Cosmic ray interaction event generator SIBYLL 2.1

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.

Figure 1

Minimum transverse momentum ($p_T^{\min }$) required for the collision to qualify as a hard scattering. Sibyll 1.7 had a constant minimum at $\sqrt{5}\mathrm{GeV}$, whereas this has been modified to change with $\sqrt{s}$ in version 2.1.

Figure 2

Minijet production, with the energy fraction carried by the minijets (left panel) and the average number of minijets produced (right panel) over a range of $\sqrt{s}$.

Figure 3

Geometric interpretation of a hard interaction (left) and soft interaction (right).

Figure 4

The total and inelastic cross section of $p$-air, $p\mathrm{\text{−}}p$ (left panel) and $\pi$-air, $\pi \mathrm{\text{−}}p$ (right panel) collision for version 2.1 (red solid lines) and 1.7 (blue dotted lines). The minijet cross section is also shown in dashed lines, where the higher one is version 2.1.

Figure 5

The Feynman $x$ ($x_F$) and rapidity ($y$) distribution of pions plotted against NA49 result of $p\mathrm{\text{−}}p$ [41] and $p\mathrm{\text{−}}C$ [42] collision at $E_{\mathrm{lab}}=158\mathrm{GeV}$. Version 2.1 (1.7) results are shown in red solid (blue dotted) lines. The left (right) panels show the production of ${\pi }^{+}$ (${\pi }^{-}$). The upper panels show the $x_F$ distribution, where the $p\mathrm{\text{−}}C$ collision results are multiplied by factor 10 in order to show both interactions on the same plot. The lower panels show the $y$ distribution: the upper (lower) set of lines and data points are from the $p\mathrm{\text{−}}C$ ($p\mathrm{\text{−}}p$) collision.

Figure 6

Inclusive cross sections of ${\pi }^{+}\mathrm{\text{−}}p$, $C$ (left panels), $K^{+}\mathrm{\text{−}}p$, $C$ (center panels), $p\mathrm{\text{−}}p$, $C$ (right panels) collisions for ${\pi }^{+}$ (upper panels) and ${\pi }^{-}$ (lower panels) production, where the events have $p_T=0.3\mathrm{GeV}$. Collision energy is $E_{\mathrm{lab}}=100\mathrm{GeV}$, and are compared with results from a FNAL fixed target experiment [43]. Version 2.1 (1.7) results are shown in red solid (blue dotted) lines.

Figure 7

Pseudorapidity ($\eta$) distribution of $p\mathrm{\text{−}}\overline{p}$ collision, for various c.m. energies, for version 1.7 (left panel) and 2.1 (right panel) Data points from top are $E_{\mathrm{c}.\mathrm{m}.}=1800\mathrm{GeV}$ [44], 630 GeV [45], 200 GeV [46], 53 GeV [47]. Note the deficit of charged particles in version 1.7 at high energies in the central region.

Figure 8

Probability of charged particle multiplicity ($n_{\mathrm{ch}}$) distribution at UA5 detector with $E_{\mathrm{c}.\mathrm{m}.}=900\mathrm{GeV}$ for three different $\eta$ ranges; $|\eta |<0.5$ ($\times 0.01$), $|\eta |<1.5$, $|\eta |<3$ ($\times 100$) [48] for version 2.1 (red solid lines) and 1.7 (blue dotted lines). The two sets of lines are for having a stable and decaying $K_s^0$.

Figure 9

Distribution of leading protons as a function of $x_F$ compared to the $p\mathrm{\text{−}}p$ collision data from the NAL bubble chamber [49]. Version 2.1 (1.7) results are shown in red solid (blue dotted) lines. The results and data points have been multiplied by factor of tens (405 GeV by 1000, 303 GeV by 100, 205 GeV by 10, 102 GeV by 1).

Figure 10

Leading proton distribution of Sibyll compared to the low-$Q^2$ [beam pipe calorimeter (BPC)] and higher-$Q^2$ [deep inelastic scattering (DIS)] ZEUS data [50, 51]. Version 2.1 (1.7) outcome is shown in red solid (blue dotted) lines. The transverse momentum of the protons are limited to $p_T^2<0.5{\mathrm{GeV}}^2$. The c.m. collision energy of Sibyll is 210 GeV.

Figure 11

Inclusive cross sections of ${\Lambda }^0$ (left panel) and $K_s^0$ (right panel) production from $p\mathrm{\text{−}}Be$ collision at $E_{\mathrm{lab}}=300\mathrm{GeV}$ for various angles [52]. Version 2.1 (1.7) results are shown in red solid (blue dotted) lines. From the top, the sets of lines and data are for angles 0.25, 1.5, 2.9, 5.0, 6.9, 8.8 mrad. The results and data have been multiplied by factors of tens to show them in one figure (0.25 mrad by ${10}^5$, 1.5 mrad by ${10}^4$, 2.9 mrad by ${10}^3$, 5.0 mrad by 100, 6.9 mrad by 10, 8.8 mrad by 1).

Figure 12

The mean $X_{\max }$ of protons and iron nuclei as a function of primary energy at zenith angle $\theta =45°$. In the case of Sibyll (red solid lines), QGSJET II-3 (orange dot-dashed lines), and EPOS 1.61 (black dashed lines), the data are taken from the hybrid simulator CONEX [58, 59] with statistical uncertainly of typically $1–3\mathrm{g}{\mathrm{cm}}^{-2}$. For Sibyll 1.6 (blue dotted lines), 500 events were simulated with Corsika 5.62 [60] (from Ref. 61) with statistical uncertainty of $1–4\mathrm{g}{\mathrm{cm}}^{-2}$.

Figure 13

Average number of muons at sea level $⟨N_{\mu }⟩$, obtained in proton showers with zenith angle $\theta =0°$. Each energy represents 5000 showers simulated with the hybrid method. The solid (dotted) line represents the values obtained with Sibyll 2.1 (Sibyll 1.7). Panels (a)–(c) show the average number of muons with energy above 30, 3- and 0.3 GeV respectively. Figure is adapted from Fig. 14 of Ref. 62.