Structure of Mass Gap between Two Spin Multiplets

Studying our semirelativistic potential model and the numerical results, which succeeds in predicting and reproducing recently discovered higher resonances of $D$, $D_s$, $B$, and $B_s$, we find a simple expression for the mass gap between two spin multiplets of heavy-light mesons, $(0^-,1^-)$ and $(0^+,1^+)$. The mass gap between chiral partners defined by $\Delta M=M(0^+)-M(0^-)$ and/or $M(1^+)-M(1^-)$ is given by $\Delta M=M(0^+)-M(0^-)=M(1^+)-M(1^-)\approx \Lambda_{\rm Q}-m_q$ in the limit of heavy quark symmetry, and including $1/m_Q$ corrections, we have $\Delta M\approx \Lambda_{\rm Q}-m_q+(1.28\times 10^{5}+4.26\times 10^{2}\cdot m_q)/m_Q$ with $\Lambda_{\rm Q}\approx 300$ MeV, a light quark mass $m_q$, and a heavy quark mass $m_Q$. This equation holds both for $D$ and $D_s$ heavy mesons. Our model calculations for the $B$ and $B_s$ also follow this formula.Comment: 6 pages, 2 figure

Decay properties of the heavy-light mesons

We study the decay properties of a heavy-light meson. We reformulate the decay amplitudes for the heavy-light systems and find a new way to calculate decay rates. Applying this formulation, we find a new sum rule for the radiative decays of one heavy-light meson into another, $H_1\to H_2+\gamma$ with various combinations of $H_i$.Comment: an invited talk at "New Frontiers in QCD 2010" held at Kyot

Schr\"odinger Equation for Heavy Mesons Expanded in 1/mQ1/m_Q

Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schr\"odinger equation for $Q\bar q$ bound states described by a hamiltonian, we systematically develop a perturbation theory in $1/m_Q$ which enables one to solve the Schr\"odinger equation to obtain masses and wave functions of the bound states in any order of $1/m_Q$. It is shown that positive energy projection with respect to the heavy quark sector of a wave function is, at each order of perturbation, proportional to the 0-th order solution. There appear also negative components of the wave function except for the 0-th order, which contribute also to higher order corrections to masses.Comment: 14 pages, uses REVTeX style file

Erratum to the paper "A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension"

This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum describes: 1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak factorization theorem for toroidal birational morphisms in [AMR], in the form utilized in [AKMR] for the proof of the weak factorization theorem for general birationla maps, avoiding the use of the above mentioned algorithm for the strong factorization, and 3. a list of corrections for a few other mistakes in [AMR], mostly pointed out by Laurent Bonavero.Comment: 3 page

Agri-Food Supply Chain Development by Various Chain Leaders: Case Studies in Japan and New Concept of High Nature Value

In this paper, firstly several different agri-food chain leaders are to be considered, such as aged and/or women farmers, supermarkets, consumers' cooperatives, and big general trade company. Secondly the high nature value of food is to be dealt with the matters Japanese consumers are concerned. The diligent working attitude of aged persons and women has led to the production in small amount, in fresh, with low pesticide use and in many varieties. Producers sell products in different modalities such as renting a space from cooperatives, consignment to cooperatives at direct sales shop, and buying-out of all products by agricultural cooperatives. Moreover some farmers shipment groups in city carry out the direct selling to supermarkets in contract. Japan's consumer cooperatives conduct two pillar businesses of "Sanchoku-Teikei" (direct transaction of food and coop-PB products under contract with producers) and operating supermarket-level stores. The co-ops have developed joint buying system in which members form small group units of 5-10 households called "Han" through which they place advance orders for various kinds of goods. The big general trading company ("Sogo Shosha") has the power for developing new businesses through closer ties with local government to assists local areas in taking new approaches to agriculture to achieve regional redevelopment. Japanese consumers seek agricultural products and their processed food with high quality, and are incessantly renewing the concept and contents regarding the high value. A movement linking consumers to agriculturalists has started, in which the concept is defined as the nature management agriculture and the products produced under it are recognized as "high nature value".Agribusiness, Consumer/Household Economics,