E-36: the First Proto-Megascience Experiment at NAL

Total Page:16

File Type:pdf, Size:1020Kb

E-36: the First Proto-Megascience Experiment at NAL FERMILAB-PUB-16-523 ACCEPTED !"#$%&'()&*+,-.&/,0.0"1)23-4+)54)&!67),+8)5.&3.&9:; Vitaly!S.!Pronskikh! Fermi!National!Accelerator!Laboratory,!Batavia,!USA! <5.,0=>4.+05& E-36,!an!experiment!,-!small!angle!proton-proton!scattering9!began!testing!equipment!in!the!National Accelerator!Laboratory’s!newl'!achieved!100-GeV!beam!on!February!12,!1972,!marking!the!beginning!of NAL’s!experimental!program.!This!experiment9!which!drew!collaborators!from!NAL9!Joint!Institute!for Nuclear! Research! (JINR! a$! Dubna,! USSR),! the! University! of! Rochester! (Rochester,! New! YorkV! and Rockefeller!University!(New!York!City)!was!significant!not!only!as!a!milestone!in!Fermilab’s!history!but!also as!%!model!of!cooperation!between!the!East!and!West!at!a!time!when!Cold!War!tensions!still!ran!high.!An examination!of!the!origin,!operation,!a-H!resoluti,-!of!E-?@!and!th2!chain!of!experiments!it!spawned reveals!the!complex!interplay!oO!science!and!politics!tha$!drove!these!experiments!as!well!as!seed.!of!the megascience!paradig3!that!has!come!to!dominate!high-energy!physi6.!research!since!the!1970s. !67),+8)5.&3()3=&0?&@AB& Quantum!chromodynamics!(QCD)! only! bega-! t,! emerge! whe-! asymptotic! freedom! was! discusseH! by! David!Gross,!Frank!Wilczek19!and!David!Politzer2!in!the!early!seventies,!when!E36!was!already!underway)! Despite!the!fact!that!QCU!is!currentl'!a!standard!tool!fo+!the!calculation!of!hadron!scattering!amplitudes,! its! application! to! the! study! of! many! processes! measured! at! high-energy! accelerators! is! still! quite! complicated)! Examples! are! such! seemingly! simple! processes! as! small! angle! scattering! of! protons! ,-! protons,! whic0! E-?@! measured.! Basically9! along! with! many! other! important! reactions! with! small! momentu3!transfer9!small!angle!proton-prot,-!scattering!generally!falls!outside!the!grasp!oO!perturbative! QCD3.! Since!the!1970s,!physicists!were!using!the!Tullio!Regge!theory4!to!explain!wha$!is!going!on!in!small!angle! proton-prot,-!scattering)!The!Regge!theory!is!a!phenomenologica&!approach59!which!in!the!1970s!was!not! linked!to!the!quar/!structure!of!the!proton!but!relieH!,-!the!so-called!S-matrix!formalis3!(an!approach! alternativ2!to!QCD,!without!elementary!particles,!which!was!almost!abandoned!sinc2!late!1970s!but!later! resulted!in!wha$!nowadays!is!known!as!string!theory))!In!the!Regge!theory,!to!describe!elastic!proton- prot,-! diffracti,-! at! hig0! energies,! unknow-! scattering! amplitudes! are! replaceH! i-! equations! wit0! structure.! containing! function.! called! Regge! trajectorie.! (or! Reggeons))! Despite! many! theoretical! attempts!undertaken!sinc2!th2!1960s,!ther2!ar2!st#&&!no!consistent!universa&!methods!to!deduce!Reggeons! from!QCD.!Sinc2!19759!theorists!have!developed!certain!approaches!of!limited!scope6,7!tha$!relate!QCD!to! the!leading!Reggeon.!The!leadinC!Reggeon8,99!which!could!effectively!explain!the!diffracti,-!behavior!of! hadrons!as!well!as!equal!co-asymptotic!cro..!section.!for!proton.!and!anti-protons!at!hig0!energies109!was! sometime.! called! the! Pomeron,! after! the! Soviet! theorist,! I.! Pomeranchuk11.! Such! approaches! as! th2! diffractive! scattering! model,! optical! theorem,!a-H! analyticity! were! the! language! useH! by! the! E36! experimentalists!for!dat%!analysis!and!interpretation12,!13.! This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The!participants!i-!E-?@!and!its!subsequent!chain!of!experiments!did!not!have!to!refe+!to!QCD!o+!the!quark! model!in!their!papers!in!order!to!interpret!their!results.!!In!his!PhD!thesis!based!on!E-?@!resultsi9!Dan!Gross! deriveH!bonds!from!Quantum!FielH!Theory!a-H!f,E-H!that!they!are!all!satisfieH!by!the!models!used.!The! experimentalists! remember! they! woulH! sometimes! talk! with! theorists! at! lunch! but! diH! not! have! any! routine!guidance!from!them.!As!Dick!Carrigan9!an!E-?@!participant,!recollects,!“we!usually!diH!not!have! much! guidance! from! theory.”! 14! By! its! conclusion,! E-?@! had! produceH! scientifically! valuable! results,! including!its!finding!that!the!ratio!oO!the!real!to!imaginary!pa+$!oO!the!proton-prot,-!scattering!amplitude! became!positive!at!about!?JJ!GeV)!This!resul$!prompteH!considerable!discussi,-!because!it!contradicted! the!accepted!models!of!th2!time15)!! However,!in!the!earliest!days!of!E-?@!ther2!was!another!factor!that!played!%!key!rol2!in!th2!justification!of! the!experiment:!politics.! C4+)5.+?+4&35=&70D+.+43D&405.)6.& The!beginning!of!the!1960s!was!marked!by!not!only!the!firs$!manned!space!flight,!but!als,!a!number!of! political!crises.!Erection!oO!the!Berlin!Wall!completed!the!separation!between!Eastern!and!Western!Blocs! in!1961,!while!the!Cuban!missile!crisis!in!1962!aggravated!tensions!between!Eas$!and!West.!The!West!had! not! yet! fully! recovered! from! the! shock! caused! by! the! launch! oO! Sputnik,! and! the! level! oO! Soviet! technological!developmen$!haH!t,!be!reckoned!with.!However,!competition!between!the!blocs,!which! extended!to!science,!was!balanced!by!an!essential!desire!t,!cooperate)!For!example,!the!year!1969!was! marked!by!signs!of!successful!scientific!collaboration!betwee-!the!East!a-H!the!West!i-!the!fielH!of!plasma! physics:! %! group! from! Culham! Laboratory,! Ud! reported! successful! measurements! of! th2! electron! temperature!in!a!tokamak!a$!the!Kurchatov!Institute,!USSR16)!! Particl2!accelerators!constituted!another!domai-!in!which!the!US!and!the!Soviets!haH!long!gone!head!to! head.!Which!country!could!boast!the!highest!energy!particle!accelerator!in!the!world?!Historian!Audra! Wolfe!wrote!about!that!period:!“The!United!States!might!have!lost!the!race!to!put!the!first!satellite!into! space,!but!it!would!wage!a!fierce!battle!to!produce!the!most!Ph.D.’s,!the!most!Nobel!laureates,!and!the! biggest!particle!accelerators.”17!! In!1949,!four!years!after!World!War!II,!%!synchrocyclotron!capable!of!accelerating!proton.!to!560!MeVii,18! was!built!fo+!the!Institute!of!Nuclear!Problems!of!Soviet!Academy!of!Sciences!in!the!city!of!Dubna9!located! about!L!hours!by!train!north!of!Moscow)!The!Join$!Institute!fo+!Nuclea+!Research!(JINRV!would!be!founded! at!Dubn%!in!1956!(the!names!“JINR”!and!“Dubna”!have!ofte-!bee-!useH!interchangeably!since!then))! However,!the!Cosmotr,-!at!the!US’s!Brookhave-!National!Laboratory!at!Long!Island,!New!York!surpassed! this!record!in!1953!when!it!started!to!produce!3-GeV!beams19)!Shortly!afterwards,!in!1954,!Lawrenc2! Berkeley!National!Laboratory!also!broke!the!GeV!barrier!with!its!6.L!GeV!Bevatron20.!The!Soviet!Union! could!not!stay!away!from!the!race,!a-H!i-!1957!their!newly!built!accelerator9!JINR’s!Synchrophasotron,! reached!a!record!oO!10!GeV21.!The!US,!not!to!be!outdone,!built!the!12.]!GeV!ZG(!at!Argonne!National! Laborator'!near!Chicago!(A.!Sessle+!evaluates!the!latte+!two!as!“th2!competition!between!Argonn2!and! Dubna!to!build!the!highest!enerC'!proton!accelerator!(th2!ZGS!and!th2!Synchro-phasotron).”)22! Soon!afterwards9!in!19599!CERN!surpassed!the!prot,-!accelerati,-!record!by!reaching!L]!GeV!with!its! Proton! Synchrotron239! and! a! year! later! the! palm! was! again! in! the! US! when! the! Alternating! Gradient! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i!D.!Gross,!PhU!Thesis,!!"#$%&'()*+",%,)-./0)1-2! ii!Because!of!secrecy,!first!ope-!publications!appeareH!ca!1956,!whe-!the!accelerator!energy!haH!bee-!elevateH!t,! @_J!MeV.! Synchrotron!at!Brookhaven!achieved!30!GeV!prot,-!beams24.!Unwilling!to!back!down,!the!Sovie$!Union! planned!to!create!a!new!record-breaking!accelerator,!this!tim2!at!the!Institute!fo+!High!Energy!Physics! (IHEPV!at!Protvino!near!Serpukhov!(called!Serpukhov!in!the!documents!of!the!time))!IHEP!was!%!USSR! national! laboratory! about! L! hours! by! train! south! of! Moscow! and! only! about! 150! miles! from! Dubna)! Scientists!at!JINR!adjusted!thei+!plans!to!form!a!use+!group!and!do!experiments!at!IHEP)!However,!since! JINR! was! an! international! institution! founded! by! the! Eastern! Bloc! countries! Albania,! Bulgaria,! Czechoslovakia,!East!Germany,!Hungary,!Poland,!Romania,!a-H!the!USSR,!along!with!China,!Mongolia,! North!Korea,!and!Vietnam!and!organized!according!to!principles!similar!to!thos2!of!CERN9!it!could!not! easily!transfer!common!resources!to!a!national!laboratory!(IHEP)!without!raising!objections!among!its! members25)!! In!1965,!China!(one!of!the!JINR!founders)!withdrew!from!membership)!One!of!the!complaints!that!drove! this!move,!as!expressed!by!the!Chinese!representative!a$!the!XII!session!oO!the!JINR!Scientific!Council!and! documenteH! i-! the! JINS! archives9! was! that! JINR! approved! the! transfe+! oO! resources! to! IHEP! without! consulting!member-countrie.!outside!the!Soviet!Union9!which!could9!the!Chinese!representative!feared,! make!JINR!“end!up!losing!its!shirt.”26!Another!allegation!was!tha$!JINR!refused!requests!by!responsible! representatives!oO!the!participating!countries!fo+!permission!to!inspect!the!institute’s!reactor!park9!while! US!visitors!“were!allowed!to!walk!around!th2!entir2!institution!without!supervision!fo+!many!hours!and! take!pictures,”!27!!often!accompanied!by!its!highest!officials.!At!the!height!of!the!ColH!War9!therefore9!JINR! appeared!to!be!committed!to!cooperation!with!the!US,!reaffirming!its!status!as!an!“international!oasisa! within!the!USSR.!! Construction!of!the!IHEP!accelerator9!U-70,!was!completed!in!1967!and!the!proton!beam!reached!76!GeV.! The!high-energy!leadership,!at!least!in!terms!of!which!lab!had!th2!highest!energy!beams,!returned!to!the!
Recommended publications
  • Regge Poles and Elementary Particles
    Regge poles and elementary particles R J EDEN Cavendish Laboratory, University of Cambridge Contents Page 1. Introduction . 996 1.l. Preliminary remarks . 996 1.2. Units . 997 1.3. Quantum numbers . 998 1.4. Two-body reactions . 998 1.5. Resonances and particles , . 999 1.6. Kinematics of r;N collisions . 1001 1.7. The physical scattering region . 1002 1.8. Cross sections and collision amplitudes . 1003 2. Experimental survey . I 1005 2.1. Total cross sections. 1006 2.2. Phases of forward amplitudes . 1007 2.3. Elastic cross sections (integrated) . 1008 2.4. Differential elastic cross sections . 1009 2.5. Exchange cross sections . 1010 2.6. Backward scattering . 1012 2.7. Polarization and spin parameters . 1013 2.8. Large-angle scattering . 1013 2.9. Quasi-two-body reactions . 1013 2.10. Photoproduction . 1014 2.1 1. Multiparticle production . * 1015 2.12. Inclusive reactions . 1016 3. Theoretical survey . 1017 3.1. Relativistic kinematics for two-body collisions . 1017 3.2. Analyticity and crossing symmetry . 1018 3.3. Dispersion relations . 1020 3.4. Scattering amplitudes and the S matrix . 1020 3.5. Partial wave expansions . 1021 3.6. Resonances and Regge poles . 1022 4. Basic ideas in Regge theory . 1023 4.1. Regge trajectories and sequences of particles . 1023 4.2. Exchanged trajectories and high-energy behaviour . 1025 4.3. Extended partial wave amplitudes and Regge poles . 1027 4.4. Partial wave series and the Sommerfeld-Watson tra.nsform . 1029 4.5. Branch cuts in the angular momentum plane . 1031 5. Applications of Regge pole models . 1032 5.1. Preliminary summary of properties .
    [Show full text]
  • Arxiv:1909.05177V2 [Hep-Th] 16 Jan 2020 3 Regge Theory 20 3.1 the Regge Limit 20 3.2 Complex Angular Momentum 22 3.3 Regge Poles 25
    SciPost Physics Lecture Notes Submission QMUL-PH-19-25 Aspects of High Energy Scattering C. D. White1* 1 Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, 327 Mile End Road, London E1 4NS, UK * [email protected] January 17, 2020 Abstract Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details of the underlying theory. This knowledge is often neglected in modern QFT courses, and the aim of these notes - aimed at graduate students - is to redress this. We review the possible singularities that amplitudes can have, before examining the generic behaviour that can arise in the high-energy limit. Finally, we illustrate the results using examples from QCD and gravity. Contents 1 Motivation 2 2 Scattering and the S-matrix 3 2.1 The S-matrix 3 2.2 Properties of the S-matrix 6 2.3 Analyticity 9 2.4 Physical regions and crossing 16 arXiv:1909.05177v2 [hep-th] 16 Jan 2020 3 Regge Theory 20 3.1 The Regge limit 20 3.2 Complex angular momentum 22 3.3 Regge poles 25 4 Examples in QCD and gravity 28 4.1 High energy scattering in QCD 28 4.2 High energy scattering in gravity 32 References 34 1 SciPost Physics Lecture Notes Submission 1 Motivation Much research in contemporary theoretical high energy physics involves scattering amplitudes (see e.g. refs. [1, 2] for recent reviews), which are themselves related to the probabilities for interactions between various objects to occur.
    [Show full text]
  • ELEMENTARY PARTICLES in PHYSICS 1 Elementary Particles in Physics S
    ELEMENTARY PARTICLES IN PHYSICS 1 Elementary Particles in Physics S. Gasiorowicz and P. Langacker Elementary-particle physics deals with the fundamental constituents of mat- ter and their interactions. In the past several decades an enormous amount of experimental information has been accumulated, and many patterns and sys- tematic features have been observed. Highly successful mathematical theories of the electromagnetic, weak, and strong interactions have been devised and tested. These theories, which are collectively known as the standard model, are almost certainly the correct description of Nature, to first approximation, down to a distance scale 1/1000th the size of the atomic nucleus. There are also spec- ulative but encouraging developments in the attempt to unify these interactions into a simple underlying framework, and even to incorporate quantum gravity in a parameter-free “theory of everything.” In this article we shall attempt to highlight the ways in which information has been organized, and to sketch the outlines of the standard model and its possible extensions. Classification of Particles The particles that have been identified in high-energy experiments fall into dis- tinct classes. There are the leptons (see Electron, Leptons, Neutrino, Muonium), 1 all of which have spin 2 . They may be charged or neutral. The charged lep- tons have electromagnetic as well as weak interactions; the neutral ones only interact weakly. There are three well-defined lepton pairs, the electron (e−) and − the electron neutrino (νe), the muon (µ ) and the muon neutrino (νµ), and the (much heavier) charged lepton, the tau (τ), and its tau neutrino (ντ ). These particles all have antiparticles, in accordance with the predictions of relativistic quantum mechanics (see CPT Theorem).
    [Show full text]
  • Everything About Reggeons” and It Will Consist of Four Parts: 1
    TAUP 2465 - 97 DESY 97 - 213 October 1997 hep - ph 9710546 EVERYTHING ABOUT REGGEONS Part I : REGGEONS IN “SOFT” INTERACTION. Eugene Levin School of Physics and Astronomy, Tel Aviv University Ramat Aviv, 69978, ISRAEL and DESY Theory, Notkrstr. 85, D - 22607, Hamburg, GERMANY [email protected]; [email protected]; Academic Training Program DESY, September 16 - 18, 1997 First revised version Abstract: This is the first part of my lectures on the Pomeron structure which I am going arXiv:hep-ph/9710546v3 7 Jan 1998 to read during this academic year at the Tel Aviv university. The main goal of these lectures is to remind young theorists as well as young experimentalists of what are the Reggeons that have re-appeared in the high energy phenomenology to describe the HERA and the Tevatron data. Here, I show how and why the Reggeons appeared in the theory, what theoretical problems they have solved and what they have failed to solve. I describe in details what we know about Reggeons and what we do not. The major part of these lectures is devoted to the Pomeron structure, to the answer to the questions: what is the so called Pomeron; why it is so different from other Reggeons and why we have to introduce it. In short, I hope that this lectures will be the shortest way to learn everything about Reggeons from the beginning to the current understanding. I concentrate on the problem of Reggeons in this lectures while the Reggeon interactions or the shadowing corrections I plan to discuss in the second part of my lectures.
    [Show full text]
  • 1 Early String Theory As a Challenging Case Study for Philosophers Elena Castellani Dipartimento Di Filosofia, Universit`Adi Firenze
    1 Early string theory as a challenging case study for philosophers Elena Castellani Dipartimento di Filosofia, Universit`adi Firenze 1.1 Introduction The history of the origins and first developments of string theory, from Veneziano’s formulation of his famous scattering amplitude in 1968 to the so- called first string revolution in 1984, provides invaluable material for philo- sophical reflection. The reasons why this episode in the history of modern physics – one still largely unknown to the philosophy of science community despite its centrality to theoretical physics – represents a particularly in- teresting case study are several and of various nature. It is the aim of the present Chapter to illustrate some of them. In general, the story of the construction of a new scientific theory has an evident interest in itself, as a concrete example of how a particular theory has been discovered and developed by a given community and over a certain period of time. On the other hand, case studies taken from the history of sci- ence are commonly used, by those philosophers of science who pay attention to actual scientific practice, to provide some evidence for or against given positions on traditional epistemological or methodological issues. In other words, historical case studies are attributed, with respect to philosophical ‘theories’ on given aspects of the scientific enterprise, a role analogous to that of the data of experience in scientific theories. These aspects can be of a very general character, such as those regarding the methodology, aim and evaluation of scientific theories; or of a more specific kind, such as the significance of a certain principle, argument or concept.
    [Show full text]
  • Derivation of Regge Trajectories from the Conservation of Angular Momentum in Hyperbolic Space
    Send Orders for Reprints to [email protected] 4 The Open Nuclear & Particle Physics Journal, 2013, 6, 4-9 Open Access Derivation of Regge Trajectories from the Conservation of Angular Momentum in Hyperbolic Space * B.H. Lavenda Università degli Studi, Camerino 62032, MC, Italy Abstract: Regge trajectories can be simply derived from the conservation of angular momentum in hyperbolic space. The condition to be fulfilled is that the hyperbolic measure of distance and the azimuthal angle of rotation in the plane be given by the Bolyai-Lobachevsky angle of parallelism. Resonances or bound states that lie along a Regge trajectory are relativistic rotational states of the particle that are quantized by the condition that the difference in angular momentum between the rest mass, assumed to be the lead particle on the trajectory, and the relativistic rotational state is an integer. Since the hyperbolic expression for angular momentum is entirely classical, it cannot take into account signature, and whether exchange degeneracy is broken or not. However, the changes in the angular momentum are in excellent agreement with non-exchange degeneracy which assumes four different rest masses in the case of , , a2, and f mesons trajectories, as well as in the case where there is only one rest mass in exchange degeneracy. A comparison is made between the critical and supercritical Pomeron trajectories; whereas the former has resonaces with higher masses, it has corresponding smaller linear dimensions. Keywords: Regge trajectories, conservation of angular momentum in hyperbolic space, relativistic rotational states. INTRODUCTION center of mass of the tube. The motion is considered relativistic, but since a uniform rotating string is not an Regge trajectories link bound states and resonances with inertial system, the Lorentz contraction cannot be employed.
    [Show full text]
  • List of Publications Peter Goddard
    List of Publications Peter Goddard 1. Anomalous Threshold Singularities in S-Matrix Theory Il Nuovo Cimento 59A, 335{355 (1969). 2. Nonphysical Region Singularities of the S-Matrix Journal of Mathematical Physics 11, 960{974 (1970). 3. with A.R. White TCP Signature and Non-Compact Covariance Conditions in Crossed Partial Wave Analysis: The Three Reggeon Vertex Nuclear Physics B17, 45{87 (1970). 4. with A.R. White The Three Reggeon Vertex: Analyticity, Asymptotics and the Toller Pole Model Nuclear Physics B17, 88{116 (1970). 5. with A.R. White Complex Helicity and the Sommerfeld-Watson Transform of Group Theoretic Expansions Il Nuovo Cimento 1A, 645{679 (1971). 6. with A.R. White Landau Singularities in Multi-Regge Theory and Fixed Angle Behaviour Il Nuovo Cimento 3A, 25{44 (1971). 7. with P.H. Frampton and D.A. Wray Perturbative Unitarity of Dual Loops Il Nuovo Cimento 3A, 755{762 (1971). 8. Analytic Renormalisation of Dual One Loop Amplitudes Il Nuovo Cimento 4A, 349{362 (1971). 9. with R.C. Brower Generalised Virasoro Models Lettere al Nuovo Cimento 1, 1075{1081 (1971). 10. with R.E. Waltz One Loop Amplitudes in the Model of Neveu and Schwarz Nuclear Physics B34, 99{108 (1971). 11. with R.C. Brower Collinear Algebra for the Dual Model Nuclear Physics B40, 437{444 (1972). 1 12. with R.C. Brower Physical States in the Dual Resonance Model Proceedings of the International School of Physics \Enrico Fermi" Course LIV (Aca- demic Press, New York and London, 1973) 98{110. 13. with A.R. White The Zero in the Three Pomeron Vertex Physics Letters 38B, 93{98 (1972).
    [Show full text]
  • 1 Hadronic Regge Trajectories in the Resonance Energy Region
    Hadronic Regge Trajectories in the Resonance Energy Region A.E. Inopin Department of Physics and Technology, V.N. Karazin Kharkov National University, Kharkov 61077, Ukraine & Virtual Teacher Ltd., Vancouver, Canada. Nonlinearity of hadronic Regge trajectories in the resonance energy region has been proved. Contents I. Introduction 2 II. Theoretical Models 2 II.1. h–expansion model 2 II.2. K-deformed alg ebra model 7 II.3. String models 9 a) Olsson model 9 b) Soloviev string quark model (SQM) 12 c) Burakovsky-Goldman string model 16 d) Sharov string model 19 II.4. Nonrelativistic quark models 22 a) Inopin model 22 b) Fabre de La Ripelle model 27 c) Martin model 32 II.5. Spectrum generating algebra model(s) 33 II.6. Relativistic and semirelativistic models 38 a) Basdevant model 38 b) Semay model 40 c) Relativistic flux tube model (RFT) 41 d) Point form of relativistic quantum mechanics 43 e) Semiclassical relativistic model 44 f) ‘t Hooft 1/N c model 46 g) Dominantly orbital state description (DOS) 50 h) Durand model 51 i) Relativistic model of Martin 54 j) Nambu-Jona-Lasinio model of Shakin 55 k) Lagae model 56 II.7. WKB -type models 57 a) Bohr-Sommerfeld quantization and meson spectroscopy 57 b) Fokker -type confinement models of Duviryak 60 II.8. Cylindrically deformed quark bag model 62 II.9. Phenomenological and analytic interpolating models 64 a) Sergeenko model 64 b) Filipponi model 69 II.10. Results based solely on work with PDG 70 a) Analysis of Tang and Norbury 70 b) Naked about hadronic RT 74 II.11.
    [Show full text]
  • Interactions in Higher-Spin Gravity: a Holographic
    Interactions in Higher-Spin Gravity: A Holographic Perspective Dissertation by Charlotte Sleight Interactions in Higher-Spin Gravity: A Holographic Perspective Dissertation an der Fakult¨atf¨urPhysik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Charlotte Sleight aus Hull, Großbritannien M¨unchen,den 2. Mai 2016 Dissertation Submitted to the faculty of physics of the Ludwig{Maximilians{Universit¨atM¨unchen by Charlotte Sleight Supervised by Prof. Dr. Johanna Karen Erdmenger Max-Planck-Institut f¨urPhysik, M¨unchen 1st Referee: Prof. Dr. Johanna Karen Erdmenger 2nd Referee: Prof. Dr. Dieter L¨ust Date of submission: May 2nd 2016 Date of oral examination: July 26th 2016 To my dad, sister, and the wonderful memory of my mum. \Die Probleme werden gel¨ost,nicht durch Beibringen neuer Erfahrungen, sondern durch Zusammenstellung des l¨angstBekannten." | Ludwig Wittgenstein Zusammenfassung Die vorliegende Dissertation widmet sich der Untersuchung der H¨ohereSpin-Gravitation auf einem Anti-de-Sitter-Raum (AdS). Es gibt Hinweise darauf, dass dem Hochen- ergiebereich der Quantengravitation eine große (H¨ohereSpin-) Symmetriegruppe zu- grundeliegt und somit eine m¨ogliche effektive Beschreibung dieses Beriechs durch eine H¨ohereSpin-Theorie gegeben ist. Die Reaslisierung einer Quantengravitation mit dieser Symmetrie ist insbesondere in der String Theorie bei hohen Energien gegeben, wenn die Stringspannung vernachl¨assigtwerden kann. Die Untersuchung der H¨ohereSpin-Theorien ist von physikalischer Relevanz, weil ihre unendlichdimensionale Symmetrie als Leitprinzip verwendet werden kann, um neue Erkenntnisse ¨uber die Quantengravitation bei Energien jenseits der heute experimen- tall erreichbaren Energieskalen zu gewinnen. Es muss dabei ber¨ucksichtigt werden, dass die verf¨ugbarennichtlinearen Formulierungen der H¨ohere-Spin-Theorien unendlich viele Hilfsfelder mit einschließen, so dass selbst grundlegende Eigenschaften wie Unitarit¨at oder Kausalit¨atnoch nicht vollst¨andigverstanden sind.
    [Show full text]
  • High Energy Scattering in the Ads/CFT Correspondence
    High Energy Scattering in the AdS/CFT Correspondence Jo˜ao Miguel Augusto Penedones Fernandes arXiv:0712.0802v2 [hep-th] 6 Feb 2008 Departamento de F´ısica Faculdade de Ciˆencias da Universidade do Porto July 2007 High Energy Scattering in the AdS/CFT Correspondence Jo˜ao Miguel Augusto Penedones Fernandes PhD Thesis supervised by Prof. Miguel Sousa da Costa Departamento de F´ısica Faculdade de Ciˆencias da Universidade do Porto July 2007 Abstract This work explores the celebrated AdS/CFT correspondence [1] in the regime of high energy scattering in Anti–de Sitter (AdS) spacetime. In particular, we develop the eikonal approxima- tion to high energy scattering in AdS and explore its consequences for the dual Conformal Field Theory (CFT). Using position space Feynman rules, we rederive the eikonal approximation for high energy scattering in flat space. Following this intuitive position space perspective, we then generalize the eikonal approximation for high energy scattering in AdS and other spacetimes. Remarkably, we are able to resum, in terms of a generalized phase shift, ladder and cross ladder Witten diagrams associated to the exchange of an AdS spin j field, to all orders in the coupling constant. In addition, we confirm our results with an alternative derivation of the eikonal approximation in AdS, based on gravitational shock waves. By the AdS/CFT correspondence, the eikonal amplitude in AdS is related to the four point function of CFT primary operators in the regime of large ’t Hooft coupling λ, including all terms of the 1/N expansion. We then show that the eikonal amplitude determines the behavior of the CFT four point function for small values of the cross ratios in a Lorentzian regime and that this controls its high spin and dimension conformal partial wave decomposition.
    [Show full text]
  • Aspects of High Energy Scattering Abstract Contents
    SciPost Phys. Lect. Notes 13 (2020) Aspects of high energy scattering Christopher D. White? Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, 327 Mile End Road, London E1 4NS, UK ? [email protected] Abstract Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details of the underlying theory. This knowledge is often neglected in modern QFT courses, and the aim of these notes - aimed at graduate students - is to redress this. We review the possible singular- ities that amplitudes can have, before examining the generic behaviour that can arise in the high-energy limit. Finally, we illustrate the results using examples from QCD and gravity. Copyright C. D. White Received 17-09-2019 This work is licensed under the Creative Commons Accepted 23-01-2020 Check for Attribution 4.0 International License. Published 07-02-2020 updates Published by the SciPost Foundation. doi:10.21468/SciPostPhysLectNotes.13 Contents 1 Motivation 1 2 Scattering and the S-matrix3 2.1 The S-matrix3 2.2 Properties of the S-matrix5 2.3 Analyticity8 2.4 Physical regions and crossing 15 3 Regge Theory 18 3.1 The Regge limit 18 3.2 Complex angular momentum 20 3.3 Regge poles 23 4 Examples in QCD and gravity 26 4.1 High energy scattering in QCD 26 4.2 High energy scattering in gravity 29 References 31 1 SciPost Phys.
    [Show full text]
  • From Dual Models to String Theory
    From Dual Models to String Theory Peter Goddard Institute for Advanced Study Olden Lane, Princeton, NJ 08540, USA A personal view is given of the development of string theory out of dual models, including the analysis of the structure of the physical states and the proof of the No-Ghost Theorem, the quantization of the relativistic string, and the calculation of fermion-fermion scattering. arXiv:0802.3249v1 [physics.hist-ph] 22 Feb 2008 This article was written in response to the invitation of Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di Vecchia to submit some personal reminiscences to the volume The Birth of String Theory. 1. A Snapshot of the Dual Model at Two Years Old When particle physicists convened in Kiev at the end of August 1970, for the 15th In- ternational Conference on High Energy Physics, the study of dual models was barely two years old. Gabriele Veneziano, reporting on the precocious subject that he had in a sense created [1], characterized it as “a very young theory still looking for a shape of its own and for the best direction in which to develop. On the other hand duality has grown up considerably since its original formulation. Today it is often seen as something accessible only to the ‘initiated’. Actually theoretical ideas in duality have evolved and changed very fast. At the same time, they have very little in common with other approaches to particle physics” [2]. Nearly forty years later, his comments might still be thought by some to apply, at least in part. In describing the theoretical developments, Veneziano stressed the progress that had been made in understanding the spectrum of the theory, obtained by factorizing the multiparticle generalizations of his four-point function in terms of the states generated from a vacuum µ state, |0i, by an infinite collection of harmonic oscillators, an, labeled by both an integral mode number, n, and a Lorentz index, µ, [3,4], µ ν µν µ† µ µ [am,an] = mg δm,−n; an = a−n; an|0i =0, for n > 0.
    [Show full text]