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Hadronization (or hadronisation) is the process of the formation of hadrons out of quarks and gluons. There are two main branches of hadronization: quark-gluon plasma (QGP) transformation^[1] and colour string decay into hadrons.^[2] The transformation of quark-gluon plasma into hadrons is studied in lattice QCD numerical simulations, which are explored in relativistic heavy-ion experiments.^[3] Quark-gluon plasma hadronization occurred shortly after the Big Bang when the quark–gluon plasma cooled down to the Hagedorn temperature (about 150 MeV) when free quarks and gluons cannot exist.^[4] In string breaking new hadrons are forming out of quarks, antiquarks and sometimes gluons, spontaneously created from the vacuum.^[5]

Statistical hadronization

A highly successful description of QGP hadronization is based on statistical phase space weighting^[6] according to the Fermi–Pomeranchuk model of particle production.^[7] This approach was developed, since 1950, initially as a qualitative description of strongly interacting particle production. It was originally not meant to be an accurate description, but a phase space estimate of upper limit to particle yield. In the following years numerous hadronic resonances were discovered. Rolf Hagedorn postulated the statistical bootstrap model (SBM) allowing to describe hadronic interactions in terms of statistical resonance weights and the resonance mass spectrum. This turned the qualitative Fermi–Pomeranchuk model into a precise statistical hadronization model for particle production.^[8] However, this property of hadronic interactions poses a challenge for the statistical hadronization model as the yield of particles is sensitive to the unidentified high mass hadron resonance states. The statistical hadronization model was first applied to relativistic heavy-ion collisions in 1991, which lead to the recognition of the first strange anti-baryon signature of quark-gluon plasma discovered at CERN.^[9]^[10]

Phenomenological studies of string model and fragmentation

The QCD (Quantum Chromodynamics) of the hadronization process are not yet fully understood, but are modeled and parameterized in a number of phenomenological studies, including the Lund string model and in various long-range QCD approximation schemes.^[5]^[11]^[12]

The tight cone of particles created by the hadronization of a single quark is called a jet. In particle detectors, jets are observed rather than quarks, whose existence must be inferred. The models and approximation schemes and their predicted jet hadronization, or fragmentation, have been extensively compared with measurement in a number of high energy particle physics experiments, e.g. TASSO,^[13] OPAL^[14] and H1.^[15]

Hadronization can be explored using Monte Carlo simulation. After the particle shower has terminated, partons with virtualities (how far off shell the virtual particles are) on the order of the cut-off scale remain. From this point on, the parton is in the low momentum transfer, long-distance regime in which non-perturbative effects become important. The most dominant of these effects is hadronization, which converts partons into observable hadrons. No exact theory for hadronization is known but there are two successful models for parameterization.

These models are used within event generators which simulate particle physics events. The scale at which partons are given to the hadronization is fixed by the shower Monte Carlo component of the event generator. Hadronization models typically start at some predefined scale of their own. This can cause significant issue if not set up properly within the Shower Monte Carlo. Common choices of shower Monte Carlo are PYTHIA and HERWIG. Each of these correspond to one of the two parameterization models.

The top quark does not hadronize

The top quark, however, decays via the weak force with a mean lifetime of 5×10⁻²⁵ seconds. Unlike all other weak interactions which typically are much slower than strong interactions, the top quark weak decay is uniquely shorter than the time scale at which the strong force of QCD acts, so a top quark decays before it can hadronize.^[16] The top quark is therefore almost a free particle.^[17]^[18]^[19]

References

^ Rafelski, Johann (2015). "Melting hadrons, boiling quarks". The European Physical Journal A. 51 (9): 114. arXiv:1508.03260. Bibcode:2015EPJA...51..114R. doi:10.1140/epja/i2015-15114-0. ISSN 1434-6001.
^ Andersson, Bo, 1937- (1998). The Lund model. Cambridge, U.K.: Cambridge University Press. ISBN 0-521-42094-6. OCLC 37755081.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
^ Müller, Berndt (2016), Rafelski, Johann (ed.), "A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature", Melting Hadrons, Boiling Quarks - From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN, Cham: Springer International Publishing, pp. 107–116, Bibcode:2016mhbq.book..107M, doi:10.1007/978-3-319-17545-4_14, ISBN 978-3-319-17544-7
^ Letessier, Jean; Rafelski, Johann (2002). Hadrons and Quark–Gluon Plasma (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511534997. ISBN 978-0-521-38536-7.
^ ^a ^b Yu; Dokshitzer, L.; Khoze, V.A.; Mueller, A. H.; Troyan, S.I. (1991). Basics of Perturbative QCD. Editions Frontieres.
^ Rafelski, Johann; Letessier, Jean (2003). "Testing limits of statistical hadronization". Nuclear Physics A. 715: 98c–107c. arXiv:nucl-th/0209084. Bibcode:2003NuPhA.715...98R. doi:10.1016/S0375-9474(02)01418-5. S2CID 18970526.
^ Hagedorn, Rolf (1995), Letessier, Jean; Gutbrod, Hans H.; Rafelski, Johann (eds.), "The Long Way to the Statistical Bootstrap Model", Hot Hadronic Matter, NATO ASI Series, vol. 346, Boston, MA: Springer US, pp. 13–46, doi:10.1007/978-1-4615-1945-4_2, ISBN 978-1-4613-5798-8, retrieved 2020-06-25
^ Torrieri, G.; Steinke, S.; Broniowski, W.; Florkowski, W.; Letessier, J.; Rafelski, J. (2005). "SHARE: Statistical hadronization with resonances". Computer Physics Communications. 167 (3): 229–251. arXiv:nucl-th/0404083. Bibcode:2005CoPhC.167..229T. doi:10.1016/j.cpc.2005.01.004. S2CID 13525448.
^ Rafelski, Johann (1991). "Strange anti-baryons from quark-gluon plasma". Physics Letters B. 262 (2–3): 333–340. Bibcode:1991PhLB..262..333R. doi:10.1016/0370-2693(91)91576-H.
^ Abatzis, S.; Barnes, R.P.; Benayoun, M.; Beusch, W.; Bloodworth, I.J.; Bravar, A.; Caponero, M.; Carney, J.N.; Dufey, J.P.; Evans, D.; Fini, R. (1990). "Λ and production in sulphur-tungsten interactions at 200 GeV/c per nucleon". Physics Letters B. 244 (1): 130–134. doi:10.1016/0370-2693(90)90282-B.
^ Bassetto, A.; Ciafaloni, M.; Marchesini, G.; Mueller, A.H. (1982). "Jet multiplicity and soft gluon factorization". Nuclear Physics B. 207 (2): 189–204. Bibcode:1982NuPhB.207..189B. doi:10.1016/0550-3213(82)90161-4. ISSN 0550-3213.
^ Mueller, A.H. (1981). "On the multiplicity of hadrons in QCD jets". Physics Letters B. 104 (2): 161–164. Bibcode:1981PhLB..104..161M. doi:10.1016/0370-2693(81)90581-5. ISSN 0370-2693.
^ Braunschweig, W.; Gerhards, R.; Kirschfink, F. J.; Martyn, H.-U.; Fischer, H.M.; Hartmann, H.; et al. (TASSO Collaboration) (1990). "Global jet properties at 14-44 GeV center of mass energy in e⁺ e⁻ annihilation". Zeitschrift für Physik C. 47 (2): 187–198. doi:10.1007/bf01552339. ISSN 0170-9739. S2CID 124007688.
^ Akrawy, M.Z.; Alexander, G.; Allison, J.; Allport, P.P.; Anderson, K.J.; Armitage, J.C.; et al. (OPAL Collaboration) (1990). "A study of coherence of soft gluons in hadron jets". Physics Letters B. 247 (4): 617–628. Bibcode:1990PhLB..247..617A. doi:10.1016/0370-2693(90)91911-t. ISSN 0370-2693. S2CID 121998239.
^ Aid, S.; Andreev, V.; Andrieu, B.; Appuhn, R.-D.; Arpagaus, M.; Babaev, A.; et al. (H1 Collaboration) (1995). "A study of the fragmentation of quarks in e⁻ p collisions at HERA". Nuclear Physics B. 445 (1): 3–21. arXiv:hep-ex/9505003. Bibcode:1995NuPhB.445....3A. doi:10.1016/0550-3213(95)91599-h. ISSN 0550-3213. S2CID 18632361.
^ Abazov, V.M.; Abbott, B.; Abolins, M.; Acharya, B.S.; Adams, M.; Adams, T.; et al. (2008). "Evidence for production of single top quarks". Physical Review D. 78 (1): 012005. arXiv:0803.0739. Bibcode:2008PhRvD..78a2005A. doi:10.1103/PhysRevD.78.012005. S2CID 204894756.
^ Seidel, Katja; Simon, Frank; Tesař, Michal; Poss, Stephane (August 2013). "Top quark mass measurements at and above threshold at CLIC". The European Physical Journal C. 73 (8): 2530. arXiv:1303.3758. Bibcode:2013EPJC...73.2530S. doi:10.1140/epjc/s10052-013-2530-7. ISSN 1434-6044. S2CID 118529845.
^ Alioli, S.; Fernandez, P.; Fuster, J.; Irles, A.; Moch, S.; Uwer, P.; Vos, M. (May 2013). "A new observable to measure the top-quark mass at hadron colliders". The European Physical Journal C. 73 (5): 2438. arXiv:1303.6415. Bibcode:2013EPJC...73.2438A. doi:10.1140/epjc/s10052-013-2438-2. ISSN 1434-6044. S2CID 20136858.
^ Gao, Jun; Li, Chong Sheng; Zhu, Hua Xing (24 January 2013). "Top-quark decay at next-to-next-to-leading order in QCD". Physical Review Letters. 110 (4): 042001. arXiv:1210.2808. Bibcode:2013PhRvL.110d2001G. doi:10.1103/PhysRevLett.110.042001. ISSN 0031-9007. PMID 25166153. S2CID 5101838.

Greco, V.; Ko, C. M.; Lévai, P. (2003). "Parton coalescence and the antiproton/pion anomaly at RHIC". Physical Review Letters. 90 (20): 202302. arXiv:nucl-th/0301093. Bibcode:2003PhRvL..90t2302G. doi:10.1103/PhysRevLett.90.202302. PMID 12785885. S2CID 35617853.
Fries, R.J.; Müller, B.; Nonaka, C.; Bass, S.A. (2003). "Hadronization in heavy-ion collisions: Recombination and fragmentation of partons hadronization in heavy-ion collisions". Physical Review Letters. 90 (20): 202303. arXiv:nucl-th/0301087. Bibcode:2003PhRvL..90t2303F. doi:10.1103/PhysRevLett.90.202303. PMID 12785886. S2CID 912540.

[1] Rafelski, Johann (2015). "Melting hadrons, boiling quarks". The European Physical Journal A. 51 (9): 114. arXiv:1508.03260. Bibcode:2015EPJA...51..114R. doi:10.1140/epja/i2015-15114-0. ISSN 1434-6001.

[2] Andersson, Bo, 1937- (1998). The Lund model. Cambridge, U.K.: Cambridge University Press. ISBN 0-521-42094-6. OCLC 37755081.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)

[3] Müller, Berndt (2016), Rafelski, Johann (ed.), "A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature", Melting Hadrons, Boiling Quarks - From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN, Cham: Springer International Publishing, pp. 107–116, Bibcode:2016mhbq.book..107M, doi:10.1007/978-3-319-17545-4_14, ISBN 978-3-319-17544-7

[4] Letessier, Jean; Rafelski, Johann (2002). Hadrons and Quark–Gluon Plasma (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511534997. ISBN 978-0-521-38536-7.

[Yu1991-5] Yu; Dokshitzer, L.; Khoze, V.A.; Mueller, A. H.; Troyan, S.I. (1991). Basics of Perturbative QCD. Editions Frontieres.

[6] Rafelski, Johann; Letessier, Jean (2003). "Testing limits of statistical hadronization". Nuclear Physics A. 715: 98c–107c. arXiv:nucl-th/0209084. Bibcode:2003NuPhA.715...98R. doi:10.1016/S0375-9474(02)01418-5. S2CID 18970526.

[7] Hagedorn, Rolf (1995), Letessier, Jean; Gutbrod, Hans H.; Rafelski, Johann (eds.), "The Long Way to the Statistical Bootstrap Model", Hot Hadronic Matter, NATO ASI Series, vol. 346, Boston, MA: Springer US, pp. 13–46, doi:10.1007/978-1-4615-1945-4_2, ISBN 978-1-4613-5798-8, retrieved 2020-06-25

[8] Torrieri, G.; Steinke, S.; Broniowski, W.; Florkowski, W.; Letessier, J.; Rafelski, J. (2005). "SHARE: Statistical hadronization with resonances". Computer Physics Communications. 167 (3): 229–251. arXiv:nucl-th/0404083. Bibcode:2005CoPhC.167..229T. doi:10.1016/j.cpc.2005.01.004. S2CID 13525448.

[9] Rafelski, Johann (1991). "Strange anti-baryons from quark-gluon plasma". Physics Letters B. 262 (2–3): 333–340. Bibcode:1991PhLB..262..333R. doi:10.1016/0370-2693(91)91576-H.

[10] Abatzis, S.; Barnes, R.P.; Benayoun, M.; Beusch, W.; Bloodworth, I.J.; Bravar, A.; Caponero, M.; Carney, J.N.; Dufey, J.P.; Evans, D.; Fini, R. (1990). "Λ and production in sulphur-tungsten interactions at 200 GeV/c per nucleon". Physics Letters B. 244 (1): 130–134. doi:10.1016/0370-2693(90)90282-B.

[Bassetto1982-11] Bassetto, A.; Ciafaloni, M.; Marchesini, G.; Mueller, A.H. (1982). "Jet multiplicity and soft gluon factorization". Nuclear Physics B. 207 (2): 189–204. Bibcode:1982NuPhB.207..189B. doi:10.1016/0550-3213(82)90161-4. ISSN 0550-3213.

[Mueller1981-12] Mueller, A.H. (1981). "On the multiplicity of hadrons in QCD jets". Physics Letters B. 104 (2): 161–164. Bibcode:1981PhLB..104..161M. doi:10.1016/0370-2693(81)90581-5. ISSN 0370-2693.

[13] Braunschweig, W.; Gerhards, R.; Kirschfink, F. J.; Martyn, H.-U.; Fischer, H.M.; Hartmann, H.; et al. (TASSO Collaboration) (1990). "Global jet properties at 14-44 GeV center of mass energy in e⁺ e⁻ annihilation". Zeitschrift für Physik C. 47 (2): 187–198. doi:10.1007/bf01552339. ISSN 0170-9739. S2CID 124007688.

[14] Akrawy, M.Z.; Alexander, G.; Allison, J.; Allport, P.P.; Anderson, K.J.; Armitage, J.C.; et al. (OPAL Collaboration) (1990). "A study of coherence of soft gluons in hadron jets". Physics Letters B. 247 (4): 617–628. Bibcode:1990PhLB..247..617A. doi:10.1016/0370-2693(90)91911-t. ISSN 0370-2693. S2CID 121998239.

[15] Aid, S.; Andreev, V.; Andrieu, B.; Appuhn, R.-D.; Arpagaus, M.; Babaev, A.; et al. (H1 Collaboration) (1995). "A study of the fragmentation of quarks in e⁻ p collisions at HERA". Nuclear Physics B. 445 (1): 3–21. arXiv:hep-ex/9505003. Bibcode:1995NuPhB.445....3A. doi:10.1016/0550-3213(95)91599-h. ISSN 0550-3213. S2CID 18632361.

[16] Abazov, V.M.; Abbott, B.; Abolins, M.; Acharya, B.S.; Adams, M.; Adams, T.; et al. (2008). "Evidence for production of single top quarks". Physical Review D. 78 (1): 012005. arXiv:0803.0739. Bibcode:2008PhRvD..78a2005A. doi:10.1103/PhysRevD.78.012005. S2CID 204894756.

[17] Seidel, Katja; Simon, Frank; Tesař, Michal; Poss, Stephane (August 2013). "Top quark mass measurements at and above threshold at CLIC". The European Physical Journal C. 73 (8): 2530. arXiv:1303.3758. Bibcode:2013EPJC...73.2530S. doi:10.1140/epjc/s10052-013-2530-7. ISSN 1434-6044. S2CID 118529845.

[18] Alioli, S.; Fernandez, P.; Fuster, J.; Irles, A.; Moch, S.; Uwer, P.; Vos, M. (May 2013). "A new observable to measure the top-quark mass at hadron colliders". The European Physical Journal C. 73 (5): 2438. arXiv:1303.6415. Bibcode:2013EPJC...73.2438A. doi:10.1140/epjc/s10052-013-2438-2. ISSN 1434-6044. S2CID 20136858.

[19] Gao, Jun; Li, Chong Sheng; Zhu, Hua Xing (24 January 2013). "Top-quark decay at next-to-next-to-leading order in QCD". Physical Review Letters. 110 (4): 042001. arXiv:1210.2808. Bibcode:2013PhRvL.110d2001G. doi:10.1103/PhysRevLett.110.042001. ISSN 0031-9007. PMID 25166153. S2CID 5101838.

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 {{short description|Process by which hadrons are formed}}
-'''Hadronization''' (or '''hadronisation''') is the process of the formation of [[hadron]]s out of [[quark]]s and [[gluon]]s. There are two main branches of hadronization: [[Quark–gluon plasma|quark-gluon plasma]] (QGP) transformation<ref>{{Cite journal|last=Rafelski|first=Johann|year=2015|title=Melting hadrons, boiling quarks|journal=The European Physical Journal A|language=en|volume=51|issue=9|pages=114|doi=10.1140/epja/i2015-15114-0|issn=1434-6001|doi-access=free}}</ref> and [[Lund string model|colour string decay]] into hadrons.<ref>{{Cite book|last=Andersson, Bo, 1937-|url=https://www.worldcat.org/oclc/37755081|title=The Lund model|publisher=Cambridge University Press|year=1998|isbn=0-521-42094-6|location=Cambridge, U.K.|oclc=37755081}}</ref> The transformation of quark-gluon plasma into hadrons is studied in [[lattice QCD]] numerical simulations, which are explored in [[Relativistic heavy-ion collisions|relativistic heavy-ion]] experiments.<ref>{{Citation|last=Müller|first=Berndt|title=A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature|work=Melting Hadrons, Boiling Quarks - From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN|pages=107–116|year=2016|editor-last=Rafelski|editor-first=Johann|place=Cham|publisher=Springer International Publishing|language=en|doi=10.1007/978-3-319-17545-4_14|isbn=978-3-319-17544-7|doi-access=free}}</ref> Quark-gluon plasma hadronization occurred shortly after the [[Big Bang]] when the [[quark–gluon plasma]] cooled down to the [[Hagedorn temperature]] (about 150&nbsp;[[MeV]]) when free quarks and gluons cannot exist.<ref>{{Cite book|last1=Letessier|first1=Jean|url=https://www.cambridge.org/core/product/identifier/9780511534997/type/book|title=Hadrons and Quark–Gluon Plasma|last2=Rafelski|first2=Johann|publisher=Cambridge University Press|year=2002|isbn=978-0-521-38536-7|edition=1|doi=10.1017/cbo9780511534997}}</ref> In string breaking new hadrons are forming out of quarks, antiquarks and sometimes gluons, spontaneously created from the [[vacuum]].<ref name=Yu1991/>
+'''Hadronization''' (or '''hadronisation''') is the process of the formation of [[hadron]]s out of [[quark]]s and [[gluon]]s. There are two main branches of hadronization: [[Quark–gluon plasma|quark-gluon plasma]] (QGP) transformation<ref>{{Cite journal|last=Rafelski|first=Johann|year=2015|title=Melting hadrons, boiling quarks|journal=The European Physical Journal A|language=en|volume=51|issue=9|pages=114|doi=10.1140/epja/i2015-15114-0|arxiv=1508.03260 |bibcode=2015EPJA...51..114R |issn=1434-6001|doi-access=free}}</ref> and [[Lund string model|colour string decay]] into hadrons.<ref>{{Cite book|last=Andersson, Bo, 1937-|url=https://www.worldcat.org/oclc/37755081|title=The Lund model|publisher=Cambridge University Press|year=1998|isbn=0-521-42094-6|location=Cambridge, U.K.|oclc=37755081}}</ref> The transformation of quark-gluon plasma into hadrons is studied in [[lattice QCD]] numerical simulations, which are explored in [[Relativistic heavy-ion collisions|relativistic heavy-ion]] experiments.<ref>{{Citation|last=Müller|first=Berndt|title=A New Phase of Matter: Quark-Gluon Plasma Beyond the Hagedorn Critical Temperature|work=Melting Hadrons, Boiling Quarks - From Hagedorn Temperature to Ultra-Relativistic Heavy-Ion Collisions at CERN|pages=107–116|year=2016|editor-last=Rafelski|editor-first=Johann|place=Cham|publisher=Springer International Publishing|language=en|doi=10.1007/978-3-319-17545-4_14|bibcode=2016mhbq.book..107M |isbn=978-3-319-17544-7|doi-access=free}}</ref> Quark-gluon plasma hadronization occurred shortly after the [[Big Bang]] when the [[quark–gluon plasma]] cooled down to the [[Hagedorn temperature]] (about 150&nbsp;[[MeV]]) when free quarks and gluons cannot exist.<ref>{{Cite book|last1=Letessier|first1=Jean|url=https://www.cambridge.org/core/product/identifier/9780511534997/type/book|title=Hadrons and Quark–Gluon Plasma|last2=Rafelski|first2=Johann|publisher=Cambridge University Press|year=2002|isbn=978-0-521-38536-7|edition=1|doi=10.1017/cbo9780511534997}}</ref> In string breaking new hadrons are forming out of quarks, antiquarks and sometimes gluons, spontaneously created from the [[vacuum]].<ref name=Yu1991/>
 == Statistical hadronization ==
-A highly successful description of QGP hadronization is based on statistical phase space weighting<ref>{{Cite journal|last1=Rafelski|first1=Johann|last2=Letessier|first2=Jean|year=2003|title=Testing limits of statistical hadronization|url=https://linkinghub.elsevier.com/retrieve/pii/S0375947402014185|journal=Nuclear Physics A|language=en|volume=715|pages=98c–107c|doi=10.1016/S0375-9474(02)01418-5|arxiv=nucl-th/0209084|s2cid=18970526 }}</ref> according to the Fermi–Pomeranchuk model of particle production.<ref>{{Citation|last=Hagedorn|first=Rolf|title=The Long Way to the Statistical Bootstrap Model|url=http://link.springer.com/10.1007/978-1-4615-1945-4_2|work=Hot Hadronic Matter|series=NATO ASI Series |volume=346|pages=13–46|year=1995|editor-last=Letessier|editor-first=Jean|place=Boston, MA|publisher=Springer US|doi=10.1007/978-1-4615-1945-4_2|isbn=978-1-4613-5798-8|access-date=2020-06-25|editor2-last=Gutbrod|editor2-first=Hans H.|editor3-last=Rafelski|editor3-first=Johann}}</ref> This approach was developed, since 1950, initially as a qualitative description of strongly interacting particle production. It was originally not meant to be an accurate description, but a phase space estimate of upper limit to particle yield. In the following years numerous hadronic resonances were discovered. [[Rolf Hagedorn]] postulated the statistical bootstrap model (SBM) allowing to describe hadronic interactions in terms of statistical resonance weights and the resonance mass spectrum. This turned the qualitative Fermi–Pomeranchuk model into a precise statistical hadronization model for particle production.<ref>{{Cite journal|last1=Torrieri|first1=G.|last2=Steinke|first2=S.|last3=Broniowski|first3=W.|last4=Florkowski|first4=W.|last5=Letessier|first5=J.|last6=Rafelski|first6=J.|year=2005|title=SHARE: Statistical hadronization with resonances|url=https://linkinghub.elsevier.com/retrieve/pii/S0010465505000755|journal=Computer Physics Communications|language=en|volume=167|issue=3|pages=229–251|doi=10.1016/j.cpc.2005.01.004|arxiv=nucl-th/0404083|s2cid=13525448 }}</ref> However, this property of hadronic interactions poses a challenge for the statistical hadronization model as the yield of particles is sensitive to the unidentified high mass hadron resonance states. The statistical hadronization model was first applied to relativistic heavy-ion collisions in 1991, which lead to the recognition of the first strange anti-baryon signature of quark-gluon plasma discovered at [[CERN]].<ref>{{Cite journal|last=Rafelski|first=Johann|year=1991|title=Strange anti-baryons from quark-gluon plasma|url=https://linkinghub.elsevier.com/retrieve/pii/037026939191576H|journal=Physics Letters B|language=en|volume=262|issue=2–3|pages=333–340|doi=10.1016/0370-2693(91)91576-H}}</ref><ref>{{Cite journal|last1=Abatzis|first1=S.|last2=Barnes|first2=R.P.|last3=Benayoun|first3=M.|last4=Beusch|first4=W.|last5=Bloodworth|first5=I.J.|last6=Bravar|first6=A.|last7=Caponero|first7=M.|last8=Carney|first8=J.N.|last9=Dufey|first9=J.P.|last10=Evans|first10=D.|last11=Fini|first11=R.|year=1990|title=Λ and production in sulphur-tungsten interactions at 200 GeV/c per nucleon|url=https://linkinghub.elsevier.com/retrieve/pii/037026939090282B|journal=Physics Letters B|language=en|volume=244|issue=1|pages=130–134|doi=10.1016/0370-2693(90)90282-B}}</ref>
+A highly successful description of QGP hadronization is based on statistical phase space weighting<ref>{{Cite journal|last1=Rafelski|first1=Johann|last2=Letessier|first2=Jean|year=2003|title=Testing limits of statistical hadronization|url=https://linkinghub.elsevier.com/retrieve/pii/S0375947402014185|journal=Nuclear Physics A|language=en|volume=715|pages=98c–107c|doi=10.1016/S0375-9474(02)01418-5|arxiv=nucl-th/0209084|bibcode=2003NuPhA.715...98R |s2cid=18970526 }}</ref> according to the Fermi–Pomeranchuk model of particle production.<ref>{{Citation|last=Hagedorn|first=Rolf|title=The Long Way to the Statistical Bootstrap Model|url=http://link.springer.com/10.1007/978-1-4615-1945-4_2|work=Hot Hadronic Matter|series=NATO ASI Series |volume=346|pages=13–46|year=1995|editor-last=Letessier|editor-first=Jean|place=Boston, MA|publisher=Springer US|doi=10.1007/978-1-4615-1945-4_2|isbn=978-1-4613-5798-8|access-date=2020-06-25|editor2-last=Gutbrod|editor2-first=Hans H.|editor3-last=Rafelski|editor3-first=Johann}}</ref> This approach was developed, since 1950, initially as a qualitative description of strongly interacting particle production. It was originally not meant to be an accurate description, but a phase space estimate of upper limit to particle yield. In the following years numerous hadronic resonances were discovered. [[Rolf Hagedorn]] postulated the statistical bootstrap model (SBM) allowing to describe hadronic interactions in terms of statistical resonance weights and the resonance mass spectrum. This turned the qualitative Fermi–Pomeranchuk model into a precise statistical hadronization model for particle production.<ref>{{Cite journal|last1=Torrieri|first1=G.|last2=Steinke|first2=S.|last3=Broniowski|first3=W.|last4=Florkowski|first4=W.|last5=Letessier|first5=J.|last6=Rafelski|first6=J.|year=2005|title=SHARE: Statistical hadronization with resonances|url=https://linkinghub.elsevier.com/retrieve/pii/S0010465505000755|journal=Computer Physics Communications|language=en|volume=167|issue=3|pages=229–251|doi=10.1016/j.cpc.2005.01.004|arxiv=nucl-th/0404083|bibcode=2005CoPhC.167..229T |s2cid=13525448 }}</ref> However, this property of hadronic interactions poses a challenge for the statistical hadronization model as the yield of particles is sensitive to the unidentified high mass hadron resonance states. The statistical hadronization model was first applied to relativistic heavy-ion collisions in 1991, which lead to the recognition of the first strange anti-baryon signature of quark-gluon plasma discovered at [[CERN]].<ref>{{Cite journal|last=Rafelski|first=Johann|year=1991|title=Strange anti-baryons from quark-gluon plasma|url=https://linkinghub.elsevier.com/retrieve/pii/037026939191576H|journal=Physics Letters B|language=en|volume=262|issue=2–3|pages=333–340|doi=10.1016/0370-2693(91)91576-H|bibcode=1991PhLB..262..333R }}</ref><ref>{{Cite journal|last1=Abatzis|first1=S.|last2=Barnes|first2=R.P.|last3=Benayoun|first3=M.|last4=Beusch|first4=W.|last5=Bloodworth|first5=I.J.|last6=Bravar|first6=A.|last7=Caponero|first7=M.|last8=Carney|first8=J.N.|last9=Dufey|first9=J.P.|last10=Evans|first10=D.|last11=Fini|first11=R.|year=1990|title=Λ and production in sulphur-tungsten interactions at 200 GeV/c per nucleon|url=https://linkinghub.elsevier.com/retrieve/pii/037026939090282B|journal=Physics Letters B|language=en|volume=244|issue=1|pages=130–134|doi=10.1016/0370-2693(90)90282-B}}</ref>
 ==Phenomenological studies of string model and fragmentation==
@@ Line 15: / Line 15: @@
 ==The top quark does not hadronize==
-The [[top quark]], however, decays via the [[weak force]] with a mean lifetime of 5×10<sup>−25</sup> seconds. Unlike all other weak interactions which typically are much slower than strong interactions, the top quark weak decay is uniquely shorter than the time scale at which the [[strong force]] of QCD acts, so a top quark decays before it can hadronize.<ref>{{cite journal |last1=Abazov |first1=V.M. |last2=Abbott |first2=B. |last3=Abolins |first3=M. |last4=Acharya |first4=B.S. |last5=Adams |first5=M. |last6=Adams  |first6=T. |last7=Aguilo |first7=E. |last8=Ahn |first8=S.H. |last9=Ahsan |first9=M. |last10=Alexeev |first10=G.D. |last11=Alkhazov |first11=G. |last12=Alton |first12=A. |last13=Alverson |first13=G. |last14=Alves |first14=G.A. |last15=Anastasoaie |first15=M. |last16=Ancu |first16=L.S. |last17=Andeen |first17=T. |last18=Anderson |first18=S. |last19=Anzelc |first19=M.S. |last20=Aoki |first20=M. |last21=Arnoud |first21=Y. |last22=Arov |first22=M. |last23=Arthaud |first23=M. |last24=Askew |first24=A. |last25=Åsman |first25=B. |last26=Assis Jesus |first26=A.C.S. |last27=Atramentov |first27=O. |last28=Avila |first28=C. |last29=Ay |first29=C. |last30=Badaud |first30=F. |display-authors=6 |year=2008 |title=Evidence for production of single top quarks |journal=Physical Review D |volume=78 |page=012005 |arxiv=0803.0739 |doi=10.1103/PhysRevD.78.012005|s2cid=204894756 }}</ref> The [[top quark]] is therefore almost a free particle.<ref>{{cite journal |last1=Seidel |first1=Katja |last2=Simon |first2=Frank |last3=Tesař |first3=Michal |last4=Poss |first4=Stephane |date=August 2013 |title=Top quark mass measurements at and above threshold at CLIC |journal=The European Physical Journal C |volume=73 |issue=8 |page=2530 |doi=10.1140/epjc/s10052-013-2530-7 |issn=1434-6044 |arxiv=1303.3758 |bibcode=2013EPJC...73.2530S|s2cid=118529845 }}</ref><ref>{{cite journal |last1=Alioli |first1=S. |last2=Fernandez |first2=P. |last3=Fuster |first3=J. |last4=Irles |first4=A. |last5=Moch |first5=S. |last6=Uwer |first6=P. |last7=Vos |first7=M. |date=May 2013 |title=A new observable to measure the top-quark mass at hadron colliders |journal=The European Physical Journal C |volume=73 |issue=5 |page=2438 |doi=10.1140/epjc/s10052-013-2438-2 |arxiv=1303.6415 |issn=1434-6044 |bibcode=2013EPJC...73.2438A|s2cid=20136858 }}</ref><ref>{{cite journal |last1=Gao |first1=Jun |last2=Li |first2=Chong Sheng |last3=Zhu |first3=Hua Xing |date=2013-01-24 |df=dmy-all |title=Top-quark decay at next-to-next-to-leading order in QCD |journal=Physical Review Letters |volume=110 |issue=4 |page=042001 |doi=10.1103/PhysRevLett.110.042001 |pmid=25166153 |issn=0031-9007 |arxiv=1210.2808|s2cid=5101838 }}</ref>
+The [[top quark]], however, decays via the [[weak force]] with a mean lifetime of 5×10<sup>−25</sup> seconds. Unlike all other weak interactions which typically are much slower than strong interactions, the top quark weak decay is uniquely shorter than the time scale at which the [[strong force]] of QCD acts, so a top quark decays before it can hadronize.<ref>{{cite journal |last1=Abazov |first1=V.M. |last2=Abbott |first2=B. |last3=Abolins |first3=M. |last4=Acharya |first4=B.S. |last5=Adams |first5=M. |last6=Adams  |first6=T. |last7=Aguilo |first7=E. |last8=Ahn |first8=S.H. |last9=Ahsan |first9=M. |last10=Alexeev |first10=G.D. |last11=Alkhazov |first11=G. |last12=Alton |first12=A. |last13=Alverson |first13=G. |last14=Alves |first14=G.A. |last15=Anastasoaie |first15=M. |last16=Ancu |first16=L.S. |last17=Andeen |first17=T. |last18=Anderson |first18=S. |last19=Anzelc |first19=M.S. |last20=Aoki |first20=M. |last21=Arnoud |first21=Y. |last22=Arov |first22=M. |last23=Arthaud |first23=M. |last24=Askew |first24=A. |last25=Åsman |first25=B. |last26=Assis Jesus |first26=A.C.S. |last27=Atramentov |first27=O. |last28=Avila |first28=C. |last29=Ay |first29=C. |last30=Badaud |first30=F. |display-authors=6 |year=2008 |title=Evidence for production of single top quarks |journal=Physical Review D |volume=78 |issue=1 |page=012005 |arxiv=0803.0739 |doi=10.1103/PhysRevD.78.012005|bibcode=2008PhRvD..78a2005A |s2cid=204894756 }}</ref> The [[top quark]] is therefore almost a free particle.<ref>{{cite journal |last1=Seidel |first1=Katja |last2=Simon |first2=Frank |last3=Tesař |first3=Michal |last4=Poss |first4=Stephane |date=August 2013 |title=Top quark mass measurements at and above threshold at CLIC |journal=The European Physical Journal C |volume=73 |issue=8 |page=2530 |doi=10.1140/epjc/s10052-013-2530-7 |issn=1434-6044 |arxiv=1303.3758 |bibcode=2013EPJC...73.2530S|s2cid=118529845 }}</ref><ref>{{cite journal |last1=Alioli |first1=S. |last2=Fernandez |first2=P. |last3=Fuster |first3=J. |last4=Irles |first4=A. |last5=Moch |first5=S. |last6=Uwer |first6=P. |last7=Vos |first7=M. |date=May 2013 |title=A new observable to measure the top-quark mass at hadron colliders |journal=The European Physical Journal C |volume=73 |issue=5 |page=2438 |doi=10.1140/epjc/s10052-013-2438-2 |arxiv=1303.6415 |issn=1434-6044 |bibcode=2013EPJC...73.2438A|s2cid=20136858 }}</ref><ref>{{cite journal |last1=Gao |first1=Jun |last2=Li |first2=Chong Sheng |last3=Zhu |first3=Hua Xing |date=2013-01-24 |df=dmy-all |title=Top-quark decay at next-to-next-to-leading order in QCD |journal=Physical Review Letters |volume=110 |issue=4 |page=042001 |doi=10.1103/PhysRevLett.110.042001 |pmid=25166153 |issn=0031-9007 |arxiv=1210.2808|bibcode=2013PhRvL.110d2001G |s2cid=5101838 }}</ref>
 ==References==