Neutrino Phenomenology. Boris Kayser INSS August, 2013 Part 1

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1 Neutrino Phenomenology Boris Kayser INSS August, 2013 Part 1 1

reaction Spin: p + p "d + e + +# 1 2 1 2 1 1 2 1

2 What Are Neutrinos Good For? Energy generation in the sun starts with the reaction Spin: p + p "d + e + +# Without the neutrino, angular momentum would not be conserved. Uh, oh 2

The Neutrinos Neutrinos and photons are by far the most abundant elementary particles in the universe. There are 340 neutrinos/cc. The neutrinos are spin 1/2, electrically neutral, leptons.

3 The Neutrinos Neutrinos and photons are by far the most abundant elementary particles in the universe. There are 340 neutrinos/cc. The neutrinos are spin 1/2, electrically neutral, leptons. The only known forces they experience are the weak force and gravity. This means that their interactions with other matter have very low strength. Thus, neutrinos are difficult to detect and study. Their weak interactions are successfully described by the Standard Model. 3

4 The Neutrino Revolution (1998 ) Neutrinos have nonzero masses! Leptons mix! 4

5 These discoveries come from the observation of neutrino flavor change (neutrino oscillation). 5

6 The Physics of Neutrino Oscillation Preliminaries 6

7 The Neutrino Flavors There are three flavors of charged leptons: e, µ, τ There are three known flavors of neutrinos: ν e, ν µ, ν τ We define the neutrinos of specific flavor, ν e, ν µ, ν τ, by W boson decays: W e ν e W µ ν µ W τ ν τ 7

8 As far as we know, when interacting, a neutrino of given flavor creates only the charged lepton of the same flavor. e µ τ ν e Detector ν µ ν τ As far as we know, neither µ W Short Journey ν µ e Detector nor any other change of flavor in the ν interaction ever occurs. Notation: denotes a charged lepton. e e, µ µ, τ τ. Lederman Schartz Steinberger 8

9 Neutrino Flavor Change ( Oscillation ) If neutrinos have masses, and leptons mix, we can have µ τ π W ν µ Long Journey ν τ Detector Give a ν time to change character, and you can have for example: ν µ ν τ The last 15 years have brought us compelling evidence that such flavor changes actually occur. 9

10 Flavor Change Requires Neutrino Masses There must be some spectrum of neutrino mass eigenstates ν i : ν 3 (Mass) 2 ν 2 ν 1 Mass (ν i ) m i 10

11 Flavor Change Requires Leptonic Mixing The neutrinos ν e,µ,τ of definite flavor (W eν e or µν µ or τν τ ) must be superpositions of the mass eigenstates: ν α > = Σ U* αi ν i >. i Neutrino of flavor Neutrino of definite mass m i α = e, µ, or τ PMNS Leptonic Mixing Matrix There must be at least 3 mass eigenstates ν i, because there are 3 orthogonal neutrinos of definite flavor ν α. 11

12 This mixing is easily incorporated into the Standard Model (SM) description of the νw interaction. For this interaction, we then have Semi-weak coupling L = " g SM 2 Left-handed! L# $ % " & L# W % + & L# $ % + ( (! L# W % ) #=e,µ,' = " g 2 ( #=e,µ,' i = 1,2,3 (! L# $ % " U #i & Li W % + & Li $ % * U #i! + L# W % ) Taking mixing into account Amp( W + + "! # +$i ) = g 2 U * #i Amp ( % " i #! $ +W + ) = g 2 U $i The SM interaction conserves the Lepton Number L, defined by L ". ( ) = L! # ( ) = #L " ( ) = #L! + ( ) =1 12

13 The Meaning of U W + W + # +! " g 2 U * "i " i g 2 U "i " i! " # U = e µ " " 1 " 2 " 3 # U e1 U e2 U e3 & % ( % U µ1 U µ2 U µ3 ( $ % U "1 U " 2 U " 3 '( The e row of U: The linear combination of neutrino mass eigenstates that couples to e. The ν 1 column of U: The linear combination of charged-lepton mass eigenstates that couples to ν 1. 13

14 Slides on The Physics of Neutrino Oscillation go here. 14

15 Neutrino Flavor Change In Matter involves This raises the effective mass of ν e, and lowers that of ν e. e ν e Coherent forward scattering via this W-exchange interaction leads to an extra interaction potential energy Fermi constant V W = + 2G F N e, ν e 2G F N e, ν e W ν e e or ν e ν e 15 e W Electron density e

16 The fractional importance of matter effects on an oscillation involving a vacuum splitting Δm 2 is Interaction energy Vacuum energy The matter effect [ 2G F N e ] / [Δm 2 /2E] x. Grows with neutrino energy E Is sensitive to Sign(Δm 2 ) Reverses when ν is replaced by ν This last is a fake CP violation, but the matter effect is negligible when x << 1. 16

17 Evidence For Flavor Change Neutrinos Solar Reactor (Long-Baseline) Evidence of Flavor Change Compelling Compelling Atmospheric Accelerator (Long-Baseline) Compelling Compelling Accelerator & Reactor (Short-Baseline) Interesting 17

18 KamLAND Evidence for O s c i l l a t o r y Behavior 18

19 The KamLAND detector studies ν e produced by Japanese nuclear power reactors ~ 180 km away. For KamLAND, x Matter < Matter effects are negligible. ( ) " e P " e # " e The survival probability,, should oscillate as a function of L / E following the vacuum oscillation formula. In the two-neutrino approximation, we expect ( ) =1$ sin 2 2% sin &m 2 ev 2 P " e # " e ' ) ( *, E(GeV ) + ( ) L(km). 19

20 Survival probability P(ν e ν e ) of reactor ν e L 0 = 180 km is a flux-weighted average travel distance. P(ν e ν e ) actually oscillates! 20

21 What We Have Learned 21

22 The (Mass) 2 Spectrum ν 3 ν 2 ν 1 } Δm 2 sol (Mass) 2 Δm 2 atm or Δm 2 atm ν ν 2 } Δm 2 sol 1 ν 3 Normal Inverted Δm 2 sol = ~ 7.5 x 10 5 ev 2, Δm 2 atm = ~ 2.4 x 10 3 ev 2 22

23 The Absolute Scale of Neutrino Mass ν 3 Δm2 atm } ν Oscillation (Mass) 2 0 ν 2 1?? Δm 2 sol } Cosmology, β Decay, How far above zero is the whole pattern? Oscillation Data Δm 2 atm < Mass[Heaviest ν i ] Mass[Heaviest ν i ] > 0.04 ev 23

24 The Upper Bound From Cosmology (Jenni Adams) m(ν i ) In the Early Universe i Large Scale Structure in the universe and the CMB probe this sum of the neutrino masses, assuming that all ν i have thermalized in the early universe. m(ν i ) < 0.23 ev i Planck + WP + ( high L + BAO ( Possible tension with terrestrial experiments if one or more Δm 2 > 1 ev 2. However, in cosmology, there are parameter degeneracies. 24

25 The Upper Bound From Tritium (Liang Yang) Cosmology is wonderful, but there are known loopholes in its argument concerning neutrino mass. The absolute neutrino mass can in principle also be measured by the kinematics of β decay. Tritium decay: 3 H" 3 He + e # + $i ; i =1, 2, or 3 BR( 3 H" 3 He + e # + $ i ) % U ei 2 3 H" 3 He + e # + $i In, the bigger m i is, the smaller the maximum electron energy is. There are 3 separate thresholds in the β energy spectrum. 25

26 The β energy spectrum is modified according to ( E 0 " E) 2 2 #[ E 0 " E] $ % U ei ( E 0 " E) ( E 0 " E) 2 2 " m i # ( E0 " m i ) " E i [ ] Maximum β energy when there is no neutrino mass β energy Present experimental energy resolution is insufficient to separate the thresholds. Measurements of the spectrum bound the average neutrino mass 2 2 m " = # U ei mi Presently: m " < 2 ev i Mainz & Troitzk 26

27 Leptonic Mixing This has the consequence that Mass eigenstate ν i > = Σ U αi ν α >. e, µ, or τ α Flavor eigenstate Leptonic Mixing Matrix Flavor-α fraction of ν i = U αi 2. When a ν i interacts and produces a charged lepton, the probability that this charged lepton will be of flavor α is U αi 2. 27

28 The spectrum, showing its approximate flavor content, is sin 2 θ 13 ν 3 ν 2 ν 1 } Δm 2 sol (Mass) 2 Δm 2 atm or Δm 2 atm ν 2 ν 1 } Δm 2 sol ν 3 sin 2 θ 13 Normal Inverted ν e [ U ei 2 ] ν µ [ U µi 2 ] ν τ [ U τi 2 ] 28

29 ν 3 Measured by reactor exps. with L ~ 1 km From max. atm. mixing, " 3 # " µ +" $ 2 (Mass) 2 Δm 2 atm { { From ν µ (Up) oscillate but ν µ (Down) don t In LMA MSW, P sol (ν e ν e ) = ν e fraction of ν 2 ν 2 ν 1 }Δm 2 sol From distortion of ν e (reactor) and ν e (solar) spectra { From max. atm. mixing, ν 1 + ν 2 includes (ν µ ν τ )/ 2 ν e [ U ei 2 ] ν µ [ U µi 2 ] ν τ [ U τi 2 ] 29

30 The 3 X 3 Unitary Mixing Matrix Caution: We are assuming the mixing matrix U to be 3 x 3 and unitary. L SM = " g 2 ( #=e,µ,' i = 1,2,3 (! L# $ % U #i & Li W " % + & Li $ % U * #i! L# W + % ) (CP)(! L" # $ & U "i % Li W $ ) (CP)&1 = % Li # $ + U "i! L" W $ Phases in U will lead to CP violation, unless they are removable by redefining the leptons. 30

31 U αi describes ν i α W + U αi α W + H ν i When ν i e iϕ ν i, U αi e iϕ U αi, all α When α e iϕ α, U αi e iϕ U αi, all i Thus, one may multiply any column, or any row, of U by a complex phase factor without changing the physics. Some phases may be removed from U in this way. 31

32 When the Neutrino Mass Eigenstates Are Their Own Antiparticles When this is the case, processes that do not conserve the lepton number L #(Leptons) #(Antileptons) can occur. + Example: W + ν i W 32

33 The amplitude for any such L-violating process contains an extra factor. When we phase-redefine ν i to remove a phase from U, that phase just moves to the extra factor. It does not disappear from the physics. Hence, when ν i = ν i, U can contain extra physically-significant phases. These are called Majorana phases. 33

34 How Many Mixing Angles and CP Phases Does U Contain? Real parameters before constraints: 18 Unitarity constraints * $ U "i U#i = % "# i Each row is a vector of length unity: 3 Each two rows are orthogonal vectors: 6 Rephase the three α : 3 Rephase two ν i, if ν i ν i : 2 Total physically-significant parameters: 4 Additional (Majorana) CP phases if ν i = ν i : 2 34

35 How Many Of The Parameters Are Mixing Angles? The mixing angles are the parameters in U when it is real. U is then a three-dimensional rotation matrix. Everyone knows such a matrix is described in terms of 3 angles. Thus, U contains 3 mixing angles. Mixing angles Summary CP phases if ν i ν i CP phases if ν i = ν i

36 The Mixing Matrix U Atmospheric Reactor (L 1 km) Solar # & # c 13 0 s 13 e "i* & # c % ( % ( 12 s 12 0& % ( U = % 0 c 23 s 23 ( )% () % "s 12 c 12 0 ( $ % 0 "s 23 c 23 '( % $ "s 13 e i* 0 c ( 13 ' $ % 0 0 1' ( c ij cos θ ij s ij sin θ ij Note big mixing! θ 12 33, θ or 48-54, θ # e i+ 1 /2 0 0& % ) 0 e i+ 2 /2 ( % 0( % $ 0 0 1( ' Majorana phases No more worry! δ would lead to P(ν α ν β ) P(ν α ν β ). CP violation But note the crucial role of s 13 sin θ

37 The Majorana CP Phases The phase α i is associated with neutrino mass eigenstate ν i : U αi = U 0 αi exp(iα i /2) for all flavors α. Amp(ν α ν β ) = Σ U αi* exp( im i2 L/2E) U βi i is insensitive to the Majorana phases α i. Only the phase δ can cause CP violation in neutrino oscillation. 37

38 There Is Nothing Special About θ 13 All mixing angles must be nonzero for CP in oscillation. For example P (" µ # " e ) $ P (" µ # " e ) = 2cos% 13 sin2% 13 sin2% 12 sin2% 23 sin& ) ' sin (m 2 L, ) sin (m 2 L, ) sin (m 2 L, * 4E - * 4E - * 4E - In the factored form of U, one can put δ next to θ 12 instead of θ

Neutrino Physics. NASA Hubble Photo. Boris Kayser PASI March 14-15, 2012 Part 1

Neutrino Physics. NASA Hubble Photo. Boris Kayser PASI March 14-15, 2012 Part 1 Neutrino Physics NASA Hubble Photo Boris Kayser PASI March 14-15, 2012 Part 1 1 What Are Neutrinos Good For? Energy generation in the sun starts with the reaction Spin: p + p "d + e + +# 1 2 1 2 1 1 2