Neutrino masses and mixings and light particles, Dark Matter, - PowerPoint PPT Presentation

Neutrino masses and mixings and light particles, Dark Matter, Dark Energy, SuperSplit SuperSymmetry Alessandro Strumia, GGI, Firenze 21/9/2005

Present Two direct evidences for violation of lepton flavour. Anomaly Solar Atmospheric first hint 1968 1986 confirmed 2002 1998 evidence 12 σ 17 σ for ν e → ν µ,τ ν µ → ν τ seen by Cl,2Ga,SK,SNO,KL SK,Macro, K2K disappearance seen seen appearance seen partly seen oscillations almost seen almost seen sin 2 2 θ 0 . 85 ± 0 . 03 1 . 02 ± 0 . 04 (8 . 0 ± 0 . 3)10 − 5 eV 2 (2 . 5 ± 0 . 3)10 − 3 eV 2 ∆ m 2 sterile? 6 σ disfavoured 7 σ disfavoured

Theory

Neutrino oscillations Ultrarelativistic neutrinos with 3 × 3 mass matrix: m ν = V ∗ diag( m 1 e − 2 iβ , m 2 e − 2 iα , m 3 ) V † where V = R 23 ( θ 23 ) · R 13 ( θ 13 ) · diag (1 , e iφ , 1) · R 12 ( θ 12 ) is the neutrino mixing matrix, oscillate in normal matter as dictated by ν e ν e     H = m † √ i d ν m ν  = H where + 2 G F N e diag(1 , 0 , 0) ν µ ν µ  ,     2 E dx   ν τ ν τ Main facts can be understood in terms of 2 ν vacuum oscillations.

2 ν vacuum oscillations (Derivation as simple as the well-known e iE i t hand-waving, and correct) Oscillations from interference between states with different mass and same E Often stationary fluxes. Always energy resolution ∆ E ≫ 1 / ∆ t : � e i ∆ E · t � = 0 At the production region x ≈ 0 | ν ( x ≈ 0) � = | ν µ � = cos θ | ν 1 � + sin θ | ν 2 � At a generic x | ν ( x ) � = e ip 1 x cos θ | ν 1 � + e ip 2 x sin θ | ν 2 � . � E 2 + m 2 Since p 2 i ≃ E − m 2 i = i / 2 E at the detection region x ≈ L P ( ν µ → ν µ ) = |� ν µ | ν ( L ) �| 2 ≃ 1 − S 12 sin 2 2 θ ∆ m 2 ∆ m 2 S ij ≡ sin 2 c 3 ij L L GeV = sin 2 1 . 27 ij . eV 2 � 4 E Km E Need low E and big L to see this macroscopic quantum phenomenon

Limiting cases 1 A Oscillations with short base-line : S ≪ 1, C reduces to perturbation theory P ( ν e → ν µ ) ∝ L 2 : 10 − 1 excluded enough to fix factor-2 ambiguity! ∆ m 2 10 − 2 B 10 − 3 A C ∆ E , ∆ L averaged oscillations : � S � = 1 / 2 10 − 2 10 − 1 1 sin 2 2 θ sin 2 θ d ( π ) sin 2 θ C ν 2 sin 2 θ sin 2 θ C 2 sin 2 2 θ = 1 − 1 c (e.g. Λ ) P ( ν e → ν e ) = sin 4 θ + cos 4 θ = ν e ν e c like cos 2 θ cos 2 θ C cos 2 θ cos 2 θ C ν 1 s ( K ) The information on the phase is lost: combine probabilities, not amplitudes B The intermediate region . Coherence is lost when neutrinos with different E have too different oscillation phases φ ∼ ∆ m 2 L/E , i.e. when ∆ φ ≈ nφ > ∼ 1. With energy resolution ∆ E one can see n ∼ E/ ∆ E oscillations (zero so far).

GZK 10 10 10 9 10 8 10 7 end of visible universe Cosmic ν rays? 10 6 Energy in GeV l l 10 5 i c l l s i o c s 10 4 m o t atmos r a a l 10 3 o s pheric 100 ν factory? NuTeV 10 Minos, CNGS 1 beams K2K 0.1 supernova LSND,Karmen 0.01 solar reactors 10 − 3 10 − 4 10 − 4 0.01 1 100 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 10 22 10 24 Path − length in km Atmospheric and solar discoveries based on careful study of natural ν sources

The atmospheric anomaly

The atmospheric anomaly SK detects ν ℓ N → ℓN distinguishing µ from e . In the multi-GeV sample ϑ ℓ ∼ ϑ ν ± 10 ◦ E ℓ < ∼ E ν ∼ 3 GeV , Without oscillations N (cos ϑ zenith ) is up/down symmetric Multi � GeV 300 p... ϑ 250 SK 200 MC ν 150 µ earth 100 p... π − ϑ e 50 0 � � � � � No doubt that there is an anomaly

Atmospheric oscillations? P µµ = 1 − sin 2 2 θ atm sin 2 ∆ m 2 atm L P ee = 1 P eµ = 0 4 E ν sin 2 2 θ atm = 2 − 2 N ↑ • = 1 ± 0 . 1 i.e. θ atm ∼ 45 N ↓ atm ∼ E ν L ∼ 3 10 − 3 eV 2 • oscillatations start ‘horizontal’, L ∼ 1000 km: ∆ m 2 P µµ ( E ν ) : the anomaly disappears at high energy, as predicted by oscillatons. P µµ ( L ) : at SK σ E ν ∼ E ν : oscillation dip averaged out ( ν µ decay, decoeherence disfavoured at 4 σ ). Restricting to cleanest events, SK sees a hint L � 10000 km 1000 100 20 1.8 1 1.6 Data/Prediction (null osc.) Survival probability 1.4 0.8 1.2 1 0.6 0.8 0.4 0.6 0.4 0.2 0.2 0 0 2 3 4 1 10 10 10 10 � � � � � L/E (km/GeV)

K2K ν µ beam sent from KEK to Kamioka. Gosplan: • Energy E ν ∼ 1 . 3 GeV ∼ m p chosen such that ϑ µ ∼ 1. • Distance L = 250 km chosen such that ∆ m 2 atm L/E ν ∼ 1. ⋆ E ν reconstructed from E µ , ϑ µ since ν source known. ◦ SK broken after beam started to really work. 151 ± 12 events without oscillations ( ± fiducial volume ± forward/near ratio) 107 observed. Hint of spectral distortion. Fit consistent with SK atmospheric K2K data K2K vs SK fit 16 Events / 0.2 (GeV) 12 8 4 0 0 1 2 3 4 5 rec (GeV) E ν

The solar anomaly

The solar ν anomaly Previously based on global fits of many ingredients: ✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏✏ PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP nuclear physics ց ւ statistics ∆ m 2 , θ Cl, Ga → ← SK, SNO Solar models ր տ MSW (sun, earth) Today we can choose best and simpler pieces of data KamLAND confirms the solar anomaly with reactor ¯ ν e . SNO measures ν e and ν µ,τ solar rates at E ν ∼ 10 MeV. Simple arguments allow to extract results quantitatively.

Fit without fit Solar mass splitting Solar mixing angle Data dominated by KamLAND: Data dominated by SNO: 1.4 � P ( ν e → ν e ) � = 0 . 357 ± 0 . 030 . KamLAND data best-fit oscillation 1.2 Second oscillation dip Theory: at largest energies 1 0.8 Ratio P ( ν e → ν e ) ≃ |� ν 2 | ν e �| 2 = sin 2 θ. 0.6 0.4 Small correction due to 0.2 0 ν e (center of sun) � = ν 2 : 20 30 40 50 60 70 80 L /E (km/MeV) 0 ν e � P ( ν e → ν e ) � ≈ 1 . 15 sin 2 θ Theory: II dip of vacuum oscillations: So: ∆ m 2 = 6 π E � = (8 . 0 ± 0 . 3)10 − 5 eV 2 � tan 2 θ = 0 . 45 ± 0 . 05 � L � dip Global fits needed to check if all the rest is consistent... and for movies

KamLAND ˇ Cerenkov scintillator that detects ¯ ν e from ter- 1 restrial (japanese) reactors using ¯ ν e p → ¯ en 0.8 Survival probability 1981 ILL 0.6 1986 Goesgen • Delayed ¯ en coincidence: ∼ no bck 1994 Krasnoyarsk 1995 Bugey (geo¯ ν e background at E vis < 2 . 6 MeV) 0.4 1999 CHOOZ 2000 Palo Verde 0.2 2002 KamLAND 0 • 258 events seen, 365 ± 24 expected 1 10 10 - 2 10 - 1 10 2 10 3 Distance from reactor in km Deficit seen at 4 σ Errors will decrease to (3 ÷ 4)% 80 No oscillations Best fit 60 Events/0.425 MeV • Most reactors at L ∼ 180 km. 40 ν ≪ m p : E ¯ ν ≈ E e + m n − m p : E ¯ L / E distortion seen at 3 σ 20 0 0 2 4 6 8 E vis = E ν e + m e in MeV _

Solar ν fluxes 4 p + 2 e → 4 He + 2 ν e ( Q = 26 . 7 MeV). The sun shines as Proceeds in steps giving a complex ν spectrum 2 p → d e + ν e ( pp ) 2 p e → d ν e ( pep ) 10 14 100 % Gallium 99.75% 0.25% 10 12 80 % pp Chlorine Survival probability Flux in cm - 2 s - 1 Water d p → 3 He γ 10 10 Be pep 60 % 86% 0.00002% CNO 10 8 ( hep ) 14% 40 % night 2 3 He → α 2 p 3 He α → 7 Be γ 3 He p → α e + ν e 10 6 B day 99.9% 0.01% 20 % 10 4 hep 7 Be e → 7 Li ν e (Be) 7 Be p → 8 B γ 10 2 0 % 0.1 1 10 Energy of solar neutrinos in MeV 7 Li p → 2 α 8 B → 2 α e + ν e (B) • pp : energy < 0 . 42 MeV ∼ 2 m p − m d − m e : too small for most expreriments. Precisly known flux Φ ∼ 2 K ⊙ /Q ∼ 6 . 5 · 10 10 / cm 2 s. 2 sin 2 2 θ . Vacuum oscillations: P ( ν e → ν e ) = 1 − 1 • B : highest energy, small flux predicted to ± 20%. Adiabatic MSW resonance: P ( ν e → ν e ) = sin 2 θ .

SNO ˇ Cerenkov detector similar to SK (smaller, cleaner) with H 2 O → D 2 O CC + 1 6NC : νe → νe CC : ν e d → ppe NC : νd → νpn 8 600 Events per 500 keV P ee = 0.3 P ee = 0.35 500 6 ν e, µ , τ flux in 10 6 cm − 2 s − 1 400 SNO NC solar models 300 4 CC 200 2 NC + bkgd 100 neutrons Bkgd SNOCC SNO ES ES SK ES 0 0 5 6 7 8 9 10 11 12 13 20 → 0 0.5 1 1.5 2 2.5 3 3.5 T (MeV) eff ν e flux in 10 6 cm − 2 s − 1 • 1st phase (2001): only e detected: distribution in ϑ e gives CC. Confirms no spectral distortion. • 2nd phase (2002): D captures n giving a 6 . 25 MeV γ ( ǫ ∼ 20%): CC/NC mainly distinguished by energy spectrum • 3rd phase (2003): salt heavy water: Cl captures n giving multiple γ ’s ( ǫ ∼ 80%). CC/NC mainly distinguished by event shapee

Global fit 20 90, 99, 99.73% CL (2 dof) 15 �� m 2 � in 10 -5 eV 2 _ 10 Reactor Ν 5 Solar Ν NuFit 0 0 0.2 0.4 0.6 0.8 1 tan 2 Θ

More oscillations?

Remaining questions θ 13 : some e ? θ 23 : more µ or τ? CP: θ,α,β ? ν µ ν τ ν 3 ν e ν µ ν τ ν 2 sun ν e ν 1 atm normal mass or ν e ν µ ν τ ν 2 inverted? atm sun ν e ν 1 ν µ ν τ ν 3 m 1 : where is the 0: degenerate ν ?