Table Of ContentFundamentals of Neutrino Physics and
Astrophysics
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Fundamentals of Neutrino Physics
and Astrophysics
Carlo Giunti
Istituto Nazionale di Fisica Nucleare, Sezione di Torino and Dipartimento di
Fisica Teorica, Universita di Torino, Italy
Chung W. Kim
Korea Institute for Advanced Study, Seoul, Korea and The Johns Hopkins
University, Baltimore, MD, USA
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PREFACE
An expert is a person who avoids the
small errors while sweeping on to the
grand fallacy.
Steven Weinberg
Studying the properties and interactions of neutrinos has been one of the most
excitingandvigorousactivitiesinparticlephysicsandastrophysicseversincePauli
firstproposedtheirexistencein1930.Inspiteoftheirweaklyinteracting(orbarely
existing,asLedermanusedtosay)nature,wehavesofaraccumulatedanenormous
amount of knowledge about neutrinos. From neutrino oscillation experiments, we
learneda few yearsagothatneutrinosaremassiveandmixed. However,westilldo
not know the absolute values of their masses and some aspects of the mixing.
In this book we have tried to gather all the basic knowledge and tools that
are necessary to understand and to infer the true nature of the neutrinos from
the experimental data, using the theories that have been developed. We have also
summarizedthe well-establishedfacts concerningneutrinos and the importantrole
playedbyneutrinosintheSunandsupernovae,andinshapingtheUniversewelive
in. Special emphases are placed on the basic knowledge of how neutrinos interact,
how they behave in matter as well as in vacuum, and on the formal aspects of
the theory of neutrino oscillations. Salient features of the oscillation experiments
in various settings and sources are given with careful analysis.
After a short history of the neutrino, leading up to the Standard Model (SM)
of electroweak interactions and the discovery of neutrino oscillations in chapter 1,
chapter 2 is devoted to a detailed discussion of the properties of spin 1/2 Dirac
particles. This chapter can be used as an introduction to the quantum field theory
ofspin1/2fermions.Wehavetriedtomakechapter2ascompleteandself-contained
as possible, especially for beginners, by including some details on the terminology
usedinquantumfieldtheoryandingaugetheory.Thesymmetrypropertiesofspin
1/2 particles under charge conjugation, C, parity, P, and time reversal, T, as well
as the space-time and Lorentz transformations are discussed. The realistic wave
packet description of a particle is also presented.
In chapter 3, the ingredients necessary for understanding the Standard Model,
suchasgaugesymmetry andthe Higgsmechanism, arepresented. Theelectroweak
behavior of quarks and leptons is explained and summarized, together with some
discussions of the gauge bosons involved.
One of the most remarkable discoveries in the past decade is the finding that
neutrinos are massive and mixed. Chapter 4 is devoted to a detailed discussion
of the three-generation mixing of quarks, which can be extended to the treatment
of mixing of three Dirac neutrinos in a straightforward way (the mixing of three
Majorana neutrinos implies the existence of two additional phases in the mixing
matrix,asexplainedinchapter6).Aconstructionofthemixingmatrixispresented
viii PREFACE
with mathematical details. The possibility of CP violation due to mixing and how
to describe and quantify it are explained.
Chapter5isdevotedtoneutrinointeractions,withdiscussionsofseveralimpor-
tant processes involving neutrinos, ranging from neutron decay to charged-current
and neutral-current deep inelastic neutrino–nucleon scattering. All the discussions
are based on the results obtained in chapter 3, where the SM was developed.
We present, in chapter 6, the description of the general, model-independent,
theory of massive neutrinos. Depending on whether they are of Dirac or Majorana
type,themathematicaldescriptiontakesdifferentforms.Inaddition,wediscussthe
famous see-sawmechanism, which explains the smallness of the neutrino masses in
a natural way. Because of their speculative nature, we have intentionally omitted
details concerning the possible neutrino mass-generating mechanisms that have
been put forward by many authors.
Equipped with the mathematical and basic physics backgroundin the previous
chapters, we present, in chapter 7, the standard derivation of the neutrino oscil-
lation probability. We have tried to make this chapter as complete as possible in
the hope that the reader can find all the necessary information on the derivation
of the standard oscillation formulas, together with how to use them in analyz-
ing experimental data. The types of experiments are as numerous as they can be:
experiments with energetic and low energy neutrinos, with reactor or accelerator
neutrinos, solar, atmospheric, and even extragalactic (SN 1987A) neutrinos, and
finally with short-baselineand long-baselinearrangements.We haveincluded help-
fuldiscussionsonallthepossiblecases.Inaddition,someconsequencesofC,CP,T
andCPTviolationfortheoscillations,andspecialcasesofoscillationswithdifferent
oscillation parameters are discussed.
In chapter 8, in view of the important role that the oscillationplays in probing
the neutrino properties, a derivation of the neutrino oscillation formulas is given
with an emphasis on the more realistic relativistic wave packet treatment. Also
presented in this chapter are answers to often raised questions concerning subtle
and confusing issues in the oscillation formulas.
One of the most interesting findings in neutrino physics is the discovery that
the properties of neutrinos change when they pass through dense matter. Due to
the difference of the weak interaction potentials that different flavor neutrinos feel
in matter, the effective mixing can be dramatically enhanced in the case of a very
smallmixinginvacuum.Iftheneutrinospassthrougharegioninwhichtheeffective
mixing is maximal, it is possible to have large flavor transitions. In chapter 9, we
explain this resonant effect, known as the MSW effect. We derive the necessary
formulas and explained the methods for analyzing the data in the simplest case
of two-neutrino mixing (three-neutrino mixing is discussed in chapter 13). Also
presented is a geometrical description of the oscillations in vacuum as well as in
matter, which, we hope, will help the reader to understand better this important
phenomenon. The geometrical description shows that the neutrino oscillation is
analogousto a classicalmagnetic moment precessing in an externalmagnetic field.
By far, the longest running neutrino experiment has been the Homestake solar
neutrinoexperiment,startedinthelate1960sbyRayDavisandcollaboratorsafter
JohnBahcallpredictedameasurablerateonthebasisofasolarmodel.Intheearly
PREFACE ix
1970s, Davis and collaborators discovered the so-called solar neutrino problem,
which has remained unsolved until recent times. It consists of a solar neutrino
detection rate which is substantially smaller than that predicted by standard solar
models. In chapter 10, we start with a brief explanation of the standard solar
models, which explain how the Sun shines and how neutrinos are produced. Then,
we listanddescribe allthe experimentsthathaveso farbeenperformed, aswellas
their results and their roles in the solar neutrino problem. We end this chapter by
presentingtheresultsofaglobalfitofallthesolarneutrinodata.Theresultsofthe
combinedanalysis ofthe data ofsolarneutrino experimentsand ofthe KamLAND
very long-baseline reactor neutrino experiment is presented later in chapter 12.
Chapter 11 explains the generating mechanism and the flux of atmospheric
neutrinos. A comprehensive survey of all the atmospheric neutrino experiments
performed so far is presented. It is interesting to note that the first undisputed
discoveryofneutrino oscillationswasmade withatmosphericneutrinos whichhave
been initially considered as unwanted background for other measurements. The
confirmation of this discovery by the accelerator long-baseline K2K experiment is
discussed later in chapter 12.
In chapter 12 we start with the introduction of the sensitivity of terrestrial
reactorandacceleratorneutrino experimentsto the measurementof the oscillation
parameters. Then, we present the main results of reactor and accelerator short-
baseline, long-baseline and very long-baseline experiments, with specific reviews of
the CHOOZ, Palo Verde, KamLAND, and K2K experiments, which are important
forourpresentknowledgeoftheneutrinooscillationparameters.Thischapterends
with a brief discussion of the future off-axis long-baseline experiments.
Deciphering the values of the squared-mass differences and the mixing angles
from the data requires a careful analysis with use of the three-generation mixing
matrix, which is often quite complex. Technical issues involved in the analysis and
some useful approximations are discussed in chapter 13. Also discussed in this
chapter are the results of a global analysis of all the existing oscillation data. The
chapter ends with some comments on the absolute scale of neutrino masses.
The most important attempts to measure directly the values of the neutrino
masses are the measurements of the end-point of the electron spectrum in nuclear
β-decays, in particular that of tritium, and neutrinoless double-β-decays. In chap-
ter 14, we review the current experimental upper bounds on the neutrino masses
obtained with tritium β-decay experiments with the effects of neutrino mixings
taken into account. Also given is a brief summary of neutrinoless double-β-decay
theory and experiments. We emphasize the salience of neutrinoless double-β-decay
experimentsindeterminingwhethertheneutrinoisaDiracoraMajoranaparticle.
Some useful comments on the results of the experiments are also given.
Chapter 15 is devoted to supernova neutrinos. In order to help the reader who
is not familiar with the subject, a short introduction to supernova physics is pre-
sented, explaining the types of supernovae and their explosion mechanisms. The
supernova which is of special interest to us, and so best studied, is SN1987A. The
neutrino burst of SN1987A was detected by three experiments: Kamiokande-II,
IMB, and Baksan. We presentthe data and compare them with theory. The limits
