The high energy asymptotics of scattering processes in QCD

High energy scattering in the QCD parton model was recently shown to be a reaction-diffusion process, and thus to lie in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the latter appears naturally in the context of the parton model. We provide a thorough numerical analysis of the mean field approximation, given in QCD by the Balitsky-Kovchegov equation. In the framework of a simple stochastic toy model that captures the relevant features of QCD, we discuss and illustrate the universal properties of such stochastic models. We investigate in particular the validity of the mean field approximation and how it is broken by fluctuations. We find that the mean field approximation is a good approximation in the initial stages of the evolution in rapidity.Comment: 31 pages, 20 figures. The code for BK evolution can be downloaded from http://www.isv.uu.se/~enberg/BK/ v2: several points clarified, discussion of the solutions to the mean-field evolution enhanced through the study of a different class of initial conditions, references added; conclusions unchanged. To appear in Phys. Rev.

Hard Pomeron in exclusive meson production at ILC

We calculate the exclusive process gamma* gamma* ->rho rho at high energy. The Born order estimate and the leading (LLA) and next to leading order (NLLA) BFKL resummation effects show the feasibility of experimental detection in a quite large range of Q2 values at future high energy e+e- linear colliders.Comment: 4 pages, Presented at Photon2005, International Conference on the Structure and Interactions of the Photon, Warsaw 31.08-04.09.2005, by Samuel Wallo

Testing the dynamics of high energy scattering using vector meson production

I review work on diffractive vector meson production in photon-proton collisions at high energy and large momentum transfer, accompanied by proton dissociation and a large rapidity gap. This process provides a test of the high energy scattering dynamics, but is also sensitive to the details of the treatment of the vector meson vertex. The emphasis is on the description of the process by a solution of the non-forward BFKL equation, i.e. the equation describing the evolution of scattering amplitudes in the high-energy limit of QCD. The formation of the vector meson and the non-perturbative modeling needed is also briefly discussed.Comment: 17 pages, 8 figures. Brief review to appear in Mod. Phys. Lett.

QCD factorizations in gamma* gamma* -> rho rho

We calculate the lowest order QCD amplitude, i.e. the quark exchange contribution, to the forward production amplitude of a pair of longitudinally polarized $\rho$ mesons in the scattering of two virtual photons $\gamma^*(Q_1) \gamma^*(Q_2) \to \rho^0_L \rho^0_L$. We show that the scattering amplitude simultaneously factorizes in two quite different ways: the part with transverse photons is described by the QCD factorization formula involving the generalized distribution amplitude of two final $\rho$ mesons, whereas the part with longitudinally polarized photons takes the QCD factorized form with the $\gamma^*_L \to \rho^0_L$ transition distribution amplitude. Perturbative expressions for these, in general, non-perturbative functions are obtained in terms of the $\rho-$meson distribution amplitude

Hard diffraction from parton rescattering in QCD

We analyze the QCD dynamics of diffractive deep inelastic scattering. The presence of a rapidity gap between the target and diffractive system requires that the target remnant emerges in a color singlet state, which we show is made possible by the soft rescattering of the struck quark. This rescattering is described by the path-ordered exponential (Wilson line) in the expression for the parton distribution function of the target. The multiple scattering of the struck parton via instantaneous interactions in the target generates dominantly imaginary diffractive amplitudes, giving rise to an "effective pomeron" exchange. The pomeron is not an intrinsic part of the proton but a dynamical effect of the interaction. This picture also applies to diffraction in hadron-initiated processes. Due to the different color environment the rescattering is different in virtual photon- and hadron-induced processes, explaining the observed non-universality of diffractive parton distributions. This framework provides a theoretical basis for the phenomenologically successful Soft Color Interaction model which includes rescattering effects and thus generates a variety of final states with rapidity gaps. We discuss developments of the SCI model to account for the color coherence features of the underlying subprocesses.Comment: 12 pages, 9 figures, REVTeX4. Somewhat expanded and modified version, two new subsections added. To appear in PR

Evolution of growth in Gulf of St Lawrence cod?

Fishing is often size selective such that the likelihood of capture increases with body size. It has therefore been postulated that fishing could favour evolution of slower growth because smaller size would reduce exposure to fishing gear (e.g. Ricker 1981). A recent study by Swain et al. (2007; hereafter referred to as SSH) makes a valuable attempt to demonstrate such an effect on length-at-age of southern Gulf of St Lawrence cod (Gadus morhua). The strength of their study lies in an innovative combination of three elements. First, as the evolving trait, they used length-at-age 4 years, an age at which cod are representatively sampled but have experienced little fishing mortality. Confounding demographic effects of size-selective fishing were therefore avoided. Second, they had time series of temperature and population density, both possibly affecting length-at-age through phenotypic plasticity. Finally, and as the most innovative element, they linked their approach to quantitative genetics theory. Using a modified breeder's equation, they modelled changes in length-at-age 4 as a function of genetic and environmental components: ΔL4=h2S+βΔE+ϵ. Here ΔL4 and ΔE are differences in length-at-age 4 and environment, respectively, between the focal cohort and its parent generation. S is the selection differential (difference in mean length-at-age 4 between fish observed at age 4 and those observed at reproducing ages). Estimated heritability h2 and parameter β are regression coefficients, and ϵ is a normally distributed error term with zero mean. SSH assumed that the environment can be described by changes in population density Δd and temperature Δt. The key point is that a significant effect of S on ΔL4 would indicate an evolutionary response in length-at-age 4. SSH's statistically favoured regression model was one including both S and Δd; they concluded that the data suggested an evolutionary response to fishing. Of course, as SSH readily pointed out, one cannot rule out the existence of alternative and untested factors. Here, we comment on some caveats in the analysis by SSH. We do not challenge their novel approach, but question some key assumptions and the strength of their conclusions

Prompt atmospheric neutrino fluxes: perturbative QCD models and nuclear effects

We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, $k_T$ factorization including low-$x$ resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for charm and bottom production and compare with the latest data on forward charm meson production from LHCb at $7$ TeV and at $13$ TeV, finding good agreement with the data. In addition, we investigate the role of nuclear shadowing by including nuclear parton distribution functions (PDF) for the target air nucleus using two different nuclear PDF schemes. Depending on the scheme used, we find the reduction of the flux due to nuclear effects varies from $10\%$ to $50 \%$ at the highest energies. Finally, we compare our results with the IceCube limit on the prompt neutrino flux, which is already providing valuable information about some of the QCD models.Comment: 61 pages, 25 figures, 11 table

Resummation in nonlinear equation for high energy factorizable gluon density and its extension to include coherence

Motivated by forthcoming p-Pb experiments at Large Hadron Collider which require both knowledge of gluon densities accounting for saturation and for processes at a wide range of $p_t$ we study basic momentum space evolution equations of high energy QCD factorization. Solutions of those equations might be used to form a set of gluon densities to calculate observables in generalized high energy factorization. Moreover in order to provide a framework for predictions for exclusive final states in p-Pb scattering with high $p_t$ we rewrite the equation for the high energy factorizable gluon density in a resummed form, similarly to what has been done in \cite{Kutak:2011fu} for the BK equation. The resummed equation is then extended to account for colour coherence. This introduces an external scale to the evolution of the gluon density, and therefore makes it applicable in studies of final states.Comment: 14 pages, appendix added, accepted for publication in JHE

The influence of process conditions during pulp storage on the optical properties of Norway spruce high-yield pulps

The influence of process conditions during pulp storage on the optical properties of Norway spruce mechanical pulps. Nordic Pulp & Paper Research Journal, Access to the published version may require subscription. N.B. When citing this work, cite the original published paper. The aim of this work was to study the influence of process conditions (time, pH, temperature and consistency) on the optical properties of mechanical pulps during storage in a clean system as a reference for further work. Laboratory storage trials were performed with unbleached and hydrogen-peroxide bleached wellwashed Norway spruce pulps. In general, the pulp darkened during storage due to an increase in light absorption, especially at shorter wavelengths. After long storage times, the light absorption coefficient, k had increased also at longer wavelengths. No specific peaks were seen in k-spectra. The increase in light absorption was most rapid initially, during the first four hours, for all pulps when stored at high temperature (80°C), and then proceeded more slowly. The corresponding change in colour, measured as a* and b*, was shifted towards red and somewhat towards yellow, and over longer periods of storage, the shift towards yellow became greater. Time and temperature were found to have the largest impact. The effects were similar regardless of the starting pH (4.3-9.7) and pulp consistency (5%-25%). The hydrogen-peroxide bleached pulps were more sensitive to storage compared to the unbleached pulp at temperatures above 50°C. At storage times of up to four hours, the unbleached pulp showed no loss of brightness at either of the storage temperatures. A slightly less bleached pulp darkened more than a highly bleached pulp at all wavelengths. The only difference measured between the two pulps was that the less bleached pulp had a higher content of iron. This higher iron content may be at least part of the reason for the more extensive darkening

Prompt neutrino fluxes from atmospheric charm

We calculate the prompt neutrino flux from atmospheric charm production by cosmic rays, using the dipole picture in a perturbative QCD framework, which incorporates the parton saturation effects present at high energies. We compare our results with the next-to-leading order perturbative QCD result and find that saturation effects are large for neutrino energies above 10^6 GeV, leading to a substantial suppression of the prompt neutrino flux. We comment on the range of prompt neutrino fluxes due to theoretical uncertainties.Comment: 13 pages with 11 figures; expanded discussion, added references, version to be published in Phys. Rev.