# The Physics of Neutrinos

Vernon Barger
Danny Marfatia
Kerry Whisnant
Pages: 256
https://www.jstor.org/stable/j.cttq94kv

1. Front Matter
(pp. i-vi)
(pp. vii-x)
3. Preface
(pp. xi-xiv)
Vernon Barger, Danny Marfatia and Kerry Whisnant
4. 1 Introduction
(pp. 1-10)

The unfolding of the physics of neutrinos has been a premier scientific achievement of the 20thcentury. The hallmark of this decades-long endeavor has been the intertwined contributions of experiment and theory in its advancement. This fascinating history has been the subject of many treatises. Our aim is to give an overview of the aggregate knowledge of neutrino physics today and to mark future pathways for still deeper understanding. In this enterprise we bring together, under one broad umbrella, what has been learned and what is now being pursued about neutrinos in a diversity of subareas–particle physics, nuclear physics,...

5. 2 Neutrino Basics
(pp. 11-32)

Massive neutrino fields are constructed from Weyl fields (also called chiral fields) that are obtained from the chirality projections of the Dirac field. The Weyl equation governing the motion of Weyl fermions tells us that Weyl fields are eigenstates of helicity and are therefore massless. Massive neutrinos may be of the Dirac or Majorana type.

We denote the 4-component Dirac spinor by$\psi =\left( \begin{matrix} \xi \\ \omega \\ \end{matrix} \right), \caption {(2.1)}$where ξ and ω are 2-component Weyl spinors; the left-handed and right-handed projections of the Dirac spinor are${{\psi }_{L}}={{(0\ \omega )}^{T}}$and${{\psi }_{R}}={{\left( \xi \ 0 \right)}^{T}}$, and their charge conjugate counterparts are$\psi _{L}^{C}$and$\psi _{R}^{C}$. By definition, a Majorana field...

6. 3 Neutrino Mixing and Oscillations
(pp. 33-44)

The dramatic increase in our knowledge of neutrino properties has come from observational evidence of neutrino oscillations. These neutrino flavor changes require that the neutrino flavor states,να, are not the same as the neutrino mass eigenstates,νi. The eigenstates are related by a unitary matrix V [18],${{\nu}_{\alpha }}=\sum{V_{\alpha i}^{*}{{\nu}_{i}}}. \caption {(3.1)}$

Vis often denoted asVMNS, where MNS represents the authors of [18].¹ For 3 neutrinos, the mixing matrixVis specified by three rotation anglesθ23,θ13,θ12$(0\le {{\theta }_{i}}\le \pi /2)$and threeCP-violating phasesδ,ϕ2andϕ3$(0\le \delta , {{\phi }_{i}}\le 2\pi )$.Vcan be conveniently written as the matrix product$V=\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & {{c}_{23}} & {{s}_{23}} \\ 0 & -{{s}_{23}} & {{c}_{23}} \\ \end{matrix} \right]\left[ \begin{matrix} {{c}_{13}} & 0 & {{s}_{13}}{{e}^{-i\delta }} \\ 0 & 1 & 0 \\ -{{s}_{13}}{{e}^{i\delta }} & 0 & {{c}_{13}} \\ \end{matrix} \right]\left[ \begin{matrix} {{c}_{12}} & {{s}_{12}} & 0 \\ -{{s}_{12}} & {{c}_{12}} & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & {{e}^{i{{\phi }_{2}}/2}} & 0 \\ 0 & 0 & {{e}^{i{{\phi }_{3}}/2}} \\ \end{matrix} \right] \caption {(3.2)}$wherecjk...

7. 4 Solar Neutrinos
(pp. 45-58)

Solar neutrinos are created by chains of fusion reactions in the sun. In the so-calledppchain, the primary reaction (which takes place with frequency 86%) is$p+p\to {{{{(}^{2}}\text{H)}}^{+}}+{{e}^{+}}+{{v}_{e}}, \caption {(4.1)}$where the neutrino can have kinetic energy in the range 0 to 0.42 MeV. A secondary branch includes the reaction (frequency 14%)${{{{(}^{7}}\text{Be)}}^{+}}+{{e}^{-}}{{\to }^{7}}\text{Li+}{{v}_{e}}, \caption {(4.2)}$where the neutrino has energy 0.86MeV or 0.38 MeV, depending on whether the ⁷Li is in the ground state (90% of the time) or an excited state (10%). A tertiary branch (frequency 0.11%) includes the reaction${{{{(}^{8}}\text{B)}}^{+}}{{\to }^{8}}\text{Be+}{{\text{e}}^{+}}+{{v}_{e}}+\gamma , \caption {(4.3)}$where the neutrino has energy 0–14.06 MeV. Much rarer than the...

8. 5 Atmospheric Neutrinos
(pp. 59-67)

The first compelling evidence for neutrino oscillations came from the measurement of atmospheric neutrinos. Interactions of cosmic rays with the atmosphere produce pions and kaons that decay to muon neutrinos, electron neutrinos, and their antineutrinos:${{\pi }^{+}},{{K}^{+}}\to {{v}_{\mu }}{{\mu }^{+}}\to {{v}_{\mu }}{{e}^{+}}{{v}_{e}}{{\bar{v}}_{\mu }}, \caption {(5.1)}$${{\pi }^{-}},{{k}^{-}}\to {{\bar{v}}_{\mu }}{{\mu }^{-}}\to {{\bar{v}}_{\mu }}{{e}^{-}}{{\bar{v}}_{e}}{{v}_{\mu }}. \caption {(5.2)}$

On average there are twice as manyνμasνeat energies of about 1GeV, although theνetend to be at somewhat lower energies since they are produced only in a secondary decay. The atmospheric neutrino flux is well understood: the normalizations are known to 20% or better (10% or better for neutrino energies below 10 GeV) and ratios of fluxes are...

9. 6 Global Three-neutrino Fits
(pp. 68-70)

As noted in section 3.1, in the limitθ13→ 0,νeνμ,ντoscillations of solar neutrinos andνμντoscillations of atmospheric neutrinos decouple, i.e., they are governed by separate parameters. However, forθ13≠ 0, solarνeand KamLAND${{\bar{v}}_{e}}$will have a further suppression due toθ13via oscillations at the$\delta m_{31}^{2}$scale, and there will be someνμνeoscillations for atmospheric neutrinos and in long-baseline experiments. Since theθ13parameter now enters into oscillations in all experiments, a global fit is necessary. Fits to some subsets of the data can also...

10. 7 Absolute Neutrino Mass
(pp. 71-75)

Neutrino oscillations tell us nothing about the absolute scale of neutrino masses, except that the heaviest eigenstate has mass above$\sqrt{\left| \delta m_{31}^{2} \right|}\simeq 0.05\text{eV}$. The standard technique for probing the absolute mass is to study the endpoint region of the electron spectrum in tritium beta-decay,$^{3}\text{H}{{\to }^{3}}\text{H}{{\text{e}}^{+}}+{{\text{e}}^{-}}+{{\bar{v}}_{e}}. \caption {(7.1)}$

The electron energy spectrum is given by$\tfrac{dN}{dE}=\tfrac{G_{F}^{2}m_{e}^{5}}{2{{\pi }^{3}}}{{\cos }^{2}}{{\theta }_{c}}{{\left| M \right|}^{2}}F(Z,E)pE({{E}_{0}}-E){{\sum\limits_{i}{{{\left| {{V}_{ei}} \right|}^{2}}\left[ {{\left( {{E}_{0}}-E \right)}^{2}}-m_{i}^{2} \right]}}^{\frac{1}{2}}}\Theta \left( {{E}_{0}}-E-{{m}_{i}} \right), \caption {(7.2)}$

whereEandpare the energy and momentum of the electron,E0is the endpoint of the spectrum,θcis the Cabibbo angle,Mis the nuclear matrix element, andF(Z,E) is the Fermi function. The step function ensures thatνiis produced only if...

11. 8 Long-baseline Neutrino Oscillations
(pp. 76-98)

Based on our current knowledge and future goals, a future neutrino program will probably include the following objectives:

Complete the measurement of the neutrino mixing angles;

Determine the sign of$\delta m_{31}^{2}$;

Measureδto determine ifCPis violated;

Search for exotic effects in neutrino oscillations.

Of these future neutrino physics goals, the search for and study ofCPviolation is of primary importance for several reasons, which we briefly address.

CPviolation has so far only been observed in the quark sector of the Standard Model. Its discovery in the neutrino sector should shed additional light on the...

12. 9 Model Building
(pp. 99-115)

The renormalizable SM Lagrangian [383] does not allow neutrino mass terms because there are no right-handed neutrino fields. Consequently, beyond the SM physics is mandated in the neutrino sector. A simple scheme for neutrino mass generation is to use the SM fields to construct a non-renormalizable addition to the Lagrangian. The unique dimension-5 lepton-number violating operator that conserves SM symmetries is schematically [384]$\left( \tfrac{k}{\Lambda } \right){{L}_{i}}{{L}_{j}}HH, \caption {(9.1)}$whereLi= (νiL,iL) andH= (ϕ+,ϕ0) areSU(2)Llepton and Higgs doublets, respectively,iandjare generation indices,kis a dimensionless coupling and Λ is the energy scale associated with...

13. 10 Supernova Neutrinos
(pp. 116-125)

Stars more massive than about8Mundergo gravitational collapse that leads to the production of a neutron star or a black hole. Neutrinos have a crucial role in the evolution of these core collapse supernovae. The variety of core collapse SN are listed in table 10.1. In stars whose mass is 8–10M, the low mass core,Mcore< 1.44M, undergoes O-Ne-Mg core collapse but the core mass is too small to ignite Ne burning. Stars with mass ≳ 10Mhave iron cores that exceed the Chandrasekar limit of about 1.44M; they can no longer be supported against gravitational collapse...

14. 11 High-energy Astrophysical Neutrinos
(pp. 126-146)

It is anticipated that neutrino telescopes will map out the sky over the next few decades. The neutrinos will point back to their sources, like gamma rays but unlike cosmic rays that are bent by magnetic fields. Neutrino telescopes should allow probes further back in time and deeper into the sources. The energy range from a TeV to a ZeV may permit the study of astrophysics and particle physics in conjunction.¹

High-energy neutrino fluxes from cosmologically distant sources are generally expected in association with the production of cosmic-rays (CR), whose energy spectrum extends to 1020eV and is likely dominated...

15. 12 Beyond Three Neutrinos
(pp. 147-171)

Our focus thus far has largely been on the three-neutrino phenomenology of massive neutrinos and its experimental validation. In addition to this, there are some neutrino experiments, though not conclusive, that may indicate other neutrino phenomena. Moreover, there are numerous theoretical possibilities that go beyond the standard three-neutrino framework. These exotic neutrino phenomena are the subject of this chapter.

The Liquid Scintillator Neutrino Detector (LSND) experiment has provided an indication for the most compelling evidence for new physics beyond the standard three-neutrino picture. New physics models have been proposed to explain the LSND data and other experiments have been carried...

16. 13 Summary and Outlook
(pp. 172-176)

In recent years we have witnessed a revolution in the physics of neutrinos. The observation of neutrino oscillations demonstrated both the quantum mechanical nature of neutrinos and that neutrinos are massive particles. These discoveries came from astrophysics sources – the neutrinos created by interactions of cosmic rays with the earth’s atmosphere and the neutrinos released by the fusion reactions in the core of the sun. The same oscillation phenomena were then found in terrestrial experiments, using detectors at long baselines from accelerators and detectors at about 180 km distances from nuclear reactors.

How convenient that nature provided neutrino mass-squared differences...

17. References
(pp. 177-220)
18. Index
(pp. 221-224)