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Primordial $k_{\perp}$

Partons are expected to have primordial $k_{\perp}$ values of the order of a few hundred MeV from Fermi motion inside the incoming hadrons. In reality, one notes a need for a larger input in the context of shower evolution, either in parton showers or in resummation descriptions. This is not yet understood, but could e.g. represent a breakdown of the DGLAP evolution equations at small $Q^2$. Until a better solution has been found, we therefore have reason to consider an effective `primordial $k_{\perp}$', at the level of the initiators, larger than the one above. For simplicity, a parametrized $Q$-dependent width

\begin{displaymath}
\sigma(Q) = \mathrm{max}\left(\frac{2.1~\mathrm{GeV} \times Q}{7~\mathrm{GeV} + Q},
\mathtt{PARJ(21)}\right)
\end{displaymath} (227)

is introduced, where $\sigma$ is the width of the two-dimensional Gaussian distribution of the initiator primordial $k_{\perp}$ (so that $\langle k_{\perp}^2 \rangle = \sigma^2$), $Q$ is the scale of the hard interaction and PARJ(21) is the standard fragmentation $p_{\perp}$ width. The remnant partons correspond to $Q=0$ and thus hit the lower limit. Apart from the selection of each individual $k_{\perp}$, there is also the requirement that the total $k_{\perp}$ of a beam adds up to zero. Different strategies can be used here, from sharing the recoil of one parton uniformly among all other initiator and remnant partons, to only sharing it among those initiator/remnant partons that have been assigned as nearest neighbours in colour space.


next up previous contents
Next: Beam-Remnant Kinematics Up: Beam Remnants (and Multiple Previous: Colour Topologies   Contents
Stephen Mrenna 2007-10-30