Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation

Phenomenological models of the dipole cross section that enters in the description of for instance deep inelastic scattering at very high energies have had considerable success in describing the available small-x data in both the saturation region and the so-called extended geometric scaling (EGS) region. We investigate to what extent such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in x of the dipole cross section in these momentum regions. We find that in the EGS region the BK equation yields results that are qualitatively different from those of phenomenological studies. In particular, geometric scaling around the saturation scale is only obtained at asymptotic rapidities. We find that in this limit, the anomalous dimension \gamma(r,x) of phenomenological models approaches a limiting function that is universal for a large range of initial conditions. At the saturation scale, this function equals approximately 0.44, in contrast to the value 0.628 commonly used in the models. We further investigate the dependence of these results on the starting distribution, the small-r limit of the anomalous dimension for fixed rapidities and the x-dependence of the saturation scale.Comment: 14 pages, 8 figures. Extensive revisions, several new results, plots, references and conclusions added; to appear in Phys.Rev.

Geometric Scaling at RHIC and LHC

We present a new phenomenological model of the dipole scattering amplitude to demonstrate that the RHIC data for hadron production in d-Au collisions for all available rapidities are compatible with geometric scaling, just like the small-x inclusive DIS data. A detailed comparison with earlier geometric scaling violating models of the dipole scattering amplitude in terms of an anomalous dimension gamma is made. In order to establish whether the geometric scaling violations expected from small-x evolution equations are present in the data a much larger range in transverse momentum and rapidity must be probed. Predictions for hadron production in p-Pb and p-p collisions at LHC are given. We point out that the fall-off of the transverse momentum distribution at LHC is a sensitive probe of the variation of gamma in a region where x is much smaller than at RHIC. In this way, the expectation for the rise of gamma from small-x evolution can be tested.Comment: 11 pages, 6 figures, minor changes, references added; version to appear in Phys.Rev.

The saturation scale and its x-dependence from Lambda polarization studies

The transverse polarization of forward Lambda hyperons produced in high-energy p-A collisions is expected to display an extremum at a transverse momentum around the saturation scale. This was first observed within the context of the McLerran-Venugopalan model which has an x-independent saturation scale. The extremum arises due to the k_t-odd nature of the polarization dependent fragmentation function, which probes approximately the derivative of the dipole scattering amplitude. The amplitude changes most strongly around the saturation scale, resulting in a peak in the polarization. We find that the observation also extends to the more realistic case in which the saturation scale Q_s is x dependent. Since a range of x and therefore Q_s values is probed at a given transverse momentum and rapidity, this result is a priori not expected. Moreover, the measurement of Lambda polarization over a range of x_F values actually provides a direct probe of the x dependence of the saturation scale. This novel feature is demonstrated for typical LHC kinematics and for several phenomenological models of the dipole scattering amplitude. We show that although the measurement will be challenging, it may be feasible at LHC. The situation at RHIC is not favorable, because the peak will likely be at too low transverse momentum of the Lambda to be a trustworthy measure of the saturation scale.Comment: 11 pages, 6 figure

Significant differentiation in the apolipoprotein(a)/lipoprotein(a) trait between chimpanzees from Western and Central Africa

Elevated Lipoprotein(a) (Lp(a)) plasma concentrations are a risk factor for cardiovascular disease in humans, largely controlled by the LPA gene encoding apolipoprotein(a) (apo(a)). Lp(a) is composed of low-density lipoprotein (LDL) and apo(a) and restricted to Catarrhini. A variable number of kringle IV (KIV) domains in LPA lead to a size polymorphism of apo(a) that is inversely correlated with Lp(a) concentrations. Smaller apo(a) isoforms and higher Lp(a) levels in central chimpanzees (Pan troglodytes troglodytes [PTT]) compared to humans from Europe had been reported. We studied apo(a) isoforms and Lp(a) concentrations in 75 western (Pan troglodytes verus [PTV]) and 112 central chimpanzees, and 12 bonobos (Pan paniscus [PPA]), all wild born and living in sanctuaries in Sierra Leone, Republic of the Congo, and DR Congo, respectively, and 116 humans from Gabon. Lp(a) levels were severalfold higher in western than in central chimpanzees (181.0 +/- 6.7 mg/dl vs. 56.5 +/- 4.3 mg/dl), whereas bonobos showed intermediate levels (134.8 +/- 33.4 mg/dl). Apo(a) isoform sizes differed significantly between subspecies (means subspecies. Human Lp(a) concentrations (mean 47.9 +/- 2.8 mg/dl) were similar to those in central chimpanzees despite larger isoforms (mean 27.1 +/- 4.9 KIV). Lp(a) and LDL, apoB-100, and total cholesterol levels only correlated in PTV. This remarkable differentiation between chimpanzees from different African habitats and the trait's similarity in humans and chimpanzees from Central Africa poses the question of a possible impact of an environmental factor that has shaped the genetic architecture of LPA. Overall, studies on the cholesterol-containing particles of Lp(a) and LDL in chimpanzees should consider differentiation between subspecies