Saturation Effects in Deep Inelastic Scattering at low Q2Q^2 and its Implications on Diffraction

We present a model based on the concept of saturation for small $Q^2$ and small $x$. With only three parameters we achieve a good description of all Deep Inelastic Scattering data below $x=0.01$. This includes a consistent treatment of charm and a successful extrapolation into the photoproduction regime. The same model leads to a roughly constant ratio of diffractive and inclusive cross section.Comment: 24 pages, 12 figures, Latex-fil

QCD analysis of the diffractive structure function F_2^{D(3)}

The proton diffractive structure function $F_2^{D(3)}$ measured in the H1 and ZEUS experiments at HERA is analyzed in terms of both Regge phenomenology and perturbative QCD evolution. A new method determines the values of the Regge intercepts in ``hard'' diffraction, confirming a higher value of the Pomeron intercept than for soft physics. The data are well described by a QCD analysis in which point-like parton distributions, evolving according to the DGLAP equations, are assigned to the leading and sub-leading Regge exchanges. The gluon distributions are found to be quite different for H1 and ZEUS. A {\it global fit} analysis, where a higher twist component is taken from models, allows us to use data in the whole available range in diffractive mass and gives a stable answer for the leading twist contribution. We give sets of quark and gluon parton distributions for the Pomeron, and predictions for the charm and the longitudinal proton diffractive structure function from the QCD fit. An extrapolation to the Tevatron range is compared with CDF data on single diffraction. Conclusions on factorization breaking depend critically whether H1 (strong violation) or ZEUS (compatibility at low $\beta$) fits are taken into account.Comment: 24 page

Spin dependent structure function g_1 at low x and low Q^2

Theoretical description of the spin dependent structure function g_1(x,Q^2) in the region of low values of x and Q^2 is presented. It contains the Vector Meson Dominance contribution and the QCD improved parton model suitably extended to the low Q^2 domain. Theoretical predictions are compared with the recent experimental data in the low x, low Q^2 region

Phase-matching conditions for nonlinear frequency conversion by use of aligned molecular gases

Includes bibliographical references (page 348).Transient birefringence can be induced in a gas of anisotropic molecules by an intense polarized laser pulse. We propose to use this birefringence to phase match nonlinear optical frequency-conversion processes. The conditions for anisotropic phase matching are derived, and experimental conditions required for phase-matched third-harmonic generation in a gas-filled hollow-core fiber are presented. We show that these conditions are experimentally feasible over a significant parameter range, making possible a new type of nonlinear optics

Observation and absolute frequency measurements of the 1S0 - 3P0 optical clock transition in ytterbium

We report the direct excitation of the highly forbidden (6s^2) 1S0 - (6s6p) 3P0 optical transition in two odd isotopes of ytterbium. As the excitation laser frequency is scanned, absorption is detected by monitoring the depletion from an atomic cloud at ~70 uK in a magneto-optical trap. The measured frequency in 171Yb (F=1/2) is 518,295,836,593.2 +/- 4.4 kHz. The measured frequency in 173Yb (F=5/2) is 518,294,576,850.0 +/- 4.4 kHz. Measurements are made with a femtosecond-laser frequency comb calibrated by the NIST cesium fountain clock and represent nearly a million-fold reduction in uncertainty. The natural linewidth of these J=0 to J=0 transitions is calculated to be ~10 mHz, making them well-suited to support a new generation of optical atomic clocks based on confinement in an optical lattice.Comment: 4 pages, 3 figure

On the behaviour of single scale hard small xx processes in QCD near the black disc limit

We argue that at sufficiently small Bjorken $x$ where pQCD amplitude rapidly increases with energy and violates probability conservation the shadowing effects in the single-scale small $x$ hard QCD processes can be described by an effective quantum field theory of interacting quasiparticles. The quasiparticles are the perturbative QCD ladders. We find, within the WKB approximation, that the smallness of the QCD coupling constant ensures the hierarchy among many-quasiparticle interactions evaluated within physical vacuum and in particular, the dominance in the Lagrangian of the triple quasiparticle interaction. It is explained that the effective field theory considered near the perturbative QCD vacuum contains a tachyon relevant for the divergency of the perturbative QCD series at sufficiently small $x$. We solve the equations of motion of the effective field theory within the WKB approximation and find the physical vacuum and the transitions between the false (perturbative) and physical vacua. Classical solutions which dominate transitions between the false and physical vacua are kinks that cannot be decomposed into perturbative series over the powers of $\alpha_s$. These kinks lead to color inflation and the Bose-Einstein condensation of quasiparticles. The account of the quantum fluctuations around the WKB solution reveals the appearance of the "massless" particles-- "phonons". It is explained that "phonons" are relevant for the black disc behaviour of small $x$ processes, leading to a Froissart rise of the cross-section. The condensation of the ladders produces a color network occupying a "macroscopic" longitudinal volume. We discuss briefly the possible detection of new QCD effects.Comment: 24 pages, 1 Figure. References added, and several misprints eliminate

Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation

We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.Comment: LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev.

Integrable spin chains and scattering amplitudes

In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large Nc and in the multi-Regge kinematics for some physical regions have the high energy behavior appearing from the contribution of the Mandelstam cuts in the complex angular momentum plane of the corresponding t-channel partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon composite states in the adjoint representation of the gauge group SU(Nc). In the leading logarithmic approximation (LLA) their contribution to the six point amplitude is in full agreement with the known two-loop result. The Hamiltonian for the Mandelstam states constructed from n gluons in LLA coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wave functions using the integrals of motion and the Baxter-Sklyanin approach.Comment: Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich (ed

Deep inelastic events containing a forward photon as a probe of small xx dynamics

We calculate the rate of producing deep inelastic events containing an energetic isolated forward photon at HERA. We quantify the enhancement arising from the leading $\log 1/x$ gluon emissions with a view to using such events to identify the underlying dynamics.Comment: 11 pages, Latex, 7 ps figure

Theoretical issues of small xx physics

The perturbative QCD predictions concerning deep inelastic scattering at low $x$ are summarized. The theoretical framework based on the leading log $1/x$ resummation and $k_t$ factorization theorem is described and some recent developments concerning the BFKL equation and its generalization are discussed. The QCD expectations concerning the small $x$ behaviour of the spin dependent structure function $g_1(x,Q^2)$ are briefly summarized and the importance of the double logarithmic terms which sum contributions containing the leading powers of $\alpha_s ln^2(1/x)$ is emphasised. The role of studying final states in deep inelastic scattering for revealing the details of the underlying dynamics at low $x$ is pointed out and some dedicated measurements, like deep inelastic scattering accompanied by an energetic jet, the measurement of the transverse energy flow etc., are briefly discussed.Comment: 17 pages, LATEX, 7 uuencoded eps figures include