On the probability distribution of the stochastic saturation scale in QCD

It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations.Comment: 9 pages, 3 figures, misprints corrected, version to appear in PL

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 traveling waves at non-asymptotic energies

Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of the Balitsky-Kovchegov saturation equation for both fixed and running coupling. A universal parametrization of the ``interior'' of the wave front is obtained and compares well with numerical simulations of the original Balitsky-Kovchegov equation, even at non-asymptotic energies. Using this universal parametrization, we find evidence for a traveling-wave pattern of the dipole amplitude determined from the gluon distribution extracted from deep inelastic scattering data.Comment: 10 pages, 5 figures, minor revision, version to appear in PL

The Balitsky-Kovchegov equation in full momentum space

We analyse the Balitsky-Kovchegov (BK) saturation equation in momentum space and solve it numerically. We confirm that, in the limit where the transverse momentum of the incident particle k is much bigger than the momentum transfer q, the equation admits travelling-wave solutions. We extract the q dependence of the saturation scale Q_s(Y) and verify that Q_s(Y=cste) scales as max(q,Q_T), where Q_T is the scale caracterizing the target.Comment: 11 pages, 7 figures, minor corrections, version appeared in Nucl. Phys.

Saturation QCD predictions with heavy quarks at HERA

The measurement of the proton structure function at HERA is often seen as a hint for the observation of saturation in high-energy QCD e.g. through the observation of geometric scaling. Accordingly, the dipole picture provides a powerful framework in which the QCD-based saturation models can be confronted to the data. In this paper, we give a parametrisation of proton structure function which is directly constrained by the dynamics of QCD in its high-energy limit and fully includes the heavy quark effects. We obtain a good agreement with the available data. Furthermore, to the contrary of various models in the literature, we do not observe a significant decrease of the saturation momentum due to the heavy quark inclusion.Comment: 8 pages, 5 figure

Geometric Scaling and QCD Dynamics in DIS

DIS data from HERA show a striking regularity as \sigma^{\gamma^* p} is a function of the ratio \tau=Q^2/Q_s^2(x) only. The scaling function shows a break at \tau ~ 1, which has been taken as an indication for saturation. However, besides saturation also the transition between dominance of k_t-ordered (DGLAP) and k_t-non-ordered (BFKL) evolution contributes to a break around this value of \tau, as well as the suppression for small Q^2 due to finite quark masses and confinement. In this paper we use a dipole cascade model based on Mueller's dipole model, which also includes energy conservation and pomeron mergins, to investigate the contributions of these different effects to the scaling behaviour. As a result we predict that the scaling function for \tau 1 GeV^2 become available. We also investigate the scaling properties of the charm contribution and the impact parameter dependence of the saturation scale.Comment: references added, figures 2, 7 and 8 updated v3: reference added, some misprints correcte

Higher Order Effects in Non Linear Evolution from a Veto in Rapidities

Higher order corrections to the Balitsky-Kovchegov equation have been estimated by introducing a rapidity veto which forbids subsequent emissions to be very close in rapidity and is known to mimic higher order corrections to the linear BFKL equation. The rapidity veto constraint has been first introduced using analytical arguments obtaining a power growth with energy, Q_s (Y) ~ exp(lambda Y), of the saturation scale of lambda ~ 0.45. Then a numerical analysis for the non-linear Balitsky-Kovchegov equation has been carried out for phenomenological rapidities: when a veto of about two units of rapidity is introduced for a fixed value of the coupling constant of alpha_s = 0.2 the saturation scale lambda decreases from ~ 0.6 to ~ 0.3, and when running coupling effects are taken into account it decreases from ~ 0.4 to ~ 0.3.Comment: 17 pages, 10 figure

Mitigating crop yield losses through weed diversity

International audienc

Facing up to the paradigm of ecological intensification in agronomy: Revisiting methods, concepts and knowledge

International audienceAgriculture is facing up to an increasing number of challenges, including the need to ensure various ecosystem services and to resolve apparent conflicts between them. One of the ways forward for agriculture currently being debated is a set of principles grouped together under the umbrella term “ecological intensification”. In published studies, ecological intensification has generally been considered to be based essentially on the use of biological regulation to manage agroecosystems, at field, farm and landscape scales. We propose here five additional avenues that agronomic research could follow to strengthen the ecological intensification of current farming systems. We begin by assuming that progress in plant sciences over the last two decades provides new insight of potential use to agronomists. Potentially useful new developments in plant science include advances in the fields of energy conversion by plants, nitrogen use efficiency and defence mechanisms against pests. We then suggest that natural ecosystems may also provide sources of inspiration for cropping system design, in terms of their structure and function on the one hand, and farmers’ knowledge on the other. Natural ecosystems display a number of interesting properties that could be incorporated into agroecosystems. We discuss the value and limitations of attempting to 'mimic' their structure and function, while considering the differences in objectives and constraints between these two types of system. Farmers develop extensive knowledge of the systems they manage. We discuss ways in which this knowledge could be combined with, or fed into scientific knowledge and innovation, and the extent to which this is likely to be possible. The two remaining avenues concern methods. We suggest that agronomists make more use of meta-analysis and comparative system studies, these two types of methods being commonly used in other disciplines but barely used in agronomy. Meta-analysis would make it possible to quantify variations of cropping system performances in interaction with soil and climate conditions more accurately across environments and socio-economic contexts. Comparative analysis would help to identify the structural characteristics of cropping and farming systems underlying properties of interest. Such analysis can be performed with sets of performance indicators and methods borrowed from ecology for analyses of the structure and organisation of these systems. These five approaches should make it possible to deepen our knowledge of agroecosystems for action