W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 1996 The strong force: Two calculations of strong interaction phenomena Richard L. Kahler College of William & Mary - Arts & Sciences Follow this and additional works at: https://scholarworks.wm.edu/etd Part of the Physics Commons Recommended Citation Kahler, Richard L., "The strong force: Two calculations of strong interaction phenomena" (1996). Dissertations, Theses, and Masters Projects. Paper 1539623887. https://dx.doi.org/doi:10.21220/s2-zpsq-v546 This Dissertation is brought to you for free and open access by the Theses, Dissertations, & Master Projects at W&M ScholarWorks. It has been accepted for inclusion in Dissertations, Theses, and Masters Projects by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back o f the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with with permission permission of the of copyright the copyright owner. owner.Further reproductionFurther reproduction prohibited without prohibited permission. without permission. THE STRONG FORCE, Two Calculations of Strong Interaction Phenomena A Dissertation Presented to The Faculty of the Department of Physics The College of William and Mary in Virginia In Partial Fulfillment Of the Requirements for the Degree of Doctor of Philosophy by Richard L. Kahler 1996 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 9720975 Copyright 1997 by Kahler, Richard L. All rights reserved. UMI Microform 9720975 Copyright 1997, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPROVAL SHEET This dissertation is submitted, in partial fulfillment of the requirements for the degree of loctcjr of Philosophy] Richard kahler Approved, August 1996 . Dirk-iWi Carl Carlson Marc Sher J. W. van Orden ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEDICATION I would like to dedicate this work to the young ladies of St. Margaret’s School, particularly my physics students past, present, and future, in the hope that they will be encouraged to participate in the greatest intellectual adventure of our culture, theoretical physics. And to another young lady, my grandmother, Helen Kahler, who celebrates her ninetieth birthday this month: Happy Birthday Grandma! Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C ontents 1 Introduction 2 1.1 Background ..................................................................................................................... 2 1 .1 . 1 The Structure of M atter ................................................................................... 3 1.1.2 The Historical Perspective................................................................................ 5 1.2 The Nucleon-Nucleon Potential ...................................................................................... 30 1.3 The Standard Model .........................................................................................................32 2 Chiral Bag Model calculation of the Nucleon-Nucleon Potential 42 2.1 Introduction ........................................................................................................................ 42 2.1.1 One Boson Exchange M odels ............................................................................. 42 2.1.2 The Bag M odel ......................................................................................................50 2.2 Calculation of the OPE potential ................................................................................... 51 2.3 Calculation of the TPE Potential ...................................................................................58 2.4 Results..................................................................................................................................63 2.5 Discussion ........................................................................................................................... 71 3 Perturbative QCD calculation of the Pion Form Factor 75 3.1 Introduction ........................................................................................................................75 3.2 Calculation of Fv ...............................................................................................................78 3.3 Determination of F*. from the decay of J / r p .................................................................84 85 4 Conclusion 93 iv 4 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS I would like to gratefully and sincerely acknowledge the gracious support, helpful advice, and stimulating teaching of my advisor, Franz Gross, who has been very patient with my trying to teach high school and get a degree at the same time. Chapter two is based in large part on a set of unpublished notes of his which he has graciously shared with me. Chapter three is taken from a paper which was co-authored with Joe Milana and his contri­ bution and guiding hand is much in evidence. It was quite generous of him to share this project with me and I appreciate it very much. Finally, I would like to thank SURA and CEBAF for a generous fellowship which supported my work during 1993 and 1994. They provided office space and access to computing facilities, and most importantly, the opportunity to meet and learn from many outstanding physicists. Reproduced with permission of the copyright owner. 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List of Tables 1.1 Properties of Low Mass Hadrons ....................................................................................18 1.2 Properties of the Quarks ...................................................................................................25 1.3 The Four Forces of Standard Model ..............................................................................33 1.4 The Leptons of the Standard M odel ..............................................................................33 2.1 Light M eso n s ..................................................................................................................... 46 2.2 Feynman rules for propagators in the static limit .......................................................... 59 2.3 Feynman rules for vertices in the static limit ..................................................................59 2.4 OBE couplings required to fit bag model potentials ...................................................... 70 2.5 OBE masses required to fit bag model potentials ........................................................... 70 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures 1-1 J. J. Thompson’s cathode ray tube ............................................................................... 7 1-2 Measuring e/m of the electron ....................................................................................... 8 1-3 Rutherford’s alpha particle experiment............................................................................ 1 2 1-4 Alpha particles deflected by a nucleus .............................................................................. 14 1-5 Elementary Particles in 1963 ...................................................................................... 16 1-6 Low mass hadrons ................................................................................................................ 19 1-7 A geometrical representation of SU(3) symmetry [9] ......................................................21 1 - 8 Forming the product of