Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach

We calculate the branching ratios and CP asymmetries for B^0 to pi^+pi^-, B^+ to pi^+pi^0 and B^0 to pi^0pi^0 decays, in a perturbative QCD approach. In this approach, we calculate non-factorizable and annihilation type contributions, in addition to the usual factorizable contributions. We found that the annihilation diagram contributions are not very small as previous argument. Our result is in agreement with the measured branching ratio of B to pi^+pi^- by CLEO collaboration. With a non-negligible contribution from annihilation diagrams and a large strong phase, we predict a large direct CP asymmetry in B^0 to pi^+pi^-, and pi^0pi^0, which can be tested by the current running B factories.Comment: Latex, 28 pages including 11 figures; added contents and figures, corrected typo

Complex Curve of the Two Matrix Model and its Tau-function

We study the hermitean and normal two matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex curve, different from the hyperelliptic curve of the one matrix model. The matrix model quantities are expressed through the periods of meromorphic generating differential on this curve and the partition function of the multiple support solution, as a function of filling numbers and coefficients of the matrix potential, is shown to be the quasiclassical tau-function. The relation to softly broken N=1 supersymmetric Yang-Mills theories is discussed. A general class of solvable multimatrix models with tree-like interactions is considered.Comment: 36 pages, 10 figures, TeX; final version appeared in special issue of J.Phys. A on Random Matrix Theor

Darboux Transformations for Supersymmetric Korteweg - de Vries Equations

\hspace{.2in}We consider the Darboux type transformations for the spectral problems of supersymmetric KdV systems. The supersymmetric analogies of Darboux and Darboux-Levi transformations are established for the spectral problems of Manin-Radul-Mathieu sKdV and Manin-Radul sKdV. Several B\"acklund transformations are derived for the MRM sKdV and MR sKdV systems.Comment: Latex, 8 pages AS-ITP-94-4

Angular momentum I ground state probabilities of boson systems interacting by random interactions

In this paper we report our systematic calculations of angular momentum $I$ ground state probabilities ($P(I)$) of boson systems with spin $l$ in the presence of random two-body interactions. It is found that the P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the $P(I_{max})$'s of bosons with spin $l$ do not follow the 1/N ($N=l+1$, referring to the number of independent two-body matrix elements) relation. The properties of the $P(I)$'s obtained in boson systems with spin $l$ are discussed.Comment: 8 pages and 3 figure

Wilson Loops in N=4 SYM and Fermion Droplets

The matrix models which are conjectured to compute the circle Wilson loop and its correlator with chiral primary operators are mapped onto normal matrix models. A fermion droplet picture analogous to the well-known one for chiral primary operators is shown to emerge in the large N limit. Several examples are computed. We find an interesting selection rule for the correlator of a single trace Wilson loop with a chiral primary operator. It can be non-zero only if the chiral primary is in a representation with a single hook. We show that the expectation value of the Wilson loop in a large representation labelled by a Young diagram with a single row has a first order phase transition between a regime where it is identical to a large column representation and a regime where it is a large wrapping number single trace Wilson loop.Comment: 32 pages, 2 figure

Radiative Kaon Decays K±→π±π0γK^\pm\to\pi^\pm\pi^0\gamma and Direct CP Violation

It is stressed that a measurement of the electric dipole amplitude for direct photon emission in \kpm decays through its interference with inner bremsstrahlung is important for differentiating among various models. Effects of amplitude CP violation in the radiative decays of the charged kaon are analyzed in the Standard Model in conjunction with the large $N_c$ approach. We point out that gluon and electromagnetic penguin contributions to the CP-violating asymmetry between the Dalitz plots of \kpm are of equal weight. The magnitude of CP asymmetry ranges from $2\times 10^{-6}$ to $1\times 10^{-5}$ when the photon energy in the kaon rest frame varies from 50 MeV to 170 MeV.Comment: Latex, 11 pages, ITP-SB-93-36, IP-ASTP-22-9

The Phospho-Dependent Dynamin-Syndapin Interaction Triggers Activity-Dependent Bulk Endocytosis of Synaptic Vesicles

Synaptic vesicles (SVs) are retrieved by more than one mode in central nerve terminals. During mild stimulation, the dominant SV retrieval pathway is classical clathrin-mediated endocytosis (CME). During elevated neuronal activity, activity-dependent bulk endocytosis (ADBE) predominates, which requires activation of the calcium-dependent protein phosphatase calcineurin. We now report that calcineurin dephosphorylates dynamin I in nerve terminals only above the same activity threshold that triggers ADBE. ADBE was arrested when the two major phospho-sites on dynamin I were perturbed, suggesting that dynamin I dephosphorylation is a key step in its activation. Dynamin I dephosphorylation stimulates a specific dynamin I-syndapin I interaction. Inhibition of this interaction by competitive peptides or by site-directed mutagenesis exclusively inhibited ADBE but did not affect CME. The results reveal that the phospho-dependent dynamin-syndapin interaction recruits ADBE to massively increase SV endocytosis under conditions of elevated neuronal activity