Inte In tern rnatio tional S l School o l on A Astro troPartic rticle le P Physic ics Euro ropean D Docto tora rate te S School Multi-Messenger Approach to Astroparticle Physics Univ iversid idad d de Z Zaragoza 1 13-22 J July ly 2 2010 Underground Physics A. Bettini Università di Padova, Dipartimento di Fisica G. Galilei; INFN - Sezione di Padova Laboratorio Subterráneo de Canfranc (Huesca) Spain July 15, 10 A. Bettini. INFN 1
Tiny signals. Go underground Physics beyond the Standard Model Neutrinos are massive Lepton numbers are violated Neutrino change flavour Discovery in underground laboratories with natural sources (sun, cosmic rays), and long base-lines Confirmation and improvement in precision with reactor and accelerator experiments, on unprecedented baselines July 15, 10 A. Bettini. INFN 2
The Models The Standard Model is the most Cosmology is now exact precise and comprehensive Tested by consistency by theory ever built observations @ different epochs Tested with high accuracy in Λ CDM experiments @ accelerators Normal Does not include gravitation Neutrinos matter 0.15-1% 4% Gravitation. Macroscopic theory only Dark matter GR - differently from other 23% interactions 2 basic constants: Coupling & Cosmological constant Cosmological constant 73% R µ � � 1 2 Rg µ � = 8 � G N T µ � � � g µ � c 4 July 15, 10 A. Bettini. INFN 3
Lepton mixing Neutrinos change flavour in two different ways • (vacuum) oscillation •in the kinetic part of the Hamiltonian ( ∆ m 2 /2 E ν ) •Disappearance atmospheric ν µ Δ m 2 •does not depend on θ ij ⇔ π /2 – θ ij [but 2 nd oscill. interference] •does not depend on sign( Δ m 2 ) [but 2 nd oscill. interference] 0 π /4 π /2 θ ij • flavour conversion in matter MSW (Sun, Supernova, Earth) • dynamical phenomenon , due to the ν e e interaction (2 G F n e ) •Disappearance (& indirectly appearance) solar ν e Δ m 2 •depends on θ ij ⇔ π /2 – θ ij •depends on sign( Δ m 2 ) 0 π /4 π /2 θ ij A. Bettini Introduction to Elementary Particle Physics. Cambridge University Press 2008 July 15, 10 A. Bettini. INFN 4
Mass eigenstates - Flavour eigenstates s 13 e � i � 1 0 0 � c 13 0 � c 12 – s 12 0 1 0 0 � e � 1 � � � � � � � � � � � � � � � � � � � � � � e i � 1 0 c 23 s 23 0 1 0 s 12 c 12 0 0 0 � µ � = � 2 � � � � � � � � � � � � � – s 13 e i � e i � 2 0 – s 23 c 23 0 c 13 0 0 1 0 0 � � � 3 � � � � � � � � � � � � What we know @ 2 σ level (95% c.l.) G. Fogli et al. hep-ph/0805.2517 � m 2 � m 2 2 � m 1 2 = 76.6 ± 3.5 meV 2 � m 2 � m 3 2 � m 2 2 + m 1 ( ) / 2 = 2380 ± 270 meV 2 2 sin 2 � 12 = 0.326 � 0.04 + 0.05 sin 2 � 23 = 0.45 � 0.09 + 0.16 sin 2 � 13 < 0.032 9 independent real parameters 3 masses m 1 , m 2 , m 3 3 mixing angles θ 12 , θ 13, θ 23 θ ij ∈ [0, π /2] 1 phase ( δ ⇒ CP violation if not δ ≠ 0, , δ ≠ π ) +2 phases ( φ 2 , φ 3 ) , if neutrinos are Majorana ⇒ irrelevant for oscillations July 15, 10 A. Bettini. INFN 5
What we know , ν 3 defined in decreasing ν e fraction ν 1 ⇒ ≈ 70% ν e , ν 2 ⇒ ≈ 30% ν e , ν 3 ⇒ ≈ 0% ν e ν 1 , , ν 2 , solar squared mass difference ⇒ δ m 2 ( >0 from solar neutrinos) atmospheric squared mass difference ⇒ Δ m 2 ( ) � 2.5% � � m 2 ( ) � 5% � � m 2 ( ) � 6% � sin 2 � 12 ( ) � 11% � sin 2 � 23 ( ) � 0.01 � sin 2 � 13 We do not know • The absolute scale • The sign of Δ m 2 � m 2 � 50 meV m 3 > m 1 , m 2 > � 50 meV � m 2 � 8.5 meV m 3 > � 8.5 meV m 2 > July 15, 10 A. Bettini. INFN 6
Oscillation probabilities •The oscillation probabilities are combinations of functions oscillating in time, hence in the distance between source and detector, better of L/E •Frequency proportional to mass square difference •Amplitude different for different processes � � ( ) L km ) sin 2 1.27 � m 2 eV 2 ( ) ( ) = A � x � � y ( P � x � � y , L � � � � ( ) E GeV � � ) � 1 ) = sin 2 2 � 23 ) cos 2 � 13 ) 1 � sin 2 � 23 cos 2 � 13 ( ( ( ( A � µ � � x Disappearance - atmosphere/acceler. 2 ) = sin 2 2 � 23 ) cos 4 � 13 ( ( ( ) � 1 A � µ � � � Appearance Observed by OPERA @ CNGS ) sin 2 2 � 13 ) = sin 2 � 23 2 ( ( ( ) � 2 � 13 A � µ � � e Rare, not yet observed ) = sin 2 2 � 13 2 ( ( ) � 4 � 13 A � e � � x Reactor experiments ) sin 2 2 � 13 ) = cos 2 � 23 2 ( ( ( ) � 2 � 13 A � e � � � July 15, 10 A. Bettini. INFN 7
The first appearance OPERA July 15, 10 A. Bettini. INFN 8
OPERA Target mass = 1.25 kt Exposure2008-9 ≈ 5 10 19 p.o.t. ( ≈ 1/5 of total) ≈ 35% completely analysed Exopected ≈ 0.5 events after selection criteria July 15, 10 A. Bettini. INFN 9
The first candidate Expected background 0.045±0.020 July 15, 10 A. Bettini. INFN 10
MSW Relevant interaction (Earth, Sun, SN) = CC ν e e Mass eigenstate in high density matter ≈ ν e . Vacuum/MSW matter term = � m 2 / 2 E � ( ) � � kinetic term 2 G F n e Sun Transition @ Δ m 12 @ E ν >> MeV Sun produces ν 2 Supernova Transitions @ Δ m 12 and Δ m 23 High neutrino density ⇒ νν νν interactions important July 15, 10 A. Bettini. INFN 11
BOREXINO Vacuum-Matter transition Before BOREXINO BOREXINO July 15, 10 A. Bettini. INFN 12
� � Helicity and Chirality � 1 � � � � � � 2 � � ( ) = � � � x = � � � � � 3 � � � � � � � � � � � � 4 Helicity is a property of a 2-component spinor, � � p h = representing a particle with v ≠ 0 p It is the spin projection on the direction of velocity � L = 1 Chirality is a property of the 4-component bispinor ( ) � , � 5 � L = � � L 2 1 � � 5 Only negative chirality fields have CC weak interactions � R = 1 The states of definite chirality are the eigenstates of γ 5 2 1 + � 5 ( ) � , � 5 � R = + � R Chirality is not an observable, we measure helicity instead Helicity content of the (Left) spinor χ ( z axis along the motion) E � p z E + p z E + p z � = 1 + 1/2 + 1 � 1/2 � m + 1/2 + 1 � � � � � � � 1/2 � � L � � L E � L � � L � � � 2 � m � 2 � m � 2 � m � If the particle is ultrarelativistic, its negative chirality state contains a m/E “wrong” helicity component, very small if E >> m July 15, 10 A. Bettini. INFN 13
Majorana bispinor The charge conjugate of a Majorana bi-spinor is the bi-spinor itself (up to a phase factor) C = i � 2 � M = � M � M Majorana neutrinos are their own antiparticles Particle and antiparticle have all the “charges” with opposite values ⇒ different particles Neutrinos and antineutrinos are possibly distinguished by a unique charge, the lepton number If lepton number is not conserved nothing distinguishes neutrino from antineutrino Neutrino may be its own antiparticle If m << E ⇒ approximate distinction between Majorana “neutrinos” and “antineutrinos” possible CC weak current � l � µ l L creates CC weak current l L � µ � l creates Dirac: � Dirac: � ( ) � ( h = + 1) ( ) � ( h = � 1) Majorana: � ( h = � 1) + m / E Majorana: � ( h = + 1) + m / E � � � � � � � � Majorana neutrino ≡ negative helicity (if m / E <<1 interacts almost as a Dirac neutrino) Majorana antineutrino ≡ positive helicity (if m / E <<1 interacts as almost a Dirac anti- ν ) July 15, 10 A. Bettini. INFN 14
ββ 2 ν and ββ ββ 0 ν Decay ββ A Majorana ν e with E ≈ + p z >> m hitting a nucleus produces e – and a fraction ( m / E ) 2 of e + [10 –20 for E =1 GeV, m =100 meV] ⇒ L eff =+1. Observation hopeless. Go to decays 2 nd order weak interaction In nuclides stable against β decay Forbidden in the Standard Model If observed @ nuclear level •Lepton number is violated ∆ L =2 ) + 2 e � + 2 � ( ) � A , Z + 2 ( A , Z •Neutrinos are Majorana e Lifetime measured for several isotopes T 2 ν 1/2 =10 19 − 10 21 yr July 15, 10 A. Bettini. INFN 15
Nuclear matrix elements Continuous progress in the nuclear matrix elements calculations in the last years Three methods • Quasi Random Phase Approximation (QRPA) • Shell Model (SM) IBM-2 Barea & Iachello 2009 • Interacting Boson Model 2 (IBM2) QRPA Simkoich et al. 2008 ShM Courier et al. 2008 116 Cd 76 Ge 82 Se 100 Mo 128 Te 130 Te 136 Xe 150 Nd 154 Sm July 15, 10 A. Bettini. INFN 16
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