Hadronic final state predictions from CCFM: the hadron-level Monte Carlo generator CASCADE

TL;DR

This paper develops a practical backward-evolution implementation of the CCFM small-x evolution equation within a new hadron-level Monte Carlo generator, Cascade. It demonstrates that backward evolution, guided by the unintegrated gluon density and angular ordering, can reproduce the forward-evolution results and efficiently generate unweighted events. Cascade predictions are then confronted with HERA data across multiple observables, including F2, forward jets, D* photoproduction, and b b̄ production, achieving reasonable agreement and highlighting CCFM as a viable framework for small-x hadronic final-state physics. The work thus provides a fast, consistent tool for exploring small-x dynamics and final-state observables, while outlining avenues for including subleading effects and complete final-state radiation in future refinements.

Abstract

We discuss a practical formulation of backward evolution for the CCFM small-$x$ evolution equation and show results from its implementation in the new Monte Carlo event-generator CASCADE.

Figures (8)

• Figure 1: Kinematic variables for multi-gluon emission. The $t$-channel gluon four-vectors are given by $k_i$ and the gluons emitted in the initial state cascade have four-vectors $p_i$. The upper angle for any emission is obtained from the quark box, as indicated with $\Xi$.
• Figure 2: Comparison of the cross section obtained from the backward evolution Monte Carlo Cascade (solid line) with Smallx (dashed line) both at parton level only. The upper plots show the cross section as a function of the quark rapidity $\eta_q$, the quark transverse momentum $p_t$ and the transverse momentum of the quark pair $p_t^{pair}$. The lower plots show the cross section as a function of the gluon transverse momentum $k_t$, and the multiplicity and transverse energy flow of the gluons from the initial state cascade as a function of the rapidity $\eta$.
• Figure 3: Comparison of quantities of the initial cascade obtained from the backward evolution Monte Carlo Cascade (solid line) with Smallx (dashed line) both at parton level only; $(a)$ shows the splitting variable $z$, $(b)$ gives the transverse momentum $k_t$, $(c)$ shows the transverse momentum of the emitted gluon $q_t$, and $(d)$ shows the ratio $k_t/q_t$.
• Figure 4: Comparison of the structure function $F_2$ as obtained from the backward evolution Monte Carlo Cascade with H1 data H1_F2_1996.
• Figure 5: The cross section for forward-jet production obtained from the Monte Carlo Cascade at hadron level (solid line); $(a-c)$ The cross section for forward-jet production as a function of $x$, for different cuts in $p_t$ compared to H1 data H1_fjets_data ($a-b$) and compared to ZEUS data ZEUS_fjets_data ($c$); $(d)$ The cross section for forward-jet production as a function of $E^2_T/Q^2$ compared to ZEUS_fjets_pt2/q2.