The cosmic ray interaction event generator Sibyll is widely used in extensive air shower simulations. We describe in detail the properties of Sibyll 2.1 and the differences with the original version 1.7. The major structural improvements are the possibility to have multiple soft interactions, introduction of new parton density functions, and an improved treatment of diffraction. Sibyll 2.1 gives better agreement with fixed target and collider data, especially for the inelastic cross sections and multiplicities of secondary particles. Shortcomings and suggestions for future improvements are also discussed.
Cosmic ray interactions in the atmosphere can be regarded as high energy fixed target collisions involving heavy particles. Because of their low intensity, cosmic rays with energies above 10 15 eV can only be studied indirectly through the extensive air showers (EAS) they initiate in the atmosphere. The analysis of EAS relies on air shower Monte Carlo simulations which uses hadronic interaction models. At higher energies, where the cosmic ray energy is beyond the reach of man-made accelerators, hadronic interaction properties have to be extrapolated. The difficulties in the extrapolation are augmented by the fact that, while the forward region contains most of the energetics and is important for shower development, most of the accelerator measurements are made in the central region.
The event generator sibyll [1] is intended for air shower cascade simulations. It is a relatively simple model that is able to reproduce many features of hadronic interactions in fixed target and collider experiments. sibyll is based on the dual parton model (DPM) [2][3][4],
the Lund Monte Carlo algorithms [5,6], and the minijet model [7][8][9][10]. The hard interaction cross section is calculated according to the minijet model. For hadron-nucleus interactions, the interaction probability for each nucleon inside the nucleus is calculated based on the impact parameter distribution. The total interaction cross section is calculated using the Glauber scattering theory [11]. For a nucleus-nucleus interaction the semisuperposition model [12] is used to determine the point of first interaction for the nucleons of the projectile nucleus. The fragmentation region is emphasized as appropriate for air shower simulations. Versions 1.6 and 1.7 of sibyll have been released and used since the early 1990s. The only difference between the two is that version 1.7 can have neutral pion interactions, which is important only for air showers above 10 19 eV because at lower energy all neutral pions decay before they interact.
Several shortcomings of sibyll 1.6 and 1.7 have been identified over the years, such as (1) the total proton-proton cross section calculated with the parton structure functions rose faster than what the experimental measurements indicate; (2) multiplicity fluctuations and average charged particle multiplicity are too small at high energy; (3) diffractive events did not agree well enough with the available data sets. For these reasons the event generator was modified and has been available as sibyll 2.1 [13] since 1999.
The most important changes in version 2.1 are in the description of soft interactions and diffraction dissociation. In order to allow multiple soft interactions, the eikonal for the soft interaction is described using Regge theory, whereas in version 1.7 the eikonal for the soft interactions was energy independent and had the same b dependence (b is the impact parameter) as used for hard interactions. While in version 1.7 the cross section for diffraction dissociation is parametrized independently of the eikonal model, a two-channel eikonal model based on the Good-Walker model [14,15] is used in sibyll 2.1. In addition, low-and highmass diffraction dissociation are treated separately in the new version. However, it should be kept in mind that diffraction dissociation is still not satisfactorily understood. The parton structure functions have been updated to agree with the HERA results. Other parameters were retuned with updated values as well. The multiple soft interaction and new parton densities give larger multiplicity at high energies and better agreement with data. The multiplicity distribution has been improved by implementing better the effect of diffraction dissociation.
The aim of this paper is to describe the current 2.1 version of sibyll to make a reference of the implemented physics models and ideas available. We will outline the overall structure and improvements made, within details of the soft interactions and diffraction dissociation.
We compare sibyll with fixed target and collider data, and we show how it performs in air shower simulations. Finally, we list some remaining shortcomings of sibyll 2.1 and outline how they can be improved.
A. Basic DPM picture sibyll 2.1 retains the DPM picture. In the DPM picture, a nucleon consists of a quark (q, color triplet) and diquark (qq, color antitriplet). Soft gluons are exchanged in an interaction and the color field gets reorganized. The projectile quark (diquark) combines with the target diquark (quark) to form two strings. Each string fragments separately following the Lund string fragmentation model [6].
The fractional energy x of the quark f q (x) is chosen from a distribution of
where α = 3.0 and µ = 0.35 GeV is the effective quark mass. The diquark energy fraction is then f qq (x) = 1 -f q (x). If particles 1, 2 collide to form strings a and b, the energy and momentum of the strings are as follows
To fragment the string, a q-q pair or qq-
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