13,941,754 research outputs found
Super congruences and Euler numbers
Let be a prime. We prove that
, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of
combinatorial nature. We also formulate many conjectures concerning super
congruences and relate most of them to Euler numbers or Bernoulli numbers.
Motivated by our investigation of super congruences, we also raise a conjecture
on 7 new series for , and the constant
(with (-) the Jacobi symbol), two of which are
and
\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$
Cusps in K --> 3 pi decays
The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As
has recently been pointed out by Cabibbo and Isidori, an accurate measurement
of the cusp may allow one to pin down the S-wave pi pi scattering lengths to
high precision. Here, we present and illustrate an effective field theory
framework that allows one to determine the structure of this cusp in a
straightforward manner. The strictures imposed by analyticity and unitarity are
respected automatically.Comment: 14 pages, 3 figures, uses Elsevier styl
On the nature of the K*2(1430), K*3(1780), K*4(2045), K*5(2380) and K*6 as K*--multi-rho states
We show that the , , ,
and a not yet discovered resonance are basically molecules made of an
increasing number of and one mesons. The idea relies on
the fact that the vector-vector interaction in s-wave with spins aligned is
very strong both for and . We extend a recent work, where
several resonances showed up as multi- molecules, to the strange
sector including the into the system. The resonant structures show
up in the multi-body scattering amplitudes, which are evaluated in terms of the
unitary two-body vector-vector scattering amplitudes by using the fixed center
approximation to the Faddeev equations
Radiative corrections in K --> 3 pi decays
We investigate radiative corrections to K --> 3 pi decays. In particular, we
extend the non-relativistic framework developed recently to include real and
virtual photons and show that, in a well-defined power counting scheme, the
results reproduce corrections obtained in the relativistic calculation. Real
photons are included exactly, beyond the soft-photon approximation, and we
compare the result with the latter. The singularities generated by pionium near
threshold are investigated, and a region is identified where standard
perturbation theory in the fine structure constant alpha may be applied. We
expect that the formulae provided allow one to extract S-wave pi pi scattering
lengths from the cusp effect in these decays with high precision.Comment: 57 pages, 17 figure
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