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Supersymmetric SO(10) unification and flavor changing weak decays [Elektronische Ressource] / Sebastian Jäger

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Published 01 January 2003
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Physik-Department
Technische Universit¨at Munc¨ hen
Institut fur¨ Theoretische Physik
Lehrstuhl Univ.-Prof. Dr. Andrzej J. Buras
Supersymmetric SO(10) unification and
flavor-changing weak decays
¨Sebastian Jager
Technische Universit¨at Munc¨ hen
Physik-Department
James-Franck-Straße
85748 Garching
Germany
Email: sjaeger@ph.tum.dePhysik-Department
Technische Universit¨at Munc¨ hen
Institut fur¨ Theoretische Physik
Lehrstuhl Univ.-Prof. Dr. Andrzej J. Buras
Supersymmetric SO(10) unification and
flavor-changing weak decays
¨Sebastian Jager
Vollst¨andiger Abdruck der von der Fakult¨at fur¨ Physik der Technischen Univer-
sit¨at Munc¨ hen zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr. Stefan Paul
Prufer¨ der Dissertation: 1. Univ.-Prof. Dr. Andrzej J. Buras
2. Univ.-Prof. Dr. Manuel Drees
Die Dissertation wurde am 9.10.2003 bei der Technischen Universit¨at Munc¨ hen
eingereicht und durch die Fakult¨at fur¨ Physik am 21.10.2003 angenommen.Abstract
Westudyflavor-changingdecaysofhadronsandleptonsinsupersymmetric grand
unified theories with universal soft-breaking terms at the Planck scale. Specifi-
cally,westudyanSO(10)modelwithaflavorstructuremotivatedbytheobserved
large atmospheric mixing angle.
In such models, the large top Yukawa coupling leads to a predictive pattern
of flavor violation among the sfermion mass matrices both in the slepton and
squark sectors. The steps taken are the following.
• We perform the first study of this model utilizing a full renormalization-
group analysis to relate Planck-scale parameters to weak-scale parameters.
This allows us to impose constraints from direct searches and vacuum sta-
bility. We provide a prescription to compute the relevant weak-scale pa-
rameters from a few weak-scale inputs.
¯• We compute and discuss the effective Lagrangians for B−B mixing, for
B →φK for τ →µγ decay.d S
¯• AdetailednumericalstudyofB −B -mixingandBR(τ →µγ )allowsustos s
assess the best way to search for signals of, and possibly falsify, this model.
• Asaby-productofourcomputation,wecomputethefullone-looprenormal-
ization-group equations in matrix form of the most general renormalizable
SUSY-SO(10) couplings of the matter fields.
¯We find that in B −B mixing, a significant (about a factor of four), but nots s
anorder-of-magnitudeenhancement ofthe standard modelprediction is possible.
For τ → µγ on the other hand, we find large signals close or even above the
experimental upper bound, so that in fact non-observation of this decay already
exludes part of the otherwise allowed parameter space.
iiiContents
1 Introduction 1
2 The standard model and its SUSY extension 5
2.1 Aspectsandproblemsofthestandardmodel............ 5
2.1.1 FieldcontentandLagrangian ............ 5
2.1.2 Flavorviolation............. 6
2.1.3 Hierarchyproblem ....... 7
2.2 Thesupersymmetricsolution.......... 8
2.2.1 Superfields....................... 9
2.2.2 Nonrenormalizationtheorem...... 11
2.2.3 Softbreaking .......... 11
2.2.4 Nonrenormalizablecase......... 12
2.2.5 Eliminating parameters in softly broken supersymmetry . . 12
2.3 TheMSSM .............................. 14
2.3.1 Softbreakingtermsandparticlemasses ...... 15
2.3.2 Electroweaksymmetrybreaking.... 15
2.3.3 Minimal flavor violation .... 17
2.3.4 Universal boundary conditions ................ 17
3 Supersymmetric grand unification 19
3.1 SO(10) unification of gauge and matter fields ........... 19
3.1.1 Lagrangian ...................... 20
3.1.2 Seesawmechanism ........... 21
3.2 UniversalitybreakinginSUSYGUTs. 21
3.2.1 Radiativeeffects ............ 21
3.2.2 D-termsfromgaugegrouprankreduction ..... 21
3.2.3 FlavorandCPphenomenology ............... 22
3.2.4 AwordongenericGUTproblems.......... 23
4 The Chang-Masiero-Murayama model 25
4.1 FieldcontentandLagrangian .................... 25
4.2 Symmetrybreakingchain ....... 27
4.3 Radiativecorrectionsandflavorviolation.............. 29
iii∆



iv CONTENTS
5 Renormalization of the CMM model 33
5.1 MSSMrenormalization ........................ 33
5.1.1 SUSYthresholdcorrectionsattheelectroweakscale 33
5.1.2 Renormalization-groupequations .............. 34
5.1.3 MSSMevolution ........ 37
5.2 GUTrenormalization......................... 38
5.2.1 Renormalization-groupequations .......... 38
5.2.2 Solution for y , fixed point of y /g, and related constraint . 43t t
5.2.3 Soft-termevolution ........... 45
5.3 Additional sources of nonuniversality ............ 48
5.3.1 D-termsfromgaugegrouprankreduction ......... 48
5.3.2 GUTthreshold ......... 49
5.4 Weak-scale mass splitting from weak-scale inputs ......... 49
6 Effective Lagrangian and weak-scale observables 51
6.1 F=2processes........................... 51
6.1.1 Massdifferences......... 53
6.1.2 CPviolation.... 54
6.2 F=1processes. 55
6.2.1 τ →µγ ............................ 55
6.2.2 B →φK . 57d S
7 Numerical study of the phenomenology 61
7.1 Fixed-pointconstraintandimplementation............. 61
7.2 Constraints on the input parameters ............ 64
7.2.1 Directsearches ............. 64
7.2.2 Vacuum stability and correct symmetry breaking. . 64
7.3 Third-generationsoftmasses.......... 65
7.3.1 Correlation of m ,a ,m (M ) with weak-scale inputs . . . 650 0 g˜ Pl
7.3.2 m , m ,and m ..................... 67˜ ˜ e˜d l RR 3 33
7.4 F=1and F=2FCNCprocesses..... 69
¯7.4.1 B –B mixing .......... 69s s
7.4.2 τ →µγ decay.... 69
8 Conclusions and outlook 73
A Crash review of SO(10) 75
A.1 LieAlgebraofSO(10) ........................ 75
A.2 Sometensorrepresentations ...... 75
A.2.1 Adjointrepresentation ......... 76
A.2.2 120-dimensional representation 76
A.2.3 252-dimensional reducible representation. Levi-Civita ten-
sor, duality transform, 252= 126+126........... 76CONTENTS v
A.3 Spinor representations ........................ 77
A.3.1 Clifford algebra and spinor generators........ 77
A.3.2 γ,chiralityprojectors,Chisholmidentity ......... 775
A.3.3 Charge conjugation matrix, irreducible bilinears . . 78
A.4 Loopcalculations ........................... 80
A.4.1 Casimirinvariants ....... 80
A.4.2 Loopfactorsandtraces......... 81
B Renormalization group equations 83
B.1 SO(10)................................. 83
B.2 SU(5) 85
C List of functions 87
C.1 Renormalizationgroupsolutions................... 87
C.2 Loopfunctions ............. 88vi CONTENTS