Null-Vectors in Integrable Field Theory

The form factor bootstrap approach allows to construct the space of local fields in the massive restricted sine-Gordon model. This space has to be isomorphic to that of the corresponding minimal model of conformal field theory. We describe the subspaces which correspond to the Verma modules of primary fields in terms of the commutative algebra of local integrals of motion and of a fermion (Neveu–Schwarz or Ramond depending on the particular primary field). The description of null-vectors relies on the relation between form factors and deformed hyper-elliptic integrals. The null-vectors correspond to the deformed exact forms and to the deformed Riemann bilinear identity. In the operator language, the null-vectors are created by the action of two operators ? (linear in the fermion) and ? (quadratic in the fermion). We show that by factorizing out the null-vectors one gets the space of operators with the correct character.
In the classical limit, using the operators ? and ? we obtain a new, very compact, description of the KdV hierarchy. We also discuss a beautiful relation with the method of Whitham.

title: Logarithmic Yangians in WZW Models
abstract: A new action of the Yangians in the WZW models is displayed. Its structure is generic and level-independent. This Yangian is the natural extension at the conformal point of the one unraveled in massive theories with current algebras. Hopefully, this new symmetry of WZW models will lead to a deeper understanding of the integrable structure of conformal field theories and their deformations.

title: Anomalous scaling in the N-point functions of a passive scalar.
abstract: A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.

title: On Root Multiplicities of Some Hyperbolic Kac–Moody Algebras
abstract: Using the coset construction, we compute the root multiplicities at level-3 for some hyperbolic Kac–Moody algebras including the basic hyperbolic extension of A11 and E10.

title: An Introduction to Yangian Symmetries
abstract: 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. 
 
 
Non-Abelian symmetries and the quantum Yangians; 
 
 
The transfer matrix and an alternative presentation of the Yangians; 
 
 
Digression on the double Yangians. 
 
 
 
 
 
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.

title: Spin-Charge Separation and the Spin Quantum Hall Effect
abstract: We use quantum field theory methods to study the network model for the spin quantum hall transition. When the couplings are fine tuned in a certain way, the spin and charge degrees of freedom, corresponding to the su-percurrent algebras su(2) 0 and osp(2|2) −2 respectively, completely decouple. This simpler theory is exactly solvable and some critical exponents are computed and shown to agree with the recent predictions based on percolation. The general network model is shown to be in a different universality class by identifying the attractive direction of the renormalization group flow.

title: Measurement of moments of the hadronic-mass and energy spectrum in inclusive semileptonic anti-B ---> X(c) l- anti-nu decays

title: On triple focusing dipole magnets
abstract: We present a general, paraxial study of triple focusing (i.e., stigmatic and non-dispersive) index-free dipole magnets. The transcendental equations which describe such magnets lead to a second-degree polynomial equation which we solve analytically. The two solutions of this equation correspond to magnets having either one or no intermediate focal points in the vertical direction. The first-order optical properties of the physical solutions are studied.

title: Laser Wakefield Acceleration of Particle in a Plasma
abstract: A review of the present situation and perspectives, in particular in the scope of a multi-Tev linear accelerator.

title: A measurement of CP-violation parameters in B0 anti-B0 mixing using partially reconstructed D*- l+ nu/l events at BaBar
abstract: CP violation in B0B0bar mixing is characterized by the value of the parameter |q/p| being different from 1, and the Standard Model predicts this difference to be smaller than 10^{-3}. We present a measurement of this parameter using a partial reconstruction of one of the B mesons in the semileptonic channel D*- l+ nu_l, where only the hard lepton and the soft pion from the D*- --> D0bar pi- decay are reconstructed. The flavor of the other B is determined by means of lepton tagging. The determination of |q/p| is then performed with a fit to the proper time difference of the two B decays. We use a luminosity of 200.8 fb^-1, collected at the Y(4S) resonance by the BaBar detector at the PEP-II asymmetrical-energy e+e- collider, in the period 1999-2004. We obtain the preliminary result: |q/p| - 1 = (6.5 +/- 3.4(stat.) +/- 2.0(syst.)) x 10^{-3}

title: Polarimetry of cosmic gamma-ray sources above $e^+e^-$ pair creation threshold
abstract: We examine the potential for gamma-ray conversion to electron-positron pairs, either in the field of a nucleus or of an electron of a detector, to measure the fraction P of linear polarization of cosmic gamma sources. For this purpose we implement, validate and use an event generator based on the HELAS amplitude calculator and on the SPRING event generator. We characterize several ways to measure P. Past proposals to increase the polarization sensitivity by the selection of a fraction of the events in a subset of the available phase space are found to be ine cient, due to the loss in statistics. The use of an optimal variable that includes the full 5D probability density function is found to improve the precision of the measurement of P of a factor of approximately 2. We then study the dilution of the asymmetry that parametrize the degradation of the precision due to experimental e ects such as multiple scattering. In a detector made with a succession of converter slabs and tracker foils, the dependence of the dilution is found to be di erent from that predicted assuming a given (the most probable) value of the pair opening angle. The limitations of a slab detector are avoided by the use of an active target, in which conversion and tracking are performed by the same device, in which case the dilution of the measurement of P is found to be manageable. Based on a realistic sizing of the detector, and for an e ective exposure of 1 year, we estimate the precision for a Crab-like source on the full energy range to be approximately 1.4 %.