Theoretical Neutrino Physics

Hitoshi Murayama (Berkeley)

EPS 2003 @ Aachen

July 22, 2003

EPS2003 Hitoshi Murayama 2

Milind Diwan

• “Neutrino physics is so simple. There are no hadronic corrections. We don’t need theorists.”

Why You Need Theoristsin Neutrino Physics

Hitoshi Murayama (Berkeley)

EPS 2003 @ Aachen

July 22, 2003

EPS2003 Hitoshi Murayama 4

Outline

• A Little Historical Perspective• Interpretation of Data & Seven Questions

– Solar Neutrino– Interpretation without LSND– Interpretation with LSND– Nature of neutrino mass

• Models of Flavor• Conclusions

A Little Historical Perspective

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Rare Effects from High-Energies

• Effects of physics beyond the SM as effective operators

• Can be classified systematically (Weinberg)

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Unique Role of Neutrino Mass

• Lowest order effect of physics at short distances

• Tiny effect (m/E)2~(eV/GeV)2=10–18!

• Interferometry (i.e., Michaelson-Morley)!– Need coherent source

– Need interference (i.e., large mixing angles)

– Need long baseline

Nature was kind to provide all of them!

• “neutrino interferometry” (a.k.a. neutrino oscillation) a unique tool to study physics at very high scales

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Grand Unification

• electromagnetic, weak, and strong forces have very different strengths

• But their strengths become the same at 1016 GeV if supersymmetry

• A natural candidate energy scale ~1016GeV

m~0.003eV• m~(m2

atm)1/2~0.03eV• m~(m2

LMA)1/2~0.007eV

Neutrino mass may be probing unification!

Interpretation of DataSeven Questions

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What we learned since Budapest

• Atmospheric s are lost. P=4.2 10–26 (SK, Hayato)

• converted most likely to (>99%CL)• Solar e is converted to either or (>5) (SNO,

Poon)

• Reactor anti-e are lost (99.95%CL) (KamLAND, Lesko)

• Only the LMA solution left for solar neutrinos• Tiny neutrino mass: the first evidence for

incompleteness of Minimal Standard Model

Solar Neutrino Problem Finally Solved After 35 Years!

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SNO Result

• Only e produced in the Sun• Wrong Neutrinos are

coming from the Sun!• Somehow some of e were

converted to on their way from the Sun’s core to the detector neutrino flavor conversion!

€

ΦCC =1.76 ± 0.05 ± 0.09 ⋅106 cm−2 sec−1

€

ΦNC = 5.09 −0.43+0.44 −0.43

+0.46 ⋅106 cm−2 sec−1

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KamLAND result

• First terrestrial expt relevant to solar neutrino problem

Dec 2002Expected #events: 86.8±5.6

Background #events: 0.95±0.99Observed #events: 54

No oscillation hypothesisExcluded at 99.95%

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No other solution than oscillation

• Neutrino decay– Wrong energy dependence

• Spin-resonant flip– Relies on a large solar magnetic field

• New flavor-changing neutral current– Relies on a high solar matter density

• Violation of the equivalence principle– Relies on the strong solar gravitational potential

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March 2002

April 2002 with SNO

Dec 2002with KamLAND

Progress in 2002 on the Solar Neutrino Problem

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Solar Neutrino Spectrum

pp7Be

8B

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We don’t get enough

We need survival probabilities of

8B: ~1/3

7Be: <1/3

pp: ~2/3

Can we get three numbers correctly with two parameters?

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Matter Effect

• CC interaction in the presence of non-relativistic electron

€

L = −GF

2e γμ (1−γ5 )ν eν eγ

μ (1−γ5 )e

= −GF

2e γμ (1−γ5 )eν eγ

μ (1−γ5 )ν e

= − 2GFneν eγ0ν e

• Neutrino Hamiltonian

€

H = common

+Δm2

4E

−cos2θ sin 2θ

sin 2θ cos2θ

⎛

⎝ ⎜

⎞

⎠ ⎟

+ 2GFne1 0

0 0

⎛

⎝ ⎜

⎞

⎠ ⎟

Electron neutrino higher energy in the Sun

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Adiabatic

• Use “instantaneous” eigenstates + and –

• For the LMA region, the dynamics is adiabatic: there is no hopping between states

20

Solar Neutrino Astrophysics

• Davis and Bahcall started solar neutrino work because they wanted to probe physics of the sun

• Finally one can fit all solar neutrino data together with KamLAND to measure all major components: pp, 7Be, 8B (Bahcall, Peña-Garay)

Solar luminosity confirmed

• Possible concern: density perturbation (Reggiani)

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Loose Ends

• Energy dependence in the solar neutrino survival probability not fully demonstrated– pp, 7Be solar neutrino experiments

• Nobody has seen “oscillation,” i.e., the survival probability dips and comes back up– Atmospheric: MINOS– Solar/reactor: continued KamLAND

• Evidence for “appearance” in atmos still not strong enough (99%CL)– OPERA, ICARUS

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Low-Energy Solar Neutrinos

• Solar neutrino data suggest energy-dependent survival probability tests MSW effect

12

Helps interpretation of CP violation, double beta decay data

7%1%

20%

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Verify Oscillation

• Even atmospheric neutrino data do not show “oscillation” yet MINOS, J-PARC

m223, 23, mass

hierarchy and 13

• KamLAND data is consistent with overall suppression continued running

m212

Interpretation Without LSND

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Three-generation Framework

• Standard parameterization of MNS matrix for 3 generations

€

UMNS =

Ue1 Ue2 Ue3

Uμ 1 Uμ 2 Uμ 3

Uτ 1 Uτ 2 Uτ 3

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

=

c12 s12

−s12 c12

1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

c13 s13e−iδ

1

−s13eiδ c13

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

1

c23 s23

−s23 c23

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

atmospheric???solar

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Three-generation

• Solar, reactor, atmospheric and K2K data easily accommodated within three generations

• sin2223 near maximal m2

atm ~ 310–3eV2

• sin2212 large m2

solar ~ 710–5eV2

• sin2213=|Ue3|2< 0.05 from CHOOZ, Palo Verde

• Because of small sin2213, solar (reactor) & atmospheric oscillations almost decouple Gonzalez-Garcia, Peña-Garay

2/dof=136/173

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Seven Questions

• Dirac or Majorana? • Absolute mass scale?

• How small is 13?

• CP Violation?• Mass hierarchy?• Verify Oscillation?• LSND? Sterile neutrino(s)? CPT violation?

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Seven Questions

• Dirac or Majorana? • Absolute mass scale?

• How small is 13?

• CP Violation?• Mass hierarchy?• Verify Oscillation?• LSND? Sterile neutrino(s)? CPT violation?

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Now that LMA is confirmed...

• Dream case for neutrino oscillation physics!• m2

solar within reach of long-baseline expts• Even CP violation may be probable

– neutrino superbeam– muon-storage ring neutrino factory

• Possible only if:– m12

2, s12 large enough (LMA)– 13 large enough

€

P(ν μ → ν e ) − P(ν μ → ν e ) = −16s12c12s13c132 s23c23

sinδ sinΔm12

2

4EL

⎛

⎝ ⎜

⎞

⎠ ⎟sin

Δm132

4EL

⎛

⎝ ⎜

⎞

⎠ ⎟sin

Δm232

4EL

⎛

⎝ ⎜

⎞

⎠ ⎟

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13 decides the future

• The value of 13 crucial for the future of neutrino oscillation physics

• Determines the required facility/parameters/baseline/energy

• Two paths to determine 13

– Long-baseline accelerator neutrino oscillation– Reactor neutrino experiment with two detectors

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Shootout (Lindner)

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Seven Questions

• Dirac or Majorana? • Absolute mass scale?

• How small is 13?

• CP Violation?• Mass hierarchy?• Verify Oscillation?• LSND? Sterile neutrino(s)? CPT violation?

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Intepretation With LSND

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ν μ

ν e?

ν ep→ e+n

μ+→ e+νeν μ

p→ π +

π+→ μ+νμ

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3.3 Signal

• Excess positron events over calculated BG

P(ν μ → ν e)

=(0.264±0.067±0.045)%

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Sterile Neutrino

• LSND, atmospheric and solar neutrino oscillation signalsm2

LSND ~ eV2

m2atm ~ 310–3eV2

m2solar < 10–3eV2

Can’t be accommodated with 3 neutrinos

Need a sterile neutrino

New type of neutrino with no weak interaction

• 3+1 or 2+2 spectrum?

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Sterile Neutrino disfavored

• 2+2 spectrum: past fits preferred– Atmospheric mostly

– Solar mostly ea (or vice versa)

– Now solar sterile getting tight due to SNO

Disfavored 1.6 10–6 (Maltoni et al)

• 3+1 spectrum: sin22LSND=4|U4e|2|U4|2

– |U4|2 can’t be big because of CDHS, SK U/D

– |U4e|2 can’t be big because of Bugey

Disfavored 5.6 10–3 (Maltoni et al)

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PLSND<0.10% PLSND< 0.20%

P(ν μ → ν e)

=(0.264±0.067±0.045)%

More Sterile Neutrinos?

• Who said there is only one sterile neutrino?

• There could well be one for each generation

• Do more sterile neutrinos help?

• Maybe 3+2 better (Sorel, Conrad, Shaevitz)

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WMAP+2dF+Lyman Maltoni, Schwetz, Tortola, Vallehep-ph/0209368

Pierce, HMHannestad

Spergel et al

∑m<0.7eV (95%)

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CPT Violation?“A desperate remedy…”

• LSND evidence:anti-neutrinos

• Solar evidence:neutrinos

• If neutrinos and anti-neutrinos have different mass spectra, atmospheric, solar, LSND accommodated without a sterile neutrino

(HM, Yanagida)

Best fit to data before KamLAND (Strumia)

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KamLAND impact

• However, now there is an evidence for “solar” oscillation in anti-neutrinos from KamLAND

• Barenboim, Borissov, Lykken: evidence for atmospheric neutrino oscillation is dominantly for neutrinos. Anti-neutrinos suppressed by a factor of 3.

• New CPT violation:

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KamLAND impact

• However, now there is an evidence for “solar” oscillation in anti-neutrinos from KamLAND

• Barenboim, Borissov, Lykken: evidence for atmospheric neutrino oscillation is dominantly for neutrinos. Anti-neutrinos suppressed by a factor of 3.

• However fit not good (Gonzalez-Garcia, Maltoni, Schwetz)

• MINOS atmospheric data will settle this

• New CPT violation:

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LSND not as oscillation

• Maybe LSND detected anomalous decay of muon (Babu, Pakvasa)

• Lepton-number violation• KARMEN disfavors it

– BR<0.009 (90%) while LSND wants BR=0.019–0.040

• No signal at Mini-BooNE• Predicts Michel parameter =0.74850.75• Current accuracy: =0.7518±0.0026• TWIST experiment at TRIUMF measures Michel

parameter down to a few times 10–4

€

+ → e+ν μ ν e

EPS2003 Hitoshi Murayama 46

Seven Questions

• Dirac or Majorana? • Absolute mass scale?

• How small is 13?

• CP Violation?• Mass hierarchy?• Verify Oscillation?• LSND? Sterile neutrino(s)? CPT violation?

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Extended Standard Model

• Massive Neutrinos Minimal SM incomplete• How exactly do we extend it?• Abandon either

– Minimality: introduce new unobserved light degrees of freedom (right-handed neutrinos)

– Lepton number: abandon distinction between neutrinos and anti-neutrinos and hence matter and anti-matter

• Dirac or Majorana neutrino• Without knowing which, we don’t know how to

extend the Standard Model

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Seesaw Mechanism

• Why is neutrino mass so small?

• Need right-handed neutrinos to generate neutrino mass

νL νR( )mD

mD

⎛

⎝ ⎜

⎞

⎠ ⎟

νL

νR

⎛

⎝ ⎜

⎞

⎠ ⎟ νL νR( )

mD

mD M

⎛

⎝ ⎜

⎞

⎠ ⎟

νL

νR

⎛

⎝ ⎜

⎞

⎠ ⎟ mν =

mD2

M<<mD

To obtain m3~(m2atm)1/2, mD~mt, M3~1015GeV (GUT!)

Neutrinos are Majorana

, but R SM neutral

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Neutrinoless Double-beta Decay

• The only known practical approach to discriminate Majorana vs Dirac neutrinos

0: nn ppe–e– with no neutrinos• Matrix element <me>=imiUei

2

• Current limit |<me>| ≤ about 1eV• m3Ue3

2<<m3 and we can typically ignore m3 • <me>=m1cos212+eim2sin212

– possible cancellation due to unknown Majorana phase

• Fortunately, they cannot cancel exactly because the maximal angle 12 excluded by SNO: cos212–sin212=cos2212>0.07 (1)

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Three Types of Mass Spectrum

• Degenerate– All three around >0.1eV with small splittings– Possible even after WMAP+2dF: m<0.23eV– May be confirmed by KATRIN, cosmology– |<me>|=|imiUei

2|>m cos2212>0.07m

• Inverted– m3~0, m1~m2~(m2

23)1/2≈0.05eV– May be confirmed by long-baseline experiment with matter effect– |<me>|=|imiUei

2|>(m223)1/2 cos2212>0.0035eV

• Normal– m1~m2~0, m3~(m2

23)1/2≈0.05eV– |<me>|=|imiUei

2| may be zero even if Majorana

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WMAP again

• WMAP constraint:– m<0.23eV each (95%CL)

• Puts upper limit on the effective neutrino mass in the neutrinoless double beta decay (Pierce, HM)

– |<me>|=|imiUei2|<imi |Uei

2|<0.23eV

– Heidelberg-Moscow: |<me>|=0.11–0.56 eV

– Reanalysis by Vogel: |<me>|=0.4–1.3 eV

Models of Flavor

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Typical Theorists’ View ca. 1990

• Solar neutrino solution must be small angle MSW solution because it’s cute

• Natural scale for m223 ~ 10–100 eV2

because it is cosmologically interesting• Angle 23 must be of the order of Vcb

• Atmospheric neutrino anomaly must go away because it needs a large angle

Wrong!

Wrong!

Wrong!

Wrong!

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Surprises

• Prejudice from quarks, charged leptons:– Mixing angles are small

– Masses are hierarchical

• In LMA, all mixing except Ue3 large

– Two mass splittings not very different

– Atmospheric mixing maximal

– Any new symmetry or structure behind it?€

e μ τ( )

big big medium?

big big big

big big big

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

ν e

ν μ

ν τ

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Δmsolar2

Δmatm2 ~0.01– 0.2

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Question of Flavor

• What distinguishes different generations?– Same gauge quantum numbers, yet different

• Hierarchy with small mixings:

Need some ordered structure

• Probably a hidden flavor quantum number

Need flavor symmetry– Flavor symmetry must allow top Yukawa

– Other Yukawas forbidden

– Small symmetry breaking generates small Yukawas

• Try to find underlying symmetries from data (bottom-up)– Repeat Heisenberg, Gell-Mann–Okubo

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Different Flavor Symmetries

Altarelli-Feruglio-Masina hep-ph/0210342

Hall, HM, Weiner

Sato, YanagidaVissani

Barbieri et al

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Lack of symmetry explains data

• Suppose there is no symmetry behind the neutrino masses and mixings (“anarchy”)

• Random 3 by 3 matrix• MNS matrix

distributed to the group invariant measure (Haba, HM)

3-D Kolmogorov–Smirnov test(de Gouvêa, HM)

P=68%

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Lower Bound on 13

• Anarchy predicts flat distribution in cos413

• 1D PKS= 2(1–cos413)~sin2213 for small 13

• Lower bounds:– sin2213>0.05 (95%CL)

– sin2213>0.01 (99%CL)

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Critical Measurements

• sin2 223=1.000.01?– Determines a need for a new symmetry to enforce the maximal

mixing

• sin2 213<0.01?– Determines if the flavor quantum number of electron is different

from , • Normal or inverted hierarchy?

– Most symmetries predict the normal hierarchy

• CP Violation?– Plausibility test of leptogenesis

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Dynamics behind flavor symmetry?

• Once flavor symmetry structure identified (e.g., Gell-Man–Okubo), what is dynamics? (e.g., QCD)

• Supersymmetry:–Anomalous U(1) gauge symmetry with Green-Schwarz mechanism

• Large Extra Dimensions:–Fat brane with physically separated left- and right-handed particles

• Technicolor:–New broken gauge symmetries at 100TeV scale

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Large 23 and quarks

• Large mixing between and

• Make it SU(5) GUT

• Then a large mixing between sR and bR

• Mixing among right-handed fields drop out from CKM matrix

• But mixing among superpartners physical

• O(1) effects on bs transition possible evading ebs constraints

(Chang, Masiero, HM)

• Expect CP violation in neutrino sector especially if leptogenesis (Rodejohann)

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Consequences in B physics

• Addt’l contrib to ms

• CP violation in Bs mixing (BsJ/ )

• Addt’l CP violation in penguin bs

(Bd Ks)

Very reasonable place for new physics to show up!

EPS2003 Hitoshi Murayama 63Harnik, Larson, HM, Pierce

also

Uli

Nie

rste

in H

eavy

Fla

vour

ses

sion

RR-dom case

EPS2003 Hitoshi Murayama 64

Conclusions

• Enormous progress in neutrino data– Solar neutrino problem solved!

• Still some loose ends– Many forthcoming experiments

• Three-generation oscillation very reasonable• LSND still unclear• Cosmological constraints beginning to be interesting• Next key: 13

– Long-baseline or reactor

• Neutrinos not stand alone– Need info from high-energy frontier, quark sector to address the origin

of masses and mixing

Do We Need Theorists?