A global analysis of inclusive diffractive cross sections at HERA

We describe the most recent data on the diffractive structure functions from the H1 and ZEUS Collaborations at HERA using four models. First, a Pomeron Structure Function (PSF) model, in which the Pomeron is considered as an object with parton distribution functions. Then, the Bartels Ellis Kowalski Wusthoff (BEKW) approach is discussed, assuming the simplest perturbative description of the Pomeron using a two-gluon ladder. A third approach, the Bialas Peschanski (BP) model, based on the dipole formalism is then described. Finally, we discuss the Golec-Biernat-W\"usthoff (GBW) saturation model which takes into account saturation effects. The best description of all avaible measurements can be achieved with either the PSF based model or the BEKW approach. In particular, the BEKW prediction allows to include the highest $\beta$ measurements, which are dominated by higher twists effects and provide an efficient and compact parametrisation of the diffractive cross section. The two other models also give a good description of cross section measurements at small $x$ with a small number of parameters. The comparison of all predictions allows us to identify interesting differences in the behaviour of the effective pomeron intercept and in the shape of the longitudinal component of the diffractive structure functions. In this last part, we present some features that can be discriminated by new experimental measurements, completing the HERA program.Comment: 32 pages, 18 figure

Hard diffraction and the nature of the Pomeron

We ask the question whether the quark and gluon distributions in the Pomeron obtained from QCD fits to hard diffraction processes at HERA can be dynamically generated from a state made of ``valence-like'' gluons and sea quarks as input. By a method combining backward Q^2-evolution for data exploration and forward Q^2-evolution for a best fit determination, we find that the diffractive structure functions published by the H1 collaboration at HERA can be described by a simple ``valence-like'' input at an initial scale of order mu^2 ~ 2.3-2.7 GeV^2. The parton number sum rules at the initial scale mu^2 for the H1 fit gives 2.1\pm .1\pm .1 and .13\pm .01 \pm .02 for gluon and sea quarks respectively, corresponding to an initial Pomeron state made of (almost) only two gluons. It has flat gluon density leading to a plausible interpretation in terms of a gluonium state.Comment: 14 pages, 9 figure

X-ray scattering study of two length scales in the critical fluctuations of CuGeO3

The critical fluctuations of CuGeO$_3$ have been measured by synchrotron x-ray scattering, and two length scales are clearly observed. The ratio between the two length scales is found to be significantly different along the $a$ axis, with the $a$ axis along the surface normal direction. We believe that such a directional preference is a clear sign that surface random strains, especially those caused by dislocations, are the origin of the long length scale fluctuations.Comment: 5 pages, 4 figures, submitted to PR

Systematics of geometric scaling

Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the original definition, or \log(Q^2)-\lambda \sqrt{Y}, which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. A ``Quality Factor'' (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept \lambda. Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation.Comment: 4 pages, 4 figure

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

Confronting next-leading BFKL kernels with proton structure function data

We propose a phenomenological study of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach applied to the data on the proton structure function F_2 measured at HERA in the small-x_{Bjorken} region. In a first part we use a simplified ``effective kernel'' approximation leading to few-parameter fits of F_2. It allows for a comparison between leading-logs (LO) and next-to-leading logs (NLO) BFKL approaches in the saddle-point approximation, using known resummed NLO-BFKL kernels. The NLO fits give a qualitatively satisfactory account of the running coupling constant effect but quantitatively the chi squared remains sizeably higher than the LO fit at fixed coupling. In a second part, a comparison of theory and data through a detailed analysis in Mellin space (x_{Bjorken} -> omega) leads to a more model independent approach to the resummed NLO-BFKL kernels we consider and points out some necessary improvements of the extrapolation at higher orders.Comment: 19 pages, 11 figures, minor corrections, one figure improved, LO fit with reunning coupling constant and references added, conclusions unchange

Structural Critical Scattering Study of Mg-Doped CuGeO3

We report a synchrotron x-ray scattering study of the diluted spin-Peierls (SP) material Cu_(1-x)Mg_xGeO_3. We find that for x>0 the temperature T_m at which the spin gap is established is significantly higher than the temperature T_s at which the SP dimerization attains long-range order. The latter is observed only for xx_c the SP correlation length quickly decreases with increasing x. We argue that impurity-induced competing interactions play a central role in these phenomena.Comment: 5 pages, 4 embedded eps figures, to appear in PR

The microscopic spin-phonon coupling constants in CuGeO_3

Using RPA results, mean field theory, and refined data for the polarization vectors we determine the coupling constants of the four Peierls-active phonon modes to the spin chains of CuGeO_3. We then derive the values of the coupling of the spin system to the linear ionic displacements, the bond lengths and the angles between bonds. Our values are consistent with microscopic theories and various experimental results. We discuss the applicability of static approaches to the spin-phonon coupling. The c-axis anomaly of the thermal expansion is explained. We give the values of the coupling constants in an effective one-dimensional Hamiltonian.Comment: 11 pages, two figures, 13 tables, PRB 59 (in press

QCD at small x and nucleus-nucleus collisions

At large collision energy sqrt(s) and relatively low momentum transfer Q, one expects a new regime of Quantum Chromo-Dynamics (QCD) known as "saturation". This kinematical range is characterized by a very large occupation number for gluons inside hadrons and nuclei; this is the region where higher twist contributions are as large as the leading twist contributions incorporated in collinear factorization. In this talk, I discuss the onset of and dynamics in the saturation regime, some of its experimental signatures, and its implications for the early stages of Heavy Ion Collisions.Comment: Plenary talk given at QM2006, Shanghai, November 2006. 8 pages, 8 figure