{"title":"Particle production in a toy model: Multiplicity distribution and entropy","authors":"Eugene Levin","doi":"10.1103/physrevd.111.016019","DOIUrl":null,"url":null,"abstract":"In this paper we found the multiplicity distribution of the produced dipoles in the final state for dipole-dipole scattering in the zero dimension toy models. This distribution shows the great differences from the distributions of partons in the wave function of the projectile. However, in spite of this difference the entropy of the produced dipoles turns out to be the same as the entropy of the dipoles in the wave function. This fact is not surprising since in the parton approach only dipoles in the hadron wave function which can be produced at t</a:mi>=</a:mo>+</a:mo>∞</a:mi></a:math> and measured by the detectors. We can also confirm the result of Kharzeev and Levin that this entropy is equal to <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:msub><c:mi>S</c:mi><c:mi>E</c:mi></c:msub><c:mo>=</c:mo><c:mi>ln</c:mi><c:mrow><c:mo stretchy=\"false\">(</c:mo><c:mi>x</c:mi><c:mi>G</c:mi><c:mo stretchy=\"false\">(</c:mo><c:mi>x</c:mi><c:mo stretchy=\"false\">)</c:mo><c:mo stretchy=\"false\">)</c:mo></c:mrow></c:math>, where we denote by <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:mi>x</i:mi><i:mi>G</i:mi></i:math> the mean multiplicity of the dipoles in the deep inelastic scattering. The evolution equations for <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:msub><k:mi>σ</k:mi><k:mi>n</k:mi></k:msub></k:math> are derived. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"164 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.016019","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we found the multiplicity distribution of the produced dipoles in the final state for dipole-dipole scattering in the zero dimension toy models. This distribution shows the great differences from the distributions of partons in the wave function of the projectile. However, in spite of this difference the entropy of the produced dipoles turns out to be the same as the entropy of the dipoles in the wave function. This fact is not surprising since in the parton approach only dipoles in the hadron wave function which can be produced at t=+∞ and measured by the detectors. We can also confirm the result of Kharzeev and Levin that this entropy is equal to SE=ln(xG(x)), where we denote by xG the mean multiplicity of the dipoles in the deep inelastic scattering. The evolution equations for σn are derived. Published by the American Physical Society2025
期刊介绍:
Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including:
Particle physics experiments,
Electroweak interactions,
Strong interactions,
Lattice field theories, lattice QCD,
Beyond the standard model physics,
Phenomenological aspects of field theory, general methods,
Gravity, cosmology, cosmic rays,
Astrophysics and astroparticle physics,
General relativity,
Formal aspects of field theory, field theory in curved space,
String theory, quantum gravity, gauge/gravity duality.