Charmed and bottomed hadronic cross sections from a statistical model

Abstract

In this work, we extended our statistical model with charmed and bottomed hadrons, and fit the quark creational probabilities for the heavy quarks, using low energy inclusive charmonium and bottomonium data. With the finalized fit for all the relevant types of quarks (up, down, strange, charm, bottom) at the energy range from a few GeV up to a few tens of GeV’s, the model is now considered complete. Some examples are also given for proton–proton, pion–proton, and proton–antiproton collisions with charmonium, bottomonium, and open charm hadrons in the final state.

Production cross sections of tetraquark states in elementary hadronic collisions

“…To estimate the energy dependent inclusive cross sections at lower energies, the inclusive sums are calculated in the two fireball scheme, as it has been done for e.g. charmonium states in [28]. Here, the previously fitted low energy quark creational probabilities, and not the ones estimated at 7 TeV are used.…”

“…The model is introduced in [26] where it was used to describe low energy exclusive cross sections and proton-antiproton annihilation at rest. In [27] the model is extended to describe inclusive cross sections at higher energies as well, while in [28] it is used to describe inclusive charmonium, bottomonium and open charm cross sections as well. In this work it is extended further to describe tetraquarks in the diquark picture which is the most straightforward way to include these states into the model.…”

“…, m n ) is the n-body phase space integral, consisting the Breit-Wigner factors for resonant particles, ρ(E) is the density of states obtained from the statistical Bootstrap, N I is a symmetry factor, and s l is the total spin of the l th particle. All of these factors are described in details in [26][27][28].…”

“…The model is used at relatively low energies (few GeV's) up to a few tens of GeV's where the quark creational probabilities are fitted through measured exclusive and inclusive cross sections [28]. At these energies a constant value for the up, down and strange quarks were satisfactory, however for the heavier quarks (charm,bottom) a simple linearly rising probability is assumed as P c,b = a c,b x.…”

“…Also it is worth to note, that due to the running nature of the charm and bottom quark creational probbilities the other parameters have to run as well, however because the charm and bottom probabilities are so small, the values shown here can be used here. The detailed explanation for these parameters and their validity is given in [28]. To validate the model for tetraquark production it will be necessary to know the quark creational probabilities at √ s = 7 TeV, which is clearly out of the range of our previous fits.…”