From the exclusive photoproduction of heavy quarkonia at HERA to the EDDE at TeVatron and LHC

Exclusive photoproduction of heavy quarkonia at HERA is analyzed in the framework of the Regge-eikonal approach together with the nonrelativistic bound state formalism. Total and differential cross-sections for the process $\gamma+p\to (Q\bar{Q})_{1S}+p$ are calculated. The model predicts cross-sections of Exclusive Double Diffractive Events (EDDE) at TeVatron and LHC.Comment: 14 pages, 6 figures, reference is adde

Energetics of a strongly correlated Fermi gas

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: E_\text{internal}=\hbar^2\Omega C/4\pi am+\sum_{\vect k\sigma}(\hbar^2 k^2/2m)(n_{\vect k\sigma}-C/k^4) where the external potential energy is not included, $a$ is the scattering length, $\Omega$ is the volume, n_{\vect k\sigma} is the average number of fermions with wave vector \vect k and spin $\sigma$, and C\equiv\lim_{\vect k\to\infty} k^4 n_{\vect k\up} =\lim_{\vect k\to\infty} k^4 n_{\vect k\down}. This result is a \textit{universal identity}. Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including the short-range structure of the one-body reduced density matrix and the pair correlation function, and the dimer-fermion scattering length, are also studied.Comment: 28 pages, 1 figur

General removal lemma

We formulate and prove a general result in spirit of hypergraph removal lemma for measurable functions of several variables.Comment: 5 page

Empirical Earth rotation model: a consistent way to evaluate Earth orientation parameters

It is customary to perform analysis of the Earth's rotation in two steps: first, to present results of estimation of the Earth orientation parameters in the form of time series based on a simplified model of variations of the Earth's rotation for a short period of time, and then to process this time series of adjustments by applying smoothing, re-sampling and other numerical algorithms. Although this approach saves computational time, it suffers from self-inconsistency: total Earth orientation parameters depend on a subjective choice of the apriori Earth orientation model, cross-correlations between points of time series are lost, and results of an operational analysis per se have a limited use for end users. An alternative approach of direct estimation of the coefficients of expansion of Euler angle perturbations into basis functions is developed. These coefficients describe the Earth's rotation over entire period of observations and are evaluated simultaneously with station positions, source coordinates and other parameters in a single LSQ solution. In the framework of this approach considerably larger errors in apriori EOP model are tolerated. This approach gives a significant conceptual simplification of representation of the Earth's rotation.Comment: To be published in the Proceedings of the Geodetic Reference Frame symposium held in Muenchen in October 2006. 6 pages, 2 table