Rho-omega mixing in asymmetric nuclear matter via QCD sum rule approach

We evaluate the operator product expansion (OPE) for a mixed correlator of the isovector and isoscalar vector currents in the background of the nucleon density with intrinsic isospin asymmetry [i.e. excess of neutrons over protons] and match it with its imaginary part, given by resonances and continuum, via the dispersion relation. The leading density-dependent contribution to $\rho-\omega$ mixing is due the scattering term, which turns out to be larger than any density dependent piece in the OPE. We estimate that the asymmetric density of $n_n-n_p \sim 2.5 \times 10^{-2} ~{\rm fm^3}$ induces the amplitude of $\rho-\omega$ mixing, equal in magnitude to the mixing amplitude in vacuum, with the constructive interference for positive and destructive for negative values of $n_n-n_p$. We revisit sum rules for vector meson masses at finite nucleon density to point out the numerical importance of the screening term in the isoscalar channel, which turns out to be one order of magnitude larger than any density-dependent condensates over the Borel window. This changes the conclusions about the density dependence of $m_\omega$, indicating $\sim 40$ MeV increase at nuclear saturation density.Comment: 8 pages, Revte

New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

ρ\rho-ω\omega mixing and spin dependent CSV potential

We construct the charge symmetry violating (CSV) nucleon-nucleon potential induced by the $\rho^0$-\o mixing due to the neutron-proton mass difference driven by the $NN$ loop. Analytical expression for for the two-body CSV potential is presented containing both the central and non- central $NN$ interaction. We show that the $\rho$$NN$ tensor interaction can significantly enhance the charge symmetry violating $NN$ interaction even if momentum dependent off-shell $\rho^0$-$\omega$ mixing amplitude is considered. It is also shown that the inclusion of form factors removes the divergence arising out of the contact interaction. Consequently, we see that the precise size of the computed scattering length difference depends on how the short range aspects of the CSV potential are treated.Comment: Accepted for publication in Phys. Rev.

Supersymmetric quantum mechanics based on higher excited states

We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward but physically quite nontrivial since it yields an infinity of new classes of susy-partner potentials, whose spectra are exactly identical except for the lowest m+1 states, if the superpotential is defined in terms of the (m+1)-st eigenfunction, with m=0 reserved for the ground state. It is shown that in case of the infinite 1-dim potential well nothing new emerges (the partner potential is still of P\"oschl-Teller type I, for all m), whilst in case of the 1-dim harmonic oscillator we get a new class of infinitely many partner potentials: for each m the partner potential is expressed as the sum of the quadratic harmonic potential plus rational function, defined as the derivative of the ratio of two consecutive Hermite polynomials. These partner potentials of course have m singularities exactly at the locations of the nodes of the generating (m+1)-st wavefunction. The susy formalism applies everywhere between the singularities. A systematic application of the formalism to other potentials with known spectra would yield an infinitely rich class of "solvable" potentials, in terms of their partner potentials. If the potentials are shape invariant they can be solved at least partially and new types of analytically obtainable spectra are expected. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.SqComment: 15 pages LaTeX file, no figures, submitted to J. Phys. A: accepted for publication

The Glasgow Benefit Inventory: a systematic review of the use and value of an otorhinolaryngological generic patient-recorded outcome measure

The Glasgow Benefit Inventory (GBI) is a validated, generic patient-recorded outcome measure widely used in otolaryngology to report change in quality of life post-intervention.To date, no systematic review has made (i) a quality assessment of reporting of Glasgow Benefit Inventory outcomes; (ii) a comparison between Glasgow Benefit Inventory outcomes for different interventions and objectives; (iii) an evaluation of subscales in describing the area of benefit; (iv) commented on its value in clinical practice and research.Systematic review.'Glasgow Benefit Inventory' and 'GBI' were used as keywords to search for published, unpublished and ongoing trials in PubMed, EMBASE, CINAHL and Google in addition to an ISI citation search for the original validating Glasgow Benefit Inventory paper between 1996 and January 2015.Papers were assessed for study type and quality graded by a predesigned scale, by two authors independently. Papers with sufficient quality Glasgow Benefit Inventory data were identified for statistical comparisons. Papers with 50% and gave sufficient Glasgow Benefit Inventory total and subscales for meta-analysis. For five of the 11 operation categories (vestibular schwannoma, tonsillectomy, cochlear implant, middle ear implant and stapes surgery) that were most likely to have a single clear clinical objective, score data had low-to-moderate heterogeneity. The value in the Glasgow Benefit Inventory having both positive and negative scores was shown by an overall negative score for the management of vestibular schwannoma. The other six operations gave considerable heterogeneity with rhinoplasty and septoplasty giving the greatest percentages (98% and 99%) most likely because of the considerable variations in patient selection. The data from these operations should not be used for comparative purposes. Five papers also reported the number of patients that had no or negative benefit, a potentially a more clinically useful outcome to report. Glasgow Benefit Inventory subscores for tonsillectomy were significantly different from ear surgery suggesting different areas of benefitThe Glasgow Benefit Inventory has been shown to differentiate the benefit between surgical and medical otolaryngology interventions as well as 'reassurance'. Reporting benefit as percentages with negative, no and positive benefit would enable better comparisons between different interventions with varying objectives and pathology. This could also allow easier evaluation of factors that predict benefit. Meta-analysis data are now available for comparison purposes for vestibular schwannoma, tonsillectomy, cochlear implant, middle ear implant and stapes surgery. Fuller report of the Glasgow Benefit Inventory outcomes for non-surgical otolaryngology interventions is encouraged

The effects of meson mixing on dilepton spectra

The effect of scalar and vector meson mixing on the dilepton radiation from hot and dense hadronic matter is estimated in different isospin channels. In particular, we study the effect of $\sigma$-$\omega$ and $\rho-a_0$ mixing and calculate the corresponding rates. Effects are found to be significant compared to standard $\pi$-$\pi$ and $K$-${\bar K}$ annihilations. While the mixing in the isoscalar channel mostly gives a contribution in the invariant mass range between the two-pion threshold and the $\omega$ peak, the isovector channel mixing induces an additional peak just below that of the $\phi$. Experimentally, the dilepton signals from $\rho$-$a_0$ mixing seem to be more tractable than those from $\sigma$-$\omega$ mixing.Comment: 10 pages, 9 figure

Comments on ``A note on first-order formalism and odd-derivative actions'' by S. Deser

We argue that the obstacles to having a first-order formalism for odd-derivative actions presented in a pedagogical note by Deser are based on examples which are not first-order forms of the original actions. The general derivation of an equivalent first-order form of the original second-order action is illustrated using the example of topologically massive electrodynamics (TME). The correct first-order formulations of the TME model keep intact the gauge invariance presented in its second-order form demonstrating that the gauge invariance is not lost in the Ostrogradsky process.Comment: 6 pages, references are adde

Molecular Tweezers with Varying Anions: A Comparative Study

Selective binding of the phosphate-substituted molecular tweezer 1a to protein lysine residues was suggested to explain the inhibition of certain enzymes and the aberrant aggregation of amyloid petide Aβ42 or α-synuclein, which are assumed to be responsible for Alzheimer’s and Parkinson’s disease, respectively. In this work we systematically investigated the binding of four water-soluble tweezers 1a−d (substituted by phosphate, methanephosphonate, sulfate, or O-methylenecarboxylate groups) to amino acids and peptides containing lysine or arginine residues by using fluorescence spectroscopy, NMR spectroscopy, and isothermal titration calorimetry (ITC). The comparison of the experimental results with theoretical data obtained by a combination of QM/MM and ab initio 1H NMR shift calculations provides clear evidence that the tweezers 1a−c bind the amino acid or peptide guest molecules by threading the lysine or arginine side chain through the tweezers’ cavity, whereas in the case of 1d the guest molecule is preferentially positioned outside the tweezer’s cavity. Attractive ionic, CH-π, and hydrophobic interactions are here the major binding forces. The combination of experiment and theory provides deep insight into the host−guest binding modes, a prerequisite to understanding the exciting influence of these tweezers on the aggregation of proteins and the activity of enzymes

Algebraic Approach to Shape Invariance

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finite-dimensional are explored.Comment: Submitted to Physical Review A. Latex file, 9 pages. Manuscript is also available at http://nucth.physics.wisc.edu/preprints