- Neutrino trident production (Neutrino trident production)

by Dr. Oleg Ruchayskiy21 Jul 2017 18:29 - Full-duplex (Full-duplex)

by Muhammad R. A. Khandaker08 Mar 2016 12:48 - Plasma physics (Plasma physics)

by Jim Crumley22 Sep 2015 16:59 - MHD equations (MHD equations)

by Jim Crumley22 Sep 2015 16:57 - Electricity and magnetism (Electricity and magnetism)

by Jim Crumley22 Sep 2015 16:54 - Quantum shot noise (Quantum shot noise)

by Prof. Carlo Beenakker04 Feb 2014 08:52 - Wigner transform (Wigner transform)

by Dr. Claude Becker06 Apr 2011 14:04 - Full counting statistics (Full counting statistics)

by Dr. Dmitri Ivanov28 Nov 2011 09:44 - Fingers of God (Fingers of God)

by Dr. Ganna Ivashchenko18 May 2011 22:42 - Gravitational lensing (Gravitational lensing)

by Prof. Koen Kuijken05 Dec 2010 22:11

- We present a centennial review of the history of the term known as the cosmological constant. First introduced to the general theory of relativity by Einstein in 1917 in order to describe a universe that was assumed to be static, the term fell from favour in the wake of the discovery of cosmic the expanding universe, only to make a dramatic return in recent times. We consider historical and philosophical aspects of the cosmological constant over four main epochs: (i) the use of the term in static cosmologies (both Newtonian and relativistic; (ii) the marginalization of the term following the discovery of cosmic expansion; (iii) the use of the term to address specific cosmic puzzles such as the timespan of expansion, the formation of galaxies and the redshifts of the quasars; (iv) the re-emergence of the term in today's Lamda-CDM cosmology. We find that the cosmological constant was never truly banished from theoretical models of the universe, but was sidelined by astronomers for reasons of convenience. We also find that the return of the term to the forefront of modern cosmology did not occur as an abrupt paradigm shift due to one particular set of observations, but as the result of a number of empirical advances such as the measurement of present cosmic expansion using the Hubble Space Telescope, the measurement of past expansion using type SN 1a supernovae as standard candles, and the measurement of perturbations in the cosmic microwave background by balloon and satellite. We give a brief overview of contemporary interpretations of the physics underlying the cosmic constant and conclude with a synopsis of the famous cosmological constant problem.Cosmological constantCosmologyDark energyExpansion of the UniverseSupernovaExpanding universeCosmological constant problemHubble Space TelescopeGalaxyQuasar...
- This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.Phase transitionsEntropyStatisticsCentral Limit TheoremRandom matrix theorySteady stateCanonical ensemblePartition functionNon-equilibrium steady statesStatistical mechanics...
- In our previous paper we constructed complete generalized covariant Hamilton systems (GCHS) and used the representation of the GCHS to deduce the acceleration flow in terms of the time, As a generalization of the GHS, The GCHS can reasonably study the curvature for different manifolds such as the Riemann manifold if we consider the Levi-Civita connection and as we will see that the Wang dynamics is the core of the GCHS. In this note we continually develop the GCHS for the curvature links, It turns out that it's necessary to consider the connection for the GCHS, the second order with respect to the coordinates of GCHS just makes the contact with curvature.CurvatureManifoldCurvature tensorLevi-Civita connectionCovariant derivativeTime operatorRicci tensorPhase spaceVelocityVector...
- The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an intrinsic 'character' is subjective or universal -- this was done by having test subjects with varying degrees of mathematical experience match mathematical arguments with paintings and music: 'does this proof feel more like Bach or Schubert?' The results suggest that such a universal connection indeed exists.Confidence intervalCrowdsourcingCountingRiesz-Thorin theoremStandard ModelSurveysPictureMaterials...
- We prove a local Faber-Krahn inequality for solutions $u$ to the Dirichlet problem for $\Delta + V$ on an arbitrary domain $\Omega$ in $\mathbb{R}^n$. Suppose a solution $u$ assumes a global maximum at some point $x_0 \in \Omega$ and $u(x_0)>0$. Let $T(x_0)$ be the smallest time at which a Brownian motion, started at $x_0$, has exited the domain $\Omega$ with probability $\ge 1/2$. For nice (e.g., convex) domains, $T(x_0) \asymp d(x_0,\partial\Omega)^2$ but we make no assumption on the geometry of the domain. Our main result is that there exists a ball $B$ of radius $\asymp T(x_0)^{1/2}$ such that $$ \| V \|_{L^{\frac{n}{2}, 1}(\Omega \cap B)} \ge c_n > 0, $$ provided that $n \ge 3$. In the case $n = 2$, the above estimate fails and we obtain a substitute result. The Laplacian may be replaced by a uniformly elliptic operator in divergence form. This result both unifies and strenghtens a series of earlier results.Dirichlet problemElliptic operatorHölder's inequalityBrownian motionCauchy-Schwarz inequalityDirichlet boundary conditionFeynman-Kac formulaDiffusion processSpectral geometryEllipticity...
- We show that quantum curves arise in infinite families and have the structure of singular vectors of a relevant symmetry algebra. We analyze in detail the case of the hermitian one-matrix model with the underlying Virasoro algebra, and the super-eigenvalue model with the underlying super-Virasoro algebra. In the Virasoro case we relate singular vector structure of quantum curves to the topological recursion, and in the super-Virasoro case we introduce the notion of super-quantum curves. We also discuss the double quantum structure of the quantum curves and analyze specific examples of Gaussian and multi-Penner models.Random matrix theoryVirasoro algebraClassical limitQuantizationExpectation ValuePartition functionSuper Virasoro algebraConformal field theoryTwo-point correlation functionSymmetry algebra...
- The radiative decay of sterile neutrinos with typical masses of 10 keV is investigated in the presence of an external magnetic field and degenerate electron plasma. Full account is taken of the modified photon dispersion relation relative to vacuum. The limiting cases of relativistic and nonrelativistic plasma are analyzed. The decay rate calculated in a strongly magnetized plasma, as a function of the electron number density, is compared with the unmagnetized plasma limit. It is found that the presence of the strong magnetic field in the electron plasma suppresses the catalyzing influence of the plasma by itself on the sterile-neutrino decay rate.Decay rateRadiative decaySterile neutrinoPhoton dispersion relation in mediumMagnetizationNeutrinoSterile neutrino decayDegenerate electron gasStrongly magnetized plasmaRadiative decay of sterile neutrino...
- The field of structural bioinformatics has seen significant advances with the use of Molecular Dynamics (MD) simulations of biological systems. The MD methodology has allowed to explain and discover molecular mechanisms in a wide range of natural processes. There is an impending need to readily share the ever-increasing amount of MD data, which has been hindered by the lack of specialized tools in the past. To solve this problem, we present HTMoL, a state-of-the-art plug-in-free hardware-accelerated web application specially designed to efficiently transfer and visualize raw MD trajectory files on a web browser. Now, individual research labs can publish MD data on the Internet, or use HTMoL to profoundly improve scientific reports by including supplemental MD data in a journal publication. HTMoL can also be used as a visualization interface to access MD trajectories generated on a high-performance computer center directly. Availability: HTMoL is available free of charge for academic use. All major browsers are supported. A complete online documentation including instructions for download, installation, configuration, and examples is available at the HTMoL website http://htmol.tripplab.com. Supplementary data are available online. Corresponding author: mauricio.carrillo@cinvestav.mxMolecular dynamicsBioinformaticsArchitectureProteinFramesSoftwareMolecular structureApplication programming interfaceVector meson dominanceHigh Performance Computing...
- We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual large N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one gets in the Vasiliev theories. Namely, the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of order 1/N. Using the slightly broken higher spin symmetry we constrain the three point functions of the theories to leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus the Chern-Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points we get the critical O(N) models, both the Wilson-Fisher one and the Gross-Neveu one. Our analysis also fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Conformal field theorySpin currentGauge fieldChern-Simons termSpinScalarP-symmetryFermionBoson...
- Quantum information theory has considerably helped in the understanding of quantum many-body systems. Since the early 2000s various measures of quantum entanglement have been employed to characterise the features of the ground and excited states of quantum matter. Furthermore, the scaling of entanglement entropy with the size of a system has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the knowledge and the methods brought by quantum information do not end with bipartite entanglement. There are other forms of quantum correlations that emerge "for free" in the ground and thermal states of condensed matter models and that can be exploited as resources for quantum technologies. The goal of this work is to review the most recent development on quantum correlations for quantum many-body systems focussing on multipartite entanglement, quantum non locality, quantum discord, mutual information but also other non classical resources like quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems.EntanglementHamiltonianQuantum correlationMany-body systemsQuantum discordQuantum phase transitionQubitBell's inequalityEntropyMutual information...
- These lecture notes are based on a series of lectures given at the XIII Modave summer school in mathematical physics. We review the construction due to Hamilton, Kabat, Lifschytz and L\"owe for reconstructing local bulk operators from CFT operators in the context of AdS/CFT and show how to recover bulk correlation functions from this definition. Building on the work of these authors, it has been noted that the bulk displays quantum error correcting properties. We will discuss tensor network toy models to exemplify these remarkable features. We will discuss the role of gauge invariance and of diffeomorphism symmetry in the reconstruction of bulk operators. Lastly, we provide another method of bulk reconstruction specified to AdS$_3$/CFT$_2$ in which bulk operators create cross-cap states in the CFT.Conformal field theoryAnti de Sitter spaceAdS/CFT correspondenceDiffeomorphismDualityTwo-point correlation functionScalar fieldIsometryEntanglementPropagator...
- We use the conformal bootstrap to perform a precision study of 3d maximally supersymmetric ($\mathcal{N}=8$) SCFTs that describe the IR physics on $N$ coincident M2-branes placed either in flat space or at a $\mathbb{C}^4/\mathbb{Z}_2$ singularity. First, using the explicit Lagrangians of ABJ(M) and recent supersymmetric localization results, we calculate certain half and quarter-BPS OPE coefficients, both exactly at small $N$, and approximately in a large $N$ expansion that we perform to all orders in $1/N$. Comparing these values with the numerical bootstrap bounds leads us to conjecture that these theories obey an OPE coefficient minimization principle. We then use this conjecture as well as the extremal functional method to reconstruct the first few low-lying scaling dimensions and OPE coefficients for both protected and unprotected multiplets that appear in the OPE of two stress tensor multiplets for all values of $N$. We also calculate the half and quarter-BPS operator OPE coefficients in the $SU(2)_k \times SU(2)_{-k}$ BLG theory for all values of the Chern-Simons coupling $k$, and show that generically they do not obey the same OPE coefficient minimization principle.OPE coefficientsSupersymmetric CFTConformal BootstrapScaling dimensionM-theoryPartition functionConformal field theoryOperator product expansionFlavour symmetryABJM theory...
- Despite widespread interests in reinforcement-learning for task-oriented dialogue systems, several obstacles can frustrate research and development progress. First, reinforcement learners typically require interaction with the environment, so conventional dialogue corpora cannot be used directly. Second, each task presents specific challenges, requiring separate corpus of task-specific annotated data. Third, collecting and annotating human-machine or human-human conversations for task-oriented dialogues requires extensive domain knowledge. Because building an appropriate dataset can be both financially costly and time-consuming, one popular approach is to build a user simulator based upon a corpus of example dialogues. Then, one can train reinforcement learning agents in an online fashion as they interact with the simulator. Dialogue agents trained on these simulators can serve as an effective starting point. Once agents master the simulator, they may be deployed in a real environment to interact with humans, and continue to be trained online. To ease empirical algorithmic comparisons in dialogues, this paper introduces a new, publicly available simulation framework, where our simulator, designed for the movie-booking domain, leverages both rules and collected data. The simulator supports two tasks: movie ticket booking and movie seeking. Finally, we demonstrate several agents and detail the procedure to add and test your own agent in the proposed framework.Natural languageReinforcement learningPythonLong short term memorySupervised learningFramesHidden layerKnowledge baseHuman dynamicsRecurrent neural network...
- One of the major drawbacks of modularized task-completion dialogue systems is that each module is trained individually, which presents several challenges. For example, downstream modules are affected by earlier modules, and the performance of the entire system is not robust to the accumulated errors. This paper presents a novel end-to-end learning framework for task-completion dialogue systems to tackle such issues. Our neural dialogue system can directly interact with a structured database to assist users in accessing information and accomplishing certain tasks. The reinforcement learning based dialogue manager offers robust capabilities to handle noises caused by other components of the dialogue system. Our experiments in a movie-ticket booking domain show that our end-to-end system not only outperforms modularized dialogue system baselines for both objective and subjective evaluation, but also is robust to noises as demonstrated by several systematic experiments with different error granularity and rates specific to the language understanding module.Reinforcement learningFramesNatural languageLong short term memorySupervised learningExperimental GroupOptimizationCrowdsourcingDeep learningClassification...
- Large $N$ melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, four-point function diagrams that are exclusively ladders, and higher-point functions that are built out of four-point functions joined together. We uncover an incredibly useful property of these theories: the six-point function, or equivalently, the three-point function of the primary $O(N)$ invariant bilinears, regarded as an analytic function of the operator dimensions, fully determines all correlation functions, to leading nontrivial order in $1/N$, through simple Feynman-like rules. The result is applicable to any theory, not necessarily melonic, in which higher-point correlators are built out of four-point functions. We explicitly calculate the bilinear three-point function for $q$-body SYK, at any $q$. This leads to the bilinear four-point function, as well as all higher-point functions, expressed in terms of higher-point conformal blocks, which we discuss. We find universality of correlators of operators of large dimension, which we simplify through a saddle point analysis. We comment on the implications for the AdS dual of SYK.Sachdev-Ye-Kitaev modelTwo-point correlation functionConformal invarianceSaddle pointAnti de Sitter spaceFeynman diagramsTheoryDimensionsAnalytic function...
- Here we present a working framework to establish finite abelian groups in python. The primary aim is to allow new A-level students to work with examples of finite abelian groups using open source software. We include the code used in the implementation of the framework. We also prove some useful results regarding finite abelian groups which are used to establish the functions and help show how number theoretic results can blend with computational power when studying algebra. The groups established are based modular multiplication and addition. We include direct products of cyclic groups meaning the user has access to all finite abelian groups.SubgroupConjugacy classPythonPermutationSoftwareCountingMaximal subgroupIsomorphismGroup theoryPrimitive permutation group...
- We add a confining potential to the Aharonov-Bohm model resulting in no contact of the particle with the solenoid (border); this is characterized by a unique self-adjoint extension of the initial Hamiltonian operator. It is shown that the spectrum of such extension is discrete and the first eigenvalue is found to be a nonconstant 1-periodic function of the magnetic flux circulation with a minimum at integers and maximum at half-integer circulations. This is a rigorous verification of the effect.SolenoidAharonov-Bohm effectHamiltonianEigenfunctionAntiunitary operatorStokes' theoremSobolev spaceContinuous spectrumUnitary operatorGauge transformation...
- The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Uncertainty principleTime energy uncertainty relationHamiltonianQuantum clockTime operatorInterferenceSelf-adjoint operatorCovarianceQuantum theoryStatistics...
- The gamma-ray burst GRB 170817A associated with GW170817 is subluminous and subenergetic compared with other typical short GRBs. It may be due to a relativistic jet viewed off-axis, or a structured jet, or cocoon emission etc. Giant flares from magnetars may possibly be ruled out. However, the luminosity and energetics of GRB 170817A is coincident with that of magnetar giant flares. After the coalescence of the binary neutron star, a hypermassive neutron star may be formed. The hypermassive neutron star may have magnetar-strength magnetic field. The subsequent collapse of this hypermassive neutron star to a black hole may launch a relativistic jet. However, the prompt emission of the jet (if it exists) may have been missed due to a large viewing angle. During the collapse of the hypermassive neutron star, the magnetic field energy will also be released. This giant-flare-like event may explain the the luminosity and energetics of GRB 170817A. In this scenario, the kilonova emission, and later X-ray/radio afterglow are unaffected. Bursts with similar luminosity and energetics are expected in future neutron star-neutron star or neutron star-black hole mergers.Neutron starGamma ray burstMagnetar Giant FlareMagnetarLuminosityMagnetic energyBinary neutron starRelativistic jetBlack holePrompt emission...
- The recent application of RNN encoder-decoder models has resulted in substantial progress in fully data-driven dialogue systems, but evaluation remains a challenge. An adversarial loss could be a way to directly evaluate the extent to which generated dialogue responses sound like they came from a human. This could reduce the need for human evaluation, while more directly evaluating on a generative task. In this work, we investigate this idea by training an RNN to discriminate a dialogue model's samples from human-generated samples. Although we find some evidence this setup could be viable, we also note that many issues remain in its practical application. We discuss both aspects and conclude that future work is warranted.Recurrent neural networkGenerative Adversarial NetRankingArchitectureHidden stateRankLanguageNetworksObjectiveLikelihood...
- We present Deep Speaker, a neural speaker embedding system that maps utterances to a hypersphere where speaker similarity is measured by cosine similarity. The embeddings generated by Deep Speaker can be used for many tasks, including speaker identification, verification, and clustering. We experiment with ResCNN and GRU architectures to extract the acoustic features, then mean pool to produce utterance-level speaker embeddings, and train using triplet loss based on cosine similarity. Experiments on three distinct datasets suggest that Deep Speaker outperforms a DNN-based i-vector baseline. For example, Deep Speaker reduces the verification equal error rate by 50% (relatively) and improves the identification accuracy by 60% (relatively) on a text-independent dataset. We also present results that suggest adapting from a model trained with Mandarin can improve accuracy for English speaker recognition.ArchitectureCosine similarityEmbeddingConvolutional neural networkStatisticsLong short term memoryClassificationFeature extractionNeural networkEntropy...
- Let $T$ be a piecewise expanding interval map and $T_H$ be an abstract perturbation of $T$ into an interval map with a hole. Given a number $\ell$, $0<\ell<1$, we compute an upper-bound on the size of a hole needed for the existence of an absolutely continuous conditionally invariant measure (accim) with escape rate not greater than $-\ln(1-\ell)$. The two main ingredients of our approach are Ulam's method and an abstract perturbation result of Keller and Liverani.
- The recent development of sensitive, high time resolution instruments at radio telescopes has enabled the discovery of millisecond duration fast radio bursts (FRBs). The FRB class encompasses a number of single pulses, many unique in their own way, so far hindering the development of a consensus for their origin. The key to demystifying FRBs lies in discovering many of them in realtime in order to localise them and identity commonalities. Despite rigorous follow-up, only one FRB has been seen to repeat suggesting the possibility of there being two independent classes of FRBs and thus two classes of possible progenitors. This paper discusses recent developments in the field, the FRB-GRB connection, some of the open questions in FRB astronomy and how the next generation telescopes are vital in the quest to understand this enigmatic population.Fast Radio BurstsGamma ray burstDispersion measureRadio telescopeTelescopesHost galaxyLine of sightPulsarIntergalactic mediumAustralian SKA Pathfinder...
- The arrival times, positions, and fluxes of multiple images in strong lens systems can be used to infer the presence of dark subhalos in the deflector, and thus test predictions of cold dark matter models. However, gravitational lensing does not distinguish between perturbations to a smooth gravitational potential arising from baryonic and non-baryonic mass. In this work, we quantify the extent to which the stellar mass distribution of a deflector can reproduce flux ratio and astrometric anomalies typically associated with the presence of a dark matter subhalo. Using Hubble Space Telescope images of nearby galaxies, we simulate strong lens systems with real distributions of stellar mass as they would be observed at redshift $z_d=0.5$. We add a dark matter halo and external shear to account for the smooth dark matter field, omitting dark substructure, and use a Monte Carlo procedure to characterize the distributions of image positions, time delays, and flux ratios for a compact background source of diameter 5 pc. By convolving high-resolution images of real galaxies with a Gaussian PSF, we simulate the most detailed smooth potential one could construct given high quality data, and find scatter in flux ratios of $\approx 10\%$, which we interpret as a typical deviation from a smooth potential caused by large and small scale structure in the lensing galaxy. We demonstrate that the flux ratio anomalies arising from galaxy-scale baryonic structure can be minimized by selecting the most massive and round deflectors, and by simultaneously modeling flux ratio and astrometric data.Anomaly detectionAnomalous flux ratioDark matter subhaloSingular isothermal ellipsoidGalaxyVelocity dispersionTime delayEllipticityGravitational lens galaxyStellar mass...
- We consider unitary CFTs with continuous global symmetries in $d>2$. We consider a state created by the lightest operator of large charge $Q \gg 1$ and analyze the correlator of two light charged operators in this state. We assume that the correlator admits a well-defined large $Q$ expansion and, relatedly, that the macroscopic (thermodynamic) limit of the correlator exists. We find that the crossing equations admit a consistent truncation, where only a finite number $N$ of Regge trajectories contribute to the correlator at leading nontrivial order. We classify all such truncated solutions to the crossing. For one Regge trajectory $N=1$, the solution is unique and given by the effective field theory of a Goldstone mode. For two or more Regge trajectories $N \geq 2$, the solutions are encoded in roots of a certain degree $N$ polynomial. Some of the solutions admit a simple weakly coupled EFT description, whereas others do not. In the weakly coupled case, each Regge trajectory corresponds to a field in the effective Lagrangian.Conformal field theoryRegge trajectoryGoldstone bosonOperator product expansionTwo-point correlation functionScaling dimensionPropagatorLight conesGlobal symmetryEffective field theory...
- Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.Operator product expansionSachdev-Ye-Kitaev modelChaosConformal field theoryDimensionsWick rotation...
- We propose an integrability setup for the computation of correlation functions of gauge-invariant operators at any value of the 't Hooft coupling and at any order in the large Nc 't Hooft expansion in N = 4 SYM theory. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a non-planar four-point correlator of large half-BPS operators at one and two loops.GraphPropagatorTwo-point correlation functionWorldsheetTorusSuper Yang-Mills theoryPerturbation theoryOperator product expansionFinite sizeN=4 supersymmetric Yang-Mills theory...
- In this work, we compute one-loop planar five-point functions in $\mathcal{N}$=4 super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight factors which depend on the cross ratios. The main new ingredient in the computation, as compared to the four-point functions studied in the previous paper, is the two-particle mirror contribution. We develop techniques to evaluate it and find agreement with the perturbative results in all the cases we analyzed. In addition, we consider next-to-extremal four-point functions, which are known to be protected, and show that the sum of one-particle and two-particle contributions at one loop adds up to zero as expected. The tools developed in this work would be useful for computing higher-particle contributions which would be relevant for more complicated quantities such as higher-loop corrections and non-planar correlators.GraphBound stateForm factorTwo-point correlation functionKinematicsYangianSuper Yang-Mills theoryMagnonFramesSymmetry algebra...
- We study general properties of the conformal basis, the space of wavefunctions in $(d+2)$-dimensional Minkowski space that are primaries of the Lorentz group $SO(1,d+1)$. Scattering amplitudes written in this basis have the same symmetry as $d$-dimensional conformal correlators. We translate the optical theorem, which is a direct consequence of unitarity, into the conformal basis. In the particular case of a tree-level exchange diagram, the optical theorem takes the form of a conformal block decomposition on the principal continuous series, with OPE coefficients being the three-point coupling written in the same basis. We further discuss the relation between the massless conformal basis and the bulk point singularity in AdS/CFT. Some three- and four-point amplitudes in (2+1) dimensions are explicitly computed in this basis to demonstrate these results.Optical theoremWavefunctionScaling dimensionScattering amplitudePropagatorMomentum spaceAnalytic continuationAdS/CFT correspondenceUnitarityConformal field theory...
- We perform conformal perturbation theory by marginal operators to first order. We explicitly check that the deformed scalar 4-point functions satisfy the bootstrap identity.Conformal field theoryOperator product expansionPerturbation theoryRegularizationEmbeddingScaling dimensionRenormalizationConformal invarianceDimensional regularizationAnalytic continuation...
- According to the "Black Box" theorem the experimental confirmation of neutrinoless double beta decay ($0 \nu 2 \beta$) would imply that at least one of the neutrinos is a Majorana particle. However, a null $0 \nu 2 \beta$ signal cannot decide the nature of neutrinos, as it can be suppressed even for Majorana neutrinos. In this letter we argue that if the null $0 \nu 2 \beta$ decay signal is accompanied by a $0 \nu 4 \beta$ quadruple beta decay signal, then at least one neutrino should be a Dirac particle. This argument holds irrespective of the underlying processes leading to such decays.NeutrinoBeta decayMajorana neutrinoMajorana fermionLepton numberNeutrinoless double-beta decayStandard ModelSubgroupNeutrino massMajorana mass...
- We study the evolution of magnetic fields in turbulent hot plasma of the early Universe accounting for the chiral magnetic effect. The magnetohydrodynamic turbulence is modeled by replacing the matter velocity in the advection term in the Faraday equation with the Lorentz force. The system of the kinetic equations for the spectra of the densities of the magnetic helicity and the magnetic energy, as well as for the chiral imbalance, is derived. The amplification of the magnetic field is shown to result from the presence of the chiral magnetic effect solely. The system of the kinetic equations is solved numerically in primordial plasma after the electroweak phase transition. The influence of the matter turbulence on the magnetic field evolution is examined for different seed magnetic fields.Chiral magnetic effectCosmological magnetic fieldKinetic equationMagnetic helicityTurbulencePrimordial plasmaElectroweak phase transitionMagnetic energyThe early UniverseMagnetohydrodynamic turbulence...
- Recent observations of the cosmic microwave background (CMB) at smallest angular scales and updated abundances of primordial elements, indicate an increase of the energy density and the helium-4 abundance with respect to standard big bang nucleosynthesis with three neutrino flavour. This calls for a reanalysis of the observational bounds on neutrino chemical potentials, which encode the number asymmetry between cosmic neutrinos and anti-neutrinos and thus measures the lepton asymmetry of the Universe. We compare recent data with a big bang nucleosynthesis code, assuming neutrino flavour equilibration via neutrino oscillations before the onset of big bang nucleosynthesis. We find a slight preference for negative neutrino chemical potentials, which would imply an excess of anti-neutrinos and thus a negative lepton number of the Universe. This lepton asymmetry could exceed the baryon asymmetry by orders of magnitude.NeutrinoCosmic microwave backgroundBig bang nucleosynthesisAbundanceFlavourLepton asymmetryWilkinson Microwave Anisotropy ProbeSouth Pole TelescopeBaryon acoustic oscillationsHelium-4...
- A cosmic lepton asymmetry $\eta_{\text{l}}=(n_{\text{l}}-n_{\bar{\text{l}}})/n_{\gamma}$ affects the primordial helium abundance and the expansion rate of the early Universe. Both of these effects have an impact on the anisotropies of the cosmic microwave background (CMB). We derive constraints on the neutrino chemical potentials from the Planck 2015 data, assuming equal lepton flavour asymmetries and negligible neutrino masses. We find $\xi=-0.002 ^{+0.114}_{-0.111}$ (95\% CL) for the chemical potentials, which corresponds to $ -0.085 \leq \eta_{\text{l}} \leq 0.084$. Our constraints on the lepton asymmetry are significantly stronger than previous constraints from CMB data analysis and we argue that they are more robust than those from primordial light element abundances. The resulting constraints on the primordial helium and deuterium abundances are consistent with those from direct measurements.Lepton asymmetryCosmic microwave backgroundNeutrinoBig bang nucleosynthesisDeuterium AbundancePlanck missionBaryon asymmetry of the UniverseLight element abundancesSystematic errorCosmological parameters...
- We consider scalar, spinor and vector matter fields transforming under arbitrary representations of a non-Abelian, compact, semisimple internal Lie group which is a physical, global symmetry of their actions. These matter fields are coupled to Abelian gauge fields through the process of {\it iterative N\"other coupling}. This procedure is shown to yield precisely the same locally gauge invariant theory (with the non-Abelian group as the gauge group) as obtained by the usual `minimal coupling' prescription originating from the {\it Gauge Principle} on which standard formulations of non-Abelian gauge field theories are founded. Prospects of this more physical alternative to gauge theories, towards better understanding of physical aspects of these theories, are briefly discussed.Gauge fieldGauge invarianceGlobal symmetryGauge theoryGeneral relativityGauge transformationScalar fieldAsymptotic freedomYang-Mills theoryFundamental Interactions...
- It is widely believed that relativistic jets in X-ray binaries and active-galactic nuclei are powered by the rotational energy of black holes. This idea is supported by general-relativistic magnetohydrodynamic (GRMHD) simulations of accreting black holes, which demonstrate efficient energy extraction via the Blandford-Znajek mechanism. However, due to uncertainties in the physics of mass-loading, and the failure of GRMHD numerical schemes in the highly-magnetized funnel region, the matter content of the jet remains poorly constrained. We investigate the observational signatures of mass-loading in the funnel by performing general-relativistic radiative transfer calculations on a range of 3D GRMHD simulations of accreting black holes. We find significant observational differences between cases in which the funnel is empty and cases where the funnel is filled with plasma, particularly in the optical and X-ray bands. In the context of Sgr A*, current spectral data constrains the jet filling only if the black hole is rapidly rotating with $a\gtrsim0.9$. In this case, the limits on the infrared flux disfavour a strong contribution from material in the funnel. We comment on the implications of our models for interpreting future Event Horizon Telescope observations. We also scale our models to stellar-mass black holes, and discuss their applicability to the low-luminosity state in X-ray binaries.FunnelingBlack holeSagittarius A*HorizonX-ray binaryLuminosityAccretionElectron temperatureAccretion flowMass accretion rate...
- We perform a detailed study of the location of brightest cluster galaxies (BCGs) on the fundamental plane of black hole (BH) accretion, which is an empirical correlation between a BH X-ray and radio luminosity and mass supported by theoretical models of accretion. The sample comprises 72 BCGs out to $z\sim0.3$ and with reliable nuclear X-ray and radio luminosities. These are found to correlate as $L_\mathrm{X} \propto L_\mathrm{R}^{0.75 \pm 0.08}$, favoring an advection-dominated accretion flow as the origin of the X-ray emission. BCGs are found to be on average offset from the fundamental plane such that their BH masses seem to be underestimated by the $M_\mathrm{BH}-M_\mathrm{K}$ relation a factor $\sim$10. The offset is not explained by jet synchrotron cooling and is independent of emission process or amount of cluster gas cooling. Those core-dominated BCGs are found to be more significantly offset than those with weak core radio emission. For BCGs to on average follow the fundamental plane, a large fraction ($\sim40\%$) should have BH masses $> 10^{10}$ M$_{\odot}$ and thus host ultramassive BHs. The local BH-galaxy scaling relations would not hold for these extreme objects. The possible explanations for their formation, either via a two-phase process (the BH formed first, the galaxy grows later) or as descendants of high-z seed BHs, challenge the current paradigm of a synchronized galaxy-BH growth.Black holeBrightest cluster galaxyMassive black holeAccreting black holeAccretionGalaxyLuminosityAccretion flowGas coolingScaling law...
- In this paper we study the semileptonic decays of $B_c^- \to (\eta_c,J/\psi)l^-\bar\nu_l$. We firstly evaluate the $B_c \to (\eta_c,J/\Psi)$ transition form factors $F_0(q^2)$, $F_+(q^2)$, $V(q^2)$ and $A_{0,1,2}(q^2)$ by employing the pQCD factorization approach, and then we calculate the branching ratios for all considered semileptonic decays. Based on the numerical results and the phenomenological analysis, we find that: (a) the pQCD predictions for the values of the $B_c \to \eta_c$ and $B_c \to J/\Psi$ transition form factors agree well with those obtained by using other methods; (b) the pQCD predictions for the branching ratios of the considered decays are $Br\left(B_c^- \to\eta_c e^-\bar\nu_e(\mu^-\bar\nu_\mu)\right) =(4.41^{+1.22}_{-1.09})\times10^{-3}$, $Br\left(B_c^- \to\eta_c\tau^-\bar\nu_\tau\right) =(1.37^{+0.37}_{-0.34})\times10^{-3}$, $Br(B_c^- \to J/\Psi e^-\bar\nu_e(\mu^-\bar\nu_\mu)) =(10.03^{+1.33}_{-1.18})\times10^{-3}$, and $Br\left(B_c^- \to J/\Psi\tau^-\bar\nu_\tau\right) =(2.92^{+0.40}_{-0.34})\times10^{-3}$; and (c) we also define and calculate two ratios of the branching ratios $R_{\eta_c}$ and $R_{J/\Psi}$, which will be tested by LHCb and the forthcoming Super-B experiments.Form factorBranching ratioSemileptonic decayDecay modePerturbative QCDLHCbElectron neutrinoHeavy quarkHamiltonianResummation...
- Among the different scenarios of New Physics, those with an extended Higgs sector are examined with a lot of attention. Recent experimental observations of several anomalies in flavour physics with respect to expectations of the Standard Model further motivate the effort of phenomenologists. First, informations about the $R_{D_s}$ ratio, a test of lepton flavour universality equivalent to $R_D$, already measured, but with the $s$ quark as spectator, are awaited in coming years to constrain the corner of an extended Higgs sector with charged doublets. On another side, leptonic widths of pseudoscalar quarkonia are particularly interesting to test an extended Higgs sector with a light CP-odd Higgs boson singlet, through the study of its mixing with quarkonia states. Hadronic parameters entering those processes have to be determined from lattice QCD with enough confidence on the control of systematic errors. We report on the very first step of a long-term program tackled with ${\rm N_f}=2$ Wilson-Clover fermions to put relevant constraints on extensions of the Higgs sector: extraction of decay constants of $D^*_s$, $\eta_c$, $\eta_c(2S)$, $J/\psi$ and $\psi(2S)$ with lattice ensembles provided by the CLS effort, considering 2 lattice spacings and a large range of pion masses to estimate cut-off effects and extrapolate results to the chiral limit.Higgs bosonPseudoscalarStandard ModelCP-oddSystematic errorTwo-point correlation functionPion massExcited stateLepton flavour universalityClover...
- A search for $B^{+} \to D_s^{+}K^{+}K^{-}$ decays is performed using $pp$ collision data corresponding to an integrated luminosity of 4.8 fb$^{-1}$, collected at centre-of-mass energies of 7, 8 and 13$\,$TeV with the LHCb experiment. A significant signal is observed for the first time and the branching fraction is determined to be \begin{equation*} \mathcal{B}(B^{+} \to D_s^{+}K^{+}K^{-} ) = (7.1 \pm 0.5 \pm 0.6 \pm 0.7) \times 10^{-6}, \end{equation*} where the first uncertainty is statistical, the second systematic and the third due to the uncertainty on the branching fraction of the normalisation mode $B^{+} \to D_s^{+} \overline{\kern -0.2em D}^{0}$. A search is also performed for the pure annihilation decay $B^{+} \to D_s^{+}\phi$. No significant signal is observed and a limit of \begin{equation*} \mathcal{B}(B^{+} \to D_s^{+}\phi) < 4.9 \times 10^{-7}~(4.2 \times 10^{-7}) \end{equation*} is set on the branching fraction at 95$\%$ (90$\%$) confidence level.Branching ratioInvariant massSystematic errorKaonMeson decaysLuminosity functionDecay modeHelicityIntegrated luminosityStandard Model...
- A measurement is reported of the ratio of branching fractions $\mathcal{R}(J/\psi)=\mathcal{B}(B_c^+\,\to\,J/\psi\tau^+\nu_\tau)/\mathcal{B}(B_c^+\,\to\,J/\psi \mu^+\nu_\mu)$, where the $\tau^+$ lepton is identified in the decay mode $\tau^+\,\to\,\mu^+\nu_\mu\overline{\nu}_\tau$. This analysis uses a sample of proton-proton collision data corresponding to 3.0$\mathrm{\,fb}^{-1}$ of integrated luminosity recorded with the LHCb experiment at center-of-mass energies $7\,\mathrm{TeV}$ and $8\,\mathrm{TeV}$. A signal is found for the decay $B_c^+\,\to\,J/\psi \tau^+\nu_\tau$ at a significance of 3 standard deviations, corrected for systematic uncertainty, and the ratio of the branching fractions is measured to be $\mathcal{R}(J/\psi) = 0.71 \pm 0.17 \mathrm{\,(stat)} \pm 0.18\mathrm{\,(syst)}$. This result lies within 2 standard deviations above the range of existing predictions in the Standard Model.Branching ratioMuonSystematic errorForm factorStandard ModelLHCbMass distributionInvariant massKinematicsDecay product...
- We argue that radiative lepton flavor violating (RLFV) decays $P \to \gamma \ell_1 \overline{\ell}_2$ of $P =B^0_q$, $\bar{D}^0$, and $K^0$ meson states are robust probes of new physics models. In particular, they could be used to put constraints on the Wilson coefficients of effective operators describing lepton flavor-changing neutral current interactions at low energy scales. We set up a generic framework for describing these transitions and review new physics constraints from $P \to \ell_1 \bar \ell_2$ decays. There is discussion of how RLFV transitions provide access to the operators that cannot be constrained in two-body decays and we in turn motivate further experimental searches via these channels.Form factorWilson coefficientsDecay rateLepton flavour violationEffective LagrangianBranching ratioStandard ModelFlavour Changing Neutral CurrentsPseudoscalarRadiative decay...
- In the present review different effects related to the orbital degrees of freedom are discussed. Leaving aside such aspects as the superexchange mechanism of the cooperative Jahn-Teller distortions and different properties of "Kugel-Khomskii"-like models, we mostly concentrate on other phenomena, which are in the focus of the modern condensed matter physics. After a general introduction we start with the discussion of the concept of effective reduction of dimensionality due to orbital degrees of freedom and consider such phenomena as the orbitally-driven Peierls effect and the formation of small clusters of ions in the vicinity of a Mott transition, which behave like "molecules" embedded in a solid. The second large section is devoted to the orbital-selective effects such as the orbital-selective Mott transition and the suppression of magnetism due to the fact that part of the orbitals start to form singlet molecular orbitals. At the end the rapidly growing field of the so-called "spin-orbit-dominated" transition metal compounds is briefly reviewed including such topics as the interplay between the spin-orbit coupling and the Jahn-Teller effect, the formation of the spin-orbit driven Mott and Peierls states, the role of orbital degrees of freedom in generation of the Kitaev exchange coupling, and the singlet (excitonic) magnetism in $4d$ and $5d$ transition metal compounds.MagnetismAntiferromagneticSuperexchangeMott transitionDegree of freedomCrystal fieldInsulatorsDopingNatriumSpin-orbit interaction...
- We review the literature on possible violations of the superposition principle for electromagnetic fields in vacuum from the earliest studies until the emergence of renormalized QED at the end of the 1940's. The exposition covers experimental work on photon-photon scattering and the propagation of light in external electromagnetic fields and relevant theoretical work on nonlinear electrodynamic theories (Born-Infeld theory and QED) until the year 1949. To enrich the picture, pieces of reminiscences from a number of (theoretical) physicists on their work in this field are collected and included or appended.Quantum electrodynamicsElectrodynamicsLight scatteringSuperposition principleIntensityPositronDelbruck scatteringMichelson interferometerSpeed of lightIndex of refraction...
- The $n$th Ramanujan prime is the smallest positive integer $R_n$ such that for all $x \geq R_n$ the interval $(x/2, x]$ contains at least $n$ primes. In this paper we undertake a study of the sequence $(\pi(R_n))_{n \in \mathbb{N}}$, which tells us where the $n$th Ramanujan prime appears in the sequence of all primes. In the first part we establish new explicit upper and lower bounds for the number of primes up to the $n$th Ramanujan prime, which imply an asymptotic formula for $\pi(R_n)$ conjectured by Yang and Togb\'e. In the second part of this paper, we use these explicit estimates to derive a result concerning an inequality involving $\pi(R_n)$ conjectured by of Sondow, Nicholson and Noe.Prime numberCountingRiemann zeta functionBertrand's postulateRight Hand Side of the expressionReal numbersProbability...
- The successful LHC operation suggests going beyond the search of excess of events for the quest of new physics. We demonstrate that the eight multipole parameters describing the spin state of the W or Z bosons are able to disentangle their hidden production mechanism. They can be separately extracted from well defined angular asymmetries in the leptonic distribution of boson decays. The discriminating power of this analysis is well illustrated by: (i) polarised top quark decays, (ii) two body decay of heavy resonances, (iii) Drell-Yan production of Z plus jets, (iv) Z boson plus missing transverse energy.Large Hadron ColliderMissing transverse energyTop quark decaysDrell-Yan processSpinEventResonanceBoson...
- We briefly review common features and overlapping issues in hadron and flavor physics focussing on continuum QCD approaches to heavy bound states, their mass spectrum and weak decay constants in different strong interaction models.Strong interactionsBound stateMass spectrumFlavour physicsWeak decayHadron...