The Lund fragmentation process for a multi-gluon string according to the area law

Abstract

The Lund Area Law describes the probability for the production of a set of colourless hadrons from an initial set of partons, in the Lund string fragmentation model. It was derived from classical probability concepts but has later been interpreted as the result of gauge invariance in terms of the Wilson gauge loop integrals. In this paper we will present a general method to implement the Area Law for a multi-gluon string state. In this case the world surface of the massless relativistic string is a geometrically bent (1 + 1)-dimensional surface embedded in the (1 + 3)-dimensional Minkowski space. The partonic states are in general given by a perturbative QCD cascade and are consequently defined only down to a cutoff in the energy momentum fluctuations. We will show that our method defines the states down to the hadronic mass scale inside an analytically calculable scenario.We will then show that there is a differential version of our process which is closely related to the generalised rapidity range λ, which has been used as a measure on the partonic states. We identify λ as the area spanned between the directrix curve (the curve given by the parton energy momentum vectors laid out in colour order, which determines the string surface) and the average curve (to be called the P-curve) of the stochastic X-curves (curves obtained when the hadronic energy-momentum vectors are laid out in rank order). Finally we show that from the X-curve corresponding to a particular stochastic fragmentation situation it is possible to reproduce the directrix curve (up to one starting vector and a set of sign choices, one for each hadron). This relationship provides an analytical formulation of the notion of Parton-Hadron Duality. The whole effort is made in order to get a new handle to treat the transition region between where we expect perturbative QCD to work and where the hadronic features become noticeable.

The λ-measure and the generalised dipoles in the Lund model

“…We note in passing that the possibility of partitioning the contributions to the λmeasure as contributions from connected flat regions has an interesting consequence for the fragmentation of a string according to the Lund model area law. Such a fragmentation scheme was presented in [8], which was closely related to the λ-measure and the X -curve. Particle production in this scheme can be thought of as partitioning the plaquettes mentioned here into smaller plaquettes, one for each hadron.…”

“…It is interesting to note that the X -curve (or rather a close relative, called the Pcurve in [8]) and the λ-measure play a major role in the String Fragmentation process for multigluon string states. In the process that we devised in [8], the final state hadron energy-momenta, laid out in rank order, constitute a curve, the X-curve.…”

“…It is interesting to note that the X -curve (or rather a close relative, called the Pcurve in [8]) and the λ-measure play a major role in the String Fragmentation process for multigluon string states. In the process that we devised in [8], the final state hadron energy-momenta, laid out in rank order, constitute a curve, the X-curve. The X-curve follows the directrix at a typical stochastically fluctuating distance and the area in between the two curves could be thought of as the area in the Lund Model Area law [8].…”

Bose-Einstein Correlations in the Lund Model for Multijet Systems

“…Recently, an alternative way to fragment the multigluon string has been developed in [3]. Unlike the approach in Pythia, this method does not try to follow the complicated surface of a multigluon string.…”

Illuminating Light

“…Measuring in detail the production of different type of particles and their correlations addresses various open questions. In the more simple case of pp collisions, the process of hadronization is described by fragmentation, but is not fully understood and requires ad hoc assumptions [38][39][40]. For heavy-ion collisions popular ways to describe hadronization is either via fragmentation-like processes as in pp collisions, or via a coalescence picture.…”