A statistical method to estimate low-energy hadronic cross sections

Abstract

In this article we propose a model based on the Statistical Bootstrap approach to estimate the cross sections of different hadronic reactions up to a few GeV in c.m.s energy. The method is based on the idea, when two particles collide a so called fireball is formed, which after a short time period decays statistically into a specific final state. To calculate the probabilities we use a phase space description extended with quark combinatorial factors and the possibility of more than one fireball formation. In a few simple cases the probability of a specific final state can be calculated analytically, where we show that the model is able to reproduce the ratios of the considered cross sections. We also show that the model is able to describe proton -antiproton annihilation at rest. In the latter case we used a numerical method to calculate the more complicated final state probabilities. Additionally, we examined the formation of strange and charmed mesons as well, where we used existing data to fit the relevant model parameters.PACS. 13.75.-n Hadron-induced low-and intermediate-energy reactions and scattering -12.40.Ee Statistical models arXiv:1711.09781v2 [nucl-th]

Charmed and bottomed hadronic cross sections from a statistical model

“…M k , and each of them ultimately decay into a specific hadronic final state. The probability of the number of fireballs is given by kinematical considerations and is described in detail in [17]. The hadronization procedure is based on the statistical bootstrap approach, which sets the probability for the number of hadrons coming from one fireball to P f b 2 = 0.69 and P f b 3 = 0.24 [25].…”

“…These parameters are fitted using experimentally measured particle multiplicities and momentum spectra for protons, pions and kaons in [26], and in [18]. It is also mentioned that T 0 could be essentially anything from 130 to 170 MeV (with some corresponding changes in E 0 and a), giving almost the same mass spectrum, therefore, as our model is not really sensitive to E 0 and a, we did our own fit to T 0 , using exclusive cross section ratios in [17], giving T 0 = 160 MeV.…”

“…For the strange, charm and bottom quarks P s , P c , P b has to be fitted from experiments or has to be estimated from some underlying theory. We choose to fit the parameters from experiments, where for the strange quark, the exclusive pp → K + K − process was used, assuming a constant P s [17]. For the up, down and strange quarks the values are P u = 0.425, P d = 0.425, and P s = 0.15.…”

“…As some of these hardly accessible processes could be important in the investigation of strongly interacting nuclear matter formed in heavy ion collisions [1,15,16], phenomenological model calculations or extrapolation from fits to available data are necessary. In [17] we proposed a model, based on the statistical Bootstrap approach [18][19][20], which were able to give reliable estimates to low/medium energy cross sections (few GeV) for exclusive hadronic processes. The model is extended in [21] to be able to give estimatations to inclusive processes as well, with an approximated error bound coming from the model uncertainties.…”

Observation of Charmonium Mass Modification in Proton Induced Reactions

“…Our transport model, originally valid in the few GeV energy range, was recently upgraded to higher energies of up to 10 AGeV [9]. We use a statistical model [10] to calculate the unknown cross sections, such aspp → J/ψπ, orpp → DD. We apply energy independent charmonium absorption cross sections for every hadron, i.e.…”