- This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between frequentism and Bayesianism fundamentally stem from differing definitions of probability, a philosophical divide which leads to distinct approaches to the solution of statistical problems as well as contrasting ways of asking and answering questions about unknown parameters. After an example-driven discussion of these differences, we briefly compare several leading Python statistical packages which implement frequentist inference using classical methods and Bayesian inference using Markov Chain Monte Carlo.Confidence intervalMonte Carlo Markov chainFrequentist approachNuisance parameterMaximum likelihoodPoint estimationStarBayesian approachPythonAlice and Bob...
- Galaxy clusters exhibit remarkable self-similar behavior which allows us to establish simple scaling relationships between observable quantities and cluster masses, making galaxy clusters useful cosmological probes. Recent X-ray observations suggest that self-similarity may be broken in the outskirts of galaxy clusters. In this work, we analyze a mass-limited sample of massive galaxy clusters from the Omega500 cosmological hydrodynamic simulation to investigate the self-similarity of the diffuse X-ray emitting intracluster medium (ICM) in the outskirts of galaxy clusters. We find that the self-similarity of the outer ICM profiles is better preserved if they are normalized with respect to the mean density of the universe, while the inner profiles are more self-similar when normalized using the critical density. However, the outer ICM profiles as well as the location of accretion shock around clusters are sensitive to their mass accretion rate, which causes the apparent breaking of self-similarity in cluster outskirts. We also find that the collisional gas does not follow the distribution of collisionless dark matter perfectly in the infall regions of galaxy clusters, leading to 10% departures in the gas-to-dark matter density ratio from the cosmic mean value. Our results have a number implications for interpreting observations of galaxy clusters in X-ray and through the Sunyaev-Zel'dovich effect and their application to cluster cosmology.Dark matterEntropy profileEntropyRadial velocityThermalisationGalaxy filamentPressure profileRadial velocity profileCluster of galaxiesCluster sampling...
- Theoretical models for the production of relativistic jets from active galactic nuclei predict that jet power arises from the spin and mass of the central black hole, as well as the magnetic field near the event horizon. The physical mechanism mechanism underlying the contribution from the magnetic field is the torque exerted on the rotating black hole by the field amplified by the accreting material. If the squared magnetic field is proportional to the accretion rate, then there will be a correlation between jet power and accretion luminosity. There is evidence for such a correlation, but inadequate knowledge of the accretion luminosity of the limited and inhomogeneous used samples prevented a firm conclusion. Here we report an analysis of archival observations of a sample of blazars (quasars whose jets point towards Earth) that overcomes previous limitations. We find a clear correlation between jet power as measured through the gamma-ray luminosity, and accretion luminosity as measured by the broad emission lines, with the jet power dominating over the disk luminosity, in agreement with numerical simulations. This implies that the magnetic field threading the black hole horizon reaches the maximum value sustainable by the accreting matter.Flat spectrum radio quasarAccretionAstrophysical jetEGRETMagnetic energyLorentz factorBlack hole spinBroad-line regionSpectral energy distributionActive Galactic Nuclei...
- The measurement of the Higgs mass at the LHC has confirmed that the Standard Model electroweak vacuum is a shallow local minimum and is not absolutely stable. In addition to a probable unacceptably fast tunneling to the deep true minimum, it is not clear how the observable present-day vacuum could be reached from the early Universe particularly following inflation. In this note it is shown that these problems can be alleviated if the Higgs field is non-minimally coupled to a higher-curvature theory of gravity which is effective in deriving inflation a la Starobinsky. Moreover, it implies that the Higgs self-coupling could be enhanced and have an observable effect at the next generation of particle colliders.Standard ModelPlanck scaleEinstein frameHiggs potentialPlanck missionHiggs bosonMixing angleE-foldingScalar fieldHiggs quartic coupling...
- Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigation. This paper considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior from any fixed prior is asymptotically normal; its mean shrinks toward the true parameter values, and its variance approaches that of the maximum empirical likelihood estimator. A more interesting case can be made for the Bayesian empirical likelihood when informative priors are used to explore commonality across quantiles. Regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas (e.g., high or low percentile levels). Through empirical likelihood, the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains. By using an MCMC algorithm in the computation, we avoid the daunting task of directly maximizing empirical likelihood. The finite sample performance of the proposed method is investigated empirically, where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels. A theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method.Bayesian approachClimateFrequentist approachStatisticsEstimating equationsCoverage probabilityIndicator functionUniform convergenceWettingCovariance...
- I apply FDR -- a recently introduced Four Dimensional Regularization approach to quantum field theories -- to compute the NLO QCD corrections to H -> gg in the large top mass limit. The calculation involves all key ingredients of massless QCD, namely ultraviolet, infrared and collinear divergences, besides alpha_s renormalization. I show in detail how the correct result emerges in FDR, and discuss the translation rules to dimensional regularization.Dimensional ReductionQuantum field theoryPhase spaceFDRStrong coupling constantPartonInfrared divergenceGauge invarianceFeynman rulesTransition rule...
- The Standard Model of particle physics is still lacking an understanding of the generation and nature of neutrino masses. A favorite theoretical scenario (the see-saw mechanism) is that both Dirac and Majorana mass terms are present, leading to the existence of heavy partners of the light neutrinos, presumably massive and nearly sterile. These heavy neutrinos can be searched for at high energy lepton colliders of very high luminosity, such as the Future electron-positron e+e- Circular Collider, FCC-ee (TLEP), presently studied within the Future Circular Collider design study at CERN, as a possible first step. A first look at sensitivities, both from neutrino counting and from direct search for heavy neutrino decay, are presented. The number of neutrinos should be measurable with a precision between 0.001 - 0.0004, while the direct search appears very promising due to the long lifetime of heavy neutrinos for small mixing angles. A sensitivity down to a heavy-light mixing of 10^{-12} is obtained, covering a large phase-space for heavy neutrino masses between 10 and 80 GeV/c2.Sterile neutrinoNeutrinoColliderTLEP experimentMixing angleCERNNeutrino massStandard ModelLuminosityMajorana mass...
- Observations of the redshifted 21 cm line from neutral hydrogen will open a new window on the early Universe. By influencing the thermal and ionization history of the intergalactic medium (IGM), annihilating dark matter (DM) can leave a detectable imprint in the 21 cm signal. Building on the publicly available 21cmFAST code, we compute the 21 cm signal for a 10 GeV WIMP DM candidate. The most pronounced role of DM annihilations is in heating the IGM earlier and more uniformly than astrophysical sources of X-rays. This leaves several unambiguous, qualitative signatures in the redshift evolution of the large-scale ($k\approx0.1$ Mpc$^{-1}$) 21 cm power amplitude: (i) the local maximum (peak) associated with IGM heating can be lower than the other maxima; (ii) the heating peak can occur while the IGM is in emission against the cosmic microwave background (CMB); (iii) there can be a dramatic drop in power (a global minimum) corresponding to the epoch when the IGM temperature is comparable to the CMB temperature. These signatures are robust to astrophysical uncertainties, and will be easily detectable with second generation interferometers. We also briefly show that decaying warm dark matter has a negligible role in heating the IGM.GalaxyIntergalactic mediumCoolingCosmologyAbsorptivityAstronomical X-ray sourceKinetic temperatureDark AgesReionizationHydrogen 21 cm line...
- The oscillation of the CMB photons into axions can cause CMB spectral distortion in the presence of large scale magnetic field. With the COBE limit on the $\mu$ parameter and a homogeneous magnetic field with strength $B\lesssim 3.2$ nG at the horizon scale, stronger lower limit on the axion mass in comparison with the limit of the ADMX experiment is found to be, $4.8\times 10^{-5}$ eV $\lesssim m_a$ for the KSVZ axion model. On the other hand, using the experimental limit on the axion mass $3.5\times 10^{-6}$ eV $\lesssim m_a$ from the ADMX experiment together with the COBE bound on $\mu$, is found $B\lesssim 53$ nG for the KSVZ axion model and $B\lesssim 141$ nG for DFSZ axion model, for a homogeneous magnetic field with coherence length at the present epoch $\lambda_B\sim 1.3$ Mpc. Limits on $B$ and $m_a$ for PIXIE/PRISM expected sensitivity on $\mu$ are derived. If CMB $\mu$ distortion would be detected by the future space missions PIXIE/PRISM and assuming that the strength of the large scale magnetic field is close to its canonical value, $B\sim 1-3$ nG, axions in the mass range $2\, \mu$eV - $3\, \mu$eV would be potential candidates of CMB $\mu$-distortion.Magnetic field strengthFaraday rotationIndex of refractionCMB temperature anisotropyCosmologyAxion modelCoupling constantQuantum electrodynamicsAxionFaraday effect...
- Evidence of a heavy neutrino, $\nu_H$, in the $K^+\to\mu^+\nu_H$ decays was sought using the E949 experimental data with an exposure of $1.70\times 10^{12}$ stopped kaons. With the major background from the radiative $K^+\to\mu^+\nu_\mu\gamma$ decay understood and suppressed, upper limits (90% C.L.) on the neutrino mixing matrix element between muon and heavy neutrino, $|U_{\mu H}|^2$, were set at the level of $10^{-7}$ to $10^{-9}$ for the heavy neutrino mass region 175 to 300 MeV/$c^2$.PionKaonBranching ratioStatisticsMonte Carlo methodScintillationStandard ModelKinematicsKaon decayBig bang nucleosynthesis...
- Both observations and modelling of magnetic fields in the diffuse interstellar gas of spiral galaxies are well developed but the theory has been confronted with observations for only a handful of individual galaxies. There is now sufficient data to consider statistical properties of galactic magnetic fields. We have collected data from the literature on the magnetic fields and interstellar media (ISM) of 20 spiral galaxies, and tested for various physically motivated correlations between magnetic field and ISM parameters. Clear correlations emerge between the total magnetic field strength and molecular gas density as well as the star formation rate. The magnetic pitch angle exhibits correlations with the total gas density, the star formation rate and the strength of the axisymmetric component of the mean magnetic field. The total and mean magnetic field strengths exhibit noticeable degree of correlation, suggesting a universal behaviour of the degree of order in galactic magnetic fields. We also compare the predictions of galactic dynamo theory to observed magnetic field parameters and identify directions in which theory and observations might be usefully developed.Mean fieldSteady stateTurbulenceSpiral armHelicityAzimuthDifferential rotationMagnetic helicityCompressibilityIntensity...
- NeutrinoInterferenceGauge fieldLepton numberWeak neutral current interactionLeptonic model of particle accelerationCharged currentSterile neutrinoElectronParticles...
- Semileptonic decayTau leptonParity violationChiralityChiral modelDalitz plotMassLeptonsP-symmetryVector...
- The spectral functions of the vector current and the axial-vector current have been measured in hadronic tau decays using the OPAL detector at LEP. Within the framework of the Operator Product Expansion a simultaneous determination of the strong coupling constant alpha_s, the non-perturbative operators of dimension 6 and 8 and of the gluon condensate has been performed. Different perturbative descriptions have been compared to the data. The Contour Improved Fixed Order Perturbation Theory gives alpha_s(mtau**2) = 0.348 +- 0.009 +- 0.019 at the tau-mass scale and alpha_s(mz**2) = 0.1219 +- 0.0010 +- 0.0017 at the Z-mass scale. The values obtained for alpha_s(mz**2) using Fixed Order Perturbation Theory or Renormalon Chain Resummation are 2.3% and 4.1% smaller, respectively. The running of the strong coupling between s_0 ~1.3 GeV**2 and s_0 = mtau**2 has been tested from direct fits to the integrated differential hadronic decay rate R_tau. A test of the saturation of QCD sum rules at the tau-mass scale has been performed.Monte Carlo methodRegularizationBranching ratioStatisticsSystematic errorQuantum chromodynamicsPionRenormalization schemeQuark massPerturbative QCD...
- We predict the spatial distribution and number of Milky Way dwarf galaxies to be discovered in the DES and LSST surveys, by completeness correcting the observed SDSS dwarf population. We apply most massive in the past, earliest forming, and earliest infall toy models to a set of dark matter-only simulated Milky Way/M31 halo pairs from Exploring the Local Volume In Simulations (ELVIS). The observed spatial distribution of Milky Way dwarfs in the LSST-era will discriminate between the earliest infall and other simplified models for how dwarf galaxies populate dark matter subhalos. Inclusive of all toy models and simulations, at 90% confidence we predict a total of 37-114 L $\gtrsim 10^3$L$_{\odot}$ dwarfs and 131-782 L $\lesssim 10^3$L$_{\odot}$ dwarfs within 300 kpc. These numbers of L $\gtrsim 10^3$L$_{\odot}$ dwarfs are dramatically lower than previous predictions, owing primarily to our use of updated detection limits and the decreasing number of SDSS dwarfs discovered per sky area. For an effective $r_{\rm limit}$ of 25.8 mag, we predict: 3-13 L $\gtrsim 10^3$L$_{\odot}$ and 9-99 L $\lesssim 10^3$L$_{\odot}$ dwarfs for DES, and 18-53 L $\gtrsim 10^3$L$_{\odot}$ and 53-307 L $\lesssim 10^3$L$_{\odot}$ dwarfs for LSST. These enormous predicted ranges ensure a coming decade of near-field excitement with these next generation surveys.Dark matter subhaloMilky WayA dwarfsUltra-faint dwarf spheroidal galaxyGalaxyAzimuthStatisticsStarAndromeda galaxyInfall model...
- In the present paper, we studied by means of the SIM introduced in Del Popolo (2009), the total and DM density profiles, and the correlations among different quantities, observed by Newman et al. (2012a,b), in seven massive and relaxed clusters, namely MS2137, A963, A383, A611, A2537, A2667, A2390. Similarly to Newman et al. (2012a,b), the total density profile, in the radius range 0.003 - 0.03$r_{200}$, has a mean total density profile in agreement with dissipationless simulations. The slope of the DM profiles of all clusters is flatter than -1. The slope, $\alpha$, has a maximum value (including errors) of $\alpha=-0.88$ in the case of A2390, and minimum value $\alpha=-0.14$ for A2537. The baryonic component dominates the mass distribution at radii $< 5-10$ kpc, while the outer distribution is dark matter dominated. We found an anti-correlation among the slope $\alpha$, the effective radius, $R_e$, and the BCG mass, and a correlation among the core radius $r_{core}$, and $R_e$. Moreover, the mass in 100 kpc (mainly dark matter) is correlated with the mass inside 5 kpc (mainly baryons). The behavior of the total mass density profile, the DM density profile, and the quoted correlations can be understood in a double phase scenario. In the first dissipative phase the proto-BCG forms, and in the second dissipationless phase, dynamical friction between baryonic clumps (collapsing to the center) and the DM halo flattens the inner slope of the density profile. In simple terms, the large scatter in the inner slope from cluster to cluster, and the anti-correlation among the slope, $\alpha$ and $R_e$ is due to the fact that in order to have a total mass density profile which is NFW-like, clusters having more massive BCGs at their centers must contain less DM in their center. Consequently the inner profile has a flatter slope.Baryon contentNavarro-Frenk-White profileCluster of galaxiesAbell 383GalaxyStarVirial massAdiabatic contraction of dark matterN-body simulationDM mass...
- By considering the kinetic equations for the relic particles and the bath particles supposed in thermal and chemical equilibrium in the early Universe, we show that the problem of finding the present relic abundance is exactly defined by a system of two equations, the usual Boltzmann equation and a new one previously not recognized. The analytical solution of the latter gives the abundance down to a matching temperature that can be identified with freeze out temperature $x_f=m/T_f$, while the usual Boltzmann equation is valid only for $x \ge x_f$. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result and not the consequence of the so called freeze out approximation. We also suggest an analytical approximation that furnishes the relic abundance accurate at the level of $1\%-2\%$ in the case of $S$-wave and $P$-wave scattering cross sections.Weakly interacting massive particleStatisticsRelic abundanceDegree of freedomFreeze-outEntropyDark matterAbundanceStandard ModelBoltzmann transport equation...
- Observations of interstellar clouds that cast shadows in the soft X-ray background can be used to separate the background Galactic halo emission from the local emission due to solar wind charge exchange (SWCX) and/or the Local Bubble (LB). We present an XMM-Newton observation of a shadowing cloud, G225.60-66.40, that is sufficiently compact that the on- and off-shadow spectra can be extracted from a single field of view (unlike previous shadowing observations of the halo with CCD-resolution spectrometers, which consisted of separate on- and off-shadow pointings). We analyzed the spectra using a variety of foreground models: one representing LB emission, and two representing SWCX emission. We found that the resulting halo model parameters (temperature $T_h \approx 2 \times 10^6$ K, emission measure $E_h \approx 4 \times 10^{-3}$ cm$^{-6}$ pc) were not sensitive to the foreground model used. This is likely due to the relative faintness of the foreground emission in this observation. However, the data do favor the existence of a foreground. The halo parameters derived from this observation are in good agreement with those from previous shadowing observations, and from an XMM-Newton survey of the Galactic halo emission. This supports the conclusion that the latter results are not subject to systematic errors, and can confidently be used to test models of the halo emission.Solar windSurface brightnessSoft X-ray backgroundAbundanceThermalisationIntensityScience analysis systemCollisional ionization equilibriumAtomDBSpectral analysis...
- Warm dark matter (WDM) has been proposed as an alternative to cold dark matter (CDM), to resolve issues such as the apparent lack of satellites around the Milky Way. Even if WDM is not the answer to observational issues, it is essential to constrain the nature of the dark matter. The effect of WDM on haloes has been extensively studied, but the small-scale initial smoothing in WDM also affects the present-day cosmic web and voids. It suppresses the cosmic "sub-web" inside voids, and the formation of both void haloes and subvoids. In N-body simulations run with different assumed WDM masses, we identify voids with the zobov algorithm, and cosmic-web components with the origami algorithm. As dark-matter warmth increases, the initial-conditions smoothing increases, and the number of voids and subvoids is suppressed. Also, void density profiles change, their shapes become flatter inside the void radius, while edges of the voids remain unchanged. Also, filaments and walls become cleaner, as the sub-structures in between have been smoothed out; this leads to a clear, mid-range peak in the density PDF. These distinct features of voids make them possible observational indicators of the warmth of dark matter.Dark matterWDM particlesGalaxyWarm dark matterThermalisationAbundanceCosmologyStructure formationRedshift-space distortionLambda-CDM model...
- This is a review of particle-theory models of inflation, and of their predictions for the primordial density perturbation that is thought to be the origin of structure in the Universe. It contains mini-reviews of the relevant observational cosmology, of elementary field theory and of supersymmetry, that may be of interest in their own right. The spectral index $n(k)$, specifying the scale-dependence of the spectrum of the curvature perturbation, will be a powerful discriminator between models, when it is measured by Planck with accuracy $\Delta n\sim 0.01$. The usual formula for $n$ is derived, as well as its less familiar extension to the case of a multi-component inflaton; in both cases the key ingredient is the separate evolution of causally disconnected regions of the Universe. Primordial gravitational waves will be an even more powerful discriminator if they are observed, since most models of inflation predict that they are completely negligible. We treat in detail the new wave of models, which are firmly rooted in modern particle theory and have supersymmetry as a crucial ingredient. The review is addressed to both astrophysicists and particle physicists, and each section is fairly homogeneous regarding the assumed background knowledge.HorizonInflatonSlow rollSlow-roll inflationCosmic Background ExplorerSupergravityGravitational waveVacuum expectation valueScalar fieldHubble time...
- Neutron stars undergoing r-mode oscillation emit gravitational radiation that might be detected on earth. For known millisecond pulsars the observed spindown rate imposes an upper limit on the possible gravitational wave signal of these sources. Taking into account the physics of r-mode evolution, we show that only sources spinning at frequencies above a few hundred Hertz can be unstable to r-modes, and we derive a more stringent universal r-mode spindown limit on their gravitational wave signal, exploiting the fact that the r-mode saturation amplitude is insensitive to the structural properties of individual sources. We find that this refined bound limits the gravitational wave strain from millisecond pulsars to values below the detection sensitivity of next-generation detectors. Young sources are therefore a more promising option for the detection of gravitational waves emitted by r-modes and to probe the interior composition of compact stars in the near future.StarCoolingRadio pulsarPulsarInstabilityDissipationLaser Interferometer Gravitational-Wave ObservatorySteady stateAccretionMode coupling...
- In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount --- or even presence --- of quark matter inside the stars.PolytropesEffective field theoryCompact starChiralitySolar massNuclear matterFirst-order phase transitionsBaryon chemical potentialSpeed of soundMassive stars...
- There is very strong circumstantial evidence that there was an inflationary epoch very early in the history of the universe. In this lecture I will describe how we might be able to piece together some understanding of the dynamics during and immediately after the inflationary epoch.InflatonReheatingDark matterReheating temperatureAbundanceThermalisationScalar fieldInflaton potentialHubble radiusModel of inflation...
- Quantum trajectories and superoperator algorithms implemented within the matrix product state (MPS) framework are powerful tools to simulate the real-time dynamics of open dissipative quantum systems. As for the unitary case, the reachable time-scales as well as system sizes are limited by the (possible) build-up of entanglement entropy. The aforementioned methods constitute complementary approaches how Lindblad master equations can be integrated relying either on a quasi-exact representation of the full density matrix or a stochastic unraveling of the density matrix in terms of pure states. In this work, we systematically benchmark both methods by studying the dynamics of a Bose-Hubbard chain in the presence of local as well as global dephasing. The build-up as well as system-size scaling of entanglement entropy strongly depends on the method and the parameter regime and we discuss the applicability of the methods for these cases as well as study the distribution of observables and time discretization errors that can become a limiting factor for global dissipation.EntropyEntanglementSteady stateOperator spaceThermalisationMixed statesHamiltonianBosonizationQuenchingExpectation Value...
- Dwarf spheroidal (dSph) galaxies are among the most promising targets for the indirect detection of dark matter (DM) from annihilation and/or decay products. Empirical estimates of their DM content - and hence the magnitudes of expected signals - rely on inferences from stellar-kinematic data. However, various kinematic analyses can give different results and it is not obvious which are most reliable. Using extensive sets of mock data of various sizes (mimicking 'ultra-faint' and 'classical' dSphs) and an MCMC engine, here we investigate biases, uncertainties, and limitations of analyses based on parametric solutions to the spherical Jeans equation. For a variety of functional forms for the tracer and DM density profiles, as well as the orbital anisotropy profile, we examine reliability of estimates for the astrophysical J- and D-factors for annihilation and decay, respectively. For large (N > 1000) stellar-kinematic samples typical of 'classical' dSphs, errors tend to be dominated by systematics, which can be reduced through the use of sufficiently general and flexible functional forms. For small (N < 100) samples typical of 'ultrafaints', statistical uncertainties tend to dominate systematic errors and flexible models are less necessary. We define an optimal strategy that would mitigate sensitivity to priors and other aspects of analyses based on the spherical Jeans equation. We also find that the assumption of spherical symmetry can bias estimates of J (with the 95% credibility intervals not encompassing the true J-factor) when the object is mildly triaxial (axis ratios b/a = 0.8, c/a = 0.6). A concluding table summarises the typical error budget and biases for the different sample sizes considered.Dark Matter Density ProfileDwarf spheroidal galaxyDark matter haloVelocity dispersionOrientationVelocity dispersion profileStarInner slopeEinasto profileClassical dwarf spherodial galaxy...
- A family of random models for bosonic quasi-particle excitations, e.g. the vibrations of a disordered solid, is introduced. The generator of the linearized phase space dynamics of these models is the sum of a deterministic and a random part. The former may describe any model of N identical phonon bands, while the latter is a d-dimensional generalization of the random matrix model of Lueck, Sommers, and Zirnbauer (LSZ). The models are constructed so as to exclude the unphysical occurrence of runaway solutions. By using the Efetov-Wegner supersymmetry method in combination with the new technique of superbosonization, the disordered boson model is cast in the form of a supermatrix field theory. A self-consistent approximation of mean-field type arises from treating the field theory as a variational problem. The resulting scheme, referred to as a coherent potential approximation, becomes exact for large values of N. In the random-matrix limit, agreement with the results of LSZ is found. The self-consistency equation for the full d-dimensional problem is solved numerically.SymplectizationEigenvalueHamiltonianSaddle pointRandom phase approximationVector spaceDensity of statesEllipticitySuperspaceTime-reversal symmetry...
- The classical Cartan-Helgason theorem characterises finite-dimensional spherical representations of reductive Lie groups in terms of their highest weights. We generalise the theorem to the case of a reductive symmetric supergroup pair $(G,K)$ of even type. Along the way, we compute the Harish-Chandra $c$-function of the symmetric superspace $G/K$. By way of an application, we show that all spherical representations are self-dual in type AIII|AIII.SupergroupSuperspaceLie group
- The compact remnants of core collapse supernovae - neutron stars and black holes - have properties that reflect both the structure of their stellar progenitors and the physics of the explosion. In particular, the masses of these remnants are sensitive to the density structure of the presupernova star and to the explosion energy. To a considerable extent, the final mass is determined by the ``fallback'', during the explosion, of matter that initially moves outwards, yet ultimately fails to escape. We consider here the simulated explosion of a large number of massive stars (10 to 100 \Msun) of Population I (solar metallicity) and III (zero metallicity), and find systematic differences in the remnant mass distributions. As pointed out by Chevalier(1989), supernovae in more compact progenitor stars have stronger reverse shocks and experience more fallback. For Population III stars above about 25 \Msun and explosion energies less than $1.5 \times 10^{51}$ erg, black holes are a common outcome, with masses that increase monotonically with increasing main sequence mass up to a maximum hole mass of about 35 \Msun. If such stars produce primary nitrogen, however, their black holes are systematically smaller. For modern supernovae with nearly solar metallicity, black hole production is much less frequent and the typical masses, which depend sensitively on explosion energy, are smaller. We explore the neutron star initial mass function for both populations and, for reasonable assumptions about the initial mass cut of the explosion, find good agreement with the average of observed masses of neutron stars in binaries. We also find evidence for a bimodal distribution of neutron star masses with a spike around 1.2 \Msun (gravitational mass) and a broader distribution peaked around 1.4 \Msun.StarBlack holeNeutron starSupernovaPopulation IIIReverse shockAccretionSupernova progenitorsMassive starsWolf-Rayet star...
- We ask whether the universe can be a patchwork consisting of distinct regions of matter and antimatter. We demonstrate that, after recombination, it is impossible to avoid annihilation near regional boundaries. We study the dynamics of this process to estimate two of its signatures: a contribution to the cosmic diffuse gamma-ray background and a distortion of the cosmic microwave background. The former signal exceeds observational limits unless the matter domain we inhabit is virtually the entire visible universe. On general grounds, we conclude that a matter-antimatter symmetric universe is empirically excluded.Cosmic microwave backgroundCosmological parametersCosmologyVoidTurbulenceSpace debrisTemperature profileIonizationFluid dynamicsStructure formation...
- We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for Renyi entanglement entropies of a one-dimensional gas trapped by a harmonic potential in all the relevant scaling regimes. We confirm our findings with accurate numerical calculations obtained by means of an ingenious discretisation of the reduced correlation matrix.EntropyRandom matrixFermi gasEigenvalueHomogenizationEntanglementFree fermionsGaussian Unitary EnsembleTwo-point correlation functionConformal field theory...
- This lecture discusses the physics implemented by Monte Carlo event generators for hadron colliders. It details the construction of parton showers and the matching of parton showers to fixed-order calculations at higher orders in perturbative QCD. It also discusses approaches to merge calculations for a varying number of jets, the interface to the underlying event and hadronization.Phase spaceQuantum chromodynamicsQuarkMonte Carlo methodKinematicsColor chargeDifferential cross sectionUnitarityInvariant massHadronic model of particle acceleration...
- Accurately predicting structural properties of dark matter halos is one of the fundamental goals of modern cosmology. We use the new suite of MultiDark cosmological simulations to study the evolution of dark matter halo density profiles, concentrations, and velocity anisotropies. The MultiDark simulations cover a large range of masses 1e10-1e15Msun and volumes upto 50Gpc**3. The total number of dark matter halos in all the simulations exceeds 60 billion. We find that in order to understand the structure of dark matter halos and to make ~1% accurate predictions for density profiles, one needs to realize that halo concentration is more complex than the traditional ratio of the virial radius to the core radius in the NFW profile. For massive halos the averge density profile is far from the NFW shape and the concentration is defined by both the core radius and the shape parameter alpha in the Einasto approximation. Combining results from different redshifts, masses and cosmologies, we show that halos progress through three stages of evolution. (1) They start as rare density peaks that experience very fast and nearly radial infall. This radial infall brings mass closer to the center producing a high concentrated halo. Here, the halo concentration increases with the increasing halo mass and the concentration is defined by the alpha parameter with nearly constant core radius. Later halos slide into (2) the plateau regime where the accretion becomes less radial, but frequent mergers still affect even the central region. Now the concentration does not depend on halo mass. (3) Once the rate of accretion slows down, halos move into the domain of declining concentration-mass relation because new accretion piles up mass close to the virial radius while the core radius is staying constant. We provide accurate analytical fits to the numerical results for halo density profiles and concentrations.Einasto profileRelaxationVirial massCircular velocityPlanck missionMass functionCore radiusVirial velocityCosmological parametersStatistics...
- We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.CurvatureGreen's functionHall conductanceFilling fractionHolomorphRegularizationQuantum Hall EffectLaplace-Beltrami operatorEntropyKahler potential...
- We include the coupling of a heavy sterile neutrino with active neutrinos in the calculation of primordial abundances of light-nuclei. We calculate neutrino distribution functions and primordial abundances, as functions depending on a renormalization of the sterile neutrino distribution function $(a)$, the sterile neutrino mass $(m_s)$ and the mixing angle $(\phi)$. Using the observable data, we set constrains on these parameters, which have the values $a < 0.60$, $\sin^2 \phi=0.15$ and $m_s \approx 4$ keV, for a fixed value of the baryon to photon ratio. When the baryon to photon ratio is allowed to vary, its extracted value is in agreement with the values constrained by Planck observations and by the Wilkinson Microwave Anisotropy Probe (WMAP). It is found that the anomaly in the abundance of $^7$Li persists, in spite of the inclusion of a heavy sterile neutrino.Active-sterile neutrino mixingMass eigen stateFactorisationStatisticsStarLuminosity functionWilkinson Microwave Anisotropy ProbeFermi-Dirac statisticsSterile neutrinoBig bang nucleosynthesis...
- We continue the study of mild transient reductions in the speed of sound of the adiabatic mode during inflation, of their effect on the primordial power spectrum and bispectrum, and of their detectability in the Cosmic Microwave Background (CMB). We focus on the regime of {\it moderately sharp} mild reductions in the speed of sound during uninterrupted slow-roll inflation, a theoretically well motivated and self-consistent regime that admits an effective single-field description. The signatures on the power spectrum and bispectrum were previously computed using a slow-roll Fourier transform (SRFT) approximation, and here we compare it with generalized slow-roll (GSR) and in-in methods, for which we derive new formulas that account for moderately sharp features. The agreement between them is excellent, and also with the power spectrum obtained from the numerical solution to the equation of motion. We show that, in this regime, the SRFT approximation correctly captures with simplicity the effect of higher derivatives of the speed of sound in the mode equation, and makes manifest the correlations between power spectrum and bispectrum features. In a previous paper we reported hints of these correlations in the Planck data and here we perform several consistency checks and further analyses of the best fits, such as polarization and local significance at different angular scales. For the data analysis, we show the excellent agreement between the CLASS and CAMB Boltzmann codes. Our results confirm that the theoretical framework is consistent, and they suggest that the predicted correlations are robust enough to be searched for in CMB and Large Scale Structure (LSS) surveys.Cosmic microwave backgroundLarge scale structureSlow rollPlanck dataLocal significanceSpeed of soundPower spectrum of primordial density perturbationsAdiabatic modeSlow-roll inflationBispectrum...
- We perform a search for localized oscillatory features in the Planck CMB power spectrum, assuming they are caused by a transient reduction in the speed of sound of the adiabatic mode during effectively single-field, uninterrupted slow-roll inflation. We find several fits, for which we calculate the expected correlated signal in the primordial bispectrum, and compare it to the search for scale dependent bispectrum features carried out by the Planck collaboration. Where both searches overlap, we reproduce the Planck results reasonably well. In addition, some of our best fits lie outside the scales and frequency ranges surveyed by Planck, which calls for an extension in frequencies and envelopes of the templates used in Planck's search. By exploiting correlations between different observables, our results strongly suggest that current data might already be sensitive enough to detect transient reductions in the speed of sound as mild as a few percent, opening a new window for the presence of extra degrees of freedom during inflation.Slow rollPower spectrumE-foldingPlanck missionCosmic microwave backgroundMonte Carlo Markov chainPower spectrum of primordial density perturbationsSpeed of soundSound horizonStatistics...
- We present constraints on the parameters of the $\Lambda$CDM cosmological model in the presence of massive neutrinos, using the one-dimensional Ly$\alpha$ forest power spectrum obtained with the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey (SDSS) by Palanque-Delabrouille et al. (2013), complemented by additional cosmological probes. The interpretation of the measured Ly$\alpha$ spectrum is done using a second-order Taylor expansion of the simulated power spectrum. BOSS Ly$\alpha$ data alone provide better bounds than previous Ly$\alpha$ results, but are still poorly constraining, especially for the sum of neutrino masses $\sum m_\nu$, for which we obtain an upper bound of 1.1~eV (95\% CL), including systematics for both data and simulations. Ly$\alpha$ constraints on $\Lambda$CDM parameters and neutrino masses are compatible with CMB bounds from the Planck collaboration. Interestingly, the combination of Ly$\alpha$ with CMB data reduces the uncertainties significantly, due to very different directions of degeneracy in parameter space, leading to the strongest cosmological bound to date on the total neutrino mass, $\sum m_\nu < 0.15$~eV at 95\% CL (with a best-fit in zero). Adding recent BAO results further tightens this constraint to $\sum m_\nu < 0.14$~eV at 95\% CL. This bound is nearly independent of the statistical approach used, and of the different combinations of CMB and BAO data sets considered in this paper in addition to Ly$\alpha$. Given the measured values of the two squared mass differences $\Delta m^2$, this result tends to favor the normal hierarchy scenario against the inverted hierarchy scenario for the masses of the active neutrino species.Cosmological parametersRedshift binsNuisance parameterFrequentist approachFlux power spectrumStatistical errorNeutrinoSystematic errorIntergalactic mediumMatter power spectrum...
- For the extension of the Standard model with light hidden photons we present preliminary estimates of the signal rate expected at the recently proposed fixed target SHiP experiment exploiting CERN SPS beam of 400 GeV protons.BremsstrahlungStandard ModelHadronizationMeson decaysBranching ratioQuarkMuonHidden photon decaysDecay widthHidden photon...
- The CFHTLS presents a unique data set for weak lensing studies, having high quality imaging and deep multi-band photometry. We have initiated an XMM-CFHTLS project to provide X-ray observations of the brightest X-ray selected clusters within the wide CFHTLS area. Performance of these observations and the high quality of CFHTLS data, allows us to revisit the identification of X-ray sources, introducing automated reproducible algorithms, based on the multi-color red sequence finder. We have also introduced a new optical mass proxy. We provide the calibration of the red sequence observed in the CFHT filters and compare the results with the traditional single color red sequence and photoz. We test the identification algorithm on the subset of highly significant XMM clusters and identify 100% of the sample. We find that the integrated z-band luminosity of the red sequence galaxies correlates well with the X-ray luminosity with a surprisingly small scatter of 0.20 dex. We further use the multi-color red sequence to reduce spurious detections in the full XMM and RASS data sets, resulting in catalogs of 196 and 32 clusters, respectively. We made spectroscopic follow-up observations of some of these systems with HECTOSPEC and in combination with BOSS DR9 data. We also describe the modifications needed to the source detection algorithm in order to keep high purity of extended sources in the shallow X-ray data. We also present the scaling relation between X-ray luminosity and velocity dispersion.Photometric redshiftSpectroscopic redshiftCluster of galaxiesPoint sourceEarly-type galaxyXMM-NewtonCOSMOS surveySloan Digital Sky SurveyAbundanceOptical identification...
- We study the possibility of having CP asymmetries in the decay Kaon(+/-) -> pion(-/+) lepton(+/-) lepton(+/-) (lepton = muon or electron). This decay violates Lepton Number by two units and occurs only if there are Majorana particles that mediate the transition. Even though the absolute rate is highly suppressed by current bounds, we search for Majorana neutrino scenarios where the CP asymmetry arising from the lepton sector could be sizeable. This is indeed the case if there are two or more Majorana neutrinos with similar masses in the range around 10^2 MeV. In particular, the asymmetry is potentially near unity if two neutrinos are nearly degenerate, in the sense that the mass difference is similar to the decay rate. The full decay, however, may be difficult to detect not only because of the suppression caused by the heavy-to-light lepton mixing, but also because of the long lifetime of the heavy neutrino, which would induce large space separation between the two vertices where the charge leptons are produced. This particular problem should be less serious in heavier meson decays, as they involve heavier neutrinos with shorter lifetimes.InterferenceBranching ratioCP-oddAbsorptivitySterile neutrinoSee-sawDecay widthNeutrino massOne particle irreducibleCP asymmetry...
- In this paper we review the main theoretical and experimental achievements in the field of Dark Matter from the Cosmological and Astrophysical point of view. We revisit it from the very first surveys of local astrophysical matter, up to the stringent constraints on matter properties, coming from the last release of data on cosmological scales. To bring closer and justify the idea of dark matter, we will go across methods and tools for measuring dark matter characteristics, and in some cases a combination of methods that provide one of the greatest direct proofs for dark matter, such as Bullet cluster.GalaxyRotation CurveCluster of galaxiesDark matterLarge scale structureCosmic microwave backgroundDark matter haloStarSpiral galaxyElliptical galaxy...
- We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by choosing appropriate initial conditions and propagators and show that the non-linear growth of the density power spectrum found in numerical simulations of cosmic structure evolution is reproduced well to redshift zero and for arbitrary wave numbers. The main difference of our approach to ordinary cosmological perturbation theory is that we do not perturb a dynamical equation for the density contrast. Rather, we transport the initial phase-space distribution of a canonical particle ensemble forward in time and extract any collective information from it at the time needed. Since even small perturbations of particle trajectories can lead to large fluctuations in density, our approach allows to reach high density contrast already at first order in the perturbations of the particle trajectories. We argue why the expected asymptotic behaviour of the non-linear power spectrum at large wave numbers can be reproduced in our approach at any order of the perturbation series.Phase spaceHamiltonianZeldovich approximationParticle massMean mass densityCanonical ensemblePermutationPerturbation theoryPrimordial density perturbationGravitational interaction...
- We show that for a class of model Hamiltonians for which certain trial quantum Hall wavefunctions are exact ground states, there is a single spectral density function which controls all two-point correlation functions of density, current and stress tensor components. From this we show that the static structure factors of these wavefunctions behaves at long wavelengths as $s_4 k^4$ where the coefficient $s_4$ is directly related to the shift: $s_4=(\mathcal S-1)/8$.Lowest Landau LevelTrial wavefunctionBosonizationQuantum Hall statesHolomorphLaughlin wavefunctionHall viscosityCyclotronPfaffian stateFactorisation...
- Modular invariant conformal field theories with just one primary field and central charge $c=24$ are considered. It has been shown previously that if the chiral algebra of such a theory contains spin-1 currents, it is either the Leech lattice CFT, or it contains a Kac-Moody sub-algebra with total central charge 24. In this paper all meromorphic modular invariant combinations of the allowed Kac-Moody combinations are obtained. The result suggests the existence of 71 meromorphic $c=24$ theories, including the 41 that were already known.Modular invarianceCentral chargeConformal field theoryChiralityPrimary fieldAlgebra