Triple Products and Yang-Baxter Equation (II): Orthogonal and Symplectic Ternary Systems

We generalize the result of the preceeding paper and solve the Yang-Baxter equation in terms of triple systems called orthogonal and symplectic ternary systems. In this way, we found several other new solutions.Comment: 38 page

Is the anomalous decay ratio of D_{sJ}(2632) due to isospin breaking?

Quark pair annihilation into gluons is suppressed at large momenta due to the asymptotic freedom. As a consequence, mass eigenvalues of heavy states should be almost diagonal with respect to up and down quark masses, thereby breaking isospin. We suggest the particle observed by the SELEX Collaboration, D_{sJ}(2632) to be to a good extent a [cd][dbar sbar] state, which would explain why its D^0 K^+ mode is anomalously suppressed with respect to D_s eta. Predictions for the rates of the yet unobserved modes D_s pi^0 and D^+ K^0 are given.Comment: 3 pages, 1 figur

Hermitian versus holomorphic complex and quaternionic generalized supersymmetries of the M-theory. A classification

Relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language,"generalized supertranslations") is provided. In each given space-time the maximal, saturated, generalized supersymmetry, compatible with the division-algebra constraint that can be consistently imposed on spinors and on superalgebra generators, is furnished. Constraining the superalgebra generators in both the complex and the quaternionic cases gives rise to the two classes of constrained hermitian and holomorphic generalized supersymmetries. In the complex case these two classes of generalized supersymmetries can be regarded as complementary. The quaternionic holomorphic supersymmetry only exists in certain space-time dimensions and can admit at most a single bosonic scalar central charge. The results here presented pave the way for a better understanding of the various $M$ algebra-type of structures which can be introduced in different space-time signatures and in association with different division algebras, as well as their mutual relations. In a previous work, e.g., the introduction of a complex holomorphic generalized supersymmetry was shown to be necessary in order to perform the analytic continuation of the standard $M$-theory to the 11-dimensional Euclidean space. As an application of the present results, it is shown that the above algebra also admits a 12-dimensional, Euclidean, $F$-algebra presentation.Comment: 25 pages, LaTe

Quadratic momentum dependence in the nucleon-nucleon interaction

We investigate different choices for the quadratic momentum dependence required in nucleon-nucleon potentials to fit phase shifts in high partial-waves. In the Argonne v18 potential L**2 and (L.S)**2 operators are used to represent this dependence. The v18 potential is simple to use in many-body calculations since it has no quadratic momentum-dependent terms in S-waves. However, p**2 rather than L**2 dependence occurs naturally in meson-exchange models of nuclear forces. We construct an alternate version of the Argonne potential, designated Argonne v18pq, in which the L**2 and (L.S)**2 operators are replaced by p**2 and Qij operators, respectively. The quadratic momentum-dependent terms are smaller in the v18pq than in the v18 interaction. Results for the ground state binding energies of 3H, 3He, and 4He, obtained with the variational Monte Carlo method, are presented for both the models with and without three-nucleon interactions. We find that the nuclear wave functions obtained with the v18pq are slightly larger than those with v18 at interparticle distances < 1 fm. The two models provide essentially the same binding in the light nuclei, although the v18pq gains less attraction when a fixed three-nucleon potential is added.Comment: v.2 important corrections in tables and minor revisions in text; reference for web-posted subroutine adde

Bounds on Dimension Reduction in the Nuclear Norm

$\newcommand{\schs}{\scriptstyle{\mathsf{S}}_1}$For all $n \ge 1$, we give an explicit construction of $m \times m$ matrices $A_1,\ldots,A_n$ with $m = 2^{\lfloor n/2 \rfloor}$ such that for any $d$ and $d \times d$ matrices $A'_1,\ldots,A'_n$ that satisfy \|A'_i-A'_j\|_{\schs} \,\leq\, \|A_i-A_j\|_{\schs}\,\leq\, (1+\delta) \|A'_i-A'_j\|_{\schs} for all $i,j\in\{1,\ldots,n\}$ and small enough $\delta = O(n^{-c})$, where $c> 0$ is a universal constant, it must be the case that $d \ge 2^{\lfloor n/2\rfloor -1}$. This stands in contrast to the metric theory of commutative $\ell_p$ spaces, as it is known that for any $p\geq 1$, any $n$ points in $\ell_p$ embed exactly in $\ell_p^d$ for $d=n(n-1)/2$. Our proof is based on matrices derived from a representation of the Clifford algebra generated by $n$ anti-commuting Hermitian matrices that square to identity, and borrows ideas from the analysis of nonlocal games in quantum information theory.Comment: 16 page

Glueball enhancements in p(gamma,VV)p through vector meson dominance

Double vector meson photoproduction, p(gamma, G -> VV)p, mediated by a scalar glueball G is investigated. Using vector meson dominance (VMD) and Regge/pomeron phenomenology, a measureable glueball enhancement is predicted in the invariant VV = rho rho and omega omega mass spectra. The scalar glueball is assumed to be the lightest physical state on the daughter pomeron trajectory governing diffractive vector meson photoproduction. In addition to cross sections, calculations for hadronic and electromagnetic glueball decays, G -> V V' (V,V'= rho, omega, phi, gamma), and gamma_v V -> G transition form factors are presented based upon flavor universality, VMD and phenomenological couplings from phi photoproduction analyses. The predicted glueball decay widths are similar to an independent theoretical study. A novel signature for glueball detection is also discussed

Theory of unitarity bounds and low energy form factors

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can beincluded in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K_l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.Comment: 11 pages latex using EPJ style files, 5 figures; v2 is version accepted by EPJA in Tools section; sentences and figures improve

Diquark-Antidiquarks with Hidden or Open Charm and the Nature of X(3872)

Heavy-light diquarks can be the building blocks of a rich spectrum of states which can accommodate some of the newly observed charmonium-like resonances not fitting a pure c-cbar assignment. We examine this possibility for hidden and open charm diquark-antidiquark states deducing spectra from constituent quark masses and spin-spin interactions. Taking the X(3872) as input we predict the existence of a 2++ state that can be associated to the X(3940) observed by Belle and re-examine the state claimed by SELEX, X(2632). The possible assignment of the previously discovered states D_s(2317) and D_s(2457) is discussed. We predict X(3872) to be made of two components with a mass difference related to (m_u-m_d) and discuss the production of X(3872) and of its charged partner X^(+-) in the weak decays of B^(+,0).Comment: 11 pages, 2 figures, revtex, minor typos correcte

Bounds on the slope and the curvature of the scalar K\pi form factor at zero momentum transfer

We derive and calculate unitarity bounds on the slope and curvature of the strangeness-changing scalar form factor at zero momentum transfer, using low-energy constraints and Watson final state interaction theorem. The results indicate that the curvature is important and should not be neglected in the representation of experimental data. The bounds can be converted also into an allowed region for the constants $C\_{12}^r$ and $C\_{34}^r$ of Chiral Perturbation Theory. Our results are consistent with, but weaker than the predictions made by Jamin, Oller and Pich in a coupled channel dispersion approach basedon chiral resonance model. We comment on the differences between the two dispersive methods and argue that the unitarity bounds are useful as an independent check involving different sources of informationComment: 25 pages, 5 figures, version to be published in Nuclear Physics