In a number of field theoretical models the vacuum angle enters physics in the combination /N, where N stands generically for the number of colors or flavors, in an apparent contradiction with the expected 2 periodicity in . We argue that a resolution of this puzzle is related to the existence of a number of different dependent sectors in a finite volume formulation, which cannot be seen in the naive thermodynamic limit V→ϱ. It is shown that, when the limit V→ϱ is properly defined, physics is always 2 periodic in for any integer, and even rational, values of N, with vacuum doubling at certain values of . We demonstrate this phenomenon in both the multiflavor Schwinger model with the bosonization technique, and four-dimensional gluodynamics with the effective Lagrangian method. The proposed mechanism works for an arbitrary gauge group. ͓S0556-2821͑98͒01717-2͔

We propose a simple method to calculate the pion form factor at not very large momentum transfers, which combines the technique of the QCD sum rules with the description of the pion in terms of the set of wave functions of increasing twist. This approach allows one to calculate the soft (end point) contribution to the form factor in a largely model-independent way. Our results confirm existing expectations that the soft contribution remains important at least up to the momentum transfers of order 10 GeV$^2$, and suggest that it comes from the region of relatively small transverse separations of order 1 GeV$^{-1}$.Comment: LATEX, 11 pages, 3 figures appended as uu-encoded file, MPI-PhT/94-

A theory of the B → Kη ′ decay is proposed. It is based on the Cabbibo favored b → ccs process followed by a direct materialization of the cc pair into the η ′ . This mechanism works due to a non-valence Zweig rule violating c-quark component of the η ′ , which is unique to its very special nature. This non-perturbative "intrinsic charm" content of the η ′ is evaluated using the Operator Product Expansion and QCD low energy theorems. Our results are consistent with an unexpectedly large Br(B → Kη ′ ) ≃ 7.8 • 10 −5 recently announced by CLEO.

BSLP is a two-dimensional dynamic model of interacting portfolio-level loss and loss intensity processes. It is constructed as a Markovian, short-rate intensity model, which facilitates fast lattice methods for pricing various portfolio credit derivatives such as tranche options, forward-starting tranches, leveraged super-senior tranches etc. A semiparametric model specification is used to achieve near perfect calibration to any set of consistent portfolio tranche quotes. The one-dimensional local intensity model obtained in the zero volatility limit of the stochastic intensity is useful in its own right for pricing non-standard index tranches by arbitrage-free interpolation.Opinions expressed in this paper are those of the authors, and do not necessarily reflect the view of JP Morgan. We would like to thank for valuable discussions. All remaining errors are our own. arXiv:0901.3398v1 [q-fin.PR]

We calculate the rate for the decay B u → lνγ using the light cone QCD sume rules. We find Br(B u → lνγ) ≃ 2 · 10 −6 . The results are used to test the applicability of the constituent quark model approximation to the same process.The latter estimate is proportional to 1/m 2 u , where m u ≃Λ u is the "constituent quark mass", indicating that the process is of long distance type. We find that the two approaches yield similar results for the total rate with the choice m u ≃ 480 MeV . This indicates that the constituent quark model may be used for estimates of the radiative "annihilation" contribution to this and other radiative decays. We point out that this decay may be useful for the measurement of |V ub |.