P,T-Odd Interactions in Atomic 129{}^{129}Xe and Phenomenological Applications

We calculate interaction constants for the contributions from \PT-odd scalar-pseudoscalar and tensor-pseudotensor operators to the electric dipole moment of ${}^{129}$Xe, for the first time in case of the former, using relativistic many-body theory including the effects of dynamical electron correlations. These interaction constants are necessary ingredients to relating the corresponding measurements to fundamental parameters in models of physics beyond the Standard Model. We obtain $\alpha_{C_S} = \left( 0.71 \pm 0.18 \right) [10^{-23}\, e~\text{cm}]$ and \alpha_{C_T}= \left( 0.520 \pm 0.049 \right) [10^{-20}\, \left_{\text{Xe}}\, e~\text{cm}], respectively. We apply our results to test a phenomenological relation between the two quantities, commonly used in the literature, and discuss their present and future phenomenological impact.Comment: 25 pages, 0 figure

NMR paramagnetic relaxation due to the S = 5/2S=5∕2 complex, Fe(III)-(tetra-p-sulfonatophenyl)porphyrin: Central role of the tetragonal fourth-order zero-field splitting interaction

The metalloporphyrins, Me-TSPP [Me = Cr(III)Me=Cr(III), Mn(III), Mn(II), Fe(III), and TSPP=meso-(tetra-pp-sulfonatophenyl)porphyrin], which possess electron spins S = 3/2S=3∕2, 2, 5/25∕2, and 5/25∕2, respectively, comprise an important series of model systems for mechanistic studies of NMR paramagnetic relaxation enhancement (NMR-PRE). For these S>1/2S>1∕2 spin systems, the NMR-PRE depends critically on the detailed form of the zero-field splitting (zfs) tensor. We report the results of experimental and theoretical studies of the NMR relaxation mechanism associated with Fe(III)-TSPP, a spin 5/25∕2 complex for which the overall zfs is relatively large (D ≈ 10 cm−1)(D≈10cm−1). A comparison of experimental data with spin dynamics simulations shows that the primary determinant of the shape of the magnetic relaxation dispersion profile of the water proton R1R1 is the tetragonal fourth-order component of the zfs tensor. The relaxation mechanism, which has not previously been described, is a consequence of zfs-induced mixing of the spin eigenfunctions of adjacent Kramers doublets. We have also investigated the magnetic-field dependence of electron-spin relaxation for S = 5/2S=5∕2 in the presence of a large zfs, such as occurs in Fe(III)-TSPP. Calculations show that field dependence of this kind is suppressed in the vicinity of the zfs limit, in agreement with observation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87861/2/184501_1.pd

Conservation Laws and Geometry of Perturbed Coset Models

We present a Lagrangian description of the $SU(2)/U(1)$ coset model perturbed by its first thermal operator. This is the simplest perturbation that changes sign under Krammers--Wannier duality. The resulting theory, which is a 2--component generalization of the sine--Gordon model, is then taken in Minkowski space. For negative values of the coupling constant $g$, it is classically equivalent to the $O(4)$ non--linear \s--model reduced in a certain frame. For $g > 0$, it describes the relativistic motion of vortices in a constant external field. Viewing the classical equations of motion as a zero curvature condition, we obtain recursive relations for the infinitely many conservation laws by the abelianization method of gauge connections. The higher spin currents are constructed entirely using an off--critical generalization of the $W_{\infty}$ generators. We give a geometric interpretation to the corresponding charges in terms of embeddings. Applications to the chirally invariant $U(2)$ Gross--Neveu model are also discussed.Comment: Latex, 31p, CERN-TH.7047/9

Single-shot non-intercepting profile monitor of plasma-accelerated electron beams with nanometric resolution

An innovative, single-shot, non-intercepting monitor of the transverse profile of plasma-accelerated electron beams is presented, based on the simultaneous measurement of the electron energy and the betatron radiation spectra. The spatial resolution is shown to be down to few tens of nanometers, important for high-precision applications requiring fine shaping of beams and detailed characterizations of the electron transverse phase space at the exit of plasma accelerating structures

Strings from Tachyons

We propose a new interpretation of the c=1 matrix model as the world-line theory of N unstable D-particles, in which the hermitian matrix is provided by the non- abelian open string tachyon. For D-particles in 1+1-d string theory, we find a direct quantitative match between the closed string emission due to a rolling tachyon and that due to a rolling eigenvalue in the matrix model. We explain the origin of the double-scaling limit, and interpret it as an extreme representative of a large equivalence class of dual theories. Finally, we define a concrete decoupling limit of unstable D-particles in IIB string theory that reduces to the c=1 matrix model, suggesting that 1+1-d string theory represents the near-horizon limit of an ultra-dense gas of IIB D-particles.Comment: 30 pages, 4 figures; v2: added references, improved discussion of Liouville boundary states, v3: small correction

On the theory of matrices with elements in the Clebsch Aronhold symbolic calculus

In the theory of invariant matrices and in the classical invariant theory there arise a considerable number of rather surprising isonorphisms relating to symmetric functions of the latent roots and to the theory of matric representations of the symmetric group. Although these relations appear sooner or later in the development of either theory it would seem, on account of their fundamental simplicity, at least desirable that they should be brought into evidence by an analysis of the algebraic nature of the systems involved. Since many of the relations referred to are merely extensions of familiar determinantal theorems, and since the totality of reducing matrices for the general invariant matrix should give a complete basis for determinantal relations, the development of these results should embody an extension of determinant theory besides all results relating to determinants with unrestricted elements in the ground field.With this end in view, the discussion given below proceeds first from an analysis of the nature of various expressions involving determinants and permanents, to a construction for the orthogonal representations of the symmetric group. The reductions given here are related to the corresponding reductions for the central cores of invariant matrices by means of an isomorphism which can be expressed in terms of certain symbolic quantities obtained by writing each element of the fundamental matrix [a i j] as a symbolic product ai αj and forming direct products oF compounds and Sohläflians of [a i j] by the use of equivalent symbols. A symbolisation of matrices in this way has been used by Professor Turnbull in his paper TTThe Invariant Theory of a General Bi- linear Form" (Proc. L.:.S. Series II, Vol. 33, Part I). The process of deduction followed in this paper is, however, essentially non -symbolic. It could have been framed equally well in the terminology of invariant matrices, in which it forms an extension of some theorems developed by Professor Aitken in his Research Lectures. The actual representations obtained are essentially the same as the orthogonal forms developed by Young.The discussion is restricted to the orthogonal case for the sake of symmetry, although rational forms can be developed in a similar manner.In the paper quoted above, Professor Turnbull uses his symbolic forms to obtain expressions representing symmetric functions of the latent roots of the matrix [a i j]. His results are easily extended to the complete homogeneous symmetric functions and to bi- alternants, and suggest the manner in which the reducing matrices for the central core might be extended to reduce the full invariant matrix. A homo-morphism is developed for this extensio