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