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 1 2 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. 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
The Neutrino Revolution (1998 ) Neutrinos have nonzero masses! Leptons mix! Neutrino masses suggest, via the See-Saw picture, new physics far above the LHC energy scale. 4
The discovery of neutrino masses and leptonic mixing has come from the observation of neutrino flavor change (neutrino oscillation). 5
The Physics of Neutrino Oscillation Preliminaries 6
The Neutrino Flavors We define the three known flavors of neutrinos, ν e, ν µ, ν τ, by W boson decays: e µ τ W ν e W ν µ W ν τ As far as we know, neither W µ Short Journey ν µ e Detector nor any other change of flavor in the ν interaction ever occurs. With α = e, µ, τ, ν α makes only α ( e e, µ µ, τ τ). 7
Neutrino Flavor Change If neutrinos have masses, and leptons mix, we can have µ τ π W ν µ Long Journey ν τ Detector Give ν time to change character ν µ ν τ The last 13 years have brought us compelling evidence that such flavor changes actually occur. 8
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 9
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. 10
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 SM = " g 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 If neutrino masses are described by an extension of the SM, and there are no new leptons, U is unitary. 11
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. 12
Slides on The Physics of Neutrino Oscillation go here. 13
Suppose an experiment cannot see the small splitting (Mass) 2 "m 2 Invisible if Δm 2 L/E = O(1) Then ( ) = sin 2 2' #% sin 2 + 1.27(m 2 ev 2 ( ) ( ) P " # $" %&# Parameters that are 1 ( ) =1% sin 2 2& ## sin 2 * 1.27'm 2 ev 2 ( ) ( ) P " # $" # ) * ( ) ( ) ( ) ( ) L km E GeV ( ) ( ) ( ) L km E GeV sin 2 2" ## = sin 2 2" #$1 + sin 2 2" #$2 No CP,. - + -, 14
Suppose the ν 3 component of ν e may be neglected A neutrino born as ν e will oscillate between ν e and one other effective flavor, ν x, which is the combination of ν 1 and ν 2 that is orthogonal to ν e. ν x is a linear combination of ν µ and ν τ. ( ) = sin 2 2$ sin 2 ( 1.27%m 2 ev 2 ( ) ( ) P " e #" x & ' ( ) ( ) ( ) L km E GeV ) + * ( ) =1$ sin 2 2% sin 2 ) 1.27&m 2 ev 2 ( ) ( ) P " e #" e Equal ' ( No CP ( ) ( ) ( ) L km E GeV *, + 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 16 e W Electron density e
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. 17
What We Have Learned Renata Zukanovich Funchal 18
The (Mass) 2 Spectrum ν 3 ν 2 ν 1 (Mass) 2 or ν 2 ν 1 ν 3 Normal Inverted Δm 2 ~ 21 = 7.4 x 10 5 ev 2, Δm 2 32 = ~ 2.3 x 10 3 ev 2 19
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! 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 % ) (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. 20
U αi describes W + ν i α U αi α W + H ν i When ν i e iϕ ν i, U αi e iϕ U αi When α e iϕ α, U αi e iϕ U αi 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. 21
Exception: If the neutrino mass eigenstates are their own antiparticles, then Charge conjugate ν i = ν i c = Cν i T One is no longer free to phase-redefine ν i without consequences. U can contain additional CP-violating phases. 22
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 23
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 3 1 3 24
The Mixing Matrix U # 1 0 0 & # c 13 0 s 13 e "i* & # c % ( % ( 12 s 12 0& % ( U = % 0 c 23 s 23 ( )% 0 1 0 () % "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 # e i+ 1 /2 0 0& % ) 0 e i+ 2 /2 ( % 0( % $ 0 0 1( ' θ 12 34, θ 23 39-51, Majorana CP phases sin 2 2θ 0.023 < sin 2 13 = 0.092 ± 0.016 (stat) 2θ 13 ± < 0.005 0.17 (syst) (Daya Bay) δ and θ 13 0 would lead to P(ν α ν β ) P(ν α ν β ). CP violation 25
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, ) + 31. sin (m 2 L, ) + 32. sin (m 2 L, + 21. * 4E - * 4E - * 4E - In the factored form of U, one can put δ next to θ 12 instead of θ 13. 26