A new analysis of $\pi K$ scattering from Roy and Steiner type equations

With the aim of generating new constraints on the OZI suppressed couplings of chiral perturbation theory a set of six equations of the Roy and Steiner type for the S- and P-waves of the scattering amplitudes is derived. The range of validity and the multiplicity of the solutions are discussed. Precise numerical solutions are obtained in the range GeV which make use as input, for the first time, of the most accurate experimental data available at GeV for both and amplitudes. Our main result is the determination of a narrow allowed region for the two S-wave scattering lengths. Present experimental data below 1 GeV are found to be in generally poor agreement with our results. A set of threshold expansion parameters, as well as sub-threshold parameters are computed. For the latter, a matching with the SU(3) chiral expansion at NLO is performed.Received: 28 October 2003, Revised: 12 December 2003, Published online: 13 February 2004Work supported in part by the EU RTN contract HPRN-CT-2002-00311 (EURIDICE) and by IFCPAR contract 2504-1.     

On the Best Constant in the Moser-Onofri-Aubin Inequality

Let S ² be the 2-dimensional unit sphere and let J _α denote the nonlinear functional on the Sobolev space H ¹(S ²) defined by

Non-Existence of Black Hole Solutions¶for a Spherically Symmetric, Static Einstein–Dirac–Maxwell System

We consider for j=?, … a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein–Dirac–Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner–Nordstr?m solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a “cloud” of spin-?-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon. Received: 2 November 1998 / Accepted: 23 February 1999     

Contribution of semi-hadronic states <Emphasis Type="Italic">P</Emphasis>γ, <Emphasis Type="Italic">S</Emphasis>γ, π<Superscript>+</Superscript>π<Superscript>−</Superscript>γ to amm of muon in the framework of the Nambu-Jona-Lasinio model

We calculate the contribution of semi-hadronic states with the pseudoscalar P = π⁰, η and scalar (σ(550)) meson accompanied with a real photon as an intermediate state of a heavy photon to the anomalous magnetic moment of the muon. We consider the intermediate states with π⁰ and σ as hadrons in the frame-work of the Nambu-Jona-Lasinio (NJL) model. The contribution of the π⁰γ state is in agreement with results obtained in previous theoretical considerations as well as with the experimental data $ a_\mu ^{\pi _0 \gamma } \approx 4.5 \times 10^{ - 10} $ a_\mu ^{\pi _0 \gamma } \approx 4.5 \times 10^{ - 10} , besides we estimate a _μ^ηγ = 0.7 × 10⁻¹⁰, a _μ^σγ ∼ 1.5 × 10⁻¹¹, $ a_\mu ^{\pi ^ + \pi ^ - \gamma } \sim 3.2 \times 10^{ - 10} $ a_\mu ^{\pi ^ + \pi ^ - \gamma } \sim 3.2 \times 10^{ - 10} . We also discuss the light-by-light (LbL) mechanism with a _μ ^lbl = 10.5 × 10⁻¹⁰.     

Statistics of Advective Stretching in Three-dimensional Incompressible Flows

We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421–432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE). We use the cellular flow model developed in Solomon and Mezic (Nature 425:376–380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient of variation of the Gaussian distribution does not decrease with time as t^-\frac12t^{-\frac{1}{2}} . However, it is observed that stretching becomes exponential log S∼t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as t^-\frac12t^{-\frac{1}{2}} . This behavior is consistent with a random multiplicative stretching process.     

Wave scattering through classically chaotic cavities in the presence of absorption: A maximum-entropy model

We present a maximum-entropy model for the transport of waves through a classically chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint 〈TrSS ^†〉 = αn: n is the dimensionality of S, and 0 ≤ α ≤ 1. For α = 1 the S-matrix distribution concentrates on the unitarity sphere and we have no absorption; for α = 0 the distribution becomes a delta function at the origin and we have complete absorption. For strong absorption our result agrees with a number of analytical calculations already given in the literature. In that limit, the distribution of the individual (angular) transmission and reflection coefficients becomes exponential — Rayleigh statistics — even for n = 1. For n ≫ 1 Rayleigh statistics is attained even with no absorption; here we extend the study to α<1. The model is compared with random-matrixtheory numerical simulations: it describes the problem very well for strong absorption, but fails for moderate and weak absorptions. The success of the model for strong absorption is understood in the light of a central-limit theorem. For weak absorption, some important physical constraint is missing in the construction of the model.     

Instantons and Yang–Mills Flows on Coset Spaces

We consider the Yang–Mills flow equations on a reductive coset space G/H and the Yang–Mills equations on the manifold \mathbbR×G/H{\mathbb{R}\times G/H}. On non-symmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang–Mills equations to f⁴{\phi^4}-kink equations on \mathbbR{\mathbb{R}}. Depending on the boundary conditions and torsion, we obtain solutions to the Yang–Mills equations describing instantons, chains of instanton–anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on \mathbbR×G/H{\mathbb{R}\times G/H}, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang–Mills flow equations and compare them with the Yang–Mills solutions on \mathbbR×G/H{\mathbb{R}\times G/H}.     

On Classification of Modular Tensor Categories

We classify all unitary modular tensor categories (UMTCs) of rank ≤ 4. There are a total of 35 UMTCs of rank ≤ 4 up to ribbon tensor equivalence. Since the distinction between the modular S-matrix S and −S has both topological and physical significance, so in our convention there are a total of 70 UMTCs of rank ≤ 4. In particular, there are two trivial UMTCs with S = (±1). Each such UMTC can be obtained from 10 non-trivial prime UMTCs by direct product, and some symmetry operations. Explicit data of the 10 non-trivial prime UMTCs are given in Sect. 5. Relevance of UMTCs to topological quantum computation and various conjectures are given in Sect. 6.     

Flux vacua in DBI type Einstein–Maxwell theory

We study compactification of extra dimensions in a theory of Dirac–Born–Infeld type gravity. We investigate the solution for Minkowski spacetime with an S ² extra space as well as that for de Sitter spacetime (S ⁴) with an S ² extra space. They are derived by the effective potential method in the presence of the magnetic flux on the extra sphere. We also consider the higher-dimensional generalization of the solutions. We find that, in a certain model, the radius of the extra space has a minimum value independent of the higher-dimensional Newton constant.     

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

The general properties of the factorized S-matrix in two-dimensional space-time are considered. The relation between the factorization property of the scattering theory and the infinite number of conservation laws of the underlying field theory is discussed. The factorization of the total S-matrix is shown to impose hard restrictions on two-particle matrix elements: they should satisfy special identities, the so-called factorization equations. The general solution of the unitarity, crossing and factorization equations is found for the S-matrices having isotopic O(N)-symmetry. The solution turns out to have different properties for the cases N = 2 and N 3. For N = 2 the general solution depends on one parameter (of coupling constant type), whereas the solution for N 3 has no parameters but depends analytically on N. The solution for N = 2 is shown to be an exact soliton S-matrix of the sine-Gordon model (equivalently the massive Thirring model). The total S-matrix of the model is constructed. In the case of N 3 there are two “minimum” solutions, i.e., those having a minimum set of singularities. One of them is shown to be an exact S matrix of the quantum O(N)-symmetric nonlinear σ-model, the other is argued to describe the scattering of elementary particles of the Gross-Neveu model.     

Leading-order actions of Goldstino fields

This paper starts with a self-contained discussion of the so-called Akulov–Volkov action S_AV\mathcal{S}_{\mathrm{AV}}, which is traditionally taken to be the leading-order action of the Goldstino field. Explicit expressions for S_AV\mathcal{S}_{\mathrm{AV}} and its chiral version S_AV^ch\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} are presented. We then turn to the issue on how these actions are related to the leading-order action S_NL\mathcal{S}_{\mathrm{NL}} proposed in the newly proposed constrained superfield formalism. We show that S_NL\mathcal{S}_{\mathrm{NL}} may yield S_AV/S_AV^ch\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} or a totally different action S_KS\mathcal{S}_{\mathrm{KS}}, depending on how the auxiliary field in the former is integrated out. However, S_KS\mathcal{S}_{\mathrm{KS}} and S_AV/S_AV^ch\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} always yield the same S-matrix elements, as one would have expected from general considerations in quantum field theory.     

From Weak to Strong Coupling in ABJM Theory

The partition function of N=6{\mathcal{N}=6} supersymmetric Chern–Simons-matter theory (known as ABJM theory) on \mathbbS³{\mathbb{S}^3} , as well as certain Wilson loop observables, are captured by a zero dimensional super-matrix model. This super–matrix model is closely related to a matrix model describing topological Chern–Simons theory on a lens space. We explore further these recent observations and extract more exact results in ABJM theory from the matrix model. In particular we calculate the planar free energy, which matches at strong coupling the classical IIA supergravity action on AdS₄×\mathbbC\mathbbP³{{\rm AdS}_4\times\mathbb{C}\mathbb{P}^3} and gives the correct N ^3/2 scaling for the number of degrees of freedom of the M2 brane theory. Furthermore we find contributions coming from world-sheet instanton corrections in \mathbbC\mathbbP³{\mathbb{C}\mathbb{P}^3} . We also calculate non-planar corrections, both to the free energy and to the Wilson loop expectation values. This matrix model appears also in the study of topological strings on a toric Calabi–Yau manifold, and an intriguing connection arises between the space of couplings of the planar ABJM theory and the moduli space of this Calabi–Yau. In particular it suggests that, in addition to the usual perturbative and strong coupling (AdS) expansions, a third natural expansion locus is the line where one of the two ’t Hooft couplings vanishes and the other is finite. This is the conifold locus of the Calabi–Yau, and leads to an expansion around topological Chern–Simons theory. We present some explicit results for the partition function and Wilson loop observables around this locus.     

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in L^￥_l{L^\infty_\ell}. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of Dudyński and Ekiel-Jeżewska (Commun Math Phys 115(4):607–629, 1985); this resolves the open question of global existence for the soft potentials.     

Complete Analysis of the ηN S-Wave Scattering-Length Values and Its Natural Limitations in Any Single-Resonance Model

We show that the S-wave ηN scattering length can be extracted in a model-independent way only if the restricting assumption is adopted that one resonance describes the behaviour of the S-wave entirely. To obtain the ηN S-wave scattering length in a model-independent way one needs only two wellknown quantities; the πN elastic S-wave T-matrix at the η-production threshold, and the near threshold π ⁻ p →ηn total cross section slope. The results are independent of the particular parametrization of the elastic πN S-wave T-matrix and of the number of channels used. These assumptions are more general than the assumptions of the existing single-resonance models employed up to now for extracting the ηN S-wave scattering length. We show that the ηN S-wave scattering length value of other single-resonance models agrees with the model-independent estimate if the input data agree with the commonly accepted values. The existence of the upper limit of the real part and the almost fixed value of the imaginary part of the ηN S-wave scattering length are demonstrated, and the nature of limitations originating directly from first principles is explained as the reduction of the full model to the single resonance in the S-wave. The expected differences from the single-resonance estimate for models that are more general is shown. A simple criterion for recognizing the importance of parts of the model that are added in addition to the single resonance in the S-wave is given as well. Received May 15, 1995; revised September 14, 1995; accepted for publication October 11, 1995     

Stability and Instability of the KDV Solitary Wave Under the KP-I Flow

We consider the KP-I and gKP-I equations in \mathbbR × (\mathbbR/2p\mathbbZ){{\mathbb{R}}\,\times\,({\mathbb{R}}/2\pi{\mathbb{Z}})}. We prove that the KdV soliton with subcritical speed 0 < c < c* is orbitally stable under the global KP-I flow constructed by Ionescu and Kenig (Ann Math Stud 163:181–211, 2007). For supercritical speeds c > c*, in the spirit of the work by Duyckaerts and Merle (GAFA 18:1787–1840, 2009), we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation.     

Anomalous dipion invariant mass distribution of the ?(4S) decays into ?(1S)π+π? and ?(2S)π+π?

To solve the discrepancy between the experimental data on the partial widths and lineshapes of the dipion emission of ϒ(4S) and the theoretical predictions, we suggest that there is an additional contribution, which had not been taken into account in previous calculations. Noticing that the mass of ϒ(4S) is above the production threshold of B[`(B)]B\bar{B}, the contribution of the sequential process \varUpsilon(4S)? B[`(B)]? \varUpsilon(nS)+S?\varUpsilon(nS)+p⁺p^-\varUpsilon(4S)\to B\bar{B}\to \varUpsilon(nS)+S\to\varUpsilon(nS)+\pi^{+}\pi^{-} (n=1,2) may be sizable, and its interference with that from the direct production would be important. The goal of this work is to investigate if a sum of the two contributions with a relative phase indeed reproduces the data. Our numerical results on the partial widths and the lineshapes d\varGamma(\varUpsilon(4S)?\varUpsilon(2S,1S)p⁺p^-)/d(m_p⁺p^-)d\varGamma(\varUpsilon(4S)\to\varUpsilon(2S,1S)\pi^{+}\pi^{-})/d(m_{\pi ^{+}\pi^{-}}) are satisfactorily consistent with the measurements; thus the role of this mechanism is confirmed. Moreover, with the parameters obtained by fitting the data of the Belle and BaBar collaborations, we predict the distributions dΓ(ϒ(4S)→ϒ(2S,1S)π ⁺ π ⁻)/dcosθ, which have not been measured yet.     

The radiative decay ϕ → γππ in a coupled-channel model and the structure of f0(980)

A coupled-channel model is used to study the nature of the scalar mesons produced in the decay ϕ → γππ. The K molecular picture of f₀(980) is found to be in a good agreement with the recent experimental data from SND and CMD-2. The structure of the light scalar mesons is elucidated by investigating the S-matrix poles and the q spectral density.     

The ADHM Construction and Non-local Symmetries of the Self-dual Yang–Mills Equations

We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat \mathbbR⁴{\mathbb{R}^4}. We show how all such connections lie in the orbit of the flat connection on \mathbbR⁴{\mathbb{R}^4} under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type.