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The Lund String model<ref>B. Andersson, “The Lund model,” Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 7 (1997) 1–471</ref> is a model for [[hadronisation]], ''i.e.'' the process of transforming a partonic final state to a hadronic one.

The model is built upon a "string" analogy, a potential linearly rising with the distance between the two quarks. At some point, the potential energy stored in the string is so large, that the string will break into hadrons. The Lund model includes the possibility for creation of hadrons with light quark content (u, d and s-type), mesons as well as baryons.

The Lund string hadronisation model is implemented in the [[Pythia]] event generator, and can be interfaced stand-alone.

==The yo-yo model for mesons==
The Lund string model is built up around a string model for mesons, where mesons are described as two massless quarks moving in 1+1 dimensions, connected by a massless string, making the quarks turn around when the string is maximally extended. This type of movement pattern (called directrix) is called the yo-yo because of its resemblance to the toy. (See ref. <ref>X. Artru, “Classical String Phenomenology. 1. How Strings Work,” Phys. Rept. 97 (1983) 147.</ref> for a through discussion of several directrices)

[[File:Lund-yoyo.png|thumb|left|alt=Sketch of the yo-yo directrix.|The yo-yo in its rest system with demarcations of its characteristic times, (1) when a period starts, (2) first point of maximal extension, (3) after half a period, the positions are back to start, while the momenta are swapped, (4) after a full period. Figure from ref. <ref>C. Bierlich, “Rope Hadronization, Geometry and Particle Production in pp and pA Collisions“ PhD thesis, Lund University, 2017 [http://bierlich.net/misc/thesis.pdf Full text]</ref>.]]

When the yo-yo is minimally extended (at ''t = 0'' in the figure), all energy is stored in the quarks. When the string is maximally stretched, all energy is stored in the string, and the quarks turn around.

==String breaking==
The string arising from an initial, colour connected parton pair, must break into smaller pieces, in order to produce hadrons. The produced hadron carries away some lightcone momentum from the string, and the when it runs out, the breaking ends. A produced hadron carries away momentum according to the Lund symmetric fragmentation function, which is a distribution function in the momentum fraction ''z'':

<math>
f(z) = N\frac{(1-z)^a}{z}\exp\left(-\frac{-bm^2_\perp}{z} \right).
</math>

Here ''a'' and ''b'' are parameters, <math>m_\perp = \sqrt{m^2 + p^2_\perp}</math> is the transverse mass and ''N'' normalises the distribution.

Since the produced hadron is massive, the quarks will be produced in one point, and must then tunnel out to the classically allowed region <ref>A. Buckley et al., “General-purpose event generators for LHC physics,” Phys. Rept. 504 (2011) 145–233, arXiv:1101.2599 [hep-ph]</ref>. Calculating the production probability using the WKB approximation gives:

<math>
\frac{1}{\kappa}\frac{d\mathcal{P}_q}{d^2p_\perp} \propto \exp(-\pi m_{\perp q}^2/\kappa) = \exp(-\pi p_\perp^2/\kappa )\exp(-\pi m_q^2/\kappa).
</math>

Here <math>\kappa</math> is the string tension, which is around 1 GeV/fm.

==In Pythia==
The Lund String Hadronization model is implemented in the Pythia event generator, and can be interfaced alone as shown in the following example code.



==References==
{{Reflist}}