Total cross sections for hadron collisions on the basis of the HPR1R2 model
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EMENTARY PARTICLES AND FIELDS Theory
Total Cross Sections for Hadron Collisions on the Basis of the HPR1R2 Model V. I. Belousov* , V. V. Ezhela, Yu. V. Kuyanov, and N. P. Tkachenko Institute for High Energy Physics, National Research Center Kurchatov Institute, pl. Nauki 1, Protvino, Moscow oblast, 142281 Russia Received February 20, 2015; in final form, August 24, 2015
Abstract—The results of a quantitative, statistically complete, description of the total-cross-section data obtained worldwide for hadron–hadron (photon–hadron) collisions and compiled in the Particle Data Group surveys are presented for several versions of a universal analytic parametrization of amplitudes for forward hadron–hadron (photon-hadron) scattering. DOI: 10.1134/S1063778816010075
INTRODUCTION New experimental data on total cross sections for nucleon–nucleon collisions at the c.m. collision energy of 7 TeV from experiments of the ATLAS Collaboration at the Large Hadron Collider (LHC, CERN) [1] required additionally tuning parameters of the HPR1R2 model. In this article, we present a parameter-dependent description of an extended set of experimental data from [2] on two observables that are determined by the elastic-scattering amplitudes T ab (s, t) for particles a and b at zero scattering angle [(θ = 0) ∼ (t = 0)]. These are the total collision ab (s) ∼ Im T ab (s, 0) and the paramcross sections σtot Re T ab (s, 0) . eter ρab (s) = Im T ab (s, 0) The variables s and t are Mandelstam variables in GeV2 units (see Kinematics, page 7, in http:// pdg.lbl.gov/2012/reviews/contents_sports.html). In the following, we will sometimes employ the ab (s ) or ρab (s ), generic symbol model(si ) instead of σtot i i thereby going over to a shorthand notation without loss of meaning of respective expressions. EXPERIMENTAL DATA An integrated compilation of data obtained over the period extending up to 1988 and saved on computer data carriers was composed by the CERNHERA group (see [3–5]). Extended data are available from the website http://pdg.lbl.gov/2014/html/ *
E-mail: [email protected]
computer_read.html. In Figs. 1 and 2, the points with total-error bars stand for experimental data, while the curves represent a parameter-dependent description of data for various collisions, the √ parameter values being fitted to experimental data at s 5 GeV. In order to avoid encumbering Fig. 1, we do not show there data on reactions involving neutrons. The arrows above the curves that represent the total cross sections indicate the lower threshold in energy for the data sample used in the fitting procedure. The parametrizations of the amplitudes are constructed as linear forms in the function ln2 (s/sM ), which specifies the asymptotic behavior according to Heisenberg [6– 8], and the functions (s/sM )−η1 and (s/sM )−η2 , which stand for the contributions of the C + and C − Reggeons, respectively. √ The table gives parameter values for s 5 GeV. A data analysis involves a simultaneous description of 20 sets of data on the total cross sections for (¯ p)p(p, n); Σ− p; π
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