Aspects of neutrino mass models in the light of recent oscillation data Thesis submitted to the University of Calcutta for the degree of Doctor of Philosophy (Science) by Soumita Pramanick Department of Physics University of Calcutta 2017 – To the journey of life – i Acknowledgements I find this section extremely hard to write as I feel I can never complete writing this. Neither the list of people to be thanked can be completed nor their contributions in my life can be acknowledged in words. No matter how vividly I express my gratitude towards them I must admit I really do not have words to acknowledge their contribution and support. “Thank you” really is too small a word. Whatever I say will only be a fraction of my gratefulness. It is a bright summer afternoon in May 2017, when I am writing this note and some M.Sc students busy in cheerful chat drags my attention in the University corridor. It seems just like yesterday when I entered this department after completing my B.Sc in Physics (Honours) from Scottish Church College, Kolkata. To be a part of this highly esteemed department of C.V. Raman, Meghnad Saha, Satyendranath Bose happened to be a dream since childhood and with the M.Sc admission a journey of close association with the department started. All my teachers from the department had been extremely student friendly in their interactions, always keen to help us in issues be it academic or administrative. Days went by and a beautiful bond resulted between the teachers and the student and unknowingly this place gradually became a home away from home and the department became an academic family. After successful completion of M.Sc examination it was a time to get parted from this integral part of my existence. I can vividly recol- lect the memory of the last M.Sc lecture in particle physics specialization course when a feeling of sadness prevailed in my heart as a very dear association with the Physics department of Rajabazar Science College (that is what we call infor- mally the University of Calcutta, Rajabazar Campus where the Department of Physics is located) was about to end. I am immensely thankful to all my teach- ers including Dr. Sudipta Bandyopadhyay, Prof. Abhijit Bhattacharyya, Prof. Subinay Dasgupta, Dr. Anindya Datta, Prof. Gautam Gangopadhyay, Prof. Deb- narayan Jana, Prof. Anirban Kundu, Prof. Indrajit Mitra, Dr. Jayashree Saha, Prof. Parongama Sen and Dr. Jayalakshmi Shamanna for their kind support and guidance in moments of need from the bottom of my heart. Then came another chance of getting associated with the department as a Ph.D. student of Prof. Amitava Raychaudhuri and work in particle physics when a new journey started. Working with Prof. Raychaudhuri was like a dream come true. He has not only taught me about the physics research problem but also has in- spired me as a human being. I am thankful to Prof. Raychaudhuri from the core of my heart for making me cognizant of various branches of particle physics including neutrinos. It was the educative discussions with him that has developed my inter- ests in diverse fields of particle physics research. I owe all my research activities in particle physics now and in future to the interest in this fascinating branch of physics that Prof. Raychaudhuri introduced me to through his discussions and guidance. His valuable advice has guided me to handle several administrative is- sues from time to time during the research. He has encouraged me to attend several schools and workshops in India and abroad. His extreme patience, inspiration and ii mental support throughout was very conducive to research. Altogether it had been fantastic learning experience. My heartfelt gratitude to Prof. Raychaudhuri for his kind support and wonderful guidance. No matter what I write, it will always remain insufficient to convey my regards and deep respect for Prof. Raychaudhuri. The academic bond with the department strengthened more during my Ph.D. research. I am indebted to the other particle physics research group members Prof. Amitava Datta, Dr. Anindya Datta and Prof. Anirban Kundu for their− discussions and help in matters academic and administrative. I wish to thank specially Dr. Sudipta Bandyopadhyay and Prof. Subinay Dasgupta for checking my office so as to ensure I am safe during my stays in University working till late in the evenings. My colleagues, the other Ph.D. students of the department, had been extremely friendly in their interactions making this period very memorable. Apart from being a constant source of inspirations, they have gifted me several moments of happiness to be cherished throughout my life. I wish to express my sincere regards to Prof. Gautam Bhattacharyya of the Saha Institute of Nuclear Physics, India. I am also thankful to the non-teaching staff of the department who had always been ready to help in administrative matters with a smile on their face. On the domestic front, my journey till date had been completely a result of someone working very hard behind the scenes, my mother. My father had been a constant source of inspiration for me. I wish to thank my sister, friends and family for their help and support to handle various practical situations. I wish to thank everyone I mentioned here for bestowing on me the wealth of good memories. This entire research was funded by CSIR (NET) Junior Research Fellowship later on upgraded to CSIR (NET) Senior Research Fellowship for which I wish to ac- knowledge the financial support under Sanction No. 09/028(0890)/2012-EMR-I of Council of Scientific and Industrial Research (CSIR), Government of India. Department of Physics, Soumita Pramanick University of Calcutta, India. May 2017. iii Abstract Neutrinos are massive and they oscillate. The three-neutrino oscillation paradigm is characterized by the three mixing angles (θ12, θ13, θ23); two mass square splittings 2 2 (∆msolar, ∆matmos) and one complex phase (δ) responsible for CP violation. It is 2 2 2 noteworthy that ∆msolar/∆matmos 10− . Earlier the experimental observations were roughly consistent with popular∼ lepton mixing patterns like the Tribimaximal (TBM), Bimaximal (BM) and Golden Ratio (GR) mixing as they give θ13 = 0 and maximal mixing in the atmospheric sector (θ23 = π/4) by construction. In 2012 short-baseline reactor anti-neutrino experiments observed non-zero θ13 which is small compared to the other two mixing angles i.e., θ 9◦. A running theme 13 ∼ of my research work is to consider a two-component Lagrangian, one of which is dominant and the other one smaller. The dominant constituent offers any of the popular lepton mixings or a scenario where all the mixing angles are either 0 or 2 maximal (π/4) to start with accompanied by ∆msolar = 0, while the sub-dominant 2 component amends the dominant part so as to generate non-zero θ13 and ∆msolar and brings the other mixing angles in concord with the experimental data while predicting the CP violation phase δ. We began with an introduction which reviews the essentials of neutrino properties and the Standard Model that were used throughout the thesis. Then we have analysed the two-component scenario in the context of different mixing patterns in a model independent fashion. Next we examined the possibility that the sub- dominant contribution could originate from a Type I seesaw mechanism. The theories result in interesting interrelationships between different oscillation param- eters making it testable. In particular, the CP phase δ, octant of θ23, ordering of neutrino masses and the lightest neutrino mass get correlated. We have also explored the possibility of such models arising from discrete flavour symmetries such as A4 and S3. We have identified the quantum numbers of the leptons such that the Type II seesaw mechanism gives rise to the dominant part of the neutrino mass matrix while the smaller Type I seesaw contribution attributes corrections which bring the mixing angles and masses into the measured range. The Lagrangian includes all terms allowed by the symmetries and no soft sym- metry breaking term is introduced. Symmetries are broken spontaneously. The models predict the octant of θ23 as well as the effective mass for neutrinoless double beta decay in terms of the lightest neutrino mass and are therefore testable. It was inferred that normal ordering is always associated with the first octant of θ23 whereas the second octant with inverted ordering. The models have rich scalar sectors which are carefully studied in terms of the local minimization of the scalar potential and the necessary conditions specific to them are obtained. iv Aspects of neutrino mass models in the light of recent oscillation data Soumita Pramanick Department of Physics, University of Calcutta Abstract Three-neutrino oscillations are characterised by the mixing angles (θ12, θ13, θ23), mass square splittings (∆m2 , ∆m2 ) and a Dirac CP phase (δ). Experiments indicate that ∆m2 / ∆m2 10 2. solar atmos solar | atmos| ∼ − Prior to the observation of θ13 = 0 in 2012, lepton mixings of the Tribimaximal, Bimaximal, and Golden 6 Ratio forms were constructed with θ13 = 0 and θ23 = π/4. Their sharp contrast with the experimental observations accentuates the necessity of amendment. A two-component formalism is the motif of 2 the thesis. The dominant contribution corresponded to ∆msolar = 0 along with any of the popular mixings or NSM (no solar mixing i.e., θ23 = π/4, θ13, θ12 = 0). The sub-dominant constituent nudged these parameters into the observed range. Predictions for the CP phase δ were obtained. Preceded by an overview of neutrino physics and the Standard Model in Chapter 1, in Chapter 2 a model independent realization of the strategy for the four mixings is presented.