Checking the transverse Ward-Takahashi relation at one loop order in 4-dimensions

Some time ago Takahashi derived so called {\it transverse} relations relating Green's functions of different orders to complement the well-known Ward-Green-Takahashi identities of gauge theories by considering wedge rather than inner products. These transverse relations have the potential to determine the full fermion-boson vertex in terms of the renormalization functions of the fermion propagator. He & Yu have given an indicative proof at one-loop level in 4-dimensions. However, their construct involves the 4th rank Levi-Civita tensor defined only unambiguously in 4-dimensions exactly where the loop integrals diverge. Consequently, here we explicitly check the proposed transverse Ward-Takahashi relation holds at one loop order in $d$-dimensions, with $d=4+\epsilon$.Comment: 20 pages, 3 figures This version corrects and clarifies the previous result. This version has been submitted for publicatio

The γγ\gamma \gamma decay of the f0(1370)f_0(1370) and f2(1270)f_2(1270) resonances in the hidden gauge formalism

Using recent results obtained within the hidden gauge formalism for vector mesons, in which the $f_0(1370)$ and $f_2(1270)$ resonances are dynamically generated resonances from the $\rho \rho$ interaction, we evaluate the radiative decay of these resonances into $\gamma \gamma$. We obtain results for the width in good agreement with the experimental data for the $f_2(1270)$ state and a width about a factor five smaller for the $f_0(1370)$ resonance, which would agree with preliminary results from the Belle collaboration, hinting at an order of magnitude smaller width for this resonance than for the $f_2(1270)$.Comment: 7 pages, 9 figures, proof of gauge invariance adde

Molecular orientational dynamics of the endohedral fullerene Sc3_{3}N@C80_{80} as probed by 13^{13}C and 45^{45}Sc NMR

We measure 13C and 45Sc NMR lineshapes and spin-lattice relaxation times (T1) to probe the orientational dynamics of the endohedral metallofullerene Sc3N@C80. The measurements show an activated behavior for molecular reorientations over the full temperature range with a similar behavior for the temperature dependence of the 13C and 45Sc data. Combined with spectral data from Magic Angle Spinning (MAS) NMR, the measurements can be interpreted to mean the motion of the encapsulated Sc3N molecule is independent of that of the C80 cage, although this requires the similar temperature dependence of the 13C and 45Sc spin-lattice relaxation times to be coincidental. For the Sc3N to be fixed to the C80 cage, one must overcome the symmetry breaking effect this has on the Sc3N@C80 system since this would result in more than the observed two 13C lines.Comment: 6 pages, 5 figure

String Theory and Water Waves

We uncover a remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain {hat c}<1 string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We observe that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context.Comment: 49 pages, 4 figure

Interpretation of Nuclear Quadrupole Resonance Spectra in Doped La2_2CuO4_4

The nuclear quadrupole resonance (NQR) spectrum of strontium doped La$_2$CuO$_4$ surprisingly resembles the NQR spectrum of La$_2$CuO$_4$ doped with excess oxygen, both spectra being dominated by a main peak and one principal satellite peak at similar frequencies. Using first-principles cluster calculations this is investigated here by calculating the electric field gradient (EFG) at the central copper site of the cluster after replacing a lanthanum atom in the cluster with a strontium atom or adding an interstitial oxygen to the cluster. In each case the EFG was increased by approximately 10 % leading unexpectedly to the explanation that the NQR spectra are only accidentally similar and the origins are quite different. Additionally the widths of the peaks in the NQR spectra are explained by the different EFG of copper centres remote from the impurity. A model, based on holes moving rapidly across the planar oxygen atoms, is proposed to explain the observed increase in frequency of both the main and satellite peaks in the NQR spectrum as the doping concentration is increased

A Dispersive Analysis on the f0(600)f_0(600) and f0(980)f_0(980) Resonances in γγ→π+π−,π0π0\gamma\gamma\to\pi^+\pi^-, \pi^0\pi^0 Processes

We estimate the di-photon coupling of $f_0(600)$, $f_0(980)$ and $f_2(1270)$ resonances in a coupled channel dispersive approach. The $f_0(600)$ di-photon coupling is also reinvestigated using a single channel $T$ matrix for $\pi\pi$ scattering with better analyticity property, and it is found to be significantly smaller than that of a $\bar qq$ state. Especially we also estimate the di-photon coupling of the third sheet pole located near $\bar KK$ threshold, denoted as $f_0^{III}(980)$. It is argued that this third sheet pole may be originated from a coupled channel Breit-Wigner description of the $f_0(980)$ resonance.Comment: 24 pages and 13 eps figures. A nuerical bug in previous version is fixed. Some results changed. References and new figures added. Version to appear in Phys. Rev.

Location, correlation, radiation: where is the σ\sigma, what is its structure and what is its coupling to photons?

Scalar mesons are a key expression of the infrared regime of QCD. The lightest of these is the $\sigma$. Now that its pole in the complex energy plane has been precisely located, we can ask whether this state is transiently ${\bar q}q$ or ${\bar {qq}} qq$ or a multi-meson molecule or largely glue? The two photon decay of the $\sigma$ can, in principle, discriminate between these possibilities. We review here how the $\gamma\gamma\to\pi^+\pi^-$, $\pi^0\pi^0$ cross-sections can be accurately computed. The result not only agrees with experiment, but definitively fixes the radiative coupling of the $\sigma$. This equates to a two photon width of $(4.1 \pm 0.3)$ keV, which accords with the simple non-relativistic quark model expectation for a ${\bar u}u, {\bar d}d$ scalar. Nevertheless, robust predictions from relativistic strong coupling QCD are required for each of the possible compositions before we can be sure which one really delivers the determined $\gamma\gamma$ coupling.Comment: 18 pages, 11 figures. To be published in Modern Physics Letters A A number of references updated and three sentences changed in the text to reflect thes

Nuclear spin-spin coupling in La_{2-x}Sr_{x}CuO_{4} studied by stimulated echo decay

We have performed copper NQR experiments in high temperature superconductors YBa_{2}Cu_{4}O_{8}, YBa_{2}Cu_{3}O_{7}, and La_{2-x}Sr_{x}CuO_{4} (x=0.12 and 0.15), using the stimulated echo technique. The stimulated echo intensity is analyzed by a model that includes the spin-lattice relaxation process (T_ {1 }-process) and the fluctuating local field due to nuclear spin-spin coupling. The model gives quantitative account of the experimental results in Y-based compounds using the known values of 1/T_{1} and 1/T_{2G}, the gaussian decay rate of the spin echo intensity. The same model applied to LSCO enables us to extract the value of T_{2G}. Our results indicate that T_{1}T/T_{2G} is independent of temperature, implying that the dynamic exponent is one in La_{2-x}Sr_{x}CuO_{4}.Comment: 14 pages, 11 fugures, The bibliography field is correcte

Research and education in management of large-scale technical programs

A research effort is reported which was conducted by NASA in conjunction with Drexel University, and which was aimed at an improved understanding of large scale systems technology and management