Analysis of the vector form factors fKπ+(Q2)f^+_{K\pi}(Q^2) and fKπ−(Q2)f^-_{K\pi}(Q^2) with light-cone QCD sum rules

In this article, we calculate the vector form factors $f^+_{K\pi}(Q^2)$ and $f^-_{K\pi}(Q^2)$ within the framework of the light-cone QCD sum rules approach. The numerical values of the $f^+_{K\pi}(Q^2)$ are compatible with the existing theoretical calculations, the central value of the $f^+_{K\pi}(0)$, $f^+_{K\pi}(0)=0.97$, is in excellent agreement with the values from the chiral perturbation theory and lattice QCD. The values of the $|f^-_{K\pi}(0)|$ are very large comparing with the theoretical calculations and experimental data, and can not give any reliable predictions. At large momentum transfers with $Q^2> 5GeV^2$, the form factors $f^+_{K\pi}(Q^2)$ and $|f^-_{K\pi}(Q^2)|$ can either take up the asymptotic behavior of $\frac{1}{Q^2}$ or decrease more quickly than $\frac{1}{Q^2}$, more experimental data are needed to select the ideal sum rules.Comment: 22 pages, 16 figures, revised version, to appear in Eur. Phys. J.

Monochromatic Progressions in Random Colorings

Let N^{+}(k)= 2^{k/2} k^{3/2} f(k) and N^{-}(k)= 2^{k/2} k^{1/2} g(k) where 1=o(f(k)) and g(k)=o(1). We show that the probability of a random 2-coloring of {1,2,...,N^{+}(k)} containing a monochromatic k-term arithmetic progression approaches 1, and the probability of a random 2-coloring of {1,2,...,N^{-}(k)} containing a monochromatic k-term arithmetic progression approaches 0, for large k. This improves an upper bound due to Brown, who had established an analogous result for N^{+}(k)= 2^k log k f(k).Comment: 5 page