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Register a new userThe soft and the hard pomerons: elastic scattering and unitarisation
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The hard pomeron component needed to reproduce small-x data seems to be present in elastic scattering at moderate energy. If this is the case, it is likely that the total cross section at the LHC will be appreciably larger than previously expected.
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Recent data from LHC13 by the TOTEM Collaboration on $sigma_{tot}$ and $rho$ have indicated disagreement with all the Pomeron model predictions by the COMPETE Collaboration (2002). On the other hand, as recently demonstrated by Martynov and Nicolescu (MN), the new $sigma_{tot}$ datum and the unexpected decrease in the $rho$ value are well described by the maximal Odderon dominance at the highest energies. Here, we discuss the applicability of Pomeron dominance through fits to the textit{most complete set} of forward data from $pp$ and $bar{p}p$ scattering. We consider an analytic parametrization for $sigma_{tot}(s)$ consisting of non-degenerated Regge trajectories for even and odd amplitudes (as in the MN analysis) and two Pomeron components associated with double and triple poles in the complex angular momentum plane. The $rho$ parameter is analytically determined by means of dispersion relations. We carry out fits to $pp$ and $bar{p}p$ data on $sigma_{tot}$ and $rho$ in the interval 5 GeV - 13 TeV (as in the MN analysis). Two novel aspects of our analysis are: (1) the dataset comprises all the accelerator data below 7 TeV and we consider textit{three independent ensembles} by adding: either only the TOTEM data (as in the MN analysis), or only the ATLAS data, or both sets; (2) in the data reductions to each ensemble, uncertainty regions are evaluated through error propagation from the fit parameters, with 90 % CL. We argument that, within the uncertainties, this analytic model corresponding to soft Pomeron dominance, does not seem to be excluded by the textit{complete} set of experimental data presently available.
Recent models of soft diffraction include a hard pomeron pole besides the usual soft term. Such models violate the black-disk limit around Tevatron energies, so that they need to be supplemented by a unitarisation scheme. Several such schemes are considered in this letter, where we show that they lead to a large uncertainty at the LHC. We also examine the impact of unitarisation on various small-t observables, the slope in t of the elastic cross section, or the ratio of the real to imaginary parts of the scattering amplitude, leading to the conclusion that the existence of a hard pomeron in soft scattering may be confirmed by LHC data.
Universality in QCD factorization of parton densities, fragmentation functions, and soft factors is endangered by the process dependence of the directions of Wilson lines in their definitions. We find a choice of directions that is consistent with factorization and that gives universality between e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the Drell-Yan process. Universality is only modified by a time-reversal transformation of the soft function and parton densities between Drell-Yan and the other processes, whose only effect is the known reversal of sign for T-odd parton densities like the Sivers function. The modifications of the definitions needed to remove rapidity divergences with light-like Wilson lines do not affect the results.
The dynamical cascade of momentum, spin, charge, and other quantum numbers from an ultra-violet process into the infra-red is a fundamental concern for asymptotically free or conformal gauge field theories. It is also a practical concern for any high energy scattering experiment with energies above tens of GeV. We present a formulation of the evolution equation that governs this cascade, the Banfi-Marchesini-Smye equation, from both an effective field theory point of view and a direct diagrammatic argument. The equation uses exact momentum conservation, and is applicable to both scattering with initial and final state hard partons. The direct diagrammatic formulation is organized by constructing a generating functional. This functional is also automatically realized with soft wilson lines and collinear field operators coupled to external currents. The two approaches are directly connected by reverse engineering the Lehman-Symanzik-Zimmermann reduction procedure to insert states within the soft and collinear matrix elements. At leading order, the cascade is completely controlled by the soft anomalous dimension. By decomposing the anomalous dimension into on-shell and off-shell regions as would be realized in the effective field theory approach with a Glauber mediating potential, we are forced to choose a transverse momentum ordering in order to trivialize the overlap between Glauber potential contributions and the pure soft region. The evolution equation then naturally incorporates factorization violating effects driven by off-shell exchanges for active partons. Finally, we examine the consequences of abandoning exact momentum conservation as well as terminating the evolution at the largest inclusive scale, procedures often used to simplify the analysis of the cascade.
We calculate the probability that the rapidity gaps in diffractive processes survive both eikonal and enhanced rescattering. We present arguments that enhanced rescattering, which violates soft-hard factorization, is not very strong. Accounting for NLO effects, there is no reason to expect that the black disc regime is reached at the LHC. We discuss the predictions for the survival of the rapidity gaps for exclusive Higgs production at the LHC.
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