CISNP 2008: Concluding Remarks

S. T. Petcov

SISSA/INFN, Trieste, Italy, and

IPMU, University of Tokyo, Japan

INRNE, Bulgarian Academy of Sciences, Sofia, Bulgaria

CISNP08, University of South Carolina

Columbia, U.S.A.

May 17, 2008

Symposium in honor of Frank Avignone,Ettore Fiorini and the late Peter Rosen

Google: Frank Avignone; Results: 588 000• Frank T. Avignone, Department of Physics and Astronomy, University of South

Carolina 712 Main Street Columbia, South Carolina 29208, (803) 777-6933 ...

www.physics.sc.edu/FacultyStaff/Bravignone.html

• USC physicist Frank Avignone

Physics professor Frank Avignone joined USC faculty 40 years ago, but it

will be another decade, he hopes, before you read about his retirement ...

www.sc.edu/usctimes/articles/2005-02/frank.avignone.html

• ORAU News: Frank Avignone Receives ORAU Outstanding Leadership Award

Frank T. Avignone III, Carolina Endowed Professor of Physics and Astronomy

at the University of South Carolina, received the Oak Ridge Associated ...

www.orau.org/news/releases/2003/fy03-14.htm

• ORLaND

V., Avignone, F. T., Mezzacappa, A., 2000. International Symposium on Neutrino

Physics in Honor of Frank Avignone, Columbia, South Carolina, 10-12 Mar 2000. ...

www.nu.to.infn.it/exp/all/orland/

• [0711.4808] The MAJORANA 76Ge neutrino less double-beta decay ...

From: Frank Avignone III Thu, 29 Nov 2007 19:40:56 GMT (776kb). Link back to:

arXiv, ... export.arxiv.org/abs/0711.4808

• LBNL CUORE Group

Frank T. Avignone (USC), (803)777-6933, Avignone@sc.edu. Ettore Fiorini* (Milan

University), 39 02 64482432,2424 / 2463 (fax), ettore.fiorini@mib.infn.it ... www-

rnc.lbl.gov/ nxu/cuore/cuore.lbnl.html

• Axions

Frank T. Avignone (USC) and W. Haxton (UW). ... K. Zioutas, C.E. Aalseth,

D. Abriola, F.T. Avignone, R.L. Brodzinski, J.I. Collar, R. Creswick, ... col-

largroup.uchicago.edu/projects/axion/index.html

• Supernova science at spallation neutron sources discussions with Frank Avignone,

John Beacom, Jeff Blackmon, Dick Boyd, David Dean,. Yuri Efremenko, Jon En-

gel, George Fuller, Wick Haxton, Ken Lande, ... www.iop.org/EJ/article/0954-

3899/29/11/008/g3.11.008.pdf

• TAUP 2003 - Convener Contacts

Frank Avignone, waters@psc.psc.sc.edu; Hiro Ejiri, ejiri@rcnpax.rcnp.osaka-u.ac.jp Jouni

Suhonen, suhonen@phys.jyu.fi int.phys.washington.edu/taup2003/contacts.html

• SUMMARY of the 1 MEETING OF THE LSC SCENTIFIC COMMITTEE Hotel ...

Aprile, Frank Avignone (Chair), Laura Baudis, Yves Declais, Juan Fuster, .... Juan Fuster

and Frank Avignone. ezpc00.unizar.es/lsc/LSC-MINSC1-08.pdf

• Fulbright US Scholar Directory: Alphabetical Index Avignone, Frank Titus III; Physics

and Astronomy; Italy. B. Baar, Kenneth K.; Architecture; Albania. Baer, Adela S.;

Biological Sciences; Malaysia ... www.cies.org/schlr-directories/usdir01/us-dir-name.htm

• Campaign Donors : Fundrace 2008 - Huffington Post Columbia SC. Democrat, Frank

Avignone Professor, University of South Carolina. Updated Q4/2007 Hillary Clinton 390,

950 WORDSWORTH DR ... fundrace.huffingtonpost.com/neighbors.

• Sticky Security: Smart Cards Versus Magnetic Stripe Credit Cards ...11 apr

2007 ... Frank Avignone Chairman International Smart Card Alliance ... Coun-

cil. www.identitytheftsecrets.com/videos/sticky-security-smart-cards-versus- magnetic-

stripe.html

• Francia - Lotte e repressione (2007). Un punto sulla situazione ...

Due ... Avignone, accusati dell’incendio della sede del .... Frank ed Ines, sono fermati il

23 ... www.informa-azione.info/ francia-lotte-e-repressione-un-punto-sulla-situazione

• CD Baby: MELISSA FAHN: F. Avignone The nine songs on ”F. Avignone” make up a

song cycle that takes the listener on a dynamic ... guitarists Chris Clermont and Jamie

Findlay, bassists Derek Frank, ... cdbaby.com/cd/melissafahn

• The Transporter Script - transcript from the screenplay and/or...

“We need you Avignone to take us to ... The deal was this far and no further. ....

You’re breaking the rules, Frank. Not good to break the rules. ...” www.script-o-

rama.com/movie-scripts/t/transporter-script-transcript-jason-statham.html

Frank Avignone: Early (pre GOOGLE) Activi-ties• Frank was trained as a nuclear physicist in the early 1960s

• He met Fred Reines in 1965; Frank’s interest in neutrinos dates from that period.

Played important role in the interpretation of the results of the νe − e− elastic scattering

experiment of Gurr, Reines and Sobel at Savannah River P-Reactor.

• In 1978 Frank met Ettore Fiorini; became interested in improving the sensitivity of Ge

detectors for fundamental physics. Started to work with Ron Brodzinski and the Pacific

Northwest Lab. group in lowering the background in Ge detectors by several orders of

magnitude.

In 1987, the group had published the first terrestrial sensitive search for CDM, which

eliminated Dirac neutrinos as the dominant component of the CDM in the halo of our

galaxy.

Used these unique detectors to search for axions from the Sun.

• Late 80’ies until now - (ββ)0ν period: IGEX, CUORICINO, CUORE, MAJORANA.

Google: Ettore Fiorini; Results: 63.800

• Universita degli Studi di Milano - Bicocca - FIORINI ETTORE FIORINI ETTORE.

professore ordinario. Settore scientifico disciplinare:. Settore FIS/04 - Fisica Nucle-

are E Subnucleare. Dipartimento: ... www.unimib.it/go/Home/Pagine-Speciali/Elenco-

Docenti/FIORINI-ETTORE

Current Academic Responsibilities:

Direttore dei Laboratori di Radioattivita‘ e di Criogenia.

Other Professional Responsabilities:

Responsabile nazionale degli esperimenti ”Mibeta” e ”Cuore”.

Coordinatore del Network Europeo sui Rivelatori Termici.

• Particle physicists plumb the depths for Roman lead - 13 July 1991 ...

The physicists, Gianni Fiorentini and Ettore Fiorini, want the lead for exper-

iments that are of critical importance in particle physics and cosmology. ...

www.newscientist.com/article/mg13117772.600- particle-physicists-plumb-the-depths-

for-roman-lead-.html

• QUANTUM CALORIMETRY - Semiconductor thermistors

Using NTD germanium thermistors and tin absorbers, Ettore Fiorini and his

group at the University of Milan currently hold the resolution record for ...

phonon.gsfc.nasa.gov/qcal/qcal-semi.html

History of Quantum Calorimetry

Calorimetry has been used since the early days of nuclear physics to measure the inte-

grated energy of various radioactivities. By the mid 1930’s, the sensitivity of cryogenic

operation had been recognized, and small calorimeters were operated at temperatures as

low as 50 mK. These devices must have been very nearly capable of detecting individual

particle or gamma ray events, but the earliest published reference that we have found to

using them in this mode is the 1974 account by Tapio Niinikoski* of spurious pulses on

a carbon resistance thermometer readout, which he associated with local heating due to

the passage of individual cosmic rays.

The first experimental development coincidentally began simultaneously on both sides of

the Atlantic in 1982. In Milan, Ettore Fiorini had been working on detecting neutrinoless

double beta decay and, intrigued by a suggestion in a preprint by Guenakh Mitselmakher

that the betas might be detected thermally, went to Niinikoski to investigate the practi-

cality of this idea. They devised an approach that was developed into the first successful

physics experiment using thermal spectrometers, obtaining a new lower limit for the life-

time for double beta decay in 130Te measured with 340 g TeO2 ingots in a dilution

refrigerator in the Gran Sasso laboratory.

• Premio Enrico Fermi 2007 della Societa Italiana di Fisica

Motivazioni: a Ettore Fiorini per il contributo alla scoperta delle correnti deboli neutre e

allo studio dei neutrini solari. www.sif.it/SIF/it/portal/attivita/concorsi

• Ortvay Kollokvium

Ettore Fiorini (Dipt. di Fisica, Universita Milano-Bicocca)

(Recepient of the Marx Medal): ”The neutrinoless beta decay and the nature of neutrino”

... ortvay-koll.elte.hu/Programs/Abstracts/marx-emlek2008tavasz.abs.html

• IUPAP COMMISSION C12: 1999-2002

E-mail: Ettore.Fiorini@MI.infn.it. JONSON, B. (1996) Department of Physics,

Chalmers University of Technology, SE-412 96 Goeteborg, SWEDEN. ...

www.physics.adelaide.edu.au/itp/C12/C12.html

• Peer review committee

Ettore Fiorini. INFN Milan. ettore.fiorini@mib.infn.it.

G. Smadja. IPN Lyon. g.smadja@ipnl.in2p3.fr.

Joe Silk. Nuclear and Astrophysics Laboratory ...

appec.in2p3.fr/pages/peer.htm

• COMUNICATO STAMPA (Press release) 11 febbraio 2008

“L’occhio” nucleare rivela: Napoleone non e stato avvelenato”

“The nuclear “eye” reveals: Napoleon was not poisoned”

11 feb 2008 ... Ettore Fiorini, docente di Fisica Nucleare all’ Universita‘

Milano Bicocca e ... e-mail: ettore.fiorini@mib.infn.it. Ezio Previtali ...

www.ricercaitaliana.it/stdoc/pdfnapoleon.pdf

• FOXNews.com - Arsenic Poisoning Ruled Out in Napoleon’s Death ...

Feb 13, 2008 ... The researchers, including Ettore Fiorini of the Italian Na-

tional Institute of Nuclear Physics and the University of Milano-Biccoca, ...

www.foxnews.com/story/0,2933,330450,00.html

Napoleon didn’t die from arsenic poisoning - Telegraph

Drs Ettore Fiorini and Ezio Previtali of INFN, who did the study with Angela

Santagostino of the University of Milan at a small nuclear reactor at the ...

www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2008/02/11/scinap111.xml

• Il Sole 24 ORE: finanza, economia, esteri, valute, borsa e fisco

Ettore Fiorini, ordinario di Fisica nucleare e subnucleare all’Universita‘ Milano Bicocca,

che da molti anni studia i processi rari legati alla radiazione ... www.ilsole24ore.com

• Attualita‘ - Ettore Fiorini

Ettore Fiorini su Wikio. ... Siamo spiacenti ma non abbiamo trovato notizie recenti a

proposito di Ettore Fiorini. Suggerimenti: ...www.wikio.it/news/Ettore+Fiorini

• YouTube - culo di Ettore

Hello, you either have JavaScript turned off or an old version of Adobe’s .... culo di

Fiorini. 00:04 From: diegoambrosetti. Views: 339 ... www.youtube.com/watch?v=Dl-

1udwR8wEfeature=related

• Photo Blog Pull Out Ravenna

Ettore ... il mitico ETTORE !!! ... FIORINI si stira !!!

JOIN THE GANG 15.03.2008 !!! www.pulloutfoto.splinder.com

Ettore Fiorini: Early (pre GOOGLE) Activities

1960’ies

• Spent one year at Duke University with M. Bloch

• Strong interactions physics: π −N interactions leading to multipion final states studied

with heavy (propane and freon) liquid bubble chamber BP3; done in collaboration with

A. Lagarrigue and the french groups related to him.

• Weak interactions:

studies (with A. Pullia and E. Bellotti) of the properties of neutral and charged K’s: Ke3

decay.

• In 1963 started the first (ββ)0ν-decay experiment with 76Ge.

1970’ies

• Neutrino Physics at CERN (Gargamelle Collab., with Lagarrique):

observation of purely leptonic NC weak interaction;

observation of ν −N NC weak interaction;

neutrino oscillations;

precocius scaling in CC interactions;

hyperon production by antineutrinos;

charm production.

1980’ies

• Parity violatin effects in nuclar physics

• Proton decay (Mont Blanc tunnel)

Late 1980’ies - now

• Solar neutrinos (GALLEX/GNO)

• (ββ)0ν-decay wiht cryo-bolometers (CUORICINO, CUORE)

Peter Rosen

Compelling Evidence for ν−Oscillations: 3-ν mixing

νlL =3∑

j=1Ulj νjL l = e, µ, τ.

B. Pontecorvo, 1957; 1958; 1967;

Z. Maki, M. Nakagawa, S. Sakata, 1962;

PMNS Matrix: Standard Parametrization

U = V

1 0 0

0 eiα21

2 0

0 0 eiα31

2

V =

c12c13 s12c13 s13e−iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13s12s23 − c12c23s13eiδ −c12s23 − s12c23s13eiδ c23c13

• sij ≡ sin θij, cij ≡ cos θij, θij = [0, π2],

• δ - Dirac CP-violation phase, δ = [0,2π],

• α21, α31 - the two Majorana CP-violation phases.

• ∆m2� ≡ ∆m2

21∼= 7.6 × 10−5 eV2 > 0, sin2 θ12

∼= 0.32, cos 2θ12 ∼> 0.26 (2σ),

• |∆m2atm| ≡ |∆m2

31| ∼= 2.4 (2.5) × 10−3 eV2, sin2 2θ23∼= 1,

• θ13 - the CHOOZ angle: sin2 θ13 < 0.033 (0.050 (0.063)) 2σ (3σ).

A.Bandyopadhyay, S.Choubey, S.Goswami, S.T.P., D.P.Roy, arXiv:0804.4857;

T. Schwetz, arXiv:0710.5027

• sgn(∆m2atm) = sgn(∆m2

31) not determined

∆m2atm ≡ ∆m2

31 > 0, normal mass ordering

∆m2atm ≡ ∆m2

32 < 0, inverted mass ordering

Convention: m1 < m2 < m3 - NMO, m3 < m1 < m2 - IMO

m1 � m2 � m3, NH,

m3 � m1 < m2, IH,

m1∼= m2

∼= m3, m21,2,3 >> ∆m2

atm, QD; mj ∼> 0.10 eV.

• Majorana phases α21, α31:

– νl ↔ νl′, νl ↔ νl′ not sensitive;

S.M. Bilenky, J. Hosek, S.T.P.,1980;

P. Langacker, S.T.P., G. Steigman, S. Toshev, 1987

– |<m>| in (ββ)0ν−decay depends on α21, α31;

– Γ(µ→ e+ γ) etc. in SUSY theories depend on α21,31;

– BAU, leptogenesis scenario: α21,31 !

Future Progress

• Determination of the nature - Dirac or Majorana, of νj .

• Determination of sgn(∆m2atm), type of ν− mass spectrum

m1 � m2 � m3, NH,

m3 � m1 < m2, IH,

m1∼= m2

∼= m3, m21,2,3 >> ∆m2

atm, QD; mj ∼> 0.10 eV.

• Determining, or obtaining significant constraints on, the absolute scale of νj-

masses, or min(mj).

• Status of the CP-symmetry in the lepton sector: violated due to δ (Dirac),

and/or due to α21, α31 (Majorana)?

• Measurement of, or improving by at least a factor of (5 - 10) the existing upper

limit on, sin2 θ13.

• High precision determination of ∆m2�, θ�, ∆m2

atm, θatm.

• Searching for possible manifestations, other than νl−oscillations, of the non-conservation of Ll, l = e, µ, τ , such as µ→ e+ γ, τ → µ+ γ, etc. decays.

• Understanding at fundamental level the mechanism giving rise to the ν− masses

and mixing and to the Ll−non-conservation. Includes understanding

– the origin of the observed patterns of ν-mixing and ν-masses ;

– the physical origin of CPV phases in UPMNS ;

– Are the observed patterns of ν-mixing and of ∆m221,31 related to the exis-

tence of a new symmetry?

– Is there any relations between q−mixing and ν− mixing? Is θ12 + θc=π/4 ?

– Is θ23 = π/4, or θ23 > π/4 or else θ23 < π/4?

– Is there any correlation between the values of CPV phases and of mixing

angles in UPMNS?

• Progress in the theory of ν-mixing might lead to a better understanding of theorigin of the BAU.

(ββ)0ν−Decay Experiments:

- Majorana nature of νj

- Type of ν−mass spectrum (NH, IH, QD)

- Absolute neutrino mass scale

3H β-decay, cosmology: mν (QD, IH)

- CPV due to Majorana CPV phases

νj− Dirac or Majorana particles, fundamental problem

νj−Dirac: conserved lepton charge exists, L = Le + Lµ + Lτ, νj 6= νj

νj−Majorana: no lepton charge is exactly conserved, νj ≡ νjThe observed patterns of ν−mixing and of ∆m2

atm and ∆m2� can be related to

Majorana νj and an approximate symmetry:

L′ = Le − Lµ − Lτ

S.T.P., 1982

See-saw mechanism: νj− Majorana

Establishing that νj are Majorana particles would be as important as thediscovery of ν− oscillations.

If νj− Majorana particles, UPMNS contains (3-ν mixing)

δ-Dirac, α21, α31 - Majorana physical CPV phases

ν-oscillations νl ↔ νl′, νl ↔ νl′, l, l′ = e, µ, τ ,

• are not sensitive to the nature of νj,S.M. Bilenky, J. Hosek, S.T.P.,1980;

P. Langacker et al., 1987

• provide information on ∆m2jk = m2

j −m2k, but not on the absolute values

of νj masses.

The Majorana nature of νj can manifest itself in the existence of ∆L = ±2

processes:

K+ → π− + µ+ + µ+

µ− + (A,Z) → µ+ + (A,Z − 2)

The process most sensitive to the possible Majorana nature of νj - (ββ)0ν-

decay

(A,Z) → (A,Z + 2) + e− + e−

of the even-even nuclei, 48Ca, 76Ge, 82Se, 100Mo, 116Cd, 130Te, 136Xe, 150Nd.

2n from (A,Z) exchange a virtual Majorana νj (via the CC weak interac-

tion) and transform into 2p of (A,Z+2) and two free e−.

Nuclear 0νββ-decaye-

e-

p

p

νn

nA,Z A,Z+2ν−

strong in-medium modification of the basic processdd → uue−e−(νeνe)

continuum

0+ (A,Z) (A,Z+1)

(A,Z+2)

0+

0+ 1+

1-

2- virtual excitationof states of all multipolaritiesin (A,Z+1) nucleus

V. Rodin, talk at Gran Sasso, 2006

A(ββ)0ν ∼ <m> M(A,Z), M(A,Z) - NME,

|<m>| =∣∣m1|Ue1|2 +m2|Ue2|2 eiα21 +m3|Ue3|2 eiα31

∣∣

=∣∣m1 c212 c

213 +m2 s212 c

213 e

iα21 +m3 s213 eiα31

∣∣, θ12 ≡ θ�, θ13- CHOOZ

α21, α31 - the two Majorana CPVP of the PMNS matrix.

CP-invariance: α21 = 0,±π, α31 = 0,±π;

η21 ≡ eiα21 = ±1, η31 ≡ eiα31 = ±1

relative CP-parities of ν1 and ν2, and of ν1 and ν3 .

L. Wolfenstein, 1981;

S.M. Bilenky, N. Nedelcheva, S.T.P., 1984;

B. Kayser, 1984.

A(ββ)0ν ∼ <m> M(A,Z), M(A,Z) - NME,

|<m>| ∼=∣∣∣√

∆m2� sin2 θ12eiα +

√∆m2

31 sin2 θ13eiβ∣∣∣ , m1 � m2 � m3 (NH),

|<m>| ∼=√m2

3 + ∆m213

∣∣cos2 θ12 + eiα sin2 θ12∣∣ , m3 < (�)m1 < m2 (IH),

|<m>| ∼= m∣∣cos2 θ12 + eiα sin2 θ12

∣∣ , m1,2,3∼= m ∼> 0.10 eV (QD),

θ12 ≡ θ�, θ13-CHOOZ; α ≡ α21, β + 2δ ≡ α31.

CP-invariance: α = 0,±π, βM = 0,±π;

|<m>| ∼< 5 × 10−3 eV, NH;

√∆m2

13 cos 2θ12∼= 0.013 eV ∼< |<m>| ∼<

√∆m2

13∼= 0.055 eV, IH;

m cos 2θ12 ∼< |<m>| ∼< m, m ∼> 0.10 eV, QD .

Best sensitivity: Heidelberg-Moscow 76Ge experiment.

Claim for a positive signal at > 3σ:

H. Klapdor-Kleingrothaus et al., PL B586 (2004),

|<m>| = (0.1 − 0.9) eV (99.73% C.L.).

IGEX 76Ge: |<m>| < (0.33 − 1.35) eV (90% C.L.).

Taking data - NEMO3 (82Se, 100Mo), CUORICINO (130Te):

|<m>| <(0.7–1.2) eV, |<m>| <(0.18–0.90) eV (90% C.L.).

Large number of projects: |<m>| ∼ (0.01 − 0.05) eV

CUORE - 130Te,GERDA - 76Ge,SuperNEMO - 82Se,EXO - 136Xe,MAJORANA - 76Ge,MOON - 100Mo,CANDLES - 48Ca,XMASS - 136Xe.

1e-05 0.0001 0.001 0.01 0.1 1mMIN [eV]

0.001

0.01

0.1

1

|<m>|

[eV

] IH

QD

NH

S. Pascoli, S.T.P., 2008

The current 2σ ranges of values of the parameters used.

1e-05 0.0001 0.001 0.01 0.1 1mMIN [eV]

0.001

0.01

0.1

1

|<m>|

[eV]

NH

IH

QD

S. Pascoli, S.T.P., 2008

sin2 θ13 = 0.015± 0.006; 1σ(∆m2�) = 4%, 1σ(sin2 θ�) = 4%, 1σ(|∆m2

atm|) = 6%;

2σ(|<m>| ) used.

0.002 0.0022 0.0024 0.0026∆ m2

A [eV2]

0

0.01

0.02

0.03

0.04

0.05

sin2

θ 13

S. Pascoli, S.T.P., 2007

NH spectrum, |<m>| > 10−3 eV

1σ(sin2 θ13) = 0.008; 1σ(∆m2�) = 3.3%, 1σ(sin2 θ�) = 4%, 1σ(|∆m2

atm|) = 4%

Absolute Neutrino Mass Measurements

The Troitzk and Mainz 3H β-decayexperiments

mνe < 2.3 eV (95% C.L.)

There are prospects to reach sensitivity

KATRIN : mνe ∼ 0.2 eV

Cosmological and astrophysical data: the WMAP result combined with data from

large scale structure surveys (2dFGRS, SDSS)

∑

j

mj ≡ Σ < (0.4 − 1.7) eV

The WMAP and future PLANCK experiments can be sensitive to∑

j

mj∼= 0.4 eV

Data on weak lensing of galaxies by large scale structure, combined with data

from the WMAP and PLANCK experiments may allow to determine∑

j

mj : δ ∼= 0.04 eV.

Mν from the See-Saw MechanismP. Minkowski, 1977.

M. Gell-Mann, P. Ramond, R. Slansky, 1979;

T. Yanagida, 1979;

R. Mohapatra, G. Senjanovic, 1980.

• Explains the smallness of ν−masses.

• Through leptogenesis theory links the ν−mass generation to the generation

of baryon asymmetry of the Universe YB.

S. Fukugita, T. Yanagida, 1986.

• In SUSY GUT’s with see-saw mechanism of ν−mass generation, the LFV decays

µ→ e+ γ, τ → µ+ γ, τ → e+ γ , etc.

are predicted to take place with rates within the reach of present and future

experiments.

F. Borzumati, A. Masiero, 1986.

• The νj are Majorana particles; (ββ)0ν−decay is allowed.

See-Saw: Dirac ν-mass mD + Majorana mass MR for NR

The See-Saw Lagrangian

Llep(x) = LCC(x) + LY(x) + LNM(x) ,

LCC = − g√2lL(x) γα νlL(x)W

α†(x) + h.c. ,

LY(x) = λilNiR(x)H†(x)ψlL(x) + YlH

c(x) lR(x)ψlL(x) + h.c. ,

LNM(x) = − 1

2MiNi(x)Ni(x) .

ψlL - LH doublet,ψTlL = (νlL lL), lR - RH singlet, H - Higgs doublet.

Basis: MR = (M1,M2,M3); DN ≡ diag(M1,M2,M3), Dν ≡ diag(m1,m2,m3).

mD generated by the Yukawa interaction:

−LνY = λilNiRH†(x)ψlL(x), v = 174 GeV, v λ = mD − complex

For MR - sufficiently large,

mν ' v2 λT M−1R λ = U∗

PMNS mdiagν U †

PMNS .

Yν ≡ λ =√DN R

√Dν (UPMNS)

†/vu, all at MR ; R-complex, RTR = 1.

J.A. Casas and A. Ibarra, 2001In GUTs, MR < MX, MX ∼ 1016 GeV;

in GUTs, e.g., MR = (109,1012,1015) GeV, mD ∼ 1 GeV.

LeptogenesisYB = nB−nB

S∼ 8.6 × 10−11 (nγ: ∼ 6.3 × 10−10)

YB∼= −10−2 ε κ

W. Buchmuller, M. Plumacher, 1998;

W. Buchmuller, P. Di Bari, M. Plumacher, 2004

κ– efficiency factor; κ∼ 10−1 − 10−3: ε ∼> 10−7.

ε: CP−, L− violating asymmetry generated in out of equilibrium NRj−decays in

the early Universe,

ε1 =Γ(N1 → Φ− `+) − Γ(N1 → Φ+ `−)

Γ(N1 → Φ− `+) + Γ(N1 → Φ+ `−)

M.A. Luty, 1992;

L. Covi, E. Roulet and F. Vissani, 1996;

M. Flanz et al., 1996;

M. Plumacher, 1997;

A. Pilaftsis, 1997.

κ = κ(m), m - determines the rate of wash-out processes:

Φ+ + `− → N1, `− + Φ+ → Φ− + `+, etc.

W. Buchmuller, P. Di Bari and M. Plumacher, 2002;

G. F. Giudice et al., 2004

Two-Flavour Regime: Individual asymmetries

Assume: M1 �M2 �M3, 109 ∼< M1 (∼ T) ∼< 1012 GeV,

ε1l = − 3M1

16πv2

Im(∑

j,km1/2j m

3/2k U∗

ljUlkR1jR1k

)

∑jmj |R1j|2

ml ≡|λ1l|2 v2

M1

=

∣∣∣∣∣∑

k

R1km1/2k U∗

lk

∣∣∣∣∣

2

, l = e, µ, τ .

The baryon asymmetry is

YB ' − 12

37g∗

(ε2 η

(417

589m2

)+ ετ η

(390

589mτ

)),

η (ml) '((

ml

8.25 × 10−3 eV

)−1

+

(0.2 × 10−3 eV

ml

)−1.16)−1

.

YB = −(12/37) (Y2 + Yτ),

Y2 = Ye+µ, ε2 = ε1e + ε1µ, m2 = m1e + m1µ

A. Abada et al., 2006; E. Nardi et al., 2006

A. Abada et al., 2006

M1 �M2 �M3, m1 � m2 � m3 (NH)

Dirac CP-violation

α32 = 0 (2π), β23 = π (0); β23 ≡ β12 + β13 ≡ arg(R12R13).

|R12|2 ∼= 0.85, |R13|2 = 1 − |R12|2 ∼= 0.15 - maximise |ετ | and |YB|:

|YB| ∼= 2.8 × 10−13 | sin δ|(s130.2

)( M1

109 GeV

).

|YB| ∼> 8 × 10−11, M1 ∼< 5 × 1011 GeV imply

| sin θ13 sin δ| ∼> 0.11 , sin θ13 ∼> 0.11 .

The lower limit corresponds to

|JCP| ∼> 2.4 × 10−2

FOR α32 = 0 (2π), β23 = 0 (π):

| sin θ13 sin δ| ∼> 0.09 , sin θ13 ∼> 0.09 ; |JCP| ∼> 2.0 × 10−2

M1 �M2 �M3, m1 � m2 � m3 (NH)

Majorana CP-violation

δ = 0, real R12, R13 (β23 = π (0));

α32∼= π/2, |R12|2 ∼= 0.85, |R13|2 = 1 − |R12|2 ∼= 0.15 - maximise |ετ | and |YB|:

|YB| ∼= 2 × 10−12

(√∆m2

31

0.05 eV

)(M1

109 GeV

).

We get |YB| ∼> 8 × 10−11, for M1 ∼> 3.6 × 1010 GeV

0 1 2 3 4 5 6∆

0

2.5

5

7.5

10

12.5

15HY B�1

01

1L

M1 �M2 �M3, m1 � m2 � m3; Dirac CP-violation, α32 = 0; 2π;

real R12, R13, |R12|2 + |R13|2 = 1, |R12| = 0.86, |R13| = 0.51, sign (R12R13) = +1;

i) α32 = 0 (κ′ = +1), s13 = 0.2 (red line) and s13 = 0.1 (dark blue line);

ii) α32 = 2π (κ′ = −1), s13 = 0.2 (light blue line);

M1 = 5 × 1011 GeV.

S. Pascoli, S.T.P., A. Riotto, 2006.

-11.5 -11 -10.5 -10 -9.5 -9Log10 YB

-0.04

-0.02

0

0.02

0.04J

CP

M1 �M2 �M3, m1 � m2 � m3; M1 = 5 × 1011 GeV;

Dirac CP-violation, α32 = 0 (2π);

|R12| = 0.86, |R13| = 0.51, sign (R12R13) = +1 (−1) (β23 = 0 (π), κ′ = +1);

The red region denotes the 2σ allowed range of YB.

S. Pascoli, S.T.P., A. Riotto, 2006.

0 1 2 3 4 5 6Α21

0

5

10

15

20

25

30

HY B�10

11

L

M1 �M2 �M3, m3 � m1 < m2; M1 = 2 × 1011 GeV;

Majorana CP-violation, δ = 0;

purely imaginary R11R12 = iκ|R11R12|, κ = −1, |R11|2 − |R12|2 = 1, |R11| = 1.2;

s13 = 0 (blue line) and 0.2 (red line).

S. Pascoli, S.T.P., A. Riotto, 2006.

0.03 0.035 0.04 0.045 0.05ÈXmΝ \È�eV

-10.3

-10.2

-10.1

-10

-9.9

-9.8L

og10

YB

M1 �M2 �M3, m3 � m1 < m2; M1 = 2 × 1011 GeV;

Majorana CP-violation, δ = 0, s13 = 0;

purely imaginary R11R12 = iκ|R11R12|, κ = +1 |R11|2 − |R12|2 = 1, |R11| = 1.05.

The Majorana phase α21 is varied in the interval [−π/2, π/2].

S. Pascoli, S.T.P., A. Riotto, 2006.

Conclusions

Determining the nature - Dirac or Majorana, of massive neutrinos is of funda-

mental importance for understanding the origin of neutrino masses.

The see-saw mechanism provides a link between ν-mass generation and BAU.

Majorana CPV phases in UPMNS: (ββ)0ν-decay, YB.

Any of the CPV phases in UPMNS can be the leptogenesis CPV parameters.

Obtaining information on Dirac and Majorana CPV is a remarkably challenging

problem.

Dirac and Majorana CPV may have the same source.

Low energy leptonic CPV can be directly related to the existence of BAU.

Understanding the status of the CP-symmetry in the lepton sector is of funda-

mental importance.

These results underline further the importance of the experiments aiming to mea-

sure the CHOOZ angle θ13 and of the experimental searches for Dirac and/or

Majorana leptonic CP-violation at low energies.

To Frank and Ettore:

Happy Anniversary!

Thank you for being the driving force in the field of (ββ)0ν-decay reserach

and inspiration for the younger generation of researchers working in this

field.

My best wishes for personal happiness and many professional successes!