Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: QGSJET-II model

The construction of a Monte Carlo generator for high energy hadronic and nuclear collisions is discussed in detail. Interactions are treated in the framework of the Reggeon Field Theory, taking into consideration enhanced Pomeron diagrams which are resummed to all orders in the triple-Pomeron coupling. Soft and “semihard” contributions to the underlying parton dynamics are accounted for within the “semihard Pomeron” approach. The structure of cut enhanced diagrams is analyzed; they are regrouped into a number of subclasses characterized by positively-defined contributions which define partial weights for various “macro-configurations” of hadronic final states. An iterative procedure for a Monte Carlo generation of the structure of final states is described. The model results for hadronic cross sections and for particle production are compared to experimental data.

Figure 1

General multi-Pomeron contribution to hadron-hadron scattering amplitude; elementary scattering processes correspond to Pomeron exchanges (vertical thick lines) or to Pomeron-Pomeron interactions.

Figure 2

A “general Pomeron” (left-hand side [lhs]) consists of the soft and semihard ones—correspondingly the 1st and the 2nd contributions in the rhs.

Figure 3

Recursive equation for projectile net-fan contribution ${\chi }_{a(j)|d(k)}^{\mathrm{net}}(y_1,{\overrightarrow{b}}_1|Y,\overrightarrow{b})$; $y_1$ and $b_1$ are rapidity and impact parameter distances between the projectile proton and the vertex in the handle of the fan. The vertex $(y_2,{\overrightarrow{b}}_2)$ couples together $m_2$ projectile net fans and $n_2$ target net fans. In addition, there are $l\ge 1$ irreducible 2-point sequences of Pomerons and Pomeron loops, exchanged between the vertices $(y_1,{\overrightarrow{b}}_1)$ and $(y_2,{\overrightarrow{b}}_2)$.

Figure 4

Recursive representations for the contributions of irreducible 2-point sequences of Pomerons and Pomeron loops ${\chi }^{\mathrm{loop}(1)}$ (top) and ${\chi }^{\mathrm{loop}}$ (bottom), exchanged between the vertices $(y_1,{\overrightarrow{b}}_1)$ and $(y_2,{\overrightarrow{b}}_2)$.

Figure 5

Recursive representations for cut net-fan diagrams characterized by a fanlike structure of cuts. The top line of the figure defines the contribution $2{\widehat{\chi }}_{a(j)|d(k)}^{\mathrm{fan}}$ of the subset of graphs in which the handle of the fan is cut; the bottom line gives the one of the diagrams with uncut handle, $2{\tilde{\chi }}_{a(j)|d(k)}^{\mathrm{fan}}$.

Figure 6

Complete set of irreducible cut diagrams characterized by a tree-like structure of cuts.

Figure 7

Example of a cut enhanced graph corresponding to a final state with two LRGs (left) and a more complicated graph which describes absorptive corrections to the same final state (right).

Figure 8

Left: Calculated total and elastic proton-proton, pion-proton, and kaon-proton cross sections—respectively solid, dashed, and dotted-dashed lines. Right: Calculated elastic scattering slope for proton-proton scattering. The compilation of experimental data (points) is from Ref. 35.

Figure 9

Left: Calculated differential elastic proton-proton cross section for different $\sqrt{s}$ in GeV (as indicated in the plot). Right: Calculated differential elastic pion-proton and kaon-proton cross sections for the projectile lab. momentum $250\mathrm{GeV}/\mathrm{c}$. Experimental data are from Refs. 36, 37, 38, 39, 40, 41.

Figure 10

Calculated proton structure function $F_2(x,Q^2)$ compared to HERA data [42].

Figure 11

Calculated proton diffractive structure function $F_2^{\mathrm{D}(3)}(x,x_{\mathbb{P}},Q^2)$ compared to ZEUS [43] (triangles) and H1 [44] (squares) data.

Figure 12

Calculated single ${\sigma }_{pp}^{\mathrm{SD}}(M_X^2/s<0.15)$ and double ${\sigma }_{pp}^{\mathrm{DD}}(y_{\mathrm{gap}}^{(0)}\ge 3)$ diffraction proton-proton cross sections (solid lines), compared to CDF data (points) [26, 27]; high mass diffraction contributions to ${\sigma }_{pp}^{\mathrm{SD}}$, ${\sigma }_{pp}^{\mathrm{DD}}$ (dashed lines); contribution to ${\sigma }_{pp}^{\mathrm{DD}}$ from a high mass diffraction of one proton and a low mass excitation of the other one (dotted-dashed line).

Figure 13

Calculated Feynman $x$ spectra of secondary protons in proton-proton collisions at 100 and $200\mathrm{GeV}/\mathrm{c}$ lab. momentum compared to data from Refs. 45 (circles) and 46 (squares).

Figure 14

Calculated Feynman $x$ spectra (left) and rapidity distributions (right) of positive (solid lines) and negative (dashed lines) pions in proton-proton collisions at $158\mathrm{GeV}/\mathrm{c}$ lab. momentum compared to NA49 data [47].

Figure 15

Calculated pseudorapidity density (top row) and transverse momentum spectra (bottom row) of charged particles produced in proton-antiproton (left panels) and proton-proton (right panels) collisions at different c.m. energies in GeV (as indicated in the plots). The data points are from Refs. 48, 49, 50, 51, 52.

Figure 16

Calculated $A$ dependence of total proton-nucleus (solid) and pion-nucleus (dashed) cross sections at, respectively, 500 and $600\mathrm{GeV}/\mathrm{c}$ lab. momentum compared to experimental data [53].

Figure 17

Calculated Feynman $x$ spectra (left) and rapidity distributions (right) of positive (solid lines) and negative (dashed lines) pions in proton-carbon collisions at $158\mathrm{GeV}/\mathrm{c}$ lab. momentum compared to experimental data [31].

Figure 18

Energy dependence of the number of cut Pomerons of different types for proton-proton interactions: exchanged between the projectile and target protons (i), exchanged between the projectile or target proton and some multi-Pomeron vertex (ii), exchanged between a pair of multi-Pomeron vertices (iii).

Figure 19

Alternative representation for the contribution $2{\widehat{\chi }}_{a(j)|d(k)}^{\mathrm{fan}}$ of fanlike cuts of net fans, the handle of the fan being cut.

Figure 20

Alternative representation for the contribution $2{\tilde{\chi }}_{a(j)|d(k)}^{\mathrm{fan}}$ of fanlike cuts of net fans, the handle of the fan being uncut.

Figure 21

Recursive representations for the contributions $2{\overline{\chi }}_{a(j)|d(k)}^{\mathrm{loop}}-2{\tilde{\chi }}_{a(j)|d(k)}^{\mathrm{loop}}$ (top) and $2{\tilde{\chi }}_{a(j)|d(k)}^{\mathrm{loop}}$ (bottom) of the subsets of fanlike cuts of net fans, which have a single cut Pomeron coupled to the projectile hadron.

Figure 22

Recursive representation for the contribution of fanlike cuts of net fans, Pomeron loops and central rapidity gaps neglected.

Figure 23

Examples of cut diagrams corresponding to a single $t$-channel sequence of cut Pomerons exchanged between the vertex $(y_1,{\overrightarrow{b}}_1)$ and the projectile hadron.

Figure 24

Lowest order zigzaglike cut diagrams.