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NeutrinoNeutrinoPhenomenologyPhenomenology

Boris Boris KayserKayserISAPPISAPP

JulyJuly,, 20112011 Part 3 Part 3

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We Must BeWe Must BeAlertAlert

ToTo SurprisesSurprises!!

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Are ThereAre ThereMoreMore Than 3 Than 3

Mass Eigenstates?Mass Eigenstates?Are ThereAre There

SterileSterile Neutrinos? Neutrinos?

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Rapid neutrino oscillation reported by theL(iquid) S(cintillator) N(eutrino) D(etector) —

The Hint From LSND

~ 1eV2 in contrast to> Δm2

sol = 7.5 x 10–5 eV2Δm2

atm = 2.3 x 10–3 eV2

At least 4 mass eigenstates.

!

P "µ #"e( ) = sin2 2$ sin2 1.27%m2 eV 2( ) L km( )E GeV( )

&

' (

)

* +

!

" µ #" e

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Such neutrinos, with no SM interactions,are called sterilesterile neutrinos.

Measured Γ(Z→νν) only 3 different flavorneutrinos made of light mass eigenstates couple to the Z.

Are There Sterile Neutrinos?At least 4 flavors.At least 4 mass eigenstates

If there are > 3 light mass eigenstates, as hinted byLSND, then the extra flavors do not couple to the Z.

In the Standard Model, flavor neutrinos that donot couple to the Z do not couple to the W either.

LSND hints at the existence of sterile neutrinos.

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Is the LSND Signal GenuineNeutrino Oscillation?The MiniBooNE experiment is

trying to confirm or refute LSND.

In MiniBooNE, both L and E are ∼ 17 timeslarger than they were in LSND,

and L/E is comparable.

MiniBooNE has recently reportedits results.

!

" µ # " e

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Direct MiniBooNE-LSND Comparison of ν Data

(Phys.Rev.Lett.105:181801, 2010)

Latest from MiniBooNE (July 25 at PANIC):Significance of νµ → νe signal reduced.

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The Reactor νe Flux SurpriseThe prediction for the un-oscillated νe fluxfrom reactors has increased by about 3%.

(Mueller et al.)

Measurements of the νe flux at (10 – 100)m from reactorcores now show a ∼ 6% disappearance.

(Mention et al.)

Disappearance at L(m)/E(MeV) ∼ 1 suggests oscillationwith Δm2 ∼ 1 eV2, like LSND and MiniBooNE.

Fits to all data with 2 extra neutrinos are improved.(Kopp et al.)

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Clearly, more information is needed.

While awaiting further news —

We will assume there areonly 3 neutrino mass eigenstates,

and no sterile neutrinos.

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Mixing,Mixing,Mass Ordering,Mass Ordering,

and CPand CP

The Central Role of θ13

Both CP violation and our ability totell whether the spectrum is normal or

inverted depend on θ13.

Determining θ13 isan important step.

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Reactor Experiments ToDetermine θ13

Looking for disappearance of reactor νe, whichhave E ~ 3 MeV, while they travel L ~ 1.5 km

is the cleanest way to determine θ13 .

P(νe Disappearance)

sin22θ13 sin2[1.27Δm2atm(eV2)L(km)/E(GeV)]

!

"

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Accelerator Experiments

Accelerator neutrino experiments can also probe θ13 .Now it is entwined with other parameters.

In addition, accelerator experiments can probewhether the mass spectrum is normal or inverted,

and look for CP violation.

All of this is done by studying νµ → νe and νµ → νe,or their inverses, while the beams travel

hundreds or thousands of kilometers.

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Generically, grand unified models (GUTS) favor —

GUTS relate the Leptons to the Quarks.

However, Majorana masses, with no quark analogues,could turn into .

The Mass Spectrum: or ?

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Recall that the matter effect raises the effective mass of νe,but lowers that of νe. Thus, it affects ν and ν oscillationdifferently, leading to:

How To Determine If TheSpectrum Is Normal Or Inverted

P(νµ → νe)

P(νµ → νe)

> 1 ;

< 1 ;

Exploit the matter effect on accelerator neutrinos.

Note fake CP

Note dependence on the mass ordering

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νe [|Uei|2] νµ[|Uµi|2] ντ [|Uτi|2]

Normal Inverted

Δm2atm

ν1

ν2

ν3

(Mass)2

Δm2sol} ν3

Δm2atm

ν1

ν2

Δm2sol}

or

The matter effect depends on whetherthe spectrum is Normal or Inverted.

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Q : Does matter still affect ν and νdifferently when ν = ν?

A : Yes!

“ν” e+ νW+

e– νW–

“ν”

Spin

Spin

The weak interactions violate parity. Neutrino – matterinteractions depend on the neutrino polarization.

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Do Neutrino InteractionsDo Neutrino InteractionsViolate Violate CP?CP?

Are we descendedAre we descendedfrom heavy neutrinos?from heavy neutrinos?

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The Challenge —A Cosmic Broken Symmetry

The universe contains baryons,but essentially no antibaryons.

Standard cosmology: Any initialbaryon – antibaryon asymmetry

would have been erased.!

nBn"

= 6 #10$10 ;nB nB

~ 0 (<10$6)

How did ?

!

nB = nB

!

nB << nB

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If quarkquark CP cannot generate the observedB–B asymmetry, can some scenario

involving leptons leptons do it?

!

nB = nB

!

nB << nBSakharov: requires CP.

The CP in the quark mixing matrix, seen in B and Kdecays, leads to much too small a B–B asymmetry.

The candidate scenario: Leptogenesis.(Fukugita, Yanagida)

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The See-Saw Mechanism

ν

NVeryheavyneutrino

Familiarlightneutrino

}{

Leptogenesis is an outgrowth of the most populartheory of why neutrinos are so light —

Yanagida;Gell-Mann, Ramond, Slansky;

Mohapatra, Senjanovic;Minkowski

Leptogenesis A Two-Step Process

N = N and ν = ν

!

m" #1mN

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In standard leptogenesis, to account for theobserved cosmic baryon – antibaryon asymmetry,

and to explain the tiny light neutrino masses,we must have —

mN ∼ 10(9–10) GeV .

This puts the heavy neutrinos N far beyond LHC range.

But these heavy neutrinos would have been madein the hot Big Bang.

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!

" Ni # !$% + H+( ) = " Ni #&$ +H0( )

By SM weak-isospin symmetry —

There are 3 × 3 = 9 independent “coupling constants”(lowest order decay amplitudes) yαi,

forming a matrix y.

Assume 3 heavy neutrinos Ni to match thenumber (3) of light lepton (α , να) families.

In the see-saw picture —

!

N " !" + H±

!

N "# + H0( )( )

andSM Higgs particle

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CP phases in the matrix y will lead to —

!

" N #!$ +H+( ) % " N #!+ +H$( )

!

" N #$ +H0( ) % " N #$ +H0& ' ( )

* +

and

This produces a universe with unequal numbersof leptons (– and ν) and antileptons (+ and ν).

In this universe the lepton number L, defined by

!

L !"( ) = L #( ) = "L !+( ) = "L # ( ) =1, is not zero.

This is Leptogenesis — Step 1

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There is now a nonzero Baryon Number.

Leptogenesis — Step 2The Standard-Model Sphaleron process,

which does not conserve Baryon Number B,or Lepton Number L, but does conserve B – L, acts.

!

Bi = 0Li " 0

!

Bf " #13Li

L f "23Li " #2Bf

SphaleronProcess

Initial statefrom N decays

Final state

There are baryons, but ∼ no antibaryons.Reasonable parameters give the observed .

!

nB n"

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Leptogenesis and CPIn Light ν Oscillation

In a convenient basis, the coupling matrixy is the only source of CP violation among the leptons.

The see-saw relation is —

!

M" = #v2UT y*MN#1y( )U

Light ν masseigenvalues

Leptonicmixing matrix

Heavy N masseigenvalues

�

The Higgs vev, a real number

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e, µ, or τ

Through U, the phases in y lead toCP in light neutrino oscillation.

Distance

EnergyNeutrino (Mass)2 splitting

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Seeking CP violation in neutrinoSeeking CP violation in neutrinooscillation is now a worldwide goal.oscillation is now a worldwide goal.

The observation of CP violation inThe observation of CP violation inneutrino oscillation would make it moreneutrino oscillation would make it moreplausible that plausible that leptogenesisleptogenesis occurred in occurred in

the early universe.the early universe.

The search will use long-baselineThe search will use long-baselineaccelerator neutrino beams to studyaccelerator neutrino beams to study

ννµµ →→ ννee and and ννµµ →→ ννee , or their inverses., or their inverses.

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Q : Can CP violation still lead toP(νµ → νe) ≠P(νµ → νe) when ν = ν?

Detector

e+“ νµ → νe ”

ν

π–

Detector

e–µ+νµ → νe

π+

ν

µ–

Compare

with

A : Certainly!

Uµi*

Uµi Uei*

Uei

!

i"

!

i"

i

i

!

exp "imi2 L 2E( )

!

exp "imi2 L 2E( )

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Accelerator ν Oscillation Probabilities( )

!

P " µ #" e[ ] $ sin 2 2%13 T1 &' sin 2%13 T2 +' sin 2%13 T3 +' 2 T4!

" # $m212 $m31

2

!

" #"m31

2 L4E

!

x "2 2GF NeE

#m312

!

T4 = cos2 "23 sin2 2"12

sin2 x#( )x2!

T1 = sin2 "23sin2 1# x( )$[ ]

1# x( )2

!

T2 = sin" sin 2#12 sin 2#23 sin$sin x$( )

xsin 1% x( )$[ ]

1% x( )

!

T3 = cos" sin 2#12 sin 2#23 cos$sin x$( )

xsin 1% x( )$[ ]

1% x( )

With , , and —

,

,

,

;

!

P " µ #" e[ ]

!

P "µ #"e[ ]= with δ → – δ and x → – x.

(Cervera et al., Freund, Akhmedov et al.)

Atmospheric

Solar

CP-odd interference

CP-even interference

m2( ) – m2( )

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What Facility Is Needed?

!

P "µ # "e( ) sin2 2$13∼

A conventional accelerator neutrino beam from π and Kdecay is mostly νµ, but has a ∼1% νe contamination.

Studying νµ → νe with a conventional beam would bedifficult if sin22θ13 < 0.01.

More Powerful Facilitiesβ Beam:

β+ emitting nuclei in a storage ring produce aflavor-pure νe beam. Look for νe → νµ.

ν Factory:

The decays µ+ → e+νeνµ of muons in a storagering, plus a magnetized detector with µ+/µ–

discrimination, yields an effectivelyflavor-pure νe beam. Look for νe → νµ.

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sin22θ13 Use

> 10–(2-3) Conventional“Superbeam”

< 10–(2-3)β Beam orν Factory