NEUTRINO PHYSICS. Neutrino Oscilla,on Theory. Fabio Bellini. Fisica delle Par,celle Elementari, Anno Accademico Lecture november 2013

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NEUTRINO PHYSICS Neutrino Oscilla,on Theory Lecture 16 11 november 2013 Fabio Bellini Fisica delle

1 NEUTRINO PHYSICS Neutrino Oscilla,on Theory Lecture november 2013 Fabio Bellini Fisica delle Par,celle Elementari, Anno Accademico

2 2 REFERENCES Review: PDG review 2013: h"p://pdg.lbl.gov/2013/reviews/rpp2012- rev- neutrino- mixing.pdf Lectures: L. Ludovici Lezioni sulle oscillazioni di neutrino : h"p:// corso.html E.Lisi Physics of Massive neutrinos : h"p:// bari- 2006/do"orato/ Interna,onal Neutrino School 2013: h"p://inss2013.ihep.ac.cn Conference: TAUP 2013: h"p:// conference.to.infn.it/taup2013.html Web page: Neutrino unbound: h"p:// Book: D. Giun,, C.W. Kim: Fundamentals of Neutrino Physics and Astrophysics, Oxford University Press B. Kayser: The physics of massive neutrinos, World Scien,fic Lecture Notes in Physics Vol.25

3 3 WHY NEUTRINO PHYSICS? Neutrino flavour: Experimental observa,on (1998- today): Neutrino flavour change Implica,ons: Leptons mix: lepton flavour not conserved Neutrinos have non zero mass: there must be some ν mass spectrum Mixing angles? Neutrino masses? Dirac or Majorana? CP viola,on in leptonic sector? Leptogenesis?

4 4 NEUTRINOS IN THE STANDARD MODEL Fermions described by a Dirac field Ψ Standard Model(MS): chiral theory SU(2) L X U(1) Y Chirality projector P L (R) =(1±γ 5 )/2, P L (R) Ψ=Ψ L (R) see lecture n.12 Ψ L and Ψ R have different proper,es under SU(2) L Ψ R SU(2) singlet doesn t couple with W,Z bosons Ψ L SU(2) doublet _ Mass term (aqer EW symmetry breaking): mψ L Ψ R + h.c. mix Ψ L and Ψ R Minimal Standard Model(MMS): neutrinos are massless! there are only 3 neutrinos lighter than M Z /2 Neutrino interac,on: Charged current: Neutral current: L W = L Z = g 2 =e,µ, ( L L W + L L W + ) g cos W =e,µ, L L Z

5 5 CHIRALITY AND HELICITY Chirality (Χ) Acts on Dirac Spinor Space Projector: P L (R) =(1±γ 5 )/2 Helicity (H) Acts on physical space: spin projec,on on momentum direc,on H=σ p/ p Projector: Π L (R) =(1±σ p/ p )/2 Lorentz invariant! Interac,ons don t depend on reference frame!! Not conserved: mass term mixes right and leq component Not Lorentz invariant for massive par,cle, momentum reversed if boost with β>β m =p/e Conserved If m=0 Helicity and Chirality coincide (not the case for neutrinos!): X=H+O(m/E) Nature has related the Weak Force to chirality eigenstates

6 6 MASS AND MIXING Higgs mechanism (like in the quark sector): Introduce Dirac Mass Term and diagonalize the mass matrix Unitary matrix appears in Interac,on Lagrangian Neutral current not affected: GIM mechanism see lecture n.12 L W = g 2 =e,µ, i=1,2,3 ( L U i Li W + Li U i L W + ) Amp(W + l α +v i )=g/ 2U αi * Orthogonality: 3 flavours at least 3 mass eigenstates = U i i i = U i i=1,2,3 =e,µ, Flavour frac,on of ν i > = U αi 2 _ ν field: creates ν and destroys ν This is why U* appear when ket ν used

7 7 NEUTRINO MIXING MATRIX If 3 mass eingentates U PMNS = c 23 s 23 0 s 23 c 23 c 13 0 s 13 e i s 13 e i 0 c 13 c 12 s 12 0 s 12 c c 12 c 13 c 13 s 12 s 13 e i c 23 s 12 c 12 s 13 s 23 e i c 12 c 23 s 12 s 13 s 23 e i c 13 s 23 s 23 s 12 c 12 c 23 s 13 e i c 12 s 23 c 23 s 12 s 13 e i c 13 c 23 = U = U e1 U e2 U e3 U µ1 U µ2 U µ3 = U 1 U 2 U ± ± ± ± ± ± ± ± ± 0.06 phase and signs neglected e row: linear combina,on of neutrino mass eigenstates that couples to e ν 1 column: linear combina,on of neutrino flavour eigenstates that couples to ν 1 Compare with the CKM Matrix: V CKM = = i = i=1,2,3 =e,µ, U i i U i

8 8 NOT THE ONLY DIFFERENCE Why neutrino masses are so small?!"##%3$85 Quarks and charged leptons are produced in ordinary processes as mass eigenstates One change of basis:mass flavour; decay rates U ij Neutrinos are produced and detected as flavour eigenstates Two changes of basis:flavour mass flavour; MQ interference Neutrinos mass difference very,ny Interference on Macroscopic scale We can produce a ν μ but not a ν 3 For this reason unitary triangles, useful because experiments can measure both sides and angles, have no pracncal use in lepton flavour mixing Neutrino OscillaNon theory

9 Sh. Rahatlou 9 MQ RECAP

10 CONSISTENT USE OF U* AND U F. Bellini from E.Lisi Physics of Massive neutrinos 10

11 CONSISTENT USE OF U* AND U F. Bellini from E.Lisi Physics of Massive neutrinos 11

12 HAMILTONIAN AND CHANGE OF BASIS same on mass basis F. Bellini from E.Lisi Physics of Massive neutrinos 12

13 EVOLUTION OPERATOR F. Bellini from E.Lisi Physics of Massive neutrinos 13

14 EVOLUTION OPERATOR F. Bellini from E.Lisi Physics of Massive neutrinos 14

15 2 NEUTRINOS CASE F. Bellini from E.Lisi Physics of Massive neutrinos 15

16 2 SLIT ANALOGY P [ ]=sin 2 (2 )sin 2 ( m 2 L/4E) Length scales L:Baseline Oscilla,on length: λ=4πe/δm 2 Franges not visibile if λ<l or large experimental smearing <sin 2 (Δm 2 L/4E)> 0.5 F. Bellini from E.Lisi Physics of Massive neutrinos 16

17 17 LOSS OF COHERENCE Neutrino oscilla,on is due to coherent interference Coherence is lost if: Poor L/E resolunon prevents you to resolve oscilla,on Wake packets don t overlap: relevant for ν only in far supernovae (important for quark) If neutrino mass is measured with enough precision to disnnguish mass ν eigenvalues Δp< p k - p j Heisenberg principle: Δx 1/Δp 2E/ m 2 k- m 2 j L osc L> L osc P i = U αi 2 independent of neutrino path length This explains why in quark sector you measure mixing but not oscilla,on Charged leptons do not oscillate, flavour defined by its mass Decay rates do not oscillate: different final states Sum Probabili,es not Amplitudes dn dt ( 3 H" 3 He + e # + $ ; t ) = % dn + & ' dt i ( 3 H" 3 He + e # + $i ; t) ( ) * 3 H 3 He +e - _ +ν 1 3 He +e - _ +ν 2 3 He +e - _ +ν 3

18 18 2 NEUTRINOS CASE Two flavour eigenstates and two mass eigenstates U = 1 2 e cos sin µ sin cos ν e = ν 1 cosϑ+ν 2 sinϑ ν μ = - ν 1 sinϑ+ν 2 cosϑ P [ ]=sin 2 (2 )sin 2 ( m 2 L/4E) P [ ]=1 sin 2 (2 )sin 2 ( m 2 L/4E) - 1 angle θ, 1 Δm 2 - no dis,nc,on between θ π/2- θ, Δm 2 - Δm 2 :;,&/ 1 1θ,&/ 1 1θ 6"&3# 3%,,&3#

SENSITIVITY TO OSCILLATION In real life: produc,on and detec,on region are not point, neutrinos not monochroma,c, experimental energy resolu,on not perfect loss of coherence oscilla,on washed out P [

19 SENSITIVITY TO OSCILLATION In real life: produc,on and detec,on region are not point, neutrinos not monochroma,c, experimental energy resolu,on not perfect loss of coherence oscilla,on washed out P [ ]=sin 2 (2 )sin 2 ( m 2 L/4E) Δm 2 L/4πE<<1 (short baseline) oscilla,on doesn t evolve Δm 2 L/4πE 1 max sensi,vity can observe n ΔE/E oscilla,ons Δm 2 L/4πE>>1 (averaged regime) phase lost due to poor L/E resolu,on sin 2 (2θ)=1 σe=e/10 ν e sin 2 θ cos 2 θ ν 2 ν 1 sin 2 θ cos 2 θ ν e F. Bellini = L/L Osc Σ Probabili,es rather than Amplitudes P(ν α ν α )=sin 4 (θ)+cos 4 (θ)=1-0.5 sin 2 (2θ) P(ν α ν β )=0.5 sin 2 (2θ) 19

20 SENSITIVITY PLOT Appearance experiment: search for ν β in a flux Φ of v α P [ ]=sin 2 (2 )sin 2 ( m 2 L/4E) Null result: P [ ] <P UP ( ) P UP PosiNve results: inclusion curves C C: Δm 2 L/4πE>>1; P(ν α ν β )=0.5 sin 2 (2θ)<P UP Φ big Flux to have small angle A: Δm 2 L/4πE<<1 Δm B 2 E 1.27 L B: (P UP, ) excluded A P(ν α ν β )=sin 2 (2θ)(Δm 2 L/4E) 2 <P UP Φ m 2 min P UP 1.27 L 2 E 2 F. Bellini big L (small Φ), small E sin 2 2θ 20

21 21 OSCILLATION: GENERAL CASE P [ ] = Amp[ ] 2 = 4 Re(U i U i U j U j )sin 2 ( m 2 ijl/4e)+2 Im(U i U i U j U j )sin( m 2 ijl/2e) i>j i>j Comments: Valid for any number of flavours and equal number of mass eigenstates: U unitary If no mixing P(ν α ν β )=δ αβ ; flavour change mixing If degenerate masses P(ν α ν β )=δ αβ ; flavour change no degenerate m ν 0 P(ν α ν β ) depends only on squared- mass splibng no absolute mass value Neutrino flavour change does not change the total flux (if no sterile νs): β P(ν α ν β )=1

22 22 OSCILLATION: GENERAL CASE P [ ] = Amp[ ] 2 = 4 Re(U i U i U j U j )sin 2 ( m 2 ijl/4e)+2 Im(U i U i U j U j )sin( m 2 ijl/2e) i>j i>j Comments: Flavour change in vacuum oscillates with L/E: macroscopic quantum interference phenomena Human units c 3 m 2 ij L 4E =1.27 m2 ij ev 2 L Km GeV E L osc = 4 E m 2 =2.48 E GeV ev 2 m 2 ij Km sin 2 (Δm 2 ijl/e) appreciable when its argument is O(1): an experiment L/E is sensi,ve to Δm 2 ij L/E E 1GeV, L 10 4 km, Δm 2 ij 10-4 ev 2 E 1MeV, L 100 km, Δm 2 ij 10-5 ev 2 Flavour change can be detected in two modes: Appearance: see ν β α in a ν α beam Disappearance: see some of known ν α disappear in ν α beam

23 23 ANTI-NEUTRINOS VACUUM OSCILLATION 4 Re(U i U i U j U j )sin 2 ( m 2 ijl/4e)+2 Im(U i U i U j U j )sin( m 2 ijl/2e) i>j i>j If CPT holds: P [ ] =P [ ] P [ ; U] =P [ ; U ] P [,U]=P [ ; U ] Imaginary term changes sign for an,- neutrinos: complex U CP violanon No CP violanon in disappearance experiment Δ αβ =P(ν α ν β ) - P(ν α ν β ) CPT: P(ν α ν β )= P(ν β ν α ) Δ αβ = - Δ βα Δ αα =0 Need at least 3 flavours If only two flavours αβ:p(ν α ν β ) =1 - P(ν α ν α )=CPT= 1 - P(ν α ν α )= P(ν α ν β )

24 MASS SPECTRUM F. Bellini from E.Lisi Physics of Massive neutrinos 24

25 25 SPECIAL CASE II: MASS SCALE DOMINANCE 3 flavours 6 parameters: 3 angles, 1 phase 2 independent Δm 2 (Δm 2 31 = Δm Δm 2 23) 3 flavours + one mass scale dominance P [ ] 4 U 3 U 3 2 sin 2 ( m 2 L/4E) P [ ] 1 4 U 3 2 (1 U 3 2 )sin 2 ( m 2 L/4E) Only 3 parameters: Δm 2,ϑ 23, ϑ 13, U α3 =sin(ϑ 13 ), U β3 =cos(ϑ 13 ) sin(ϑ 23 ) Invariant for Δm 2 - Δm 2 (no hierarchy) and U U* (no CP viola,on) Experiment with Δm 2 L/E=O(1) sensi,ve to U α3 measure flavour content of ν 3 At first order in δm 2 : Δm 2 Δm 2 + δm 2 ( U α1 2 - U α2 2 )/2( U α1 2 + U α2 2 ) not invariant for Δm 2 - Δm 2 but suppressed: P ee U e3 2 few% P μμ 1/180

26 26 νe OSCILLATION ν e ν μ Short Baseline ν τ ν e Long Baseline ν τ ν μ

27 27 νμ OSCILLATION ντ ν e ν μ Short Baseline ν μ ν τ Long Baseline ν e

28 28 ντ OSCILLATION ν τ ν e ν μ Short Baseline ν τ ν μ Long Baseline ν e

The Physics of Neutrino Oscillation. Boris Kayser INSS August, 2013

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