Commutator Relations Reveal Solvable Structures in Unambiguous State Discrimination

We present a criterion, based on three commutator relations, that allows to decide whether two self-adjoint matrices with non-overlapping support are simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they can be simultaneously brought into a diagonal structure with 2x2-dimensional blocks. Application of this criterion to unambiguous state discrimination provides a systematic test whether the given problem is reducible to a solvable structure. As an example, we discuss unambiguous state comparison.Comment: 5 pages, discussion of related work adde

Explicit form of the Isgur-Wise function in the BPS limit

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope rho^2 = -xi'(1) of the Isgur-Wise function xi(w) attains its lower bound 3/4, then all the derivatives (-1)^L xi^(L)(1) attain their lower bounds (2L+1)!!/2^(2L), obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function xi(w) = [2/(w+1)]^(3/2). Since the so-called BPS condition proposed by Uraltsev implies rho^2 = 3/4, it implies also that the IW function is given by the preceding expression.Comment: 19 page

Relation between Light Cone Distribution Amplitudes and Shape Function in B mesons

The Bakamjian-Thomas relativistic quark model provides a Poincar\'e representation of bound states with a fixed number of constituents and, in the heavy quark limit, form factors of currents satisfy covariance and Isgur-Wise scaling. We compute the Light Cone Distribution Amplitudes of $B$ mesons $\phi_{\pm}^B(\omega)$ as well as the Shape Function $S(\omega)$, that enters in the decay $B \to X_s \gamma$, that are also covariant in this class of models. The LCDA and the SF are related through the quark model wave function. The former satisfy, in the limit of vanishing constituent light quark mass, the integral relation given by QCD in the valence sector of Fock space. Using a gaussian wave function, the obtained $S(\omega)$ is identical to the so-called Roman Shape Function. From the parameters for the latter that fit the $B \to X_s\gamma$ spectrum we predict the behaviour of $\phi_{\pm}^B(\omega)$. We discuss the important role played by the constituent light quark mass. In particular, although $\phi_-^B(0) \not= 0$ for vanishing light quark mass, a non-vanishing mass implies the unfamiliar result $\phi_-^B (0) = 0$. Moreover, we incorporate the short distance behaviour of QCD to $\phi_+^B (\omega)$, which has sizeable effects at large $\omega$. We obtain the values for the parameters $\bar{\Lambda} \cong 0.35$ GeV and $\lambda_B^{-1} \cong 1.43$ GeV$^{-1}$. We compare with other theoretical approaches and illustrate the great variety of models found in the literature for the functions $\phi_{\pm}^B (\omega)$; hence the necessity of imposing further constraints as in the present paper. We briefly review also the different phenomena that are sensitive to the LCDA.Comment: 6 figure

One Interesting New Sum Rule Extending Bjorken's to order {1/m_Q}

We explicitly check quark-hadron duality to order $(m_b-m_c)\Lambda/m_b^2$ for $b \to c l\nu$ decays in the limit $m_b-m_c \ll m_b$ including ground state and orbitally excited hadrons. Duality occurs thanks to a new sum rule which expresses the subleading HQET form factor $\xi_3$ or, in other notations, $a_+^{(1)}$ in terms of the infinite mass limit form factors and some level splittings. We also demonstrate the sum rule, which is not restricted to the condition $m_b-m_c \ll m_b$, applying OPE to the longitudinal axial component of the hadronic tensor without neglecting the $1/m_b$ subleading contributions to the form factors. We argue that this method should produce a new class of sum rules, depending on the current, beyond Bjorken, Voloshin and the known tower of higher moments. Applying OPE to the vector currents we find another derivation of the Voloshin sum rule. From independent results on $\xi_3$ we derive a sum rule which involves only the $\tau_{1/2}^{(n)}$ and $\tau_{3/2}^{(n)}$ form factors and the corresponding level splittings. The latter strongly supports a theoretical evidence that the $B$ semileptonic decay into narrow orbitally-excited resonances dominates over the decay into the broad ones, in apparent contradiction with some recent experiments. We discuss this issue.Comment: 9 page

: Volcanoes and Humans since the Last InterglaciaL in Basse Auvergne (Massif Central, France)

pdf du manuscritThe impact of volcanic eruptions needs to be considered more closely from the point of view of human behaviour in an area of volcanic activity . In the Massif Central, selected case-studies allow us to discuss the effect of local volcanism on the vegetal cover and the patterns of human settlement.La perception de ce que furent les comportements humains en zone volcanique active aux temps préhistoriques reste encore très floue. On examine ici l'enregistrement de l'activité de la Chaîne des Puys dans la plaine adjacente de la Limagne au Pléistocène récent et à l'Holocène. Les impacts environnementaux sont discutés et des perspectives archéologiques sont esquissées

Duality in the non-relativistic harmonic oscillator quark model in the Shifman-Voloshin limit : a pedagogical example

The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\delta m/m_b^2$.Comment: 11 pages, Latex2e, AMS-LaTe

Proposal to study Bs→DˉsJB_s \to \bar D_{sJ} transitions

It is proposed to clear some of the puzzles of B decay to the broad $\bar{D}^{\ast\ast}$ states by studying the corresponding decay with strange states $B_s^0 \to D_{s0}^{\ast -} \pi^+$ at LHCb. Interpretation of the results should be easier due to the narrowness of the $D_{s0}^{\ast -}$ state.Comment: 21 page

Innovation management from fractal infinite paths integral point of view

While a mastery of management innovation is crucial for the future of the economy, to date, there is no theory able to base with objectivity the management of creativity and entrepreneurship. This absence is not due to the lack of methods but to ignorance of mathematical foundations which justify the paradigmatic transgression. These foundations exist nevertheless. It can be mentioned the fractal geometry and the role played by the singularities and correlations over long distances. In the set theory, let us mention Cohen's forcing methods and its engineering consequences through CK theory. In the categories theory, we can mention the principles of Kan extension herein applied by the mean of holomorphic analysis and the analytical extensions. All these methods are based on the recognition of the incompleteness of any structure axiomatically closed (Goedel). At the junction between the physics and the economy, the goal of the present work is to show that the lack of recognition of the role of singularities in this science must be searched in mental biases and the paradigms that affect our concept of equilibrium. We show that this concept must be generalized. If the criticism of the concept of equilibrium in economics is already known, it does not lead, quite as much, to a theory of innovation. We would like to address the issue of creativity by backing the reasoning by the questioning of the concept of equilibrium, using an analogy coming from the physics in fractal structures. The idea is to consider the equilibrium as some steady state limit of a fractional dynamics. The fractional dynamics is a dynamics controlled by non integer fractional equation. These equations will be considered in the Fourier space and by the means of their hyperbolic geodesics. Due to the intrinsic incompleteness of the fractality and of its cardinality, the thickening of the infinite will be used to show that there is no even physical balance but only pseudo-equilibria. The practical use of this observation leads to the design of a dynamic model of creativity, named DQPl (Dual Quality Planning), giving a topologic content to the innovation process. New principles of management of innovation emerge in naturally

Regularization of a three-body problem with zero-range potentials

We propose a coordinate-space regularization of the three-body problem with zero-range potentials. We include the effective range and the shape parameter in the boundary condition of the zero-range potential. The proposed extended zero-range model is tested against atomic helium trimers and is shown to provide an adequate quantitative description of these systems