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Hadron Structures and Decays Within Quantum Chromodynamics Alaa Abd El-Hady Iowa State University

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Hadron Structures and Decays Within Quantum Chromodynamics Alaa Abd El-Hady Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1998 Hadron structures and decays within Quantum Chromodynamics Alaa Abd El-Hady Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Elementary Particles and Fields and String Theory Commons, and the Nuclear Commons Recommended Citation El-Hady, Alaa Abd, "Hadron structures and decays within Quantum Chromodynamics " (1998). Retrospective Theses and Dissertations. 11585. https://lib.dr.iastate.edu/rtd/11585 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfihn master. UMI fihns 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 aligimient can adversely affect 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 comer 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 of 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 Noith Zed) Road, Ann Aibor MI 48106-1346 USA 313/761-4700 800/521-0600 Hadron structures and decays within Quantum Chromodynamics by Alaa Abd El-Hady A dissertation submitted to the graduate faculty in partial fuifillnient of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Nuclear Physics Major Professor: James P. Vary Iowa State University Ames. Iowa 1998 Copyright © Alaa Abd El-Hady. 1998. .-Vll rights reserved. XIMI N\imber: 9826506 Uivn Microform 9826506 Copyright 1998, 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 11 Graduate College Iowa State University This is to certify that the Doctoral dissertation of Alaa Abd El-Hady has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Major Professor Signature was redacted for privacy. For the Major Program Signature was redacted for privacy. For the Graduate College Ill TABLE OF CONTENTS ABSTRACT vii INTRODUCTION 1 MESON SPECTROSCOPY AND IN-MEDIUM EFFECTS 7 Meson spectroscopy 7 Medium effects 11 HEAVY QUARK SYMMETRY AND B DECAYS iO [sgur-VV'ise function and lc6 from Betlie-Salpeter equations 20 B —)• D{D') form factors in a Bethe-Salpeter model ."{l) Decay constants, semileptonic, and nonleptonic B decays 45 CHIRAL SYMMETRY AND HYPERON DECAYS 58 Clural Lagrangian for hyperon nonleptonic decays 59 Hyperon nonleptonic decay amplitudes CP VIOLATION IN B DECAYS FROM ANOMALOUS tbW INTERACTIONS . 75 High energy effective Lagrangian 75 Low energy effective interactions 7(5 CP violation in neutral B decays 77 CONCLUSIONS AND OUTLOOK 81 BIBLIOGRAPHY 8:5 ACKNOWLEDGEMENTS 88 IV LIST OF TABLES Table 1 Fitting parameters and RMS 9 Table 2 Fitted spectra for reductions A and B 10 Table 8 Values of Vcb in the units of 10"^ from different sets of experimental data. ... 80 Table 4 The values of the form factors at a-- = 1 87 Table 5 Decay constants of the B and D mesons in MeV 51 Table 6 Nonleptonic decay rates for B meson o(j Table 7 Experimental data for S-wave and P-wave amplitudes for A/ = 1/2 78 Table 8 Fitting results for A/ = 1/2 S-wave amplitudes for parameter values hj — 0.75. and = 4.0 74 Table 9 Fitting results for A/ = 1/2 P-wave amplitudes using the same parameter values 74 V LIST OF FIGURES Figure I Plot of the mass and the DD threshold as a function of c/cto i;{ Figure 2 Plot of the O mass and the KK threshold as a function of (T/<ro 14 Figure Medium effects on the masses of charmonium states 17 Figure -I Medium effects on the average radii of charmonium states 18 Figure 5 Medium effects on the radiative decay widths of charmonium states 19 Figure 6 Radial wavefunction for the B meson 'J.'J Figure 7 Radial wavefunction for the D' meson "24 Figure 8 The Isgur-VVise function. The deviation of the IVV function from unity at zero recoil is due to the finite heavy quark mass effects incorporated in our BSE model. 26 Figure 9 Plot of V'^b vs. from ARGUS 93 data 27 Figure 10 Plot of ^(u;) vs. from CLEO 93 data 28 Figure II Plot of I'cb vs. uj from CLEO 94 data 29 Figure 12 The calculated form factors ^,(u;) without perturbative QCD corrections and the calculated Isgur-VVise funrtinn $(x') from Eq. 21 38 Figure 13 The mass parameter .V e.vtracted from the form factors ) 40 Figure 14 The l/mg correction functions \i(u--)/A. \2(u.)/.\. \3(^)/.V and ^3(^)/.V^(^) e.\tracted from the form factors "11 Figure 15 The calculated form factors ^, (w) with perturbative QCD corrections with // = 0.6 GeV 43 Figure 16 The differential decay rate with and without the QCD correction, together with the corresponding values of Vet, 44 Figure 17 The calculated form factors FQ, F\.V, AQ. A\. and .IT as a function of g- 53 Figure 18 The differential decay rate for B —> D'lu with and without the QCD correction. together with the corresponding values of V'cb 54 Figure 19 F{u;)lVc6| versus u; for 5 —)• Dli) 55 VI Figure 20 Tree level S-wave diagram. Solid lines denote octet baryons and dashed lines denote mesons. A square denotes a weak vertex fj-l Figure 21 Tree level P-wave diagrams. Solid lines denote octet baryons and dashed lines denote mesons. A square denotes a weak vertex, and a circle denotes a strong vertex (55 Figure 22 One loop S-wave diagrams, octet contribution (5(5 Figure 2:? One loop S-wave diagrams, decuplet contribution. Double solid lines denote baryon decuplet (56 Figure 24 Source of difference between our calculations and Jenkins" calculations. See text for explanation ()7 Figure 25 One loop P-wave diagrams, octet contribution (i!) Figure 26 One loop P-wave diagrams, decuplet contribution 70 Figure 27 VVavefunction renormalization for baryons 72 Figure 28 VVavefunction renormalization for mesons 7;{ VII ABSTRACT We have evaluated the meson spectrum using a relativistic model based on reductions of Bethe- Salpeter equation. We included one gluon exchange from Quantum Chromodynamics (QCD) and phenomenological confinement in the interaction kernel. We used an ansatz for the running of the coupling constant with the meson masses. We fitted more than forty states ranging from a hundred .MeV to a few GeV using seven parameters, with root mean square deviation from e.xperimental data of lO-oO .VIeV. This establishes our successful QCD-based model for many applications which we investigate. We employed our model to e.xamine the strong interaction medium effects on meson properties. We have evaluated the masses of specific mesons as the confinement strength is weakened by the medium. VV'e have shown how these effects may be observed experimentally in specific examples. Wo liave shown how charmonium and o meson hadronic decay channels may be closed, and leptonic yield may be enhanced. We demonstrated how radiative decays of charmonium states may also be useful for investigating our predicted in-medium effects. We next applied our model to investigate B meson decays. We showed the consistency of our model with the heavy quark symmetry, which enabled us to calculate the Isgur-Wise function and extract the Cabibbo-Kobayashi-.VIaskawa (CKM) mixing matri.x element from recent experiments. We have evaluated the leptonic decay constants, semileptonic decay form factors and used factorization to calculate the nonleptonic decays of B mesons. Looking forward to future experiments which will investigate domains within and beyond the stan­ dard model, we have applied chiral perturbation theory (\PT) to evaluate hyperon nonleptonic decays. We invoked the heavy baryon formalism and included the decuplet baryon contribution. We have ob­ tained the A/ = 1/2 octet amplitudes and the A/ = 3/2 27-plet amplitudes to one loop. We discussed the convergence of \PT amplitudes for both the S-wave and the P-wave for hyperon decays. We have evaluated CP violation in B decays from a certain anomalous /6tr coupling appearing in many versions of models which go beyond the standard model. The effect of this anomalous interaction may be large enough to be seen experimentally in B factories. This may help us in the search for physics beyond the standard model. I INTRODUCTION Ai present, it is widely believed that we have a successful theory, "the standard model", which can describe particles and their interactions down to lO""' m or.
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