Transverse momentum correlations of quarks in recursive jet models

In the symmetric string fragmentation recipe adopted by PYTHIA for jet simulations, the transverse momenta of successive quarks are uncorrelated. This is a simplification but has no theoretical basis. Transverse momentum correlations are naturally expected, for instance, in a covariant multiperipheral model of quark hadronization. We propose a simple recipe of string fragmentation which leads to such correlations. The definition of the jet axis and its relation with the primordial transverse momentum of the quark is also discussed.

Figure 1

Comparison of the splitting functions of Eq. (13) and Eqs. (6), (8), and (9) in the $(Z,k_x^{\prime })$ plane, for $k_y^{\prime }=k_y=0$. Vertical scales: $k_x^{\prime }$ in ${\mathrm{fm}}^{-1}$. Upper figures: $k_x=0$; lower figures: $k_x=2{\mathrm{fm}}^{-1}$. Left figures: Eq. (13) with $c=0$; middle figures: Eq. (13) with $c=1$; right figures: Eqs. (6), (8), and (9). The other parameters are $a=1$, $b_{\mathrm{T}}=1{\mathrm{fm}}^2$, $b_{\mathrm{L}}=0.25{\mathrm{fm}}^2$, $m_h=m_{\pi }=0.7{\mathrm{fm}}^{-1}$.

Figure 2

Space-time picture of the string fragmentation model. The string breaks at points $Q_2\cdots Q_4$. Hadrons are liberated at points $H_1\cdots H_4$ (choice $c=0$), but they can be considered as really “born” at points $C_1\cdots C_4$ (choice $c=1$).

Figure 3

Multiperipheral diagram illustrating Eq. (23).