Present Aspects and Future Prospects of Neutrino Mass and ...library/ghosh_m_2015_abst.pdf · DECLARATION I, Mr. Monojit Ghosh, S/o Mr. Monoranjan Ghosh, resident of RN-011, PRL student

Present Aspects and Future Prospectsof Neutrino Mass and Oscillation

A THESIS

submitted for the Award of Ph.D. degree of

MOHANLAL SUKHADIA UNIVERSITY

in the

Faculty of Science

by

Monojit Ghosh

Under the Supervision of

Prof. Srubabati Goswami

Professor

Theoretical Physics Division

Physical Research Laboratory

Ahmedabad, India.

DEPARTMENT OF PHYSICS

MOHANLAL SUKHADIA UNIVERSITY

UDAIPUR

Year of submission: 2015

DECLARATION

I, Mr. Monojit Ghosh, S/o Mr. Monoranjan Ghosh,

resident of RN-011, PRL student hostel campus, Thaltej, Ahmed-

abad 380058, hereby declare that the research work incorporated

in the present thesis entitled, “Present Aspects and Future

Prospects of Neutrino Mass and Oscillation” is my own work

and is original. This work (in part or in full) has not been submit-

ted to any University for the award of a Degree or a Diploma. I

have properly acknowledged the material collected from secondary

sources wherever required. I solely own the responsibility for the

originality of the entire content.

Date:

(Monojit Ghosh)

CERTIFICATE

I feel great pleasure in certifying that the thesis entitled,

“Present Aspects and Future Prospects of Neutrino Mass

and Oscillation” embodies a record of the results of investiga-

tions carried out by Mr. Monojit Ghosh under my guidance. He

has completed the following requirements as per Ph.D regulations

of the University.

(a) Course work as per the university rules.

(b) Residential requirements of the university.

(c) Regularly submitted six monthly progress reports.

(d) Presented his work in the departmental committee.

(e) Published minimum of one research papers in a refereed re-

search journal.

I am satisfied with the analysis, interpretation of results and

conclusions drawn. I recommend the submission of thesis.

Date:

Prof. Srubabati Goswami

(Thesis Supervisor)

Professor, THEPH,

Physical Research Laboratory,

Ahmedabad - 380 009

Countersigned by

Head of the Department

i

Acknowledgements

I want to take this opportunity to express my sincere and deep gratitude to my

supervisor Prof. Srubabati Goswami, for her invaluable guidance, support and

involvement throughout my work. Her immense knowledge, perspective and ex-

pertise in the subject have helped me during my research and writing of the thesis.

Discussing physics with her was fun. We had a great compatibility in understand-

ing the views of each other. She always encouraged me to have a deep and critical

understanding of the subject. Due to her friendly nature I could discuss any of

my problems with her and she was always there to help me. Her continuous

encouragement and motivation gave me confidence to continue research in this

field. I could not have imagined having a better advisor for my Ph.D study.

I would specially like to thank Dr. Bijaya Sahoo, Prof. Hiranmaya Mishra,

Prof. Jitesh Bhatt, Dr. Namit Mahajan, Dr. Partha Konar, Prof. Raghavan

Rangarajan and Prof. Subhendra Mohanty for taking courses on quantum me-

chanics, particle physics, quantum field theory and mathematical methods. My

special thanks goes to my thesis expert Prof. S. Mohanty and the academic com-

mittee for reviewing my work thoroughly. I also thank Prof. Amol Dighe, Prof.

Raj Gandhi, Prof. Sandhya Choubey, Dr. Sanjib Agarwala and Prof. Uma

Shankar for various physics discussions. I would also like to thank Prof J.W.F.

Valle for giving me the opportunity to visit IFIC, Valencia. I thank him and

Prof. Mariam Tortolla for very useful discussions at IFIC.

I specially thank Dr. Shivani Gupta with whom I have carried out my first

research project. I learned a lot of things from her during my initial days of re-

search. I offer my heartiest thanks to Dr. Pomita Ghoshal and Dr. Sushant Raut

whose contributions have shaped my knowledge and understanding of neutrino

oscillation physics. I thank them for answering my infinite number of questions

with patience. I can never forget those long stimulating discussion sessions in my

supervisor’s office. I also want to thank Animesh Chatterjee, Moon Moon Devi

and Reetanjali Moharana with whom I have spent sleepless nights to finish our

project at WHEPP 2013. It has been a nice experience to work with all of you.

ii

I thank my senior Subrata da, my batch mate Gulab and my juniors Chandan

Gupta, Chandan Hati, Newton and Vishnu for various useful discussions. I also

want to express my gratitude to Abhay, Kuldeep Suthar, Tanmoy Mondal and

Ujjal with whom I shared my office space at PRL. They helped me greatly in my

research work. A special thanks to Ujjal for a thorough proofreading of my thesis.

My stay at PRL hostel will be memorable due to the presence of all the stu-

dents including all my seniors, juniors, project associates, project students and

my batchmates. The festival celebrations, the sports events, our hundred kilo-

meter long bike trips, hangouts, mind boggling discussions on cinema, politics,

literature and many other things will remain unforgettable and will stay close

to my heart throughout my life. I want thank you all: Aadhi, Anjali, Arko,

Avdhesh, Bhavya, Damu, Dillip, Dinesh, Gaurav Tomar, Girish Chakravarty,

Lata, Lekshmy, Midhun, Naveen, Nigam, Priyanka, Reddy, Tanmoy Chattopad-

hay, Upendra, Wageesh, Yashpal, Abhishek da, Akhilesh, Amrendra, Amzad da,

Aravind Saxena, Aravind Thakur, Arun Awasthi, Asish, Bhaswar da, Chin-

may da, Fazlul da, Ketan, Koushik da, Moumita di, Pankaj, Prashant, Ra-

biul da, Shashi, Siddhartha da, Soumya, Srinu, Suman da, Sunil, Sushanta,

Tanushree di, Tapas da, Vimal, Vineet, Zeen, Ananta, Gaveshna, Ila, Mansi,

Nabyendu da, Ranjita, Shweta, Sudip da, Alok, Anirban, Arun Pandey, Chi-

trabhanu, Gaurav Jaiswal, Girish Kumar, Guru, Ikshu, Manu, Sanjay, Shradha,

Apurv, Ashim, Bivin, Deepak, Dipti, Jiniya, Lalit, Pankaj, Rahul, Sukanya,

Venky, Ali, Jabir, Kuldeep Pandey, Kumar, Navpreet, Prahlad, Rukmani, Rupa,

Satish, Wriju, Balaji, Bose, Dharak, Ejaz, Jayesh Khunt, Nitesh, Ranjit, Rishi,

Santosh, Sharad, Sneha, Subha Anand, Vijayan, Abhishek, Ankur, Dipanweeta,

Jayesh Agarwal, Rashika, Ria, Sameer, Sudha and Vasu for spending such beau-

tiful times with me.

I am grateful to all the PRL library, computer center, dispensary and admin-

istration staff and also to the staff members of Theoretical Physics Division of

PRL for their sincere support.

I also acknowledge Biswajit, Dipankar, Kamakhya, Sabyasachi, Suprabh and

Tuhin whom I met in different conferences and became very good friends. We

iii

discussed physics whenever we meet and spent precious time together. I could not

forget the warm hospitality of Biswajit when we went for the DAE 2014 meeting.

I would also like to thank few of my university friends Anupam, Arghya,

Barun, Kalpana, Koushik, Soubhik, Sudip and Suman who frequently keep on

asking that how my work is going on and supported me in difficult times. I also

want to thank few of my school friends Sandipan, Subho and Tamoghna who were

always there to greet me whenever I went home.

I express my deepest gratitude to my family: my parents and my brother for

supporting me throughout and for their unconditional love. They always stood

beside and encouraged me to pursue a career that I like. This thesis would never

be possible without their constant support.

And last but not the least I would also like to thank Anushmita, for proof

reading of my thesis partially and motivating me by the following Hemingway’s

advice on writing at the time when I was struggling to write my thesis by thinking

if a 10 page paper takes several months to write then how it will be possible to

manage a thesis consisting of 200 pages:

“Advice on how to write? Sit on a typewriter and start typing. That’s the

easiest and the hardest part.”

Monojit

v

ABSTRACT

Neutrinos are neutral, spin-12particles which undergo only weak interactions.

The experimentally observed phenomenon of neutrino oscillation establishes the

fact that neutrinos are massive and there is mixing between different neutrino

flavours. This constitutes the first unambiguous hint towards the physics Beyond

Standard Model (BSM). In the BSM theories, the neutrino mass terms in the

Lagrangian lead to the non-diagonal neutrino mass matrix in the flavour basis

which depends on neutrino mass and mixing parameters. Thus knowledge of the

neutrino oscillation parameters and understanding the underlying symmetries of

the neutrino mass matrix are very important as they can give an insight to the

new physics beyond Standard Model. Therefore the measurement of different

oscillation parameters and studying the structure of the neutrino mass matrix

are some of the main goals in neutrino physics at present.

Currently the paradigm of neutrino oscillation between three flavours is well

established from different experiments and the oscillation parameters are get-

ting measured with continued precision. The current unknowns in the neutrino

oscillation physics in the standard three generation framework are: the neu-

trino mass hierarchy, octant of θ23 and the leptonic phase δCP . There are many

ongoing/future experiments where these unknown oscillation parameters can be

probed. These experiments utilize different sources and detectors as well as differ-

ent baselines along which oscillations can develop. As the oscillation probabilities

depend differently on the parameters in different oscillation experiments, com-

bination of different experiments can often be useful. Apart from three flavours

oscillations there are also evidences of oscillation involving sterile neutrinos. In

the presence of a sterile neutrino there will be new mixing angles and phases

contributing to the oscillation of the neutrinos. This gives rise to the possibil-

ity that the well understood phenomenological behaviour of the neutrino mass

matrix may change in the presence of sterile neutrinos.

In this thesis we have studied the potential of present/future neutrino os-

cillation experiments and synergy between them to determine the unknown pa-

vi

rameters in the neutrino sector in the light of current experimental results. We

consider the beam based experiments T2K, NOνA, LBNO, LBNE, the atmo-

spheric experiment INO@ICAL and the ultra high energy neutrino experiment

IceCube for our analysis. We find that the data from atmospheric neutrino ex-

periment ICAL can significantly improve the CP sensitivity of the long-baseline

experiments T2K/NOνA in their unfavourable parameter space. To improve

the sensitivity beyond what can be achieved in T2K/NOνA, it is important to

study the physics potential of the proposed long-baseline experiments LBNO

and LBNE in view of the current experiments. We have shown that the required

exposure of LBNO and LBNE in determining neutrino mass hierarchy, octant of

θ23 and δCP can be reduced significantly when data from T2K, NOνA and ICAL

are added to them. We have also explored the possibility to constrain the CP

phase δCP by analyzing the IceCube data in terms of the flavour compositions

of the ultra high energy neutrinos.

We have also studied the phenomenological consequences of texture zeros in

the neutrino mass matrices in the presence of a sterile neutrino. We have carried

out a detailed analysis of the two-zero and one-zero textures in the 3+1 scenario

which involves three active neutrinos and one sterile neutrino. We find that

in the 3+1 picture, conclusions differ significantly as compared to the standard

3 generation case. The allowed two-zero textures in the 3 × 3 structure are

more phenomenologically constrained as compared to the 4 × 4 structure. The

correlations between the different oscillation parameters are also very different

when the texture zero conditions between the 3 generation and 3+1 generations

are compared.

Keywords : Neutrino Physics, Neutrino Oscillation, Long-Baseline Neutrino

Experiments, Atmospheric Neutrino Experiments, Ultra High Energy Neutrinos,

Leptonic CP Phase, Neutrino Mass Matrix, Sterile Neutrino, Texture Zero

LIST OF PUBLICATIONS

Publications contributing to this thesis :

1. Two Zero Mass Matrices and Sterile Neutrinos,

M. Ghosh, S. Goswami and S. Gupta, JHEP 1304, 103 (2013).

2. Implication of a vanishing element in the 3+1 scenario,

M. Ghosh, S. Goswami, S. Gupta and C. S. Kim, Phys. Rev. D 88, no.

3, 033009 (2013).

3. Can atmospheric neutrino experiments provide the first hint of leptonic CP

violation?,

M. Ghosh, P. Ghoshal, S. Goswami and S. K. Raut, Phys. Rev. D 89,

no. 1, 011301 (2014).

4. Synergies between neutrino oscillation experiments: an ’adequate‘ configu-

ration for LBNO,

M. Ghosh, P. Ghoshal, S. Goswami and S. K. Raut, JHEP 1403, 094

(2014).

5. Probing CP violation with the first three years of ultrahigh energy neutrinos

from IceCube,

A. Chatterjee, M. M. Devi, M. Ghosh, R. Moharana and S. K. Raut,

Phys. Rev. D 90, no. 7, 073003 (2014).

6. Evidence for leptonic CP phase from NOνA, T2K and ICAL: A chrono-

logical progression,

M. Ghosh, P. Ghoshal, S. Goswami and S. K. Raut, Nucl. Phys. B 884,

274 (2014).

7. Economizing the LBNE configuration with current experiments,

M. Ghosh, S. Goswami and S. K. Raut, arXiv:1412.1744 [hep-ph] (com-

municated for publication).

viii

Other publications :

1. Can the hint of δCP from T2K also indicate the hierarchy and octant?,

M. Ghosh, S. Goswami and S. K. Raut, arXiv:1409.5046 [hep-ph] (com-

municated for publication).

2. Identifying and resolving the degeneracies in neutrino oscillation parame-

ters in current experiments,

M. Ghosh, P. Ghoshal, S. Goswami, N. Nath and S. K. Raut, arXiv:1504.06283

[hep-ph] (communicated for publication).

ix

List of Abbreviations

BSM Beyond Standard Model

SM Standard Model

CC Charge Current Interaction

NC Neutral Current Interaction

LEP Large Electron-Positron collider

VEV Vacuum Expectation Value

PMNS Pontecorvo Maki Nakagawa Sakata Matrix

0νββ Neutrinoless Double Beta Decay

SSM Standard Solar Model

SK Super-Kamiokande Experiment

DAR Decay at Rest

DIF Decay in Flight

IBD Inverse Beta Decay

UHE Ultra High Energy

AGN Active Galactic Nuclei

GRB Gamma Ray Burst

GUT Grand Unified Theories

NSI Non Standard Interaction

OMSD One Mass Scale Dominance Approximation

MSW Mikheyev Smirnov Wolfenstein Effect

PREM Preliminary Reference Earth Model

GLoBES General Long Baseline Experiment Simulator

NH Normal Hierarchy

IH Inverted Hierarchy

QD Quasi-Degenerate

x

LO Lower Octant

HO Higher Octant

LHP Lower Half-Plane of δCP

UHP Upper Half-Plane of δCP

T2K Tokai to Kamioka

POT Protons on Target

NOνA NuMI Off-axis νe Appearance

LAGUNA Large Apparatus studying Grand Unification and

Neutrino Astrophysics

LBNO Long-Baseline Neutrino Oscillation Experiment

LBNE Long-Baseline Neutrino Experiment

LArTPC Liquid Argon Time Projection Chamber

SURF Sanford Underground Research Facility

DUNE Deep Underground Neutrino Experiment

INO India-based Neutrino Observatory

ICAL Iron Calorimeter Detector

LBL Long Baseline Experiments

CPV CP Violation

TASD Totally Active Scintillator Detector

ND Near Detector

FD Far Detector

TBM Tri-bimaximal Mixing

SBL Short Baseline Experiments

Contents

Acknowledgements i

Abstract v

List of Publications vii

List of Abbreviations ix

Contents xi

List of Tables xvii

List of Figures xix

1 Introduction 1

1.1 The Origin of Neutrinos . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Neutrinos in Standard Model . . . . . . . . . . . . . . . . . . . . 2

1.3 Neutrino Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Evidences of Neutrino Oscillation . . . . . . . . . . . . . . . . . . 7

1.4.1 Solar Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4.2 Atmospheric Neutrinos . . . . . . . . . . . . . . . . . . . . 9

1.4.3 Accelerator Neutrinos . . . . . . . . . . . . . . . . . . . . 10

1.4.4 Reactor Neutrinos . . . . . . . . . . . . . . . . . . . . . . 12

1.4.5 Ultra High Energy Neutrinos . . . . . . . . . . . . . . . . 13

1.5 Neutrino Mass Matrix . . . . . . . . . . . . . . . . . . . . . . . . 14

xi

xii CONTENTS

1.6 Unknown Oscillation Parameters and Future Prospects: Three

Generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.7 Sterile Neutrinos: Beyond Three Generations . . . . . . . . . . . . 18

1.8 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Neutrino Oscillation 23

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Derivation of Oscillation Probability . . . . . . . . . . . . . . . . 24

2.2.1 Two Flavour Oscillation in Vacuum . . . . . . . . . . . . . 24

2.2.2 N Flavour Oscillation in Vacuum . . . . . . . . . . . . . . 28

2.2.3 Two Flavour Oscillation in Matter . . . . . . . . . . . . . 30

2.2.4 Three Flavour Oscillation in Matter: The OMSD Approx-

imation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2.5 Three Flavour Oscillation in Matter: The α− s13 Approx-

imation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3 Current Status of the Oscillation Parameters . . . . . . . . . . . . 40

2.4 Degeneracies in Oscillation Parameters . . . . . . . . . . . . . . . 46

2.4.1 The Hierarchy-δCP Degeneracy . . . . . . . . . . . . . . . 48

2.4.2 The Octant-δCP Degeneracy . . . . . . . . . . . . . . . . . 52

2.5 Salient Features of the Present/Future Generation Oscillation Ex-

periments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.5.1 T2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.5.2 NOνA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.5.3 LBNO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.5.4 LBNE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.5.5 INO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

2.5.6 IceCube . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3 Probing Neutrino Oscillation Parameters in Future Experiments 61

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2 Evidence for Leptonic CP Phase from NOνA, T2K and ICAL . . 63

3.2.1 Experimental Specification . . . . . . . . . . . . . . . . . . 64

CONTENTS xiii

3.2.2 Details of the Simulation . . . . . . . . . . . . . . . . . . . 65

3.2.3 CP Sensitivity of T2K and NOνA with Their Projected

Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.2.4 CP Sensitivity of Atmospheric Neutrinos . . . . . . . . . . 69

3.2.5 Effect of ICAL on the CP Sensitivity of T2K and NOνA . 71

3.2.6 A Chronological Study of δCP Using T2K, NOνA and ICAL 74

3.2.6.1 CP Sensitivity of T2K and NOνA . . . . . . . . . 75

3.2.6.2 CP Violation Discovery Potential of T2K/NOνA:

Synergies and Dependence on Parameters . . . . 84

3.2.6.3 CP Violation Discovery and δCP Precision with

Combined NOνA, T2K and Atmospheric Neutrinos 90

3.3 Physics Potential of LBNO in Conjunction with T2K, NOνA and

ICAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

3.3.1 Experimental Specifications and Other Simulation Details 98

3.3.2 Determination of Mass Hierarchy . . . . . . . . . . . . . . 100

3.3.3 Determination of Octant of θ23 . . . . . . . . . . . . . . . 104

3.3.4 Evidence for CP Violation . . . . . . . . . . . . . . . . . . 109

3.4 Physics Potential of LBNE in Conjunction with T2K, NOνA and

ICAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

3.4.1 Experimental Specifications and Other Simulation Details 113

3.4.2 Adequate Exposure for LBNE . . . . . . . . . . . . . . . . 115

3.4.2.1 Hierarchy Sensitivity . . . . . . . . . . . . . . . . 115

3.4.2.2 Octant Sensitivity . . . . . . . . . . . . . . . . . 117

3.4.2.3 Detecting CP Violation . . . . . . . . . . . . . . 118

3.4.3 Role of the Near Detector in Reducing Systematics . . . . 119

3.4.4 Significance of the Second Oscillation Maximum . . . . . . 121

3.4.5 Optimising the Neutrino-Antineutrino Runs . . . . . . . . 123

3.5 Constraining δCP using First Three Years of IceCube Data . . . . 128

3.5.1 Astrophysical Sources . . . . . . . . . . . . . . . . . . . . . 129

3.5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

3.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

xiv CONTENTS

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

4 Neutrino Mass Matrices 143

4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

4.2 Texture Zero Results for 3 Generation . . . . . . . . . . . . . . . 145

4.3 Masses and Mixing in the 3+1 Scheme . . . . . . . . . . . . . . . 147

4.4 Analysis of Two-Zero Textures . . . . . . . . . . . . . . . . . . . . 150

4.4.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

4.4.2 Results and Discussions . . . . . . . . . . . . . . . . . . . 153

4.4.2.1 Results for 3 Active Neutrino Mass Matrix . . . . 153

4.4.2.2 Results for 3+1 Scenario . . . . . . . . . . . . . . 155

4.5 Analysis of One-Zero Textures . . . . . . . . . . . . . . . . . . . . 165

4.5.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

4.5.2 Neutrino Mass Matrix Elements . . . . . . . . . . . . . . . 166

4.5.2.1 The Mass Matrix Element mee . . . . . . . . . . 166

4.5.2.2 The Mass Matrix Element meµ . . . . . . . . . . 170

4.5.2.3 The Mass Matrix Element meτ . . . . . . . . . . 174

4.5.2.4 The Mass Matrix Element mµµ . . . . . . . . . . 177

4.5.2.5 The Mass Matrix Element mµτ . . . . . . . . . . 181

4.5.2.6 The Mass Matrix Element mττ . . . . . . . . . . 183

4.5.2.7 The Mass Matrix Elements mes, mµs, mτs and

mss . . . . . . . . . . . . . . . . . . . . . . . . . 188

4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

5 Conclusion: Present Aspects and Future Prospects 195

A Expressions for Neutrino Oscillation Probabilities 201

A.1 Expressions for OMSD Approximation . . . . . . . . . . . . . . . 201

A.2 Expressions for α− s13 Approximation . . . . . . . . . . . . . . . 202

A.3 Expressions in Vacuum . . . . . . . . . . . . . . . . . . . . . . . . 204

B Calculation of Events and χ2 Analysis 205

CONTENTS xv

C Extraction of the Sterile Mixing Parameters 209

Bibliography 211

Publications attached with the thesis 231

List of Tables

2.1 The best-fit values and 3σ ranges of neutrino oscillation parame-

ters from global analysis by the Nu-fit group [124]. . . . . . . . . 42

2.2 Resonance energies at different baselines assuming average PREM

density profile as calculated in [129]. . . . . . . . . . . . . . . . . 45

2.3 The data taking period of T2K in neutrino mode as given in [53]. 56

3.1 Values of maximal CP violation discovery χ2 in the favourable

and unfavourable half-planes and percentage of true δCP values

allowing CP violation discovery at 2σ/3σ for different exposures

of T2K, NOνA and ICAL. . . . . . . . . . . . . . . . . . . . . . . 97

3.2 Experimental characteristics of the LBNO options. . . . . . . . . 99

3.3 Adequate exposures of LBNO for determining hierarchy, octant

and CP in units of POT-kt. . . . . . . . . . . . . . . . . . . . . . 104

3.4 Adequate exposures of LBNE for determining hierarchy, octant

and CP in units of MW-kt-yr for NH (IH). . . . . . . . . . . . . . 116

3.5 CPV coverage fraction of LBNE at 3σ for total 600 MW-Kt-yr

exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

3.6 Reduction in systematic errors in LBNE with the addition of a

near detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

3.7 Effect of the second oscillation maximum on the sensitivity of LBNE.124

3.8 Theoretical values of track by shower ratio for πS, µDS and nS

sources along with value calculated from IceCube data. . . . . . . 137

4.1 Possible two-zero textures in the three generation scenario. . . . . 146

xvii

xviii LIST OF TABLES

4.2 Oscillation parameters [127, 255, 257] used in two-zero texture

analysis in 3+1 scenario. . . . . . . . . . . . . . . . . . . . . . . . 152

4.3 Allowed two-zero textures in the 3+1 scenario. . . . . . . . . . . . 154

4.4 The allowed mass spectra in 3 and 3+1 scenarios. . . . . . . . . . 155

4.5 Oscillation parameters [127, 257, 258] used in one-zero texture

analysis in 3+1 scenario. . . . . . . . . . . . . . . . . . . . . . . . 167

List of Figures

1.1 Fluxes of neutrinos at different energies. The figure is taken from

Ref. [20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1 CC and NC interactions of neutrinos. . . . . . . . . . . . . . . . . 30

2.2 Comparison between OMSD and α− s13 approximation. . . . . . 40

2.3 Two possible mass orderings of neutrinos. . . . . . . . . . . . . . 41

2.4 Comparison of the best-fit values and 3σ ranges of the oscillation

parameters. The figure is taken from Ref. [126]. . . . . . . . . . . 43

2.5 Pµe vs energy for L=812 km. The blue band corresponds to NH

and the red band corresponds to IH. . . . . . . . . . . . . . . . . 49

2.6 Similar plot as that of Fig. 2.5 but for 1300 km baseline. . . . . . 50



2.9 Pµe vs energy for L=812 km. The blue band corresponds to LO

and the red band corresponds to HO. . . . . . . . . . . . . . . . . 53

3.1 CPV discovery vs true δCP for NOνA(3+3)+T2K(8+0) taking

θtrµµ = 39◦, 45◦ and 51◦ and sin2 2θ13 = 0.1. . . . . . . . . . . . . . 68

3.2 CP sensitivity of ICAL experiment. . . . . . . . . . . . . . . . . . 70

3.3 CPV discovery potential of ICAL as a function of the detector

energy and angular resolutions. . . . . . . . . . . . . . . . . . . . 71

3.4 CPV discovery vs true δCP for NOνA(3+3)+T2K(8+0)+ICAL(500

kt-yr) taking θtrµµ = 39◦, 45◦ and 51◦ and sin2 2θ13 = 0.1. . . . . . . 72

xix

xx LIST OF FIGURES

3.5 CPV discovery vs true δCP for NOνA(3+3)+T2K(8+0) and for

NOνA(3+3)+T2K(8+0)+ICAL(500 kt yr) taking two sets of ICAL

detector resolutions for θtrµµ = 39◦ and sin2 2θ13 = 0.1. . . . . . . . 73

3.6 CPV discovery vs true δCP for NOνA(3+3)+T2K(8+0) and for

NOνA(3+3)+T2K(8+0)+ICAL taking two sets of ICAL exposure

for θtrµµ = 39◦ and sin2 2θ13 = 0.1. . . . . . . . . . . . . . . . . . . 74

3.7 CPV discovery and 90% C.L. δCP precision for T2K(5+0)/(3+2)

and T2K(5+0)/(3+2)+NOνA(3+3) taking θtrµµ = 39◦ and sin2 2θ13 =

0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.8 CPV discovery and 90%/95% C.L. δCP precision for the combina-

tion of T2K(5+0)+NOνA(5+5) taking θtrµµ = 39◦ and sin2 2θ13 = 0.1. 79

3.9 CPV discovery and 90%/95% C.L. δCP precision for the combina-

tion of T2K(5+5)+NOνA(5+5) taking θtrµµ = 39◦ and sin2 2θ13 = 0.1. 80

3.10 Allowed CP fraction (90% C.L.) corresponding to each true δCP

for T2K(5+5) and NOνA(5+5) taking θtrµµ = 39◦ and sin2 2θ13 = 0.1. 81

3.11 90% C.L. δCP precision for T2K(5+5) and NOνA(5+5) taking

θtrµµ = 39◦ and sin2 2θ13 = 0.1. . . . . . . . . . . . . . . . . . . . . 82

3.12 Pµe vs energy for T2K and NOνA taking neutrinos and antineu-

trinos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.13 CPV discovery vs true δCP for appearance and disappearance

channels of T2K(5+0) and NOνA(5+5) taking θtrµµ = 39◦ and

sin2 2θ13 = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.14 CPV discovery potential of T2K(5+0)+NOνA(5+5) as a function

of true θ13 for two maximally CP-violating values of true δCP tak-

ing θtrµµ = 39◦. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.15 CPV discovery vs true δCP for T2K(5+0)+NOνA(5+5) for sin2 2θtr13 =

0.07 and 0.13 taking θtrµµ = 39◦, 45◦ and 51◦. . . . . . . . . . . . . 87

3.16 CPV discovery potential of T2K(5+0)+NOνA(5+5) as a function

of true θµµ for two maximally CP-violating values of true δCP

taking sin2 2θ13 = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . 88

LIST OF FIGURES xxi

3.17 CPV discovery vs true δCP for T2K(5+0)+NOνA(5+5) for θtrµµ =

43◦ and 49◦ taking sin2 2θ13 = 0.1. . . . . . . . . . . . . . . . . . . 89

3.18 CPV discovery and 90%/95% C.L. δCP precision for the combi-

nation of T2K(5+0)+NOνA(5+5)+ICAL(250 kt yr) taking θtrµµ =

39◦ and sin2 2θ13 = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . 91

3.19 CPV discovery vs true δCP for T2K(5+0)+NOνA(5+5)+ICAL(500

kt yr) taking θtrµµ = 39◦ and sin2 2θ13 = 0.1. . . . . . . . . . . . . . 92

3.20 CPV discovery potential of T2K(5+0)+NOνA(5+5)+ICAL(500

kt yr) as a function of true θµµ for two maximally CP-violating

values of true δCP taking sin2 2θ13 = 0.1. . . . . . . . . . . . . . . 93


kt yr) for θtrµµ = 43◦ and 49◦ taking sin2 2θ13 = 0.1. . . . . . . . . . 93

3.22 CPV discovery and 90%/95% C.L. δCP precision for the combi-

nation of T2K(5+5)+NOνA(5+5)+ICAL(250 kt yr) taking θtrµµ =

39◦ and sin2 2θ13 = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . 95


kt yr) taking θtrµµ = 39◦ and sin2 2θ13 = 0.1. . . . . . . . . . . . . . 96

3.24 Hierarchy sensitivity χ2 of LBNO vs true δCP for the 2290 km and

1540 km baselines. . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3.25 Hierarchy sensitivity χ2 vs LBNO exposure for the 2290 km and

1540 km baselines. . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.26 Hierarchy sensitivity χ2 of LBNO for the 2290 km and 1540 km

baselines taking different combinations of experiments, demon-

strating the synergy between them. . . . . . . . . . . . . . . . . . 103

3.27 Octant sensitivity χ2 of LBNO vs true θ23 for the baselines 2290

km and 1540 km. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

3.28 Octant sensitivity χ2 vs LBNO exposure, for the 2290 km and

1540 km baselines. . . . . . . . . . . . . . . . . . . . . . . . . . . 106

3.29 Octant sensitivity χ2 of LBNO vs true θ23 for the 130 km baseline. 107

3.30 Octant sensitivity χ2 vs LBNO exposure, for the 130 km baseline. 108

xxii LIST OF FIGURES

3.31 Octant sensitivity χ2 of LBNO for the 2290 km and 1540 km base-

lines taking different combinations of experiments, demonstrating

the synergy between them. . . . . . . . . . . . . . . . . . . . . . . 108

3.32 CP violation detection χ2 of LBNO vs true δCP for the 2290 km

and 1540 km baselines. . . . . . . . . . . . . . . . . . . . . . . . . 109

3.33 Fraction of the full δCP range for which it is possible to detect CP

violation at 3σ vs LBNO exposure, for the 2290 km and 1540 km

baselines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

3.34 CP violation detection χ2 of LBNO vs true δCP for the 130 km

baseline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.35 Fraction of the full δCP range for which it is possible to detect CP

violation at 3σ vs LBNO exposure, for the 130 km baseline and

both hierarchies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.36 CP detection sensitivity χ2 of LBNO for the 130 km baseline tak-

ing different combinations of experiments, demonstrating the syn-

ergy between them. . . . . . . . . . . . . . . . . . . . . . . . . . . 112

3.37 Hierarchy/Octant/CPV discovery χ2 vs LBNE exposure, for both

hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

3.38 Hierarchy/Octant/CPV discovery χ2 of LBNE vs true δCP show-

ing effect of including a near detector. . . . . . . . . . . . . . . . . 117

3.39 χ2 vs δCP for LBNE, showing the effect of including the near

detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

3.40 νµ flux and neutrino oscillation probability Pµe for various repre-

sentative values of δCP and normal hierarchy, for the NOνA and

LBNE baselines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

3.41 Hierarchy/Octant/CPV discovery χ2 of LBNE vs true δCP show-

ing effect of the second oscillation maximum. . . . . . . . . . . . . 123

3.42 Sensitivity of LBNE for various combinations of neutrino and an-

tineutrino run by itself and in conjunction with T2K, NOνA and

ICAL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

LIST OF FIGURES xxiii

3.43 Fit of the IceCube data to δCP considering a single source i.e.,

πS (k1 = 1, k2 = 0, k3 = 0), µDS (k1 = 0, k2 = 1, k3 = 0), nS

(k1 = 0, k2 = 0, k3 = 1). . . . . . . . . . . . . . . . . . . . . . . . . 133

3.44 Similar plot as that of Fig. 3.43 but for neutrinos within energy

60 TeV to 3 PeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

3.45 Fit of the IceCube data to δCP considering contribution from two

sources at a time, in equal proportion i.e., k1 = k2 = 0.5, k3 = 0,

k1 = 0, k2 = k3 = 0.5 and k1 = k3 = 0.5, k2 = 0. . . . . . . . . . . . 135

3.46 Fit of the IceCube data to δCP considering equal contribution from

all the sources, i.e., k1 = k2 = k3 = 0.33. . . . . . . . . . . . . . . 136

3.47 Contour plots for allowed region in the k1 − δCP plane, for three

representative values of k2. . . . . . . . . . . . . . . . . . . . . . . 137





4.1 The allowed 3+1 mass ordering. . . . . . . . . . . . . . . . . . . . 149

4.2 The values of ym(=m1

m3) as a function of the lowest mass (m1 or

m3) for the 3+1 case when the known oscillation parameters are

varied in Gaussian distributions peaked at their respective best-fit

values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

4.3 Correlation plots for A and E class. . . . . . . . . . . . . . . . . . 159

4.4 The effective mass governing 0νββ as a function of the lowest mass.162

4.5 The values of ym(=m1

m3) as a function of the lowest mass (m1 or

m3) for the 3+1 case when parameters are varied randomly. . . . 165

4.6 Plots of |mee| versus the lowest mass. . . . . . . . . . . . . . . . . 168

4.7 Plots of |meµ| vs m1 for normal hierarchy. . . . . . . . . . . . . . 172

4.8 Plots of |meµ| vs m3 for inverted hierarchy. . . . . . . . . . . . . . 173

4.9 Plots of |meτ | vs m1 for normal hierarchy. . . . . . . . . . . . . . . 175

4.10 Plots of |meτ | vs m3 for inverted hierarchy. . . . . . . . . . . . . . 177

xxiv LIST OF FIGURES

4.11 Plots of |mµµ| vs m1 for normal hierarchy. . . . . . . . . . . . . . 179

4.12 Plots of |mµµ| vs m3 for inverted hierarchy. . . . . . . . . . . . . . 180

4.13 Plots of |mµτ | vs m1 for normal hierarchy. . . . . . . . . . . . . . 183

4.14 Plots of |mµτ | vs m3 for inverted hierarchy. . . . . . . . . . . . . . 184

4.15 Plots of |mττ | vs m1 for normal hierarchy. . . . . . . . . . . . . . 186

4.16 Plots of |mττ | vs m3 for inverted hierarchy. . . . . . . . . . . . . . 187

4.17 Plots of |mks| versus the lowest mass. . . . . . . . . . . . . . . . . 189

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Present Aspects and Future Prospects of Neutrino Mass and ...library/ghosh_m_2015_abst.pdf · DECLARATION I, Mr. Monojit Ghosh, S/o Mr. Monoranjan Ghosh, resident of RN-011, PRL student