783 research outputs found
R-matrix-valued Lax pairs and long-range spin chains
In this paper we discuss -matrix-valued Lax pairs for
Calogero-Moser model and their relation to integrable quantum long-range spin
chains of the Haldane-Shastry-Inozemtsev type. First, we construct the
-matrix-valued Lax pairs for the third flow of the classical Calogero-Moser
model. Then we notice that the scalar parts (in the auxiliary space) of the
-matrices corresponding to the second and third flows have form of special
spin exchange operators. The freezing trick restricts them to quantum
Hamiltonians of long-range spin chains. We show that for a special choice of
the -matrix these Hamiltonians reproduce those for the Inozemtsev chain. In
the general case related to the Baxter's elliptic -matrix we obtain a
natural anisotropic extension of the Inozemtsev chain. Commutativity of the
Hamiltonians is verified numerically. Trigonometric limits lead to the
Haldane-Shastry chains and their anisotropic generalizations.Comment: 12 pages, Introduction added, minor correction
LHC soft physics and TMD gluon density at low x
We study the unintegrated, or transverse momentum dependent (TMD) gluon
distribution obtained from the best description of the LHC data on the
inclusive spectra of hadrons produced in the mid-rapidity region and low
transverse momenta at starting scale Q0^2 = 1 GeV^2. To extend this gluon
density at higher Q^2 we apply the Catani-Ciafoloni-Fiorani-Marchesini (CCFM)
evolution equation. The influence of the initial (starting) non-perturbative
gluon distribution is studied. The application of the obtained gluon density to
the analysis of the ep deep inelastic scattering allows us to get the results
which describe reasonably well the H1 and ZEUS data on the longitudinal proton
structure function FL(x,Q^2). So, the connection between the soft processes at
LHC and small x physics at HERA has been confirmed and extended to a wide
kinematical region.Comment: 8 pages, 3 figures, 1 tabl
Quark-diquark model for p(\bar p)-p elastic scattering at high energies
A model for elastic scattering of protons at high energies based on the
quark-diquark representation of the proton is discussed. The predictions of the
model are compared with experimental data for the differential elastic
cross-sections from available databasesComment: 4 pages, 5 figure
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