Topics in the Structure of Hadronic Systems [thesis]

136 Pages·1994·8.672 MB·English

LBL-35371
UC-414
• Topics in the Structure of Hadronic Systems
Richard Felix Lebed
Ph.D. Thesis
Physics Department
University of California
and
Physics Division
Lawrence Berkeley Laboratory
University of California
Berkeley, CA 94720
April 1994
This work was supported bythe Director, Office of Energy Research, Office of High Energy and
Nuclear Physics, Division of High Energy Physics ofthe U.S. Department of Energy under
Contract No. DE-AC03-76SF00098. I_ _. T _ R
DISTRIBUTIONOFTHIS DOCUMENT ISUNLIMITED
Topics in the Structure of Hadronic Systems
Copyright © 1994
by
RichardFelix Lebed
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Abstract
• Topics in the Structure of Hadronic Systems
by
b
RichardFelixLebed
Doctor of Philosophy in Physics
University of California at Berkeley
Professor Mahiko Suzuki, Chair
In this dissertation we examine a variety of different problems in the
physics of strongly-bound systems. Each is elucidated by a different standard
method of analysis developed to probe the properties of such systems.
We begin with an examination of the properties and consequences of the
current algebra ofweak currents in the limit of heavy quark spin-flavor symmetry. In
particular, we examine the assumptions in the proof of the Ademollo-Gatto theorem
in general and for spin-flavor symmetry, and exhibit the constraints imposed upon
matrix elements by this theorem.
Then we utilize the renormalization-group method to create composite
fermions in a three-generation electroweak model. Such a model is found to re-
. produce the same low energy behavior as the top-condensate electroweak model,
although in general it may have strong constraints upon its Higgs sector.
• Next we uncover subtleties in the nonrelativistic quark model that drasti-
cally alter our picture of the physical origins of meson electromagnetic and hyperfine
mass splittings; in particular, the explicit contributions due to (rod- rr'tu) and elec-
trostatic potentials may be overwhelmed by other effects. Such novel effects axe used
to explain the anomalous pattern of mass splittings recently measured in bottom
1
mesons.
Finally, we consider tl_e topic of baryon masses in heavy fermion chiral
perturbation theory, including both tree-level and loop effects. We find that certain
mass relations holding at second-order in symmetry breaking (O(m_)and O(Q_))
have finite, computable, and numerically small loop corrections within the theory.
The numerical values of these corrections are found to be in excellent agreement with
experiment. We also find that, within chiral perturbation theory, the experimentally
measured baryon masses None are not enough to place stringent constraints upon
the light quark masses.
To Allyson
OQ I
111
h
Contents
List of Figures J vi
List of Tables vii
Akcn oweldg ements vm"'"
List of Publications ix
Introduction 1
1 Current Algebra and O(1/m) Corrections in Heavy Quark Spin-
Flavor Symmetry 3
1.1 Introduction ............................... 3
1.2 The Spin-Flavor Current Algebra ................... 6
1.3 The Algebra of Effective Weak Currents ............... 10
1.4 The Ademollo-Gatto Theorem ..................... 13
1.5 The Ademollo-Gatto Theorem in Spin-Flavor Symmetry ...... 16
1.6 Scalar, Tensor, and Pseudoscalar Densities .............. 19
1.7 A Sample Application ......................... 21
2 Composite Fermions in a Three-Generation Electroweak Model 23
2.1 Introduction ............................... 23
2.2 Three Generations in the Top-Condensate Model .......... 26
2.3 The Composite-tR Model ........................ 29
2.4 Extending the Composite-tR Model .................. 32
2.4.1 One Generation with One Higgs Doublet ........... 32
2.4.2 One Generation with Two Higgs Doublets .......... 34
2.4.3 More Than One Fermion Generation ............. 35
2.5 A Composite Left-Handed Fermion Model .............. 37
2.5.1 One Generation ......................... 38
2.5.2 More Than One Fermion Generation ............. 39
2.6 Conclusions ............................... 39
iv
3 Meson Mass Splittings in Potential Models 41
3.1 Introduction ............................... 41
3.2 Mass Computation in Field Theory .................. 43
3.3 The Nonrelativistic Limit ....................... 50
3.4 Mass Splitting Formulas ................... : .... 53
3.5 Quantum-mechanical Theorems .................... 55
3.6 Example: V(r) - r/a 2- tc/r ...................... 57
3.7 Numerical Results ............................ 60
3.8 Conclusions ............................... 65
4 Baryon Masses 1: Group Theory 68
4.1 Introduction ................................ 68
4.2 The Structure of SU(3) Breaking ................... 69
4.3 Baryon Mass Relations ......................... 73
4.4 Quark Mass Parameters ........................ 77
4.5 Decuplet Mass Measurements ..................... 80
5 Baryon Masses 2: Chiral Dynamics 84
_5.1 Introduction ............................... 84
5.2 Heavy Baryon Theory and the Effective Lagrangian ......... 86
5.3 Constructing the Lagrangian ...................... 88
5.3.1 Field Transformation Properties ................ 88
5.3.2 Lagrangian Terms ........................ 91
5.4 Parameter Counting .......................... 95
5.5 Loop Corrections ............................ 99
5.6 Method of Calculation ......................... 102
5.7 Results and Predictions ......................... 105
5.7.1 Estimating Parameters ..................... 105
5.7.2 Decuplet Predictions: A1,2,3,4 ................. 106
5.7.3 Octet Prediction: AcG ..................... 108
5.7.4 Octet Prediction: As ...................... 108
5.8 Conclusions ............................... 109
Bibliography 111
A Loop Corrections: Decuplet 118
B Loop Corrections: Octet 122
List of Figures
2.1 Fermion chain diagrams in the top-condensate model ......... 27
2.2 Chain diagrams in the composite-tR model ............... 31
3.1 Diagrammatical representation of A4I_................. 45
3.2 Diagram for A,4fl in the mesonic system ................ 46
3.3 Free quark Feynman amplitude A4................... 47
3.4 Notation and conventions for the mesonic system ........... 48
5.1 "Keyhole" (quartic vertex) diagram contributing to baryon masses. 92
5.2 Trilinear vertex diagram contributing to baryon masses ........ 93
vi
List of Tables
I Contributiontsomasssplittinogfsheavymesons:Isospinpairs... 61
II Contributiontsomasssplittinogfsheavymesons:(1-,0-)pairs.. 62
Ill Meson masssplittincgosmparedtoexperiment............ 63
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Acknowledgements
First and foremost, I wish to thank my advisor Mahiko Suzuki, without
whose encouragement and wisdom this research would never have been possible.
The gems of his insights from our discussions are to be found sprinkled liberally
throughout the pages of this dissertation. Likewise, I wish to acknowledge the
invaluable assistance of Dave Jackson, who taught me particle theory here at U. C.
Berkeley, and who has helped me to answer more questions than I can count.
Were I to recognize individually every person in the LBL Theory Group
who has aided me at one time or another during my graduate research, I would
do as well to reproduce the whole group roster. But I would like to single out
the following individuals: Lawrence Hall, who on more than one occasion pointed
out to me some recent results which I subsequently incorporated into my research;
Markus Luty, whose passion for discovery enhanced the quality of our work; and
Paul Watts, whose incisive comments and painstaking exactitude helped to improve
my understanding of numerous topics.
This work has also been enriched by my conversations or correspondences
with Orlando Alvarez, Dick Arndt of Virginia Polytechnic Institute, John Donoghue
of the University of Massachusetts, Amherst, Harris Kagan of Ohio State University,
Joe Schechter of Syracuse University, and Charles Wohl of the LBL Particle Data
Group.
Without the kind assistance of the Theory Group secretaries, Betty Mourn
and Luanne Neumann, I would forever have been lost in the maze of LBL bureau-
cracy. To them I convey my appreciation and gratitude.
I would also like to thank my earliest advocates, my parents Walter F.
and Sally Lebed, for their encouragement which has sustained me from my earliest
times to the present.
Finally, I would like to thank my beloved Allyson Ford, partly for her
critical reading ofthis manuscript, but especially for her compassion and the infusion
to m_ of her great emotional strength.
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