Tribute to Samoil Bilenky

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Tribute to Samoil Bilenky

A Great Physicist, A Mentor, A Friend

23 May 1928, Zmerinka (Ukraine), USSR 5 November 2020, Vancouver, Canada

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−1/20

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I I am presenting this tribute because I knew Samoil well: we spent long times together, with many interesting

discussions, and we collaborated on many studies since 1992.

I For me he was a friend, a mentor and my main collaborator for many years.

Torino, September 2015

Munich, May 2002 Barcelona, November 2002

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Samoil BILENKY — a world-famous scientist, teacher and

personality Renowned theoretical physicist Samoil Mikhelevich Bilenky passed away in Vancouver on 5 November 2020 at the age of 92. When in 1999 his friends, colleagues and pupils celebrated his 70th birthday at the conference spe- cially organized for the occasion in Torino, P. Bernabeu suggested as a joke to change Bilenky’s patronymic name to “Neutrino”. Already at that time the reason was obvi- ous. The many important contributions of S. Bilenky to neutrino physics during his life-long and brilliant career, now perhaps more than ever, justify a sort of canonization of such a suggestion.

✍❯❑❬ ❨❩❴✂▲❪❲✜❲

IN MEMORY OF THE SCIENTIST

[JINR News 2021, No.1]

[CERN Courier, May/June 2021]

I See also: Serguey Petcov, Commemoration of Samoil Bilenky, XIX International Workshop on Neutrino Telescopes, February 2021

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−3/20

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I Samoil was born in Ukraine in 1928.

I He and his family left Ukraine when it was invaded by German troops during the Second World War.

I They went to some place in Siberia, far from the front.

I After the War, he studied in Moscow and graduated “cum laude” in 1952 under the supervision of I. Pomeranchuk.

I A short time later he started to work at the Laboratory for Nuclear Problems in Dubna, which was classified until 1954 and became JINR (Joint Institute for Nuclear Research) in 1956.

I Since 1956 Samoil was a staff member of JINR. He also gave lectures in Moscow.

S.M. Bilenky in 1966

I Although born in Ukraine, Samoil considered himself Russian.

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I The early scientific career of Samoil was mainly devoted to the study of scattering of polarized particles (hadrons and leptons).

I He remained interested in this topic.

I Our second paper, in 1993, was on polarized p ¯ p scattering!

I He was very interested in nucleon properties, especially form factors.

I Samoil was the driving force of several papers on this topic with different collaborators (mainly Wanda Alberico, Torino) from about 1995 to 2009.

Wanda Alberico and Sofia Bilenkaya Torino, 2018

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−5/20

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I Samoil and Bruno Pontecorvo were friends since the 50’s, together with their families.

I He liked to tell stories of Bruno Pontecorvo and their adventures (hiking, camping, etc.

together with their families).

I Around 1970 Samoil started to work on neutrino physics:

I Bardin, Bilenky, Pontecorvo, On the ν − ν interaction (1970); On the ν ¯

_e

+ e → ¯ ν

_e

+ e process (1970)

I Andryushin, Bilenky, Gershtein, Possible

method of measuring the electromagnetic

form factor of the neutrino (1971)

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I In the middle 70’s Samoil started to work with Pontecorvo on the theory of massive neutrinos and neutrino

oscillations.

I The deep physical intuition of Pontecorvo and the profound

theoretical knowledge and wisdom of Samoil led to fundamental contributions to the development of the theory and phenomenology of massive neutrinos:

I The theory and phenomenology of neutrino oscillations in vacuum I The theory and phenomenology of

massive Majorana neutrinos obtained from the diagonalization of the Dirac + Majorana mass Lagrangian

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−7/20

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I Bilenky, Pontecorvo, Quark-Lepton Analogy and Neutrino Oscillations (1975) I Bilenky, Pontecorvo, Again on

Neutrino Oscillations (1976) I Bilenky, Petcov, Pontecorvo,

Lepton Mixing, µ → e + γ Decay and Neutrino Oscillations (1977) I Bilenky, Pontecorvo, Majorana

and Dirac Masses, Neutrino

Oscillations and the Number of

Charged Leptons (1980)

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First complete review on massive neutrinos and oscillations

PHYSICS REPORTS(Section C of Physics Letters)41, No, 4(1978)225-261. NORTH-HOLLAND PUBLISHING COMPANY

LEPTON MIXING AND NEUTRINO OSCILLATIONS

S.M. BILENKY and B. PONTECORVO

Joint institute forNuclear Research. Dubna,USSR

Received 27 June 1977

Contents:

5.4. The solar neutrino “puzzle” and neutrino oscilla-

1. Introduction 227 tions 248

2. Weak interaction theories with neutrino mixing 229 5.5.Oscillations and future solar neutrino experiments 249 2.1. Electron and muon lepton numbers 229 5.6. Solar neutrinos, time intensity variations and

2.2. Majorana neutrinos 231 oscillation lengths 249

2.3. Dirac neutrinos 234 5.7, A question about coherence of neutrino beams 251

2.4. Comparison of theories with neutrino mixing 236 5.8. Oscillations and cosmic neutrinos 252 3. Neutrino oscillations 237 6. Oscillations in the general case ofNneutrino types 253 4. Possible experiments in which the hypothesis of neu- 6.1. Left-handed fields 253

trino mixing might be tested 239 6.2. The general case of left-handed and right-handed

4.1. General considerations 239 neutrino fields 254

4.2. Limits imposed on the parameterM2by existing 6.3. Concluding remarks 255

data 241 7. Theji~-e~’decay and neutrino oscillations 256

4.3. Possible experiments 242 7.!. The case when there are only neutrinos 256

5. Solar and cosmic neutrinos 245 7.2. Heavy leptons 257

5.1. The Brookhaven experiment 245 7.3. The~i—~ey decay and neutrino oscillations 258

5.2. The experimental results 245 8. Conclusions 258

5.3. Conclusions 247 References 260

Single orders for this issue

PHYSICS REPORT (Section C of PHYSICS LETTERS) 41,No. 4 (1978) 225—261.

Copies of this issue may be obtained at the price given below. All orders should be sent directly to the Publisher. Orders must be accompanied by check.

Single issue price Dfl. 18.00, postage included.

PHYSICS REPORTS(Section C of Physics Letters)41, No, 4(1978)225-261. NORTH-HOLLAND PUBLISHING COMPANY

LEPTON MIXING AND NEUTRINO OSCILLATIONS

S.M. BILENKY and B. PONTECORVO

Joint institute forNuclear Research. Dubna,USSR

Received 27 June 1977

Contents:

5.4. The solar neutrino “puzzle” and neutrino oscilla-

1. Introduction 227 tions 248

2. Weak interaction theories with neutrino mixing 229 5.5.Oscillations and future solar neutrino experiments 249 2.1. Electron and muon lepton numbers 229 5.6. Solar neutrinos, time intensity variations and

2.2. Majorana neutrinos 231 oscillation lengths 249

2.3. Dirac neutrinos 234 5.7, A question about coherence of neutrino beams 251

2.4. Comparison of theories with neutrino mixing 236 5.8. Oscillations and cosmic neutrinos 252 3. Neutrino oscillations 237 6. Oscillations in the general case ofNneutrino types 253 4. Possible experiments in which the hypothesis of neu- 6.1. Left-handed fields 253

trino mixing might be tested 239 6.2. The general case of left-handed and right-handed

4.1. General considerations 239 neutrino fields 254

4.2. Limits imposed on the parameterM2by existing 6.3. Concluding remarks 255

data 241 7. Theji~-e~’decay and neutrino oscillations 256

4.3. Possible experiments 242 7.!. The case when there are only neutrinos 256

5. Solar and cosmic neutrinos 245 7.2. Heavy leptons 257

5.1. The Brookhaven experiment 245 7.3. The~i—~ey decay and neutrino oscillations 258

5.2. The experimental results 245 8. Conclusions 258

5.3. Conclusions 247 References 260

Single orders for this issue

PHYSICS REPORT (Section C of PHYSICS LETTERS) 41,No. 4 (1978) 225—261.

Copies of this issue may be obtained at the price given below. All orders should be sent directly to the Publisher. Orders must be accompanied by check.

Single issue price Dfl. 18.00, postage included.

Monumental review

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−9/20

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I In the early 80’s Samoil published fundamental papers on the physics of Majorana neutrinos:

I Bilenky, Hosek, Petcov, On Oscillations of Neutrinos with Dirac and Majorana Masses (1980)

I Bilenky, Niedermayer, A Possible Test of CP Invariance in Neutrino Oscillations (1981)

I Bilenky, Nedelcheva, Petcov, Some Implications of the CP Invariance for Mixing of Majorana Neutrinos (1984) I A very good review on weak neutral

current interactions:

I Bilenky, Hosek, Glashow-Weinberg-Salam theory of electroweak interactions and the neutral currents (1982)

S.M. Bilenky at the Neutrino Telescopes Workshop in the

1990s

From: Serguey Petcov,Commemoration of Samoil Bilenky,XIX International Workshop on

Neutrino Telescopes, February 2021

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I After the fall of Soviet Union, in 1992 Samoil lived mostly out of Russia, always accompanied by his very kind wife Sofia (a physicist until 1992).

I They spent considerable time in many places: Barcelona (J.A. Grifols, E.

Masso), Munich (W. Potzel, F. von Feilitzsch), Padova (A. Masiero), Seoul (C.W. Kim), Trieste (S.T. Petcov), Torino (W. Alberico, CG), Tübingen (A. Faessler, F. Simkovic), Valencia (J. Bernabeu), Vienna (W. Grimus).

I They finally settled in Vancouver (Canada) where their son Mikhail (Misha) was already living (he was a physicist until about 1999 and now he is a brilliant biologist working on the human genome).

Mikhail Bilenky cartoons in B. Pontecorvo office, JINR, Dubna

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−11/20

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International Pontecorvo Neutrino Physics School

Initiated by Samoil Bilenky in 1998 (with A. Sissakian and S. Ivanova of JINR)

VII International Pontecorvo Neutrino Physics School 2017 http://theor.jinr.ru/~neutrino17

August 20 –September 1, 2017 Prague, Czech Republic

O r g a n i z e d b y Joint Institute for Nuclear Research (Dubna, Russia) Czech Technical University (Prague, Czech Republic) Charles University (Prague, Czech Republic) Comenius University (Bratislava, Slovakia) Institute of Nuclear Physics (Krakow, Poland) M e m b e r s Bednyakov V.A. (JINR)Leitner R. (ChU) Zalewska A. (INP) Brudanin V.B. (JINR) Rondio E. (NCBJ, Swierk) Kolganova E.A. (JINR)

S e c r e t a r i e s HodákR. (CTU)Rusakovich E. (JINR) Rukhadze E. (CTU)VanišováM. (CTU) Introduction to ν-physics Bilenky S. (JINR Dubna)

Theory of ν-masses and mixing King S.F. (Southampton Univ.) ν-oscillation phenomenology Kayser B. (Fermilab) Solar ν-experiments and theory Smirnov A. (MPI Heidelberg) Accelerator ν-experiments Feldman G.J. (Harvard Univ.) Reactor ν-experiments Wang Y. (IHEP) Measurement of ν-mass Tkachev I. (INR RAS, Moscow)

Gastaldo L. (Heidelberg Univ.) 0νββ-decay experiments Barabash A. (ITEP Moscow) 0νββ-decay nuclear matrix elementsVogel P. (Caltech) ν-nucleus interactions Sobczyk J. (Wroclaw Univ.) Sterile neutrinos Link J. (Virginia Tech.)

Giunti C. (INFN Torino)

Leptogenesis Davidson S. (IPNL Lyon)

ν-astronomy Tamborra I. (Copenhagen Univ.)

ν-telescopes Spiering C. (DESY)

ν-cosmology Mangano G. (INFN Naples)

Dark matter experiments Fornengo N. (INFN Torino) Observation of gravitational wavesBarish B. (CALTECH) Neutrino physics at CERN Elsen E. (CERN) Future colliders Blondel A. (CERN) Statistics for Nucl. and Particle Phys.Dyk D.V. (IC, London)

O r g a n i z i n g C o m m i t t e e Matveev V.A. (JINR) Bilenky S.M. (JINR) Štekl I. (CTU) Olshevskiy A.G. (JINR) Šimkovic F. (CU/JINR) Jezabek M. (INP)

Český Krumlov KutnáHora

- chairman - scientific program - vice-chairman - vice-chairman - vice-chairman - vice-chairman

VI International Pontecorvo Neutrino Physics School VI International Pontecorvo

Neutrino Physics School

Organizing Committee:

Chairman - V. A. Matveev Scientific Program - S. M. Bilenky Vice-chairmen: I. Stekl F. Simkovic A. G. Olshevskiy V. A. Bednyakov R. Leitner V. B. Brudanin E. A. Kolganova O. Matyukhina – secretary D. Stefanik - secretary

Chairman - V. A. Matveev Scientific Program - S. M. Bilenky Vice-chairmen: I. Stekl F. Simkovic A. G. Olshevskiy V. A. Bednyakov R. Leitner V. B. Brudanin E. A. Kolganova O. Matyukhina – secretary D. Stefanik - secretary VI International Pontecorvo

Neutrino Physics School August 27 – September 4, 2015 Horný Smokovec, Slovakia

Lectures at School:

Neutrinos in SM and beyond: Samoil Bilenky (JINR Dubna) Phenomenology of ν-mixing and oscillations: Serguey Petcov (SISSA) Long baseline ν-oscillation experiments: David Wark (Oxford U.) Reactor ν experiments: Rupert Leitner (Charles U.) Atmospheric neutrinos: Yoichiro Suzuki (U. of Tokyo) Solar- and geo-neutrinos: Oleg Smirnov (JINR Dubna) Sterile neutrinos: Carlo Giunti (INFN Torino) Vyacheslav Egorov (JINR Dubna) Theory of ν –masses: Werner Rodejohann (MPI Heidelberg) Baryogenesis from Leptogenesis: Sasha Davidson (IPNL Lyon) Direct ν-mass search: Christian Weinheimer (U. of Muenster) Theory of 0νbb-decay : Martin Hirsch (U. of Valencia)

V. A. Matveev - chairman S. M. Bilenky - scientific program F. Šimkovic - vice-chairman A. G. Olshevskiy - vice-chairman I. Štekl - vice-chairman V. A. Bednyakov (http://theor.jinr.ru/~neutrino15/)

ν2

Double Beta Decay Matrix Elements: Francesco Iachello (Yale U.) 0νββ-decay: EXO and KamLAND-Zen: Andreas Piepke (U. of Alabama) 0νββ-decay : GERDA: Stefan Schoenert (TU Muenchen) Neutrinos in cosmology and astronomy : Steen Hannestadt (Aarhus U.) Physics at IceCube: Elisa Resconi (TU Muenchen) Baikal experiment: Zhan-Arys Dzhilkibaev (INR Moscow) Supernova and relic neutrinos: Petr Vogel (CATLTECH) Dark Matter: Walter Potzel (TU Muenchen) News from CERN: Sergio Bertolucci (CERN) Progressive detection techniques: Ettore Fiorini (U. di Milano-Bicocca) Progressive detection techniques II: Ivan Štekl (CTU Prague) Statistics for Nuclear and Particle Physics: Louis Lyons (U. of Oxford) R. Leitner V. B. Brudanin E. A. Kolganova O. Matyukhina D. Štefánik ν3

ν1

VI International Pontecorvo Neutrino Physics School VI International Pontecorvo

Neutrino Physics School

Chairman - V. A. Matveev Scientific Program - S. M. Bilenky Vice-chairmen: I. Stekl

F. Simkovic A. G. Olshevskiy V. A. Bednyakov R. Leitner V. B. Brudanin E. A. Kolganova O. Matyukhina – secretary D. Stefanik - secretary

Chairman - V. A. Matveev Scientific Program - S. M. Bilenky Vice-chairmen: I. Stekl

F. Simkovic A. G. Olshevskiy V. A. Bednyakov R. Leitner V. B. Brudanin E. A. Kolganova O. Matyukhina – secretary D. Stefanik - secretary VIII International Pontecorvo

Neutrino Physics School September 1 – September 10, 2019 Sinaia, Romania Organizing Committee: Members:

V. A. Matveev - chairman S. M. Bilenky- scientific program A.G. Olshevskiy - vice-chairman S. Stoica -vice-chairman F. Šimkovic - vice-chairman I. Štekl - vice-chairman http://theor.jinr.ru/~neutrino19/

ν2

V.A. Bednyakov V.B. Brudanin C. Giunti E.A. Kolganova R. Leitner ν3

ν1Secretaries:

A. Babič, J, D. Ali, O. Nitescu, A. Neascu C. Militaru

Introduction to ν-physics Samoil Bilenky (JINR Dubna) Theory of ν-masses and mixingAlexei Smirnov (MPI Heidelberg) ν-oscillation phenomenology Boris Kayser (Fermilab) ν-oscillations experiments:

Solar ν–experiments Oleg Smirnov (JINR Dubna) Atmospheric ν–experiments Juan Pablo Yanez (Univ. of Alberta) Accelerator ν–experiments Maury Goodman (Argonne National Lab) Reactor ν-experiments-Dmitry Naumov (JINR Dubna) Spectra of ν ’s from reactor Anna Hayes (Los Alamos National Lab) Light sterile neutrinos

theory - Carlo Giunti (INFN)

experiments - Yuri Shitov (JINR Dubna) Heavy sterile neutrinos Dmitry Gorbunov (INR RAS Moscow)

Measurement of ν-mass Kathrin Valerius (KIT in Karlsruhe) 0νββ−decay experiments Andrea Giuliani (CSNSM in Paris) 0νββ−decay NMEs Javier Menendez (Univ. of Tokyo) Coherent scattering of ν ’s Henry Wong (Academia Sinica, Taipei) ν-nucleus interactions Jan Sobczyk (Univ. of Wroclaw) Leptogenesis Pascuale DiBari (Univ. of Southampton ν-telescopes Nathan Whitehorn (Univ. of California) ν-properties from cosmology Richard Battye (Univ. of Manchester) Dark matter searches Suchita Kulkarni (HEPHY Vienna) Physics of gravitational waves Imre Bartos (Univ. of Florida) Everything about Higgs boson Guenakh Mitselmakher*(Univ. of Florida) Statistics for ν-experiments Thomas Schwetz (KIT in Karlsruhe)

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5 Books!

I Introduction to Feynman diagrams (1970 in Russian; 1971 in English) I Introduction to the physics of electroweak interactions (1980 in Russian;

1981 in English)

I Introduction to scattering theory (1985 in Russian)

I Basics of introduction to Feynman diagrams and electroweak interactions physics (1994)

I Introduction to the Physics of Massive and Mixed Neutrinos (2010 1st Edition; 2018 2nd Edition)

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−13/20

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Several Awards

I 1999 Humboldt Research Award I 2002 Pontecorvo Prize

I Russian state medal “For Distinguished Service to the State”

I Medal of First Degree of the Faculty of Physics and Mathematics of Charles University in Prague

I Honorable diploma of the Lomonosov

Moscow State University [2002 Pontecorvo Prize]

Well-Known PhD Students

Dimitri Bardin, Serguey Petcov, Victor Semikoz, Fedor Simkovic

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Samoil’s Conjectures on Sterile Neutrinos

Eur. Phys. J. C 1, 247–253 (1998)

T

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Neutrino mass spectrum from the results of neutrino oscillation experiments

S.M. Bilenky^1,2C. Giunti²W. Grimus³

1Joint Institute for Nuclear Research, Dubna, Russia

2INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Universit`a di Torino, Via P. Giuria 1, I–10125 Torino, Italy 3Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, A–1090 Vienna, Austria

Received: 5 January 1997 / Revised version: 17 March 1997

Abstract.All the possible schemes of neutrino mixing with four massive neutrinos inspired by the existing experimental indications in favor of neutrino mixing are considered in a model independent way. Assuming that in short-baseline experiments only one mass-squared difference is relevant, it is shown that the scheme with a neutrino mass hierarchy is not compatible with the experimental results. Only two schemes with two pairs of neutrinos with close masses separated by a mass difference of the order of 1 eV are in agreement with the results of all experiments. One of these schemes leads to possibly observable effects in³H and (ββ)⁰νexperiments.

1 Introduction

Neutrino masses and neutrino mixing are natural and plau- sible phenomena of modern gauge theories (see, for exam- ple, [1]). However, for the time being, the values of the neutrino masses and mixing angles cannot be predicted on theoretical grounds. The determination of these quan- tities is the key problem of today’s experimental neutrino physics.

At present there are several indications in favor of neutrino masses and mixing. One of the most important indications comes from solar neutrino experiments (Home- stake [2], Kamiokande [3], GALLEX [4] and SAGE [5]).

As it is well-known, in all four presently operating solar neutrino experiments the observed event rates are signifi- cantly smaller than the values predicted by the Standard Solar Model (SSM) [6]. Moreover, if the survival probabil- ity of solarνe’s is equal to one, the data ofdifferentexperi- ments cannot be explained even if the total neutrino fluxes are considered as free parameters [7]. Assuming the valid- ity of the SSM, the experimental data can be described by the MSW matter effect [8] for∆m²∼10⁻⁵eV²[9] or by vacuum oscillations in the case of∆m²∼10⁻¹⁰eV²[10]

(∆m²is the neutrino mass-squared difference).

The second indication in favor of neutrino mixing comes from the data of the Kamiokande [11], IMB [12]

and Soudan [13] atmospheric neutrino experiments. The ratio of muon-like to electron-like events measured in these experiments is less than the expected ratio. The sub-GeV and multi-GeV data of the Kamiokande collaboration can be explained byνµ⇆ντorνµ⇆νeoscillations with

∆m²∼10⁻²eV².

Finally, in the LSND experiment [14] ¯νep→ e⁺n events produced by neutrinos originating fromπ⁺and subsequentµ⁺decays at rest were observed. These events can be explained by ¯νµ⇆¯νeoscillations with∆m²∼ 1 eV².

Therefore, from the existing experimental data we have three different indications in favor of non-zero neutrino masses, each with a particular scale of∆m². However, we must also take into account the fact that in several short-baseline experiments neutrino oscillations were not observed. The results of these experiments allow to ex- clude large regions in the space of the neutrino oscillation parameters.

In the present paper we will examine what information on the neutrino mass spectrum can be inferred from the results of all short-baseline neutrino oscillation experiments if we also take into account the results of the solar and atmospheric neutrino experiments. We will present a general discussion which does not assume a definite model of neutrino mixing. We will show that the experimental results favor two rather particular possibilities for the neutrino mass spectrum.

We will start with the presentation of the general for- mulas for the neutrino transition probabilities in short- baseline neutrino oscillation experiments (for details see [15]). Our basic assumption is that only one neutrino mass- squared difference is relevant for short-baseline neutrino oscillations. This assumption means that the neutrino mass spectrum consists of two groups of close masses, separated by a mass difference in the eV range. Denot- ing the neutrinos of the two groups byν1, . . . , νrand νr+1, . . . , νn, respectively, with massesm1≤. . .≤mr

andmr+1≤. . .≤mn, we can quantify our assumption

Eur. Phys. J. C 1, 247–253 (1998)

T

HE

E

UROPEAN

P

HYSICAL

J

OURNAL

C

c

Springer-Verlag 1998

Neutrino mass spectrum from the results of neutrino oscillation experiments

S.M. Bilenky^1,2C. Giunti²W. Grimus³

1Joint Institute for Nuclear Research, Dubna, Russia

2INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Universit`a di Torino, Via P. Giuria 1, I–10125 Torino, Italy 3Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, A–1090 Vienna, Austria

Received: 5 January 1997 / Revised version: 17 March 1997

Abstract.All the possible schemes of neutrino mixing with four massive neutrinos inspired by the existing experimental indications in favor of neutrino mixing are considered in a model independent way. Assuming that in short-baseline experiments only one mass-squared difference is relevant, it is shown that the scheme with a neutrino mass hierarchy is not compatible with the experimental results. Only two schemes with two pairs of neutrinos with close masses separated by a mass difference of the order of 1 eV are in agreement with the results of all experiments. One of these schemes leads to possibly observable effects in³H and (ββ)⁰νexperiments.

1 Introduction

Neutrino masses and neutrino mixing are natural and plau- sible phenomena of modern gauge theories (see, for exam- ple, [1]). However, for the time being, the values of the neutrino masses and mixing angles cannot be predicted on theoretical grounds. The determination of these quan- tities is the key problem of today’s experimental neutrino physics.

At present there are several indications in favor of neutrino masses and mixing. One of the most important indications comes from solar neutrino experiments (Home- stake [2], Kamiokande [3], GALLEX [4] and SAGE [5]).

As it is well-known, in all four presently operating solar neutrino experiments the observed event rates are signifi- cantly smaller than the values predicted by the Standard Solar Model (SSM) [6]. Moreover, if the survival probabil- ity of solarνe’s is equal to one, the data ofdifferentexperi- ments cannot be explained even if the total neutrino fluxes are considered as free parameters [7]. Assuming the valid- ity of the SSM, the experimental data can be described by the MSW matter effect [8] for∆m²∼10⁻⁵eV²[9] or by vacuum oscillations in the case of∆m²∼10⁻¹⁰eV²[10]

(∆m²is the neutrino mass-squared difference).

The second indication in favor of neutrino mixing comes from the data of the Kamiokande [11], IMB [12]

and Soudan [13] atmospheric neutrino experiments. The ratio of muon-like to electron-like events measured in these experiments is less than the expected ratio. The sub-GeV and multi-GeV data of the Kamiokande collaboration can be explained byνµ⇆ντorνµ⇆νeoscillations with

∆m²∼10⁻²eV².

Finally, in the LSND experiment [14] ¯νep→ e⁺n events produced by neutrinos originating fromπ⁺and subsequentµ⁺decays at rest were observed. These events can be explained by ¯νµ⇆¯νeoscillations with∆m²∼ 1 eV².

Therefore, from the existing experimental data we have three different indications in favor of non-zero neutrino masses, each with a particular scale of∆m². However, we must also take into account the fact that in several short-baseline experiments neutrino oscillations were not observed. The results of these experiments allow to ex- clude large regions in the space of the neutrino oscillation parameters.

In the present paper we will examine what information on the neutrino mass spectrum can be inferred from the results of all short-baseline neutrino oscillation experiments if we also take into account the results of the solar and atmospheric neutrino experiments. We will present a general discussion which does not assume a definite model of neutrino mixing. We will show that the experimental results favor two rather particular possibilities for the neutrino mass spectrum.

We will start with the presentation of the general for- mulas for the neutrino transition probabilities in short- baseline neutrino oscillation experiments (for details see [15]). Our basic assumption is that only one neutrino mass- squared difference is relevant for short-baseline neutrino oscillations. This assumption means that the neutrino mass spectrum consists of two groups of close masses, separated by a mass difference in the eV range. Denot- ing the neutrinos of the two groups byν1, . . . , νrand νr+1, . . . , νn, respectively, with massesm1≤. . .≤mr

andmr+1≤. . .≤mn, we can quantify our assumption

S.M. Bilenky handwriting

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−15/20

hep-ph/9607372

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I In the last years Samoil was very skeptical about the existence of light sterile neutrinos for reasons of economy and simplicity, as indicated by the seesaw mechanism:

If light sterile neutrinos will be discovered in future short baseline and other neutrino experiments in this case our ideas about the origin of small neutrino masses will be com-

pletely changed. [arXiv:1907.01472]

I However, he emphasised that the question of the existence of light sterile neutrinos must be answered experimentally. See:

I Neutrino Masses from the Point of View of Economy and Simplicity, arXiv:1907.01472

I Neutrinos: Majorana or Dirac?, arXiv:2008.02110

I His last contribution to physics is the nice pedagogical review

Basics of General Theory of Relativity for Beginners, arXiv:2010.11823

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Prague, 23 May 2018

Celebrating Neutrinos: Colloquium in honor of prof. S. Bilenky at occasion of his 90th birthday

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−17/20

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NEUTRINOMIXING

Meeting in Honour of Samoil Bilenky's 70-th Birthday TORINO, March 25-27, 1999

W. Alberico (Univ. of Torino) V. de Alfaro (Univ. of Torino) M. Baldo Ceolin (Univ. of Padova) R. Bernabei (Univ. of Roma II) J. Bernabeu (Univ. of Valencia) S. Bilenky (JINR, Dubna) A. Bottino (Univ. of Torino) F. Buccella (Univ. of Napoli) M. Chaichian (Univ. of Helsinki) F. von Feilitzsch (Tech.Un. of Muenchen) E. Fiorini (Univ. of Milano) G. Fogli (Univ. of Bari) C. Giunti (INFN, Torino)

W. Grimus (Univ. of Wien) J. Hosek (Univ. of Prague) A. Masiero (Univ. of Padova) G. Navarra (Univ. of Torino) F. Niedermayer (Univ. of Bern) S. Petcov (SISSA, Trieste) A. Santamaria (Univ. of Valencia) P. Strolin (Univ. of Napoli)

AulaMagna,IstitutodiFisica,ViaP.Giuria1,Torino

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Dubna, 20 June 2018

Jubilee of Samoil Mihelevich Bilenky

C. Giunti−Tribute to Samoil Bilenky−TAUP 2021−3 September 2021−19/20

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Tribute to Samoil Bilenky