Saturation of counterterms by resonances inK ����e + e ? decays

The decaysK ⁺???? ⁺ e ⁺ e ^?,K _S???? ⁰ e ⁺ e ^? andK _L???? ⁰ e ⁺ e ^? are reinvestigated within the framework of chiral perturbation theory. The counterterms induced by strong, electromagnetic and weak interactions are determined assuming the resonance exchange. The weak deformation model, the factorization model and the largeN _c limit are used to create a weak Lagrangian. It is found that the results of the first two approaches depend on theH ₁ coupling, defined in the effective chiral Lagrangian of theO(p ⁴) order. The set of parameters used in the extended Nambu and Jona-Lasinio model can accommodeteK ⁺???? ⁺ e ⁺ e ^? decay rate within the factorization approach. The CP violatingK _L???? ⁰ e ⁺ e ^? decay rate is discussed.     

Magnetic moments of K isomers as indicators of octupole collectivity

The relation between the quadrupole-octupole deformation and the structure of high-K isomers in heavy even-even nuclei is studied through a reflection asymmetric deformed shell model including a BCS procedure with constant pairing interaction. Two-quasiparticle states with K ^?? = 4^?, 5^?, 6^?, 6⁺ and 7^? are considered in the region of actinide nuclei (U, Pu and Cm) and rare-earth nuclei (Nd, Sm and Gd). The behaviour of two-quasiparticle energies and magnetic dipole moments of these configurations is examined over a wide range in the plane of quadrupole and octupole deformations (?? ₂ and ?? ₃. In all considered actinide nuclei, the calculations show that there is pronounced sensitivity of the magnetic moments to the octupole deformation. In the rare-earth nuclei, the calculations for ^{154, 156}Gd show stronger sensitivity of the magnetic moment to the octupole deformation than in the other considered cases.     

Phenomenological implications of light stop and higgsinos

We examine the phenomenological implications of light $\tilde t_R $ and higgsinos in the Minimal Supersymetric Standard Model, assuming tan² ??<m _t m _b and heavy $\tilde t_L $ and gauginos. In this simplified setting, we study the contributions to ??m _{B d},?? _K,BR(b??s??),R _b???(Z??bb) /??(Z??hadrons),BR(t??bW), and their interplay.     

Invariant Measures of Gaussian Type for 2D Turbulence

Gaussian measures ?? ^??,?? are associated to some stochastic 2D models of turbulence. They are Gibbs measures constructed by means of an invariant quantity of the system depending on some parameter ?? (related to the 2D nature of the fluid) and the viscosity???. We prove the existence and the uniqueness of the global flow for the stochastic viscous system; moreover the measure ?? ^??,?? is invariant for this flow and is the unique invariant measure. Finally, we prove that the deterministic inviscid equation has a ?? ^??,?? -stationary solution (for any ??>0).     

A Sublinear Variance Bound for Solutions of a Random Hamilton–Jacobi Equation

We estimate the variance of the value function for a random optimal control problem. The value function is the solution w ^? of a Hamilton?CJacobi equation with random Hamiltonian H(p,x,??)=K(p)?V(x/?,??) in dimension d??2. It is known that homogenization occurs as ???0, but little is known about the statistical fluctuations of w ^? . Our main result shows that the variance of the solution w ^? is bounded by O(?/|log?|). The proof relies on a modified Poincaré inequality of Talagrand.     

Multiplicity distributions inb ��s gluon decays

The final states for the processb??sy have been extensively discussed in the literature. Similarly-detailed analyses for the caseb??s gluon have not been performed. Generally this process is searched for in 2-body decays such as B⁰??K⁺ ?? ^?. We present simple arguments to suggest that most of the time the quark-level process will give rise to final states with rather high multiplicities. Comments are made about the applicability of these results tob??d gluon and hadronicb??u decays.     

Recent Developments in Reactions of Astrophysical Interest

We present different models used in nuclear astrophysics. In particular the role of microscopic cluster theories is emphasized. Recent applications on the triple-?? process, and on the ¹²C(??, ??)¹⁶O and ³He(??, ??)⁷Be reactions are discussed.     

Contribution of vector resonances to the \bar{B}_{d}^{0}\to\bar {K}^{*0}\mu^{+}\mu^{-} decay

The fully differential angular distribution for the rare flavor-changing neutral current decay $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) \mu^{+}\mu^{-} $ is studied. The emphasis is placed on accurate treatment of the contribution from the processes $\bar{B}_{d}^{0} \to\bar{K}^{*0} (\to K^{-} \pi^{+}) V $ with intermediate vector resonances V=??(770),??(782),?(1020),J/??,??(2S),?? decaying into the ?? ⁺ ?? ^? pair. The dilepton invariant-mass dependence of the branching ratio, longitudinal polarization fraction f _L of the $\bar{K}^{*0}$ meson, and forward?Cbackward asymmetry A _FB is calculated and compared with data from Belle, CDF and LHCb. It is shown that inclusion of the resonance contribution may considerably modify the branching ratio, calculated in the SM without resonances, even in the invariant-mass region far from the so-called charmonia cuts applied in the experimental analyses. This conclusion crucially depends on values of the unknown phases of the B ⁰??K ^?0 J/?? and B ⁰??K ^?0 ??(2S) decay amplitudes with zero helicity.     

Perturbative and nonperturbative contributions to the strange quark asymmetry in the nucleon

There are two mechanisms for the generation of an asymmetry between the strange and anti-strange quark distributions in the nucleon: nonperturbative contributions originating from nucleons fluctuating into virtual baryon?Cmeson pairs such as ??K and ??K, and perturbative contributions arising from gluons splitting into strange and anti-strange quark pairs. While the nonperturbative contributions are dominant in the large-x region, the perturbative contributions are more significant in the small-x region. We calculate this asymmetry taking into account both nonperturbative and perturbative contributions, thus giving a more accurate evaluation of this asymmetry over the whole domain of x. We find that the perturbative contributions are generally a few times larger in magnitude than the nonperturbative contributions, which suggests that the best region to detect this asymmetry experimentally is in the region 0.02<x<0.03. We find that the asymmetry may have more than one node, which is an effect that should be taken into account, e.g. for parameterizations of the strange and anti-strange quark distributions used in global analysis of parton distributions.     

New approach to analyzing and evaluating cross sections for partial photoneutron reactions

The presence of substantial systematic discrepancies between the results of different experiments devoted to determining cross sections for partial photoneutron reactions??first of all, (??, n), (??, 2n), and (??, 3n) reactions??is a strong motivation for studying the reliability and authenticity of these data and for developing methods for taking into account and removing the discrepancies in question. In order to solve the first problem, we introduce objective absolute criteria involving transitional photoneutron-multiplicity functions F ₁, F ₂, F ₃, ??; by definition, their values cannot exceed 1.0, 0.5, 0.33, ??, respectively. With the aim of solving the second problem, we propose a new experimental-theoretical approach. In this approach, reaction cross sections are evaluated by simultaneously employing experimental data on the cross section for the total photoneutron yield, ?? ^expt(??, xn) = ?? ^expt(??, n) + 2?? ^expt(??, 2n) + 3?? ^expt(??, 3n) + ??, which are free from drawbacks plaguing experimental methods for sorting neutrons in multiplicity, and the results obtained by calculating the functions F _theor ¹ , F _theor ² , F _theor ³ , ?? on the basis of the modern model of photonuclear reactions. The reliability and authenticity of data on the cross sections for (??, n), (??, 2n), and (??, 3n) partial reactions???? ^eval(??, in) = F _i ^theor ?? ^expt(??, xn)??were evaluated for the ⁹⁰Zr, ¹¹⁵In, ^{112,114,116,117,118,119,120,122,124}Sn, ¹⁵⁹Tb, and ¹⁹⁷Au nuclei.     

Twisted Elliptic Genus for K3 and Borcherds Product

We discuss the relation between the elliptic genus of K3 surface and the Mathieu group M ₂₄. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M ₂₄, can be represented in a very simple manner in terms of the ?? product of the corresponding conjugacy classes. It is shown that our formula is a consequence of the identity between the Borcherds product and additive lift of some Siegel modular forms.     

Stimulated Raman scattering in natural crystals of SrSO4, BaSO4 and PbSO4: High-order Stokes and anti-Stokes generation with?single-wavelength UV, visible, and near-IR excitation, as?well?as cascaded up-conversion nonlinear �� (3)?�� (3) lasing effects under dual-wavelength picosecond collinear coherent pumping

Orthorhombic crystals of SrSO₄, BaSO₄, and PbSO₄, known as natural crystals celestine, barite, and anglesite, were found to be attractive ?? ⁽³⁾-active nonlinear optical materials. High-order Stokes and anti-Stokes picosecond generation that spans almost two octaves has been recorded with single-wavelength laser excitation in the UV, visible, and near-IR ranges. All recorded Raman induced lasing components were identified and attributed to the SRS-promoting vibration modes of the studied crystals (?? _SRS??999?cm^?1 for SrSO₄,?? _SRS??985?cm^?1 for BaSO₄ and ?? _SRS??977?cm^?1 for PbSO₄). Under dual-wavelength (?? _f1=1.06415???m + ?? _f2=0.53207???m) collinear coherent picosecond pumping several new manifestations of cascaded ?? ⁽³⁾??? ⁽³⁾ nonlinear up-conversion lasing effects were observed in BaSO₄ and SrSO₄ crystals. We classify all three studied sulfate crystals as promising SRS-active materials for Raman laser frequency converters and as efficient ?? ⁽³⁾-crystals that efficiently generate Stokes and anti-Stokes frequency combs, which can enable experiments of ultra-short pulse syntheses.     

Three-Frequency Composite Multipulse Nuclear Quadrupole Resonance Technique for Explosive Detection

New method of multifrequency nuclear quadrupole resonance (NQR) for the explosive detection has been proposed. This technique consists of application of the series of composite excitation circles, each consisting of two or three successive pulses of different frequencies. In this work, we study in detail the multipulse sequence consisting of n excitation sets, each set consists of three pulses. The first pulse is applied with frequency ?? _?, the second pulse with frequency ?? ₀, and the third pulse with frequency ?? _?C, but with a shifted phase. The NQR signal is detected at the frequency ?? ₊. The maximal amplitude of the detected signal is obtained by tuning the pulse parameters at frequencies ?? _? and ?? ₀. We have shown that the phase of the NQR signal at the frequency ?? ₊ second part of the composite pulse with the frequency ?? ₀ the signals with different phases to suppress the spurious signals. The method could be used for increasing the NQR signal, avoiding the spurious signals and improving the reliability of NQR detection. Possible applications of the method for the explosive detection are also discussed.     

Non-normal tracer diffusion from stirring by swimming microorganisms

The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ??(??) with long time behaviour ??(??) ?? ?? ^?1??? and a step size distribution p(??x) ?? (??x)^?2??? . The experimentally observed behaviour that ??x ²?? ?? t is obtained for a one-parameter family of exponents with ?? = 2??. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.      

Chiral SU(3) dynamics and the quasibound K – pp cluster

The prototype of a $\bar{K}$ nuclear cluster, K ^???pp, has been investigated using effective $\bar{K}N$ potentials based on chiral SU(3) dynamics. Variational calculation shows a bound state solution with shallow binding energy B(K ^???pp)?=?20±3 MeV and broad mesonic decay width $\Gamma(\bar{K}NN \rightarrow \pi Y N)=40$ –70 MeV. The $\bar{K}N(I=0)$ pair in the K ^???pp system exhibits a similar structure as the Λ(1405). We have also estimated the dispersive correction, p-wave $\bar{K}N$ interaction, and two-nucleon absorption width.     

Nonlinear optical properties of novel tunable, one dimensional molecular superlattice polymers (heteroarylene methines) containing alternating aromatic and quinoid segments

We have investigated the spectral dispersion of second molecular hyperpolarizability ?? (?????; ??, ???, ??) of three derivatives of heteroarylene methine by antiresonant ring interferometric nonlinear spectroscopic technique using femtosecond modelocked Ti:sapphire laser in the spectral range of 725?C820?nm. The observed dispersion of ?? has been explained in the framework of three-essential states model involving the ground state, a one-photon excited state and a two-photon excited state. The spectral response of the hyperpolarizability has been correlated with the electronic and chemical structures of the three derivatives of heteroarylene methine. The estimated ?? values have been compared to the fundamental quantum mechanical limit. We have found for the first time that the heteroarylene methines approach this limit within a factor of 2 while even the best known molecule so far falls short of this limit by a factor of 30.     

���Ѧ� Interaction Leading to N* and ��* Resonances

We have performed a calculation for the three-body ????? system by using the fixed center approximation to Faddeev equations, taking the interaction between ?? and ??, ?? and ??, and ?? and ?? from the chiral unitary approach. We find several peaks in the modulus squared of the three-body scattering amplitude, indicating the existence of resonances, which can be associated to known I?=?1/2, 3/2 and J ^P ?=?1/2⁺, 3/2⁺ and 5/2⁺ baryon states.     

Muon Capture on Deuteron and 3He

We present the results of a recent simultaneous study of the muon capture reactions ²H(?? ^?, ?? _?? )nn and ³He(?? ^?, ?? _?? )³H. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v ₁₈ or chiral N3LO two-nucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A?=?3. The weak current consists of polar- and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (??EFT) framework. In the first case, there is one parameter which is fixed by reproducing the Gamow-Teller matrix element in tritium ??-decay (GT^EXP). In the second case, the low-energy constants, two in the polar and one in the axial-vector current, are fixed, respectively, by reproducing the A?=?3 magnetic moments and GT^EXP. The total rates are found to be 392.0 ± 2.3 s^?1 for A?=?2, and 1484 ± 13 s^?1 for A?=?3, where the spread accounts for the model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the ??EFT currents).     

Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose ?? is the shift acting on Bernoulli space X={1,2,??,d}^?, and, consider a fixed continuous cost function c:X×X???. Denote by ?? the set of all Borel probabilities ?? on X×X, such that, both its x and y marginals are ??-invariant probabilities. We are interested in the optimal plan ?? which minimizes ??c? d?? among the probabilities in ??. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan ?? by convex combinations of plans such that the support projects in periodic orbits.