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| Lund string model | |
|---|---|
| Name | Lund string model |
| Caption | Schematic of string fragmentation |
| Developer | Gösta Gustafson; Bo Andersson |
| Introduced | 1970s |
| Field | Particle physics |
| Applications | Large Hadron Collider, Deep inelastic scattering, Electron–positron annihilation |
Lund string model
The Lund string model is a phenomenological framework for hadronization used in high-energy particle physics. It describes how quarks and gluons produced in processes such as Electron–positron annihilation, Deep inelastic scattering, and Proton–proton collision evolve into observable hadrons. The model underpins widely used Monte Carlo event generators and connects quantum chromodynamics with experimental measurements at facilities like the Large Hadron Collider and the CERN experiments.
The Lund string model was developed in the 1970s by researchers including Gösta Gustafson and Bo Andersson and was motivated by parton-level insights from Quantum chromodynamics and measurements from experiments such as PETRA and SPS. It treats the color field between separating partons as a one-dimensional relativistic string with energy proportional to length, providing a mechanism for nonperturbative confinement and hadron formation observed in detectors like ALEPH and ATLAS. The approach complements perturbative calculations performed in frameworks associated with DGLAP evolution and BFKL dynamics.
The model rests on principles drawn from Quantum chromodynamics including color flux tube formation between color charges, approximate linear confinement as suggested by lattice studies such as those by Kenneth G. Wilson and results related to the Wilson loop. It posits string tension parameters inspired by phenomenology and lattice estimates, connecting to concepts like Regge phenomenology and the Regge trajectory picture used in hadron spectroscopy. Conservation laws enforced by symmetries studied in contexts like Noether's theorem and experimental constraints from collaborations such as OPAL guide model choices. The interpretation of string breaking involves quantum tunneling notions akin to the Schwinger effect applied to color fields.
The core mathematical ingredients include a linear potential V(r) ≈ κ r with string tension κ, fragmentation functions encoding momentum sharing among produced hadrons, and probabilities for quark–antiquark pair production given by tunneling rates exp(−π m^2/κ) where m denotes flavor mass parameters. The model employs light-cone kinematics familiar from analyses by Paul A. M. Dirac and uses invariant measures to generate hadron four-momenta consistent with phase space and cluster mass distributions studied in analyses such as those by Enrico Fermi. Fragmentation is often implemented via iterative algorithms using Lund symmetric fragmentation functions, which balance constraints from sum rules and fits to data collected by collaborations like TASSO and DELPHI.
Practical implementations appear in major Monte Carlo generators such as PYTHIA, Herwig (in hybrid forms), and components of SHERPA via interfaces to fragmentation modules. Parameters like string tension, transverse momentum width, and strangeness suppression are tuned using data from experiments including LEP, Tevatron, and LHC detectors such as CMS. The generators integrate perturbative parton showers modeled after formalisms by authors of Catani–Seymour and Altarelli–Parisi with nonperturbative string fragmentation stages. Generator tuning efforts are coordinated through initiatives like the Professor project and data preservation efforts by HEPData.
Predictions of the Lund string model are tested against observables including charged particle multiplicities, fragmentation functions, jet shapes, baryon-to-meson ratios, and heavy-flavor hadron spectra measured by collaborations such as ALICE, LHCb, and STAR. The model describes the soft hadron production and the so-called string effect in three-jet events first examined at PETRA and later at LEP experiments. Discrepancies in heavy baryon yields, strangeness enhancement in heavy-ion collisions at facilities like RHIC and LHC lead to refinements and additional mechanisms interfacing with collective models developed by groups associated with ALICE.
Extensions include models of junction topologies for baryon production, color reconnection schemes tuned by ATLAS and CMS to describe underlying event observables, and hybrid approaches combining string fragmentation with cluster models as realized in Herwig. Alternative hadronization frameworks include the cluster model originally used in some versions of HERWIG and statistical hadronization approaches applied in heavy-ion physics by collaborations such as PHENIX. Novel ideas explore connections to string-inspired descriptions in the context of the AdS/CFT correspondence studied by theorists in string theory communities.
The Lund string model is indispensable for full-event simulations used in detector design, acceptance corrections, and background modeling for searches for new phenomena at facilities like CERN and Fermilab. It informs precision measurements of Standard Model parameters in experiments such as LEP electroweak analyses, parton distribution fits involving data from HERA, and studies of jet substructure at LHC experiments. The model's parameter tunes form part of global analyses coordinated by projects like the MCnet network and influence data–theory comparisons in a wide array of particle and nuclear physics programs.
Category:Particle physics models