C IV-quasar cross-correlation at $< z > \approx 1.6$.
QuasarCosmologyLarge scale structureBaryon acoustic oscillationsAbsorptivityIntergalactic mediumLyman-alpha forestExpansion of the UniverseAbsorption lineLine of sight...
• #### On the core-halo distribution of dark matter in galaxies

We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (`inos') at selected temperatures and degeneracy parameters within general relativity. The most general solutions present, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) a decreasing density distribution $\rho\propto r^{-2}$ leading to flat rotation curves fulfilling the classical Boltzmann statistics. The mass of the inos is determined as an eigenfunction of the mass of the inner quantum cores. We compare and contrast this mass value with the lower limit on the particle mass by Tremaine and Gunn (1979), and show that the latter is approached for the less degenerate quantum cores in agreement with the fixed halo observables. Consequences of this alternative approach to the massive core in SgrA* and to dwarf galaxies are outlined.
Phase space densityDark matter haloBlack holeSpiral galaxyCircular velocityCore radiusParticle massStarPhase spaceGalactic halo...
• #### $\nu=1/2$ Fractional Quantum Hall Effect in Tilted Magnetic Fields

Magnetotransport measurements on two-dimensional electrons confined to wide GaAs quantum wells reveal a remarkable evolution of the ground state at filling factor $\nu=1/2$ as we tilt the sample in the magnetic field. Starting with a compressible state at zero tilt angle, a strong $\nu=1/2$ fractional quantum Hall state appears at intermediate angles. At higher angles an insulating phase surrounds this state and eventually engulfs it at the highest angles. This evolution occurs because the parallel component of the field renders the charge distribution increasingly bilayer-like.
Fractional Quantum Hall EffectGaAs QWsPhase diagramWigner crystalReciprocal spaceFractional quantum Hall stateMoore-Read Pfaffian wavefunctionSuperconductivityLandau levelCompressibility...
• #### Testing X-ray Measurements of Galaxy Cluster Outskirts with Cosmological Simulationsver. 3

The study of galaxy cluster outskirts has emerged as one of the new frontiers in extragalactic astrophysics and cosmology with the advent of new observations in X-ray and microwave. However, the thermodynamic properties and chemical enrichment of this diffuse and azimuthally asymmetric component of the intracluster medium (ICM) are still not well understood. This work, for the first time, systematically explores potential observational biases in these regions. To assess X-ray measurements of galaxy cluster properties at large radii ($>{R}_{500c}$), we use mock Chandra analyses of cosmological galaxy cluster simulations. The pipeline is identical to that used for Chandra observations, but the biases discussed in this paper are relevant for all X-ray observations outside of ${R}_{500c}$. We find the following from our analysis: (1) filament regions can contribute as much as $50\%$ at $R_{200c}$ to the emission measure; (2) X-ray temperatures and metal abundances from model fitted mock X-ray spectra in a multi-temperature ICM respectively vary to the level of $10\%$ and $50\%$; (3) resulting density profiles vary to within $10\%$ out to $R_{200c}$, and gas mass, total mass, and baryon fractions all vary to within a few percent; (4) the bias from a metal abundance extrapolated a factor of five higher than the true metal abundance results in total mass measurements biased high by $20\%$ and total gas measurements biased low by $10\%$; and (5) differences in projection and dynamical state of a cluster can lead to gas density slope measurements that differ by a factor of $15\%$ and $30\%$, respectively. The presented results can partially account for some of the recent gas profile measurements in cluster outskirts by, e.g., Suzaku. Our findings are pertinent to future X-ray cosmological constraints from cluster outskirts.
AbundanceLine of sightTemperature profileAccretionX-ray spectrumHydrostatic massSystematic errorOutskirt of a galaxy clusterCoolingRelaxation...
• #### The Dark Matter Halos of Moderate Luminosity X-ray AGN as Determined from Weak Gravitational Lensing and Host Stellar Masses

Understanding the relationship between galaxies hosting active galactic nuclei (AGN) and the dark matter halos in which they reside is key to constraining how black-hole fueling is triggered and regulated. Previous efforts have relied on simple halo mass estimates inferred from clustering, weak gravitational lensing, or halo occupation distribution modeling. In practice, these approaches remain uncertain because AGN, no matter how they are identified, potentially live a wide range of halo masses with an occupation function whose general shape and normalization are poorly known. In this work, we show that better constraints can be achieved through a rigorous comparison of the clustering, lensing, and cross-correlation signals of AGN hosts to a fiducial stellar-to-halo mass relation (SHMR) derived for all galaxies. Our technique exploits the fact that the global SHMR can be measured with much higher accuracy than any statistic derived from AGN samples alone. Using 382 moderate luminosity X-ray AGN at z<1 from the COSMOS field, we report the first measurements of weak gravitational lensing from an X-ray selected sample. Comparing this signal to predictions from the global SHMR, we find that, contrary to previous results, most X-ray AGN do not live in medium size groups ---nearly half reside in relatively low mass halos with Mh~10^12.5 Msun. The AGN occupation function is well described by the same form derived for all galaxies but with a lower normalization---the fraction of halos with AGN in our sample is a few percent. By highlighting the relatively "normal" way in which moderate luminosity X-ray AGN hosts occupy halos, our results suggest that the environmental signature of distinct fueling modes for luminous QSOs compared to moderate luminosity X-ray AGN is less obvious than previously claimed.
Halo Occupation DistributionMock catalogWeak lensingLensing signalAccretionHost galaxyGalaxy galaxy lensingDark matterBlack holeObscured AGN...
• #### Be-CoDiS: An epidemiological model to predict the risk of human diseases spread worldwide. Application to the 2014 Ebola Virus Disease epidemic

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the national and international health authorities due to important outbreaks concurring in some Western African countries and possible spread to other continents, which has already occurred in the USA and Spain. Regarding the emergency of this situation, there is a need of development of decision tools to help the authorities to focus their efforts in important factors that can help to eradicate Ebola. Mathematical modeling and, more precisely, epidemiological modeling can help to predict the possible evolution of the Ebola outbreaks and to give some recommendations in the region to be prioritized for surveillance. In this work, we present a first formulation of a new spatial-temporal epidemiological model, called Be-CoDiS (Between-COuntries Disease Spread), based on the combination of a deterministic Individual-Based model (modelling the interaction between countries, considered as individual) for between country spread with a deterministic compartmental model, based on ordinary differential equations, for within-country spread. The goal is to simulate the spread of a particular disease and identify risk zones worldwide. This model is a particular adaptation of a previous epidemiological software, called Be-FAST, used to predict the spatial spread of animal diseases. The main interesting characteristics of Be-CoDiS are the consideration of migratory flux between countries, control measure effects and time dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model. Next, to validate our approach, we consider various numerical experiments regarding the 2014 Ebola epidemic. The results are compared to current data and other models outputs found in literature. Finally, a parameter sensitivity analysis is done.
HorizonLeast squaresClimateEbola VirusHuman diseasesEpidemiological modelingBetweenness centralityNumerical simulationClassificationNonlinear regression...
• #### On the Feasibility and Implications of Self-Contained Search Engines in the Browser

JavaScript engines inside modern browsers are capable of running sophisticated multi-player games, rendering impressive 3D scenes, and supporting complex, interactive visualizations. Can this processing power be harnessed for information retrieval? This paper explores the feasibility of building a JavaScript search engine that runs completely self-contained on the client side within the browser---this includes building the inverted index, gathering terms statistics for scoring, and performing query evaluation. The design takes advantage of the IndexDB API, which is implemented by the LevelDB key-value store inside Google's Chrome browser. Experiments show that although the performance of the JavaScript prototype falls far short of the open-source Lucene search engine, it is sufficiently responsive for interactive applications. This feasibility demonstration opens the door to interesting applications in offline and private search across multiple platforms as well as hybrid split-execution architectures whereby clients and servers collaboratively perform query evaluation. One possible future scenario is the rise of an online search marketplace in which commercial search engine companies and individual users participate as rational economic actors, balancing privacy, resource usage, latency, and other factors based on customizable utility profiles.
• #### Bayes-X: a Bayesian inference tool for the analysis of X-ray observations of galaxy clustersver. 2

We present the first public release of our Bayesian inference tool, Bayes-X, for the analysis of X-ray observations of galaxy clusters. We illustrate the use of Bayes-X by analysing a set of four simulated clusters at z=0.2-0.9 as they would be observed by a Chandra-like X-ray observatory. In both the simulations and the analysis pipeline we assume that the dark matter density follows a spherically-symmetric Navarro, Frenk and White (NFW) profile and that the gas pressure is described by a generalised NFW (GNFW) profile. We then perform four sets of analyses. By numerically exploring the joint probability distribution of the cluster parameters given simulated Chandra-like data, we show that the model and analysis technique can robustly return the simulated cluster input quantities, constrain the cluster physical parameters and reveal the degeneracies among the model parameters and cluster physical parameters. We then analyse Chandra data on the nearby cluster, A262, and derive the cluster physical profiles. To illustrate the performance of the Bayesian model selection, we also carried out analyses assuming an Einasto profile for the matter density and calculated the Bayes factor. The results of the model selection analyses for the simulated data favour the NFW model as expected. However, we find that the Einasto profile is preferred in the analysis of A262. The Bayes-X software, which is implemented in Fortran 90, is available at http://www.mrao.cam.ac.uk/facilities/software/bayesx/.
TelescopesPressure profilePrior probabilityCluster of galaxiesBayesian evidenceNavarro-Frenk-White profileAbundanceLine emissionEffective areaContinuum emission...
• #### Word Storms: Multiples of Word Clouds for Visual Comparison of Documents

Word clouds are a popular tool for visualizing documents, but they are not a good tool for comparing documents, because identical words are not presented consistently across different clouds. We introduce the concept of word storms, a visualization tool for analysing corpora of documents. A word storm is a group of word clouds, in which each cloud represents a single document, juxtaposed to allow the viewer to compare and contrast the documents. We present a novel algorithm that creates a coordinated word storm, in which words that appear in multiple documents are placed in the same location, using the same color and orientation, in all of the corresponding clouds. In this way, similar documents are represented by similar-looking word clouds, making them easier to compare and contrast visually. We evaluate the algorithm in two ways: first, an automatic evaluation based on document classification; and second, a user study. The results confirm that unlike standard word clouds, a coordinated word storm better allows for visual comparison of documents.
ClassificationPolymersTerm frequencyCosine similarityInformation and communication technologiesDimensional ReductionSubcategorySupport vector machineOverfittingOrientation...
• #### CMB constraints on mass and coupling constant of light pseudoscalar particlesver. 3

Transformation of CMB photons into light pseudoscalar particles at post big bang nucleosynthesis epoch is considered. Using the present day value of a large scale magnetic field to estimate it at earlier cosmological epochs, the oscillation probability of photons into light pseudoscalar particles with an account of coherence breaking in cosmological plasma is calculated. Demanding that the photon transformation does not lead to an exceedingly large CMB spectral distortion and temperature anisotropy, the constraints on the coupling constant of axion like particles to photons, $g_{\phi\gamma} B \lesssim (10^{-15} - 10^{-12}) \textrm{nG}\times \textrm{GeV}^{-1}$, are found for the axion like particle mass in the interval $10^{-25}$ eV $\lesssim m_{\phi}\lesssim 10^{-5}$ eV, where $B$ is the strength of the large scale magnetic field at the present time. Our results update the previously obtained ones since we use the density matrix formalism which is more accurate than the wave function approximation for the description of oscillations with an essential coherence breaking. In the axion like particle mass range $10^{-25}$ eV $\lesssim m_{\phi}\lesssim 10^{-14}$ eV, weaker limits, by at least 2 orders of magnitude $g_{\phi\gamma} B \lesssim 10^{-11}\textrm{nG}\times \textrm{GeV}^{-1}$, are obtained in comparison with the wave function approximation. In the mass range $10^{-14}$ eV $\lesssim m_{\phi}\lesssim 10^{-5}$ eV, on the other hand, limits that are stronger, by more than an order of magnitude are obtained. Our results are derived by using upper limits on spectral distortion parameter $\mu$ and temperature anisotropy $\Delta T/T$ found by COBE and expected sensitivities by PIXIE/PRISM.
Axion-like particleIndex of refractionALP parameter spaceCompton scatteringIonization fractionAbsorptivityAxionKinetic equationQuantum electrodynamicsBig bang nucleosynthesis...
• #### Evolution equations beyond one loop from conformal symmetry

We study implications of exact conformal invariance of scalar quantum field theories at the critical point in non-integer dimensions for the evolution kernels of the light-ray operators in physical (integer) dimensions. We demonstrate that all constraints due the conformal symmetry are encoded in the form of the generators of the collinear sl(2) subgroup. Two of them, S_- and S_0, can be fixed at all loops in terms of the evolution kernel, while the generator of special conformal transformations, S_+, receives nontrivial corrections which can be calculated order by order in perturbation theory. Provided that the generator S_+ is known at the k-1 loop order, one can fix the evolution kernel in physical dimension to the k-loop accuracy up to terms that are invariant with respect to the tree-level generators. The invariant parts can easily be restored from the anomalous dimensions. The method is illustrated on two examples: The O(n)-symmetric phi^4 theory in d=4 to the three-loop accuracy, and the su(n) matrix phi^3 theory in d=6 to the two-loop accuracy. We expect that the same technique can be used in gauge theories e.g. in QCD.
Anomalous dimensionEvolution equationConformal invarianceSubgroupPerturbation theorySpecial conformal transformationCritical pointConformal symmetryQuantum field theoryGauge theory...