Pierre Valin

Bio: Pierre Valin is an academic researcher from Université de Moncton. The author has contributed to research in topics: Unitarity. The author has an hindex of 1, co-authored 1 publications receiving 8 citations.

Eikonal representation in the momentum-transfer space

Abstract: By means of empirical fits to the differential cross section data on pp and $\bar{p}p$ elastic scattering, above 10 GeV (center-of-mass energy), we determine the eikonal in the momentum-transfer space (q 2- space). We make use of a numerical method and a novel semi-analytical method, through which the uncertainties from the fit parameters can be propagated up to the eikonal in the q 2- space. A systematic study of the effect of the experimental information at large values of the momentum transfer is developed and discussed in detail. We present statistical evidence that the imaginary part of the eikonal changes sign in the q 2- space and that the position of the zero decreases as the energy increases; after the position of the zero, the eikonal presents a minimum and then goes to zero through negative values. We discuss the applicability of our results in the phenomenological context, outlining some connections with nonperturbative QCD. A short review and a critical discussion on the main results concerning “model-independent” analyses are also presented.

A study on analytic parametrizations for proton–proton cross-sections and asymptotia

Abstract: A comparative study on some representative parametrizations for the total and elastic cross-sections as a function of energy is presented. The dataset comprises pp and scattering in the c.m. energy interval 5 GeV–8 TeV. The parametrization for the total cross-section at low and intermediate energies follows the usual reggeonic structure (non-degenerate trajectories). For the leading high-energy pomeron contribution, we consider three distinct analytic parametrizations: either a power (P) law, or a log-squared (L2) law or a log-raised-to-γ (Lγ) law, where the exponent γ is treated as a real free fit parameter. The parametrizations are also extended to fit the elastic (integrated) cross-section data in the same energy interval. Our main conclusions are the following: (1) the data reductions with the logarithmic laws show strong dependence on the unknown energy scale involved, which is treated here either as a free parameter or fixed at the energy threshold; (2) the fit results with the P law, the L2 law (free scale) and the Lγ law (fixed scale and exponent γ above 2) are all consistent within their uncertainties and with the experimental data up to 7 TeV, but they partially underestimate the high-precision TOTEM measurement at 8 TeV; (3) once compared with these results, the L2 law with fixed scale is less consistent with the data and, in the case of a free scale, this pomeron contribution decreases as the energy increases below the scale factor (which lies above the energy cutoff); (4) in all cases investigated, the predictions for the asymptotic ratio between the elastic and total cross-sections, within the uncertainties, do not exceed the value 0.430 (therefore, below the black-disc limit) and the results favor rational limits between 1/3 and 2/5. We are led to conclude that the rise of the hadronic cross-sections at the highest energies still constitutes an open problem, demanding further and detailed investigation.

A study on analytic parametrizations for proton-proton cross-sections and asymptotia

Abstract: A comparative study on some representative parametrizations for the total and elastic cross-sections as a function of energy is presented. The dataset comprises pp and \bar{p}p scattering in the c.m energy interval 5 GeV-8 TeV. The parametrization for the total cross-section at low and intermediate energies follows the usual reggeonic structure (non-degenerate trajectories). For the leading high-energy pomeron contribution, we consider three distinct analytic parametrizations: either a power (P) law, or a log-squared (L2) law or a log-raised-to-gamma (Lgamma) law, where the exponent gamma is treated as a real free fit parameter. The parametrizations are also extended to fit the elastic (integrated) cross-section data in the same energy interval. Our main conclusions are the following: the data reductions with the logarithmic laws show strong dependence on the unknown energy scale involved, which is treated here either as a free parameter or fixed at the energy threshold; the fit results with the P law, the L2 law (free scale) and the Lgamma law (fixed scale and exponent gamma above 2) are all consistent within their uncertainties and with the experimental data up to 7 TeV, but they partially underestimate the high-precision TOTEM measurement at 8 TeV; once compared with these results, the L2 law with fixed scale is less consistent with the data and, in the case of a free scale, this pomeron contribution decreases as the energy increases below the scale factor (which lies above the energy cutoff); in all cases investigated, the predictions for the asymptotic ratio between the elastic and total cross-sections, within the uncertainties, do not exceed the value 0.430 (therefore, below the black-disc limit) and the results favor rational limits between 1/3 and 2/5. We are led to conclude that the rise of the hadronic cross-sections at the highest energies still constitutes an open problem.

Erratum: Elementary amplitudes in the multiple diffraction theory of pp and p-barp elastic scattering

Abstract: We discuss some fundamental aspects of the pure-geometrical models related to the connection between the scattering amplitude of composite hadrons and the scattering amplitude of the constituents partons in the multiple diffraction theory. A comparative study of the parton-parton amplitudes currently used in these models is presented, showing its main mathematical and physical features and also a comparison with results from a model-independent analysis, for the dynamical part of the eikonal.

Applicability Of A Representation For The Martin's Real-part Formula In Model-independent Analyses

Abstract: Using a novel representation for the Martin's real-part formula without the full scaling property, an almost model-independent description of the proton–proton differential cross-section data at high energies (19.4 GeV–62.5 GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted inelastic overlap function presents a peripheral effect (tail) above 2 fm and the extracted opacity function is characterized by a zero (change of sign) in the momentum transfer space, confirming results from previous model-independent analyses. Analytical parametrization for these empirical results are introduced and discussed. The importance of investigations on the inverse problems in high-energy elastic hadron scattering is stressed and the relevance of the proposed representation is commented. A short critical review on the use of Martin's formula is also presented.