Phenomenology 2010 Symposium University of Wisconsin, Madison 10-12 - PowerPoint PPT Presentation

Phenomenology 2010 Symposium University of Wisconsin, Madison 10-12 May, 2010 Marek Zralek University of Silesia 5/11/10

Outline Introduc.on Neutrino Oscilla.on in the Standard Model Neutrino oscilla.on beyond the SM Conclusions

1) Introduc.on In frame of the Standard Model (SM) only left handed neutrinos (right-handed antineutrinos) are produce and detected, the neutrino flavour states are well defined, they are orthogonal, phenomenon of neutrino oscillation is well described, At higher energies (e.g. at LHC), beyond the SM can appears and can be tested (e.g. supersymmetry), in such models, standard neutrino oscillation theory does not work, Generally there are many models with Non Standard neutrino Interaction (NSI) where the existing theory of oscillation can not be applied, Here we propose the general approach for neutrino oscillation, valid for any NSI where, neutrinos in positive and negative helicity states can be produced, and neutrino flavour states are only approximately defined, We found the necessary and sufficient conditions for the NSI, under which the standard neutrino oscillation theory is correct.

Different processes for neutrino production π + → µ + + ν µ π − → µ − + ν µ  Beta beams Average E cms = 1.937 MeV n → p + e − + ν e 6 Li e − ν e 6 He → 3 2 p → n + e + + ν e 18 F e + ν e 18 Ne → 10 9 Average E cms = 1.86 MeV µ − → e − + ν µ + ν e  Neutrino factories µ + → e + + ν µ + ν e

1) Water Cerenkov Detector Processes for 2) Liquid Argon Detector 3) Iron Calorimeter neutrino detection 4) Emulsion Detector ν e + n → p + e − Z + 1 + e − ν e + A J Z → A J ' A J Z = 12 C 6 , 20 Ne 10 , 37 Cl 17 , 71 Ga 31 , 100 Mo 42 , 127 I 53 Z − 1 + e + ν e + A J Z → A J ' 18 , 71 Ge 32 , 100 Tc 43 , 115 Sn 50 , 127 Xe 54 Z = 37 Ar A J ' ν e + p → n + e + ν α + e − → ν α + e − ν α + e − → ν α + e − ν α + d → p + n + ν α ν α + d → p + p + e −

Neutrino oscilla.on in the SM

For production and detection processes - charge current − + h . c e ∑ γ µ (1 − γ 5 )U α i ν i W µ L CC = l α 2 2 sin θ W α , i Relativistic (anti)neutrinos are produced in pure Quantum Mechanical flavour state ∑ ∑ ν α ↓ = ν i ↓ ν β ↑ = ν i ↑ * U U β i α i i i Neutrinos always with Antineutrinos always Z. Maki, M. Nakagawa, S. Sakata, negative helicity with positive helicity Prog.Theor.Phys. 28(1962)870

Neutrino propagation in the vacuum or in a matter – - neutral current e ∑ L NC = ν i γ µ (1 − γ 5 ) ν i Z µ 4sin θ W cos θ W i = 1,2,3 ∑ ∑ ν α ↓ = ν i ↓ U * ν β ↓ = ν i ↓ U * No spin flip α i β i i i D P ∑ ∑ ν α ↑ = ν i ↑ ν β ↑ = ν i ↑ No spin flip U β i U α i i i

Neutrinos oscillation rate in a detector is described by the factorized formula: ν α → ν β L ν α ν β P D ν β ν α Δ N D ( L , E ) = j α ( E ) P α → β ( L , E ) σ β ( E ) N D Probability of the α to β Number of the β Flux of Detection Number the neutrino neutrinos with cross of active initial conversion energy E, which section for neutrinos scattering β neutrinos reach detector of the centres in a unit time α type in a detector Oscillation rate is the same for Dirac and Majorana neutrinos

There are models which predict NonStandard neutrino Interaction (NSI) in the weak scale range, which can modify  neutrino production process,  oscillation inside matter, and  detection process  Models which try to resolve problem of neutrino mass e.g. see‐saw  Charged Higgs,  Right handed currents,  Supersymmetric models. What we should change to describe future experiment with NSI of neutrinos??

Oscilla.on beyond the SM

For the neutrino production (detection - for low energy) dimensional six operators - four-fermions effective Hamiltonian e.g for muon decay (in neutrino factory) 3 H = 4 G F ∑ ∑ δ ) i , k ( l α Γ δ ν i , ε )( ν k , η Γ δ l β ) + h . c . ( g ε , η 2 δ = S , V , T i , k = 1 ε , η = L , R First suggestion that a result of neutrino oscillation depends on three ingredients, on the production process, on the propagation inside matter and on their detection, appeared in 1995 Y. Grossman, Phys.Lett.B359,141(1995)

ν i l α Neutrio masses are uknown- but are very small, experiments cannot obserwed neutrinos as mass eigenstates. But the mass ν i CC basis is well define. Such states are process independent. ν α P l α Neutrinos are produced by charged current interaction. This process defines neutrino P flavour. Such states are process dependent: P = ∑ CC ν α ν i P U α , i ν β D i l β Detection process measures different state – the detection flavour neutrino states: D D = ∑ ν β ν i D U β , i i

2 ∝ ν i ; f P H P l α ; i P Production and detection 2 P U α , i flavour mixing matrices are constucted from the 2 ∝ l β ; f D H D ν i ; i D 2 production and detection D U β , i interaction Hamiltonians. ν β The probability of finding neutrinos in a states in D ν β D the original beam at the time t is given by P e − iHt ν α 2 α → β ( t ) = ν β D P Two types of such approaches can be found in the literature: NSI and internal or external wave packets: Kayser(81),Giunti,Kim,Lee(91),Rich(93). Field theory and of mass shell neutrino Grimus and Stckinger(96), MZ(98), propagation: Cardall(00), Giunti(02), Beuthe(03).

In these approaches, as in the Standard Model: 1) Production and detection states are pure Quantum Mechanical states ν β ν α D P 2) It is possible to define flavour change probability P e − iHt ν α 2 α → β ( t ) = ν β D P which factorize: Δ N D ( L ≈ t , E ) = j α ( E ) P α → β ( t ) σ β ( E ) N D

In the proper approach - neutrino states are calculated in the standard way State of the neutrinos produced in the process A → B + l α + ν i is described by the density matrix (if initial particle (A) is not polarized and polarizations of the final particles (B, l) are not measured): λ , i ; µ , k = 1 ∑ α ( λ A ; λ B , λ l ∫ ρ α , λ ) f k α * ( λ A ; λ B , λ l , µ ) f i N α α ( λ A ; λ B , λ l , λ ) where is the amplitude for the f i A → B + l α + ν i production process .

We need the density matrix in the laboratory (detector) frame = Lorentz boost + time evolution Calculated in the CM of decaying particle: Beta beam Accelerator neutrinos Neutrino factory α ( L = 0) ≅ ρ CM α ρ LAB M.Ochman,R.Szafron and MZ, arXiv:0707.4089 Neutrino propagation in the vacuum or in a matter H – vacuum or matter Hamiltonian

Any detection process: A β ( Ω ) ≡ A k β ( λ k , λ C ; λ β , λ D ; Ω ) p f 1 1 ∑ ∫ A β ( Ω α ( L = T ) A β * ( Ω ) σ α → β ( L , E ) = d Ω ) ρ LAB 64 π 2 s 2 s C + 1 p i spins There is no factorization for the detection rate

For muon decay For Dirac neutrinos 3 ν e = ν ( λ = + 1) ∑ ν e = ν i U e i Pure i = 1 In the SM dis.ngishable QM 3 ∑ ν µ = ν i ν µ = ν ( λ = − 1) * U µ i STATES i = 1 ν e ν ( λ = + 1) Beyond the SM Mixed QM STATES ν µ ν ( λ = − 1) Density matrix For Majorana neutrinos required In the SM ν e ν ( λ = + 1) or QM mixed STATE ν µ ν ( λ = − 1) beyond ρ α − 1, i ; − 1, k , ρ α + 1, i ; + 1, k , ρ α − 1, i ; + 1, k , ρ α + 1, i ; − 1, k Non–standard description

If only positive(negative) helicity neutrinos(antineutrinos) are produced -- Theorem: The necessary and sufficient condition for pure initial state of produced neutrinos with negative helicities is the factorization for spin and mass production amplitudes α ≡ g µ α ( λ A ; λ B , λ l , λ = − 1) = g α ( λ A ; λ B , λ l , λ = − 1) ∗ h i α h i α f i If we introduce the shortcut notation µ = ( λ A ; λ B , λ l ) Then: α ≡ g µ α ( µ ) = g α ( µ , λ = − 1) ∗ h i α h i α f i

Then the density matrix is given by: α h k β * α = h i ρ α ( i , λ = − 1; k , µ = − 1) ≡ ρ i , k α χ k α * = χ i ∑ α 2 h i i where α α = h i χ i ∑ α 2 h i i which is equivalent to the pure QM state : ∑ ∑ ν α = χ i α ν i ν α = ν i * U α i i i ν SM ∑ ν α ν β = χ i α χ i β * ≠ δ αβ ( = 1 for α = β ) α = U α i i χ i * which are normalized but not necessarily orthogonal

Factorization for the final oscillation rate σ α → β ( L , E ) = p f 1 1 ∑ ∫ d Ω β ( λ , λ C , λ l , λ D ; Ω ) ρ α ( i , λ ; k , λ ; L , E ) A k β * ( λ , λ C , λ l , λ D ; Ω ) A i 64 π 2 s f + 1 2 s p i i , k , λ , λ C , λ l , λ D The density matrix after oscillation − δ m i , k 2 ρ α ( i , λ = − 1; k , µ = − 1; L , E ) = ρ i , k α ( L , E ) e 2 E L If the detection amplitudes factorize β ( λ = − 1, λ C , λ l , λ D ; Ω ) = e η β ( θ , ϕ ) ∗ k i β A i Then the final cross section factorize σ α → β ( L , E ) = − δ m i , k 2 p f β ∗ k i β * ∗ k k 1 1 ∑ ∫ α e 2 E L )( e η d Ω ( e η β )( ρ i , k β * ) = 32 π s 2 s f + 1 p i i , k , η = P α → β ( L , E ) σ β ( E )