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NNLO Vacuum Stability Analysis in the SM and the Higgs Bosons of the MSSM at Three-Loop Accuracy

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NNLO Vacuum Stability Analysis in the SM and the Higgs Bosons of the MSSM at Three-Loop Accuracy NNLO Vacuum Stability Analysis in the SM and the Higgs Bosons of the MSSM at Three-Loop Accuracy Edilson Alfonso Reyes Rojas Universidad Nacional de Colombia Facultad de Ciencias, Departamento de F´ısica Bogot´a,Colombia 2020 NNLO Vacuum Stability Analysis in the SM and the Higgs Bosons of the MSSM at Three-Loop Accuracy Edilson Alfonso Reyes Rojas Trabajo de grado presentado como requisito para optar al t´ıtulode: Doctor en Ciencias F´ısica Director: Ph.D. Angelo Raffaele Fazio Grupo de Campos y Part´ıculas Universidad Nacional de Colombia Facultad de Ciencias, Departamento de F´ısica Bogot´a,Colombia 2020 This thesis is based on the author's work conducted at the Universidad Nacional de Colombia in Bogot´a.Main results of this work have already been published in the articles: [1] E. A. Reyes R., A. R. Fazio, EPJ Web Conf. 192, 00033 (2018). DOI: 10.1051/epjconf/201819200033 [2] A. R. Fazio and E. A. Reyes R., Nucl. Phys. B 942, 164-183 (2019). [arXiv:1901.03651 [hep-ph]]. DOI: 10.1016/j.nuclphysb.2019.03.008 [3] E.A. Reyes R., A.R. Fazio, Phys. Rev. D 100, no.11, 115017 (2019). [arXiv:1908.00693 [hep-ph]]. DOI: 10.1103/PhysRevD.100.115017 The author have presented and discussed the results of this thesis in different events: The Higgs Boson Masses of the MSSM at Three-Loop Accuracy Katharsis of Ultimate Theory Standards 7 (KUTS7) Karlsruhe - Karlsruhe Institute of Thechnology (KIT) (2017). The Higgs Boson Masses of the MSSM at Three-Loop Accuracy XXVII Congreso Nacional de F´ısica Cartagena - Colombia (2017). The Lightest Higgs Boson Mass of the MSSM at Three-Loop Accuracy 2nd Colombian Meeting on High Energy Physics Bogot´a,D.C. - Universidad Nacional de Colombia (UNAL) (2017). The Lightest Higgs Boson Mass of the MSSM at Three-Loop Accuracy MASS2018: Origin of Mass at the High Energy and Intensity Frontier Odense - University of Southern Denmark (SDU) (2018). The light CP-even Higgs boson mass of the MSSM at three-loop accuracy International Workshop on Quantum Chromodynamics Theory and Experiment QCD@Work 2018. Matera - Italy (2018). Acknowledgements Empiezo agradeciendo al profesor A. Raffaele Fazio quien fue mi director de esta tesis doctoral, pero mas importante aun un valioso amigo que me ha acompa~nadoen mi proceso de formaci´oncomo investigador en el ´areade la f´ısicade part´ıculas.Agradezco su apoyo continuo en medio del complejo camino que deci- dimos seguir en este proyecto, las valiosas discusiones que hemos tenido, sus consejos para poder realizar exitosamente el doctorado y sobretodo su paciencia y confianza en medio de los problemas que se nos han presentado. Espero sinceramente haber contribuido a su vida personal y profesional de la misma manera que el contribuyo a la m´ıa. Por otra parte quiero agradecer a varias personas que han formado parte a lo largo de este proceso. Al Prof. Dr. Bernd A. Kniehl, quien me presto su hospitalidad y apoyo incondicional en mi estancia realizada con su grupo en DESY en el a~no2017. A la doctora Sophia C. Borowka, quien estuvo en la Universidad Nacional de Colombia con nuestro grupo en el a~no2016 como profesora invitada y con quien iniciamos este camino. Su amable disponibilidad para discutir acerca de los detalles t´ecnicosde nuestro c´alculohicieron realizable este proyecto. Al profesor Alexis Irlande por ayudarnos con la instalaci´onde nuestro propio servidor en la UNAL y por su apoyo t´ecnico todos estos a~nos.Al profesor Sven Heinemeyer por las diferentes discusiones en el evento KUTS y via e-mail. Al equipo de KUTS por permitirme exponer mis resultados y por todas las discusiones llevadas a cabo en su evento. Al profesor Ayres Freitas por sus discusiones acerca del c´odigo TVID que es una pieza importante en nuestro c´alculo. Al profesor Mikhail Kalmykov por sus discusiones acerca del estado de arte de las integrales master a tres-loop. Al profesor German Rodrigo y al profesor William Torres, quien es tambi´enun antiguo amigo, por su amable invitaci´ona presentar un seminario en su grupo de investigaci´onen el IFIC de la universidad de Valencia - Espa~na,por las discusiones llevadas a cabo y por incluirme como miembro de COST. A la profesora Heidi Rzehak por su colaboraci´ony apoyo financiero para participar en el evento MASS2018 realizado en Odense { Dinamarca. Al profesor C. Coriano y en general a los organizadores del seminario QCD@Work 2018 por su apoyo financiero, por permitirme presentar un poster y por las discusiones en su evento. Quiero agradecer a las instituciones que han financiado este proyecto. La Universidad Nacional de Colombia a trav´esde la beca: CONVOCATORIA NACIONAL DE PROYECTOS PARA EL FORTALECIMIENTO DE LA INVESTIGACION,´ CREACION´ E INNOVACION´ DE LA UNIVERSIDAD NACIONAL DE CO- LOMBIA 2016-2018 con el proyecto N. 34729, Minimal Supersymmetric Standard Model Higgs Boson to High Accuracy. Colciencias a trav´esde la beca: CONVOCATORIA 727 DE COLCIENCIAS PARA DOC- TORADOS NACIONALES 2015 con el Proyecto N. 39844, NNLO Vacuum Stability Analysis in the SM and the Higgs Bosons of the MSSM at Three-Loop Accuracy. Finalmente, quiero agradecer el apoyo de mi familia, necesario para hacer mas f´acilel camino que escog´ı. Este documento esta dedicado a ellos: Celia, Alfonso, Diego, Freddy, Cristian, Susana y en especial a Paola por su paciencia y apoyo en estos ultimos a~nos.Amorem nostrae memoriam spero sempiternam fore. ix Resumen En esta tesis proporcionamos un c´alculodiagram´atico a orden fijo de las correcciones cu´anti- cas a la masa del boson de Higgs liviano en el modelo super-sim´etricominimal con par´ametros reales. Hemos calculado las contribuciones provenientes del sector de la QCD super-sim´etri- 2 ca con una precisi´onde tres-loops al orden O(αtαs). El procedimiento de regularizaci´on adoptado esta basado en el esquema de reducci´ondimensional con el fin de preservar la super-simetr´ıaen todos los ordenes perturbativos. El c´alculoextiende la regi´onde validez de estudios previos al espacio completo de par´ametrossuper-sim´etricos.Las correcciones a la masa del Higgs son expresadas en t´erminosde un conjunto de integrales del vac´ıoa tres-loops las cuales han sido calculadas explotando las t´ecnicasdel m´etodo de dispersi´on que permite realizar su evaluaci´onnum´ericapara una jerarqu´ıaarbitraria de las escalas de masa involucradas. Por otro lado, hemos realizado una comparaci´onnum´ericade nuestros resultados con las dem´aspredicciones te´oricasencontradas en la literatura. En particular, el c´odigoFeynHiggs combina c´alculosa orden fijo con los c´alculosprovenientes de la teor´ıa efectiva de campos cu´anticos dando una predicci´onconfiable para la masa del boson de Higgs hasta el orden de tres-loops. Las dos predicciones num´ericasson compatibles en el escenario donde solo hay una escala de la super-simetr´ıaque toma valores menores a 10 TeV y donde el par´ametrode mezcla del quark stop se anula. Para escalas mayores a 10 TeV observamos diferencias num´ericassignificativas. La diferencia crece sin acotarse al aumentar la escala de la super-simetr´ıadebido a los efectos de los t´erminoscon logaritmos grandes en el c´alculoa orden fijo que da~nanla perturbatividad de las correcciones cu´anticas. Por lo tanto, hemos realizado un an´alisisnum´erico adicional donde buscamos restricciones al valor que puede tomar la escala super-sim´etrica.El valor experimental combinado para la masa del boson de Higgs obtenido por los laboratorios CMS y ATLAS y el problema de la estabilidad del vac´ıoen el modelo est´andarson usados para derivar cotas superiores sobre esta escala. En el escenario considerado en este trabajo, para un valor grande de la raz´onentre los valores esperados en el vac´ıode los dos campos de Higgs pares bajo CP (tanβ 10), hemos encon- ≥ trado que valores de la escala super-sim´etricasuperiores a 12:5 1:2 TeV est´anexcluidos. ± Para valores peque~nosde tanβ 1, una cota superior muy grande de alrededor de 1011 GeV ≈ fue encontrada. Abstract In this thesis we provide a fixed-order Feynman diagrammatic computation of the quan- tum corrections to the lightest CP-even Higgs Boson mass in the real version of the Mi- nimal Supersymmetric Standard Model. We have computed the contributions coming from 2 the SUSY-QCD sector with a precision of three-loops at order O(αtαs). The adopted re- x gularization procedure is based on the dimensional reduction scheme in order to preserve supersymmetry to all perturbative orders. The calculation extends the region of validity of previous studies to the whole supersymmetric parameter space. The Higgs mass corrections are expressed in terms of a set of three-loop vacuum integrals which have been computed by exploiting dispersion relation techniques which allows their numerical evaluation for an arbitrary hierarchy of the involved mass scales. A numerical comparison of our results with the other predictions found in literature has been done. In particular, the code FeynHiggs combines one- and two-loop fixed-order with the effective-field-theory calculations and gives a reliable prediction for the same Higgs mass at three-loop level. The two numerical pre- dictions agree considering the scenario of only one SUSY-scale and vanishing stop mixing parameter below 10 TeV. For large scales above 10 TeV we have observed sizeable numerical differences between the two predictions. The difference grows monotonically with the SUSY scale due to the effects of large logarithmic terms in the fixed-order computation which spoil the perturbativity of the corrections. Therefore, we have developed an additional nu- merical analysis where we look for constraints on the supersymmetric scale.
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