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University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations Summer 2010 Phenomenology of Heterotic String Theory: With Emphasis on the B-L/EW Hierarchy Michael Ambroso University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Elementary Particles and Fields and String Theory Commons Recommended Citation Ambroso, Michael, "Phenomenology of Heterotic String Theory: With Emphasis on the B-L/EW Hierarchy" (2010). Publicly Accessible Penn Dissertations. 236. https://repository.upenn.edu/edissertations/236 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/236 For more information, please contact [email protected]. Phenomenology of Heterotic String Theory: With Emphasis on the B-L/EW Hierarchy Abstract E8 x E8 heterotic string and M-theory, when appropriately compactified, can give rise to realistic, N = 1 supersymmetric particle physics. In particular, the exact matter spectrum of the MSSM is obtained by compactifying on Calabi-Yau manifolds admitting specific SU(4) vector bundles. These "heterotic standard models" have the SU(3)C x SU(2)L x U(1)Y gauge group of the standard model augmented Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Physics & Astronomy First Advisor Burt Ovrut Keywords Heterotic, String Theory, Renormalization group equations Subject Categories Elementary Particles and Fields and String Theory This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/236 PHENOMENOLOGY OF HETEROTIC STRING THEORY: WITH EMPHASIS ON THE B-L/EW HIERARCHY Michael Ambroso A DISSERTATION in Physics and Astronomy Presented to the Faculties of the University of Pennsylvania in Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy 2010 Supervisor of Dissertation Burt Ovrut, Professor, Physics and Astronomy Graduate Group Chair Ravi Sheth, Professor, Physics and Astronomy Dissertation Committee: Vijay Balasubramanian, Associate Professor, Physics and Astronomy Justin Khoury, Assistant Professor, Physics and Astronomy Paul Heiney Professor, Physics and Astronomy Hugh Williams, Professor, Physics and Astronomy Acknowledgments I would like to thank my wife, Kathleen, for an incredible amount of support and understanding during this long endeavor. I would also like to thank my advisor, Burt Ovrut, and the Department of Physics at Penn for their support. In addition, I would like to thank my parents for their continued encouragement over the last many years. Lastly, I would like to thank the LORD for His grace and strength in this process. ii ABSTRACT PHENOMENOLOGY OF HETEROTIC STRING THEORY: WITH EMPHASIS ON THE B-L/EW HIERARCHY Michael Ambroso Burt Ovrut, Advisor E8 £ E8 heterotic string and M-theory, when appropriately compacti¯ed, can give rise to realistic, N = 1 supersymmetric particle physics. In particular, the exact matter spectrum of the MSSM is obtained by compactifying on Calabi-Yau mani- folds admitting speci¯c SU(4) vector bundles. These \heterotic standard models" have the SU(3)C £ SU(2)L £ U(1)Y gauge group of the standard model augmented by an additional gauged U(1)B¡L. In this thesis, we report on the phenomenological viability of these compacti¯cations. Through a series of increasingly sophisticated analyses, we consider a wide variety of phenomenological e®ects and compare them to present experimental bounds. We have found that, given the constraints con- sidered, phenomenologically viable regions of parameter space exist and lead to interesting phenomenology, including exact predictions of new particle mass spec- tra. iii Contents 1 Introduction 1 2 Two Higgs Pair Model: A Simpli¯ed Analysis 8 2.1 Discussion of the Superpotential . 11 2.2 A Simpli¯ed Model . 19 2.2.1 The Spectrum . 20 2.2.2 Discrete Symmetry . 22 2.2.3 The Vacuum State . 26 2.2.4 Flavor-Changing Neutral Currents . 29 2.2.5 Phenomenology . 31 3 Single Higgs Pair Model: Quasi Analytic Analysis 38 3.1 The N = 1 Supersymmetric Theory . 40 3.2 The Renormalization Group and B-L . 44 3.3 The RGEs for Higgs Fields and Squarks . 59 3.4 The B-L/Electroweak Hierarchy . 86 iv 3.5 Conclusions . 89 4 Single Higgs Pair: Numerical Analysis 92 4.1 Dimensionless quantities . 95 4.2 Dimensionful Couplings . 101 4.3 The N = 1 Supersymmetric Theory . 107 4.4 Initial Parameter Space . 111 4.4.1 Gauge Coupling Parameters . 111 4.4.2 Gaugino Mass Parameters . 113 4.4.3 Higgs, Squark and Slepton Masses . 114 4.4.4 The A and B Parameters . 115 4.4.5 The ¹ Parameter . 116 4.4.6 Tan¯ and the Yukawa Couplings . 117 4.4.7 Parameterizing the Initial Conditions . 119 4.4.8 Phenomenological Constraints . 124 4.5 Numerical Analysis . 129 4.5.1 All m2 > 0............................ 130 2 4.5.2 mQ3 < 0............................. 145 2 4.5.3 me3 < 0 ............................. 159 4.5.4 Summary . 170 4.6 Some hº3i 6= 0 Phenomenology . 172 4.6.1 Lepton Number Violation . 172 v 4.6.2 Baryon Number Violation . 177 5 Appendices 180 vi List of Figures 2.1 Kaluza-Klein mode mediated supergraphs giving rise to W4 and ef- fective Yukawa couplings of quarks/leptons to the second Higgs pair. 13 0 2.2 Kaluza-Klein mode mediated supergraphs giving rise to W4 and ef- fective ¹ terms in the superpotential. 15 2.3 Feynman diagrams of the tree level contributions to neutral meson mixing mediated by Higgs bosons. 32 4.1 This plot shows the running of the gauge couplings . 96 4.2 This plot shows the running of the gauge couplings . 97 4.3 This table shows values of various Yukawa couplings . 99 4.4 This plot shows the running of the Log10 of the inverse Yukawa cou- plings . 100 4.5 We see the running of ¹=¹0 for several values of tan¯ . 102 4.6 This plot shows the running of the gaugino mass couplings . 103 4.7 In this plot, we show At=A0 over the whole scaling range of t for several di®erent values of tan¯ and for A0 = M0 and M3(0) = 1:5M0. 104 vii 4.8 In these plots, we show At=A0 and At=M0 over the whole scaling range of t ................................ 105 4.9 In this plot, we show Bt=B0 . 106 4.10 The c¹(0)-tan ¯ plane corresponding to the point cq(0) = 0:75; cº3 (0) = 0:75. 132 4.11 A plot of the cq(0)-cº3 (0) plane for which all soft susy breaking masses remain positive over the entire scaling range. 136 4.12 The c¹(0)-tan ¯ plane corresponding to the point cq(0) = 1:4; cº3 (0) = 1:2..................................... 138 4.13 The hierarchy at point (A) in Figure 4.11 . 141 4.14 The hierarchy at point (B) in Figure 4.11 . 144 2 4.15 A plot of the cq(0)-cº3 (0) plane for which mD3 < 0. 150 4.16 The c¹(0)-tan ¯ plane corresponding to the point cq(0) = 1:0; cº3 (0) = 1:1. 151 4.17 The hierarchy at point (C) in Figure 4.15 . 155 4.18 A plot of the cq(0)-cº3 (0) plane showing both the blue and red regions presented in Figures 4.11 and 4.15 respectively. 156 4.19 The c¹(0)-tan ¯ plane corresponding to the point cq(0) = 1:0; cº3 (0) = 0:9..................................... 157 2 4.20 A plot of the cq(0)-cº3 (0) for which me3 < 0 . 166 viii 4.21 The c¹(0)-tan ¯ plane corresponding to the point cq(0) = 1:1; cº3 (0) = 0:5..................................... 167 0 4.22 E®ective operators generated by the dimension 4 interactions ¸ijkLiQjdk 00 and ¸ijkuidjdk. ............................. 178 2 2 5.1 This plot shows a representative set of points of jM3(0)j =mH (0) (black dots) for di®erent values of T 02 as well as the accuracy of the ¯t of equation (5.6) (blue line) to these representative points. 183 2 2 5.2 These plots show representative points mH (t) =mH (0) (black dots) obtained by numerical solution of (3.108) for di®erent values of t in our scaling range as well as the ¯t of equations (5.7),(5.8) (blue line) to these points. 184 R 2 t 2 2 5.3 Graph (a) is a plot of the term ¡ 3¼2 0 g3jM3j over the entire scaling R 02 1 t 2 0 range taking T =40. Graph (b) is the term 64¼2 0 g4S 1 plotted over the same range. 186 2 2 5.4 In this graph, hhº3ii /mº(0) is plotted over the entire scaling range. 187 5.5 In this graph, we demonstrate the dependence of the running of 2 2 hhmQ3 ii on D . ............................. 188 5.6 This plot shows representative points of D2 (black dots) for di®erent values of T 02 and the ¯t of equation (5.12) (blue line) to these points. 189 ix List of Tables 2.1 Table of data pertinent to the calculation of ¢MF . 34 4.1 Experimental lower bounds on the Higgs ¯elds and sparticles in the MSSM. 128 4.2 The predicted spectrum at point (P) in Figure 4.10(e). 135 4.3 The predicted spectrum at point (Q) in Figure 4.12. 139 4.4 The predicted spectrum at point (R) in Figure 4.16. 153 4.5 The predicted spectrum at point (S) in Figure 4.19. 158 4.6 The spectrum at point (T) in Figure 4.21. 169 x Chapter 1 Introduction In this thesis, we report on the work that lead to the results presented in [2, 3, 4, 5].
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