Cumulant Expansion and Monthly Sum Derivative

Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed, that $1/\sqrt{N}$ can be used as a small parameter in Edgeworth expansion. First two leading terms of this expansion are calculated here. It is shown that the suggest closed-form approximation is in a good agreement with numerical results for typical mode parameters.Comment: 8 pages, 2 figure

Soft Modes Contribution into Path Integral

A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $\omega^2 >\omega^2_0$) and soft (with frequencies $\omega^2 <\omega^2_0$) ones, $\omega_0$ is a some parameter. Hard modes contribution is considered by weak coupling expansion. A low energy effective Lagrangian for soft modes is used. In the case of soft modes we apply a strong coupling expansion. To realize this expansion a special basis in functional space of trajectories is considered. A good convergency of proposed procedure in the case of potential $V(x)=\lambda x^4$ is demonstrated. Ground state energy of the unharmonic oscillator is calculated.Comment: 16 pages, 1 Figure, CEBAF-93-03.(Standard LATEX file

Delta-Isobar Magnetic Form Factor in QCD

We consider the QCD sum rules approach for Delta-isobar magnetic form factor in the infra-red region $0<Q^2<1GeV^2$. The QCD sum rules in external variable field are used. The obtained formfactor is in agreement with quark model predictions for the Delta-isobar magnetic moment.Comment: 13 pages, CEBAF-TH-93-02, Latex, 1 Figur

Magnetic Moments of Heavy ΞQ\Xi_{Q} Baryons in Light Cone QCD Sum Rules

The magnetic moments of heavy $\Xi_{Q}$ baryons containing a single charm or bottom quark are calculated in the framework of light cone QCD sum rules method. A comparison of our results with the predictions of the quark models is presented.Comment: 26 Pages, 8 Figures and 1 Tabl

Positive and negative-parity flavor-octet baryons in coupled QCD sum rules

We apply the method of the QCD sum rule, in which positive- and negative-parity baryons couple with each other, to the flavor-octet hyperons and investigate the parity splittings. We also reexamine the nucleon in the method, which was studied in our previous paper, by carefully choosing the Borel weight. Both in the nucleon and hyperon channels the obtained sum rules turn out to have a very good Borel stability and also have a Borel window, an energy region in which the OPE converges and the pole contribution dominates over the continuum contribution. The predicted masses of the positive- and negative-parity baryons reproduce the experimental ones fairly well in the $\Lambda$ and $\Sigma$ channels, if we assign the $\Lambda(1670)$ and the $\Sigma(1620)$ to the parity partners of the $\Lambda$ and the $\Sigma$, respectively. This implies that the $\Lambda(1405)$ is not the party partner of the $\Lambda$ and may be a flavor-singlet or exotic state. In the $\Xi$ channel, the sum rule predicts the mass of the negative-parity state to be about 1.8 GeV, which leads to two possibilities; one is that the observed state with the closest mass, $\Xi(1690)$, is the parity partner and the other is that the parity partner is not yet found but exists around 1.8 GeV.Comment: 15 pages, 4 figure

Vector, Axial, Tensor and Pseudoscalar Vacuum Susceptibilities

Using a recently developed three-point formalism within the method of QCD Sum Rules we determine the vacuum susceptibilities needed in the two-point formalism for the coupling of axial, vector, tensor and pseudoscalar currents to hadrons. All susceptibilities are determined by the space-time scale of condensates, which is estimated from data for deep inelastic scattering on nucleons

Lattice and Continuum Theories

We investigate path integral formalism for continuum theory. It is shown that the path integral for the soft modes can be represented in the form of a lattice theory. Kinetic term of this lattice theory has a standard form and potential term has additional nonlocal terms which contributions should tend to zero in the limit of continuum theory. Contributions of these terms can be estimated. It is noted that this representation of path integral may be useful to improve lattice calculations taking into account hard modes contribution by standard perturbative expansion. We discuss translation invariance of correlators and the possibility to construct a lattice theory which keeps rotary invariance also.Comment: (Latex, 6 pages), preprint CEBAF-TH-94-1