Some Simple (Integrable) Models of Fractional Statistics

In the first part, we introduce the notion of fractional statistics in the sense of Haldane. We illustrate it on simple models related to anyon physics and to integrable models solvable by the Bethe ansatz. In the second part, we describe the properties of the long-range interacting spin chains. We describe its infinite dimensional symmetry, and we explain how the fractional statistics of its elementary excitations is an echo of this symmetry. In the third part, we review recent results on the Yangian representation theory which emerged from the study of the integrable long-range interacting models.Comment: 18 pages, Latex. Two lectures presented at 1994 Les Houches Summer School ``Fluctuating Geometries in Statistical Mechanics and Field Theory'' (also available at http://xxx.lanl.gov/lh94/

Low-energy hadronic cross sections measurements at BABAR and g-2 of the muon

The LO hadronic vacuum polarization (VP) contribution to the muon anomalous magnetic moment $a_\mu$ is obtained as the integral as a function of energy of an expression that involves the ratio of the $e^+e^- \rightarrow \mathrm{hadron}$ cross section to the pointlike muon pair cross section. The former is extracted from experimental data for individual hadronic final states at low energies, and from perturbative QCD at high energies. The BaBar experiment at SLAC has a programme of systematic measurement of the production of the lowest-rest-mass hadronic final states, those that contribute most significantly to the integral. To that purpose, we use a method in which, while the PEP-II storage ring is operated at a constant energy in the center of mass system, $\sqrt{s}$, of about 10.6 GeV, events are reconstructed and selected which have been produced with a hadronic final state together with a high-energy photon which may (photon tagging) or may not (no tagging) be observed. In our kinematic configuration the photon is almost always emitted by the electron or by the positron of the initial state, hence the name "initial-state radiation" (ISR). The cross section for the direct $e^+e^- \rightarrow f$ production of a final state $f$ at an energy $\sqrt{s'}$ is then extracted from the differential cross section of the ISR production of the state $f$ with invariant mass $\sqrt{s'}$. The programme is almost completed and has lead to a number of first measurements and to an improvement of up to a factor of three of the uncertainties on the contributions of individual channels to $a_\mu$.Comment: On behalf of the BaBar Collaboration. Talk given at QCD 16, 19th International Conference in Quantum Chromodynamics, 4 - 8 July 2016, Montpellier, France. Proceedings submitted to Nuclear and Particle Physics Proceeding

An Introduction to Yangian Symmetries

We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 1 - The classical Heisenberg model: Non-Abelian symmetries; The generators of the symmetries and the semi-classical Yangians; An alternative presentation of the semi-classical Yangians; Digression on Poisson-Lie groups. 2 - The quantum Heisenberg chain: Non-Abelian symmetries and the quantum Yangians; The transfer matrix and an alternative presentation of the Yangians; Digression on the double Yangians. Talk given at the "Integrable Quantum Field Theories" conference held at Come, Italy , September 13-19, 1992.Comment: 14 pages, SPTh-92-134, (The Tex has been corrected

On The Three Point Velocity Correlation Functions in 2d Forced Turbulence

We present a simple exact formula for the three point velocity correlation functions in two dimensional turbulence which is valid on all scales and which interpolates between the direct and inverse cascade regimes. As expected, these correlation functions are universal in these extreme regimes. We also discuss the effect of anisotropy and friction.Comment: 6 pages, LateX, a small remark adde

Quantum Symmetries in 2D Massive Field Theories

We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions is shortly described.Comment: 40 page

Results on conventional and exotic charmonium at BaBar

The B factories provide a unique playground for studying the properties of conventional and exotic charmonium states. We present recent results in initial state radiation and two-photon fusion, obtained using the full data set collected by the BaBar experiment. Amongst BaBar 's harvest presented in this talk, the determination of the quantum numbers of the X(3915) resonance, a body of concording evidence pointing to JPC = 1++ for the X(3872), and updates on the family of the Y resonance to the full integrated luminosity.Comment: Presented at DIS2013, the XXI International Workshop on Deep-Inelastic Scattering and Related Subject -DIS2013, 22-26 April 2013 Marseille, France. To appear in Proceedings of Scienc