History of the Neutrino. Nuclear Beta 1. Robert D. McKeown. Since 1920 s physicists have observed beta decay: e.g. 14 C 14 N + e -

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1 The Universe, Vol. 5, No. 2 April-June 2017 Popular Sciecne Article 1 Nuclear Beta Decay History of the Neutrino Robert D. McKeown Nuclear Beta 1 Decay 1 Caltech and Jefferson Lab Since 1920 s physicists have observed beta decay: e.g. 14 C 14 N + e - But the electron energy distribution is continuous: Since 1920 s physicists have observed beta decay: e.g. 14 C 14 N + e. But the electron energy distribution is continuous: E e Where did the energy go?? Fig. 1: β-ray spectra. Where did the energy go?? 2 3 Fig. 2: Famous Pauli s letter. I have done something very bad today by proposing a particle that cannot be detected; it is something that no theorist should ever do. by Wolfgang Pauli. This popular-science article on the history of neutrinos has been modified by the Editor-in-chief, W-Y. Pauchy Hwang. 1

2 Popular Science Article The Universe, Vol. 5, No. 2 April-June Fermi Theory of β Decay (1934) Golden Rule: dn de e density of final states. Fermi Theory of b decay (1934 n p + e - + n Golden Rule: n p + e + ν (1) W = 2p G 2 M 2 ћ dn de e W = 2π G2 M 2 dn (2) de e p e - density of final sta M = <p J m n> <e J m n> n n Fig. 3: Actually is G = g 2 /M W /GeV 2 (actually is G = g 2 /M W2 ~ 1x10-5 /GeV 2 ) M =< p J µ n >< e J µ ν > (3) 5 So we can explain the observed spectrum: (e.g., Kurie plot) 1.2 Inverse Beta Decay The related process also should occur: Estimate cross section (neglect e + mass): dn = 4πp2 edp e 4πp 2 νdp ν h 3 h 3 δ(e o E ν E e ) (Integrate over E ν = p ν, m ν = 0) = 16π 2 p e E e (E 0 E e ) 2 de e (4) σ G 2 E 2 ν ( c) 2 W p e E e (E 0 E e ) 2 (5) ν + p n + e + (6) (10 6 )( ) 2 cm 2 (E = 1MeV ) cm 2 (7) λ = (σρ) 1 ( ) 1 cm = cm 10 l.y!! (8) 2

The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article 2 Discovery of the Neutrino 1956 F.

Discovery of the Neutrino 1956 Fig. 4: F. Reines, Nobel Lecture, 1995.

decay reaction has to be there, as Hans Bethe and Rudolf Peierls recognized, and as I m sure did Fermi,

Reines, Nobel Lecture, 1995 The original Reines-Cowan experiment is sketched below in Fig.

3 The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article 2 Discovery of the Neutrino 1956 F. Reines, et. al. obtained the first Nobel prize (until 1995) for neutrinos. Discovery of the Neutrino 1956 Fig. 4: F. Reines, Nobel Lecture, Finally, we chose to look for the reaction ν e +p n+e + If the free neutrino exists, this inverse beta decay reaction has to be there, as Hans Bethe and Rudolf Peierls recognized, and as I m sure did Fermi, but they had no occasion to write it down in the early days. Reines-Cowan Experiment F. Reines, Nobel Lecture, 1995 The original Reines-Cowan experiment is sketched below in Fig.5: 8 Water + Fig. 5: Reines-Cowan Experiment. 9 In Fig. 6, the original suggestion for parity nonconservation was made by T.D. Lee and C.N. Yang. Fig. 6: The paper by T.D. Lee and C.N. Yang 10 3

Popular Science Article The Universe, Vol. 5, No. 2 April-June 2017 2.

2 Chirality States Implication for the Neutrino! Fig.

8: Implication for the neutrino! Pauli (1933) Dirac Eq.

4 Popular Science Article The Universe, Vol. 5, No. 2 April-June A Year of Revolution Fig. 7 are the portrait of T.D. Lee and C.N. Yang (on the theory) and of C.S. Wu (on the experiment), on parity1956 nonconservation. A Year of Revolution (A. Zee) 11 Fig. 7: For the first time a force of nature was Asymmetric. 2.2 Chirality States Implication for the Neutrino! Fig. 8 shows the different chirality states: (See the Fig. 8.) Fig. 8: Implication for the neutrino! Pauli (1933) Dirac Eq.: (p m)ψ = 0 (9) X γ 5 : (p + m)γ 5 Ψ = 0 (10) define Ψ R 1 2 (1 + γ 5); Ψ L 1 2 (1 γ 5) p Ψ R mψ L = 0 p Ψ L mψ R = 0 (11) m 0 : pψ R = 0; pψ L = 0. (12) note: m 0 must have both Ψ R, Ψ L. 4 12

5 The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article Free ( fermions ) obey ( the Dirac ) equation ( (p m)ψ ) = 0 where p = γ µ p µ. Use the representation: σ 1 0 γ 0 = γ = γ 1 0 σ 0 5 =. 0 1 ( Now) rewrite the four component Dirac equation as two coupled two component equations Ψ = ψ+ : ψ mψ + (E σ p)ψ + = 0 (E + σ p)ψ mψ + = 0 (13) In the limit m 0 these equations decouple and we obtain the Weyl equations describing states with a definite helicity σ ˆpψ ± = ±ψ ±. ψ is the left-handed neutrino (E > 0) or a right-handed antineutrino (E < 0). ψ + describes ν R or ν L. Neutrino Helicity Measurement 2.3 Neutrino Helicity Measurement 152 Eu(0 + ) + e 152 Sm (1 + ) + ν 152 Sm(0 + ) + γ (14) 152 Let p ν = p ν ẑ so that p = p Sm ẑ. Eu (0 + ) + e Sm * (1 + ) + n 152 Sm(0 + ) + g LH ν J Sm +ẑ Let p n = p ^ n z so that p Sm = - p Sm z ^ J γ +ẑ(lh) (15) LH n J Sm ~ + z ^ p Sm J Sm J g ~ + ^ z (LH) k g Fig. 9: The chirality determination of the neutrino 15 Neutrino Helicity Measurement (1958) as in Eqs. (14) and (15) g spin analyzer select E g p Sm 16 Fig. 10: Neutrino Helicity Measurement (1958). 5

Popular Science Article The Universe, Vol. 5, No. 2 April-June 2017 3 Subsequent History Creating a Neutrino Beam Magnetic Focusing Horns Fig. 11: Creating a Neutrino Beam. π + µ + ν µ.

6 Popular Science Article The Universe, Vol. 5, No. 2 April-June Subsequent History Creating a Neutrino Beam Magnetic Focusing Horns Fig. 11: Creating a Neutrino Beam. π + µ + ν µ. p + m + n 60 s and 70 s: ν s studied in accelerator-based production: m ν e ν µ (16). 1968: 1st solar ν anomaly evidence present: the quest for neutrino mass and oscillations ν s as dark matter?? All you have to do is imagine something that does practically nothing. You can use your son-in-law as a prototype The Standard Model (1967) ν R does not exist! Neutral currents! L = ( νl l L ) ψ R = l R (17) L F = ( ψ i i m i gm ) ih ψ i 2M i W g 2 ψ i γ µ (1 γ 5 )(T + W µ + + T Wµ )ψ i 2 i e q i ψi γ µ ψ i A µ i g ψ i γ µ (gv i g 2 cos θ Aγ i 5 )ψ i Z µ. (18) W i 3.2 Neutral Current Discovery (1973) g i V t 3L (i) 2q i sin 2 θ W, g i A t 3L (i). (19) The so-called November revolution refers to the discovery of neutral currents (the interaction mediated by the Z 0 boson) and the discovery of the J/Ψ particle. 6

12: Major Triumph for the Standard Model!

7 Co ma Dar The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article Neutral Current Discovery (1973) n m N W X m - n m N Z X n m (unobserved) 4 A Puzzle from Astrophysics Major Triumph for the Standard Model!! Fig. 12: Major Triumph for the Standard Model!! A Puzzle from Astro 20 The masses of the neutrinos (of three flavors), since they are tiny (at most in the range of sub ev or smaller), will represent one of the most difficult experimental problems. Fig. 13: Galactic Rotation Curves gravitational clustering of neutral matter. Could neutrinos have mass and explain the Dark Matter? Neutrino mass and three-body decays (in particular β decay where two light particles are emitted): Galactic Rotation Curves gravita Z A (Z + 1) A + e + ν e (20) of neutral matter For T e Q β neutrino can become nonrelativistic. 7

8 Popular Science Article The Universe, Vol. 5, No. 2 April-June 2017 Fig. 14: E ν + T e = Q β (electron kinetic energy, since Q β represents atomic mass diff.) Momentum is automatically conserved (nuclear recoil). 4.1 Electron Spectrum in Nuclear β Decay The transition probability per unit time is given by Fermi s golden rule dw = (2π) 5 d 3 p e d 3 p ν δ(e e + E ν ) A fi 2 (21) 22 Since the lepton energies are of order m e their debroglie wavelength (λ /m e c = cm) is much larger than the nuclear radius, and we can neglect the variation of their wave function over the nuclear volume. In addition, we neglect all recoil terms (E e + E ν )/m N and terms involving nucleon velocity. This is so called allowed approximation, p e R 1. A fi = G F 2 cos θ C [C V 1 j 0 (0) C A σ j(0)] (22) Here C V = 1 and C A = 1.26 are coupling constants and 1 and σ are the Fermi and Gammow- Teller nuclear matrix elements. The lepton currents j(0) and j(0) depend on lepton spins and directions. After squaring, summing over spins, and integrating over angles we obtain the transition probability. dw = G2 F cos2 θ C 2π 3 ξf (Z + 1, E e )E e p e E ν p ν de e (23) Here ξ = CV CA 2 σ 2 and F (Z, E) is the easily calculable correction for the Coulomb effect on the emitted electron (ratio of the square of the electron wave function at r = R with and without Coulomb field.) In the last formula one must substitute E ν = E e = Q β T e and p ν = Eν 2 m 2 ν. The last expression gives the clue to the sensitivity to the neutrino mass. Obviously, when p ν 0 or T e Q β, i.e., near the endpoint of β spectrum, that sensitivity is more pronounced. 4.2 Kurie Plot Lets call dw/de N(E) and consider [ ] N(E) 1/2 K(E) const [p ν E ν ] 1/2. (24) F (Z, E)p e E e For massless neutrinos this quantity, called Kurie plot, is a straight line K(E e ) E e, with the intersect at the endpoint (or Q [ β if the electron kinetic energy is used). Rewriting [p ν E ν ] 1 2 = ( E e ) 1 m2 ( E e) ]. One can see that 2 The spectrum ends at m ν and not at as for massless neutrinos. More importantly, the slope of Kurie plot becomes infinite near the endpoint for massive neutrinos. 8

9 The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article Effects like finite resolution, background, etc. neutrino mass, that makes it steeper. will make the slope less steep, unlike the Thus, if such effects are incorrectly included we might get m 2 ν < 0 from a fit to the data. Fig. 15: Graph from Fermi s famous paper on the theory of beta decay, showing how the shape of the emitted electron s energy spectrum varies with neutrino mass. 25 Fig Tritium Kurie Plot The efforts to investigate the tritium β decays to get the neutrino mass are underway. 5.1 Tritium Beta Decay and Neutrino Mass Let s try to show some related results on tritium beta decays (for tiny neutrino masses). We should admire the efforts of these experimental endeavors. 9

10 Popular Science Article The Universe, Vol. 5, No. 2 April-June 2017 Tritium Kurie Plot Fig. 17: The Kurie plot of the end point region for molecular tritium. The solid curve is a fit to the data of run (b) with zero neutrino mass. Tritium The subtractedbeta backgroundecay is 26 counts/channel. and neutrino mass 3 H 27 Requirements: Fig. 18: Requirements: Strong source; Excellent energy resolution; Small endpoint energy E Strong source 0; Long term stability; Low background rate. Excellent energy resolution Small endpoint energy E 0 Long term stability 6 Perhaps Neutrinos are not so Useless After All 6.1 Neutrino Oscillations Low background rate We began with a brief introduction to the physics of neutrino oscillations in free space. We discuss the case of two flavors of neutrino, ν µ and ν e. The generalization to three flavors is straightforward. These neutrinos are those created (and absorbed) via weak interaction processes. However, we postulate that they are not the mass eigenstates. Rather, they are a mixture of two mass eigenstates designated ν 1 and ν 2 with masses m 1 and m 2 (m 1 m 2 ). The weak interaction states are obtained by a unitary transformation of these mass eigenstates: ν e = cos θ ν 1 + sin θ ν 2 (25) ν µ = sin θ ν 1 + cos θ ν 2 (26) where θ is a mixing angle and a parameter of the theory. A weak interaction process like nuclear beta decay generates a ν e, which then propagates as a function of time as ν(t) = e ie 1t cos θ ν 1 + e ie 2t sin θ ν 2. (27) At t = 0 we have a pure ν e but because of the phase slippage as a function of time, the relative degree of ν µ and ν e in the state vector varies. If the mass difference is small, m 2 m 2 2 m2 1 p2 (p = E 1 = E2 is the momentum) then the energies are related by 28 E 1 E 2 m 2 = 2 m2 1. (28) 2p 10

11 The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article Requirements: Strong source llent energy resolution all endpoint energy E 0 Long term stability ow background rate 28 Previous Tritium Fig. 19Measurements 29 Fig. 20: Previous Tritium Measurements Then the probabilities for detecting a ν e or ν µ at a distance x(= t) are given by ( P e (x) = ν e ν t 2 = 1 sin 2 2θ sin 2 πx ) L ( P µ (x) = ν µ ν t 2 = sin 2 2θ sin 2 πx ) L (29) (30) where the characteristic oscillation length (in vacuum) is defined by L 4πp m 2. (31) 6.2 Length & Energy Scales E ν = 1 MeV, m 2 = 1 ev 2, L = 1.24 meters (P e minimum) (32) Super-K: Chooz, Palo Verde Kam LAND E ν = 1 GeV, m 2 = 10 3 ev 2, L = 1240 km (33) E ν = 1 MeV, m 2 = 10 3 ev 2, L = 1.2 km (34) E ν = 1 MeV, m 2 = 10 5 ev 2, L = 125 km (35) 11

35 Popular Science Article The Universe, Vol. 5, No.

21: KATRIN sensitivity and discovery potential 30 Expectation for 3 full beam years: syst ~ stat 5 discovery potential: m n = 0.35eV (5 ) m n = 0.3eV (3 ) Sensitivity: m n < 0.

KATRIN will improve the sensitivity by one order of magnitude; will check the whole cosmological relevant mass range; will detect background neutrinos (if they are will check the whole cosmological

12 35 Popular Science Article The Universe, Vol. 5, No. 2 April-June 2017 KATRIN at Forschungszentrum Karlsruhe unique facility for closed T 2 cycle: Tritium Laboratory Karlsruhe 5 countries 13 institutions 100 scientists TLK ~ 75 m long with 40 s.c. solenoids KATRIN: Fig. 21: KATRIN sensitivity and discovery potential 30 Expectation for 3 full beam years: syst ~ stat 5 discovery potential: m n = 0.35eV (5 ) m n = 0.3eV (3 ) Sensitivity: m n < 0.2eV (90%CL) KATRIN will improve the sensitivity by 1 order of magnitude Fig. 22: KATRIN: sensitivity and discovery potential. KATRIN will improve the sensitivity by one order of magnitude; will check the whole cosmological relevant mass range; will detect background neutrinos (if they are will check the whole cosmological relevant mass range degenerate). will detect background neutrinos (if they are 31 degen.) 6.3 Atmospheric Neutrinos Implications of SuperK observation, Mixing angle is quite large (θ 15 ). Note: SuperK seems to be observing m 2 = ev 2 0 at least 1 m ν 0 (36) ν µ ν τ (37) up to January 2012 (when this lecture was given). W.A. Fowler, Nobel Lecture, 1983: My deepest personal interest is in experimental data, in the analysis of the data and in the proper use of the data in theoretical stellar models. I continue to be encouraged in this regard by this one-hundred and nine year old quotation from Mark Twain: There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact. Atmospheric neutrinos Cosmic proton p m + n m m e + n m + n e N s, p s, Fig. 23: π µ + ν µ; µ e + ν µ + ν e ν µ+ ν µ ν e+ ν e 12 n m + n m n e + n e = 2

The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article 30 kton H 2 0 Cherenkov 11000 20 PMT s Fig.

The experimentalist must try to eliminate the word trifling through his endeavors in uncovering, the facts of nature.

13 The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article 30 kton H 2 0 Cherenkov PMT s Fig Life on the Mississippi 1874 For me Twain s remark is a challenge to the experimentalist. The experimentalist must try to eliminate the word trifling through his endeavors in uncovering, the facts of nature. Maybe there is something wrong with these astrophysical neutrinos??? We need a aboratory experiment!! Appendix Neutrino s mass would be in the range of ev or smaller. Negation of the LSND result is thus very essential. 13

Popular Science Article The Universe, Vol. 5, No. 2 April-June 2017 37 Fig.

26: SuperKamiokande Result (1998) 38 The LSND Experiment (1993-98) Nearly 49,000 Coulombs of protons

14 Popular Science Article The Universe, Vol. 5, No. 2 April-June Fig. 25 SuperKamiokande Result (1998) q Monte Carlo Where are the upward muon neutrinos?? Fig. 26: SuperKamiokande Result (1998) 38 The LSND Experiment ( ) Nearly 49,000 Coulombs of protons on target Baseline 30 m Neutrino Energy MeV, 1280 phototubes 167 tons Liquid scintillator Fig. 27: The LSND Experiment ( ) 44 14

: 45 Fig. 28: LSND Result. Excess: 87.9 ± 22.4 ± 6.0 ν ep e + n events. Osc.

15 The Universe, Vol. 5, No. 2 April-June 2017 Popular Science Article LSND Result Excess: Osc. Prob.: 45 Fig. 28: LSND Result. Excess: 87.9 ± 22.4 ± 6.0 ν ep e + n events. Osc. Prob.: (0.264 ± ± 0.045)% LSND Fig. 29: was LSND was not unconfirmed (New MiniBOONE result) (New MiniBOONE result) 46 15

1 Neutrinos. 1.1 Introduction

1 Neutrinos. 1.1 Introduction 1 Neutrinos 1.1 Introduction It was a desperate attempt to rescue energy and angular momentum conservation in beta decay when Wolfgang Pauli postulated the existence of a new elusive particle, the neutrino.