Neutrino Oscillationand CPT Violation

Hitoshi Murayama

Caltech

April 12, 2002

2

Puzzle with Beta Spectrum

• Three-types of radioactivity:

• Both discrete spectrum because

E= Ei – Ef

• But spectrum continuous

F. A. Scott, Phys. Rev. 48, 391 (1935)

Bohr: At the present stage of atomic theory, however, we may say that we have no argument, either empirical or theoretical, for upholding the energy principle in the case of -ray disintegrations

3

Desperate Idea of Pauli

4

Three Kinds of Neutrinos

• There are three • And no more

5

• Very strong evidence for neutrino oscillation from atmospheric and solar neutrinos

• What about LSND?

6

Outline

• LSND• LSND and SN1987A• Sterile Neutrinos• CPT Violation• Models of CPT Violation• Implications on Experiments• Conclusions

7

LSND

8

ν μ

ν e?

ν ep→ e+n

μ+→ e+νeν μ

p→ π+

π+→ μ+νμ

9

3.3 Signal

• Excess positron events over calculated BG

P(ν μ → ν e)

=(0.264±0.067±0.045)%

10

Neutrino mode

• They also studied DIF (decay in flight) negative muons

• Claimed signal in to e at ~2 sigma level

• Final analysis reduced the significance. Not even mentioned any more.

11

Mini-BooNE

• LSND unconfirmed• Neutrino beam from

Fermilab booster• Settles the issue of

LSND evidence• Start data taking later

this year

LSND and SN1987A

13

Kamiokande-II

• SN1987A in Large Magellanic Cloud

• ~150,000 light years away

• Burst of neutrino events at Kamiokande-II and IMB

14

SN1987A Neutrino Burst

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SN1987A Neutrino Burst

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SN1987A neutrino burstdoesn’t like LSND

HM, Yanagida

• Kamiokande’s 11 events:– 1st event is forward

may well be e from deleptonization burst

(p e- n e to become neutron star)– Later events most likely e because its cross section of inverse beta

decay is much larger than elastic scattering for other neutrino species

• LSND parameters cause complete MSW conversion ofeif light side (e lighter)

eif dark side (e heavier)

• Either mass spectrum disfavored

_

_ _

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The Light side

• eif light side (e lighter)– You will lose the precious first event from

neutronization burst into

– Of course, based on one event, you can’t say it strongly, though. The weakest argument in this talk.

18

The Dark Side

• eif dark side (e heavier)– Temperature hierarchy from supernova– T(e)~10–12MeV– T(e)~14–17MeV– T()~24–27MeV

• Observed at Kamiokande-II– T(e)~7–14MeV

• If complete conversion, the events must be much hotter

_

_

_ _

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Nuclear r-process

• For the neutrino-driven wind in the supernova envelope to be the site for nuclear r-process, you want it to be neutron-rich

• Enemy: n e p e– to lose neutrons

• If e hotter due to conversion from you would lose more neutrons and destroy the r-process

(Qian-Fuller)

20

SN1987A neutrino burstdoesn’t like LSND

HM, Yanagida

Posc<90% Posc<35%

Sterile Neutrinos

22

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?

23

Sterile Neutrino getting tight

• 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

– Marginally allowed (90% excl. vs 99% allw’d)

– (Barger et al, Giunti et al, Gonzalez-Garcia et al, Strumia)

24

3+1 spectrum

Strumia

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Sterile Neutrino getting tight

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

– Solar mostly es (or vice

versa)

– Now solar sterile getting tight(Barger et al, Giunti et al, Gonzalez-

Garcia et al, Strumia)

26

27

28Josh Klein, Lepton Photon 2001

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SNO

• SNO: e

• SuperK: e+/7

3.3 difference

are coming from the Sun!

Φν =1.75±0.07−0.11+0.12±0.05⋅106cm−2sec−1

Φν =2.32±0.03−0.07+0.08⋅106cm−2sec−1

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SNO result

• Total 8B flux:

(5.440.99)10-9cm-2s-1

• BP2000 calculation

(5.05+0.1-0.8)10-9cm-2s-1

Remarkable agreement!

Not much room for sterile neutrinos

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Wrong Neutrinos

• 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 oscillation!

SNO is further studying

neutral current reaction

e++

Expect result in April!

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2+2 Spectrum also disfavored

• Global fit to four-neutrino oscillation– Solar, Atmospheric,

LSND(Gonzalez-Garcia, Maltoni, Peña-

Garay@EPS01)

• One can look for a compromise solution with 2+2 spectrum Disfavored at 90-99%

CL

es

e s

CPT Violation

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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, atmos-pheric, solar, LSND accommodated without a sterile neutrino(HM, Yanagida)

35

CPT violation in atmospheric neutrinos

• CPT violation not needed, but allowed

(Strumia)• Anti-neutrino mass-

squared less constrained because of lower event rates

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Best Global Fit

• CPT violation provides much better fit to solar, atmospheric, LSND, and other limits

(Strumia)

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Is it allowed???

• We need CPT violation in neutrino mass of ~0.1–1eV

• Neutral kaon mass limit

• But, consider mass-squared as a natural parameter:

• LSND mass range compatible€

mK 0 − m

K 0< 0.4 ⋅10−9 eV

€

mK 0

2 − mK 0

2 < 0.2eV2

38

CPT Theorem

• Based on three assumptions:– Locality– Lorentz invariance– Hermiticity of Hamiltonian

• Violation of any one of them: big impact on fundamental physics

• Neutrino mass: tiny effect from high-scale physics– Non-commutative geometry? (HM, Yanagida)

– Brane world? (Barenboim, Borissov, Lykken, Smirnov)

Models of CPT Violation

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Trivial Idea

• If you write down the Hamiltonian in momentum space, it is easy to break CPT

• Still Lorentz invariant, but cannot be written in terms of a local field.

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Extra Dimensions

• Right-handed neutrinos SM gauge singlet• Can propagate in the “bulk”• Makes neutrino mass small

(Arkani-Hamed, Dimopoulos, Dvali, March-Russell;Dienes, Dudas, Gherghetta; Grossman, Neubert)

• m ~ 1/R if one extra dim R~10m• An infinite tower of sterile neutrinos• Need also inter-generational mixing now

42

CPT Violation in the Bulk

• Write down CPT-violating Hamiltonian for the right-handed neutrinos in the bulk

• The only particle on the brane that picks up that effect would be neutrinos through the mass terms.

• CPT-violation appears only in the neutrino mass(Barenboim, Borissov , Lykken Smirnov)

43

Dipole Field Theory

• Start with a standard quantum field theory

• Make it non-local by introducing a “dipole vector” L to every field

• Product of fields is defined by

• Can be obtained as a limit of string theory

(Bergman, Dasgupta, Ganor, Karczmarek, Rajesh)€

Φ1 ˜ ∗Φ2( )(x) = Φ1(x − 12

L2 )Φ2 (x + 12

L1)

• Non-local Lorentz-violating theory

• Dipole vector L changes sign for conjugate field

• But electric dipole moment CPT-even

• CPT violation!(Ganor; private communication)

Implications on Experiments

45

Mini-BooNE

• Plans to run in neutrino mode

• If CPT violated, won’t neither refute nor confirm LSND

• They can run in anti-neutrinos

• Lower rate requires twice as much running time

46

KamLAND

• Reactor anti-neutrino experiment

• KamLAND will exclude or verify LMA definitively

• But if CPT violated, KamLAND won’t confirm neutrino oscillation

47

KamLAND

• If KamLAND sees LMA, it excludes CPT violation of this particular type

• If KamLAND doesn’t see LMA, it may still be LMA together with CPT violation

• LMA then needs to be established by exclusion

48

Day/Night Effectin CC @ SNO

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VAC by seasonal variation

• 7Be neutrino monochromatic

• seasonal effect probes VAC region

(de Gouvêa, Friedland, HM)

• Borexino crucial• Hopefully

KamLAND, too!

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VAC by seasonal variation

• Fit to seasonal variation to measure parameters

Can pep resolve degeneracy?

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LOW by day/night effect

• 7Be neutrino monochromatic

• Day/night effect probes LOW region

• (de Gouvêa, Friedland, HM)

• Borexino crucial• Hopefully

KamLAND, too!

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LOW by zenith angle dependence

• More information in zenith angle depend. (de Gouvêa, Friedland, HM)

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SMA by pp neutrinos

• SMA: Sharp falloff in probability in the pp neutrino region the survival

• Because of the condition for the level crossing

• Measure the falloff m2 measurement

Δm2

2E< 2GFne(0)

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Can pp neutrinos be studied?

• CC+NC (electron recoil)– gaseous He TPC

– HERON: superfluid He (phonon & roton)

– liquid Xe

– GENIUS: Ge

• CC (e capture)– LENS: Yb or In

– MOON: Mo

LENS-Yb

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By exclusion…

• If none of these attempts succeed, solar neutrinos must be LMA by exclusion

• Negative signal at KamLAND then implies CPT violation

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Lepton-number Violation?

• Neutrino Hamiltonian analogou to neutral kaons:

• m: CPT-conservating mass

• : CPT-violating mass

• y: lepton-number violating mass

57

0

• LSND mass scale 0.1–1eV is interesting from the point of view of neutrinoless double beta decay

• If CPT violated, LSND mass scale may show up in the neutrinoless double beta decay

• 0<m<0.1mLSND

(Barenboim, Beacom, Borissov, Kayser)

58

Conclusions

• If all data and indications taken literally, CPT violation the most preferred explanation to data

• Of course, it is a highly exotic possibility• But after all, we are interested in neutrinos

because they tell may us something about extremely rare phenomena from very-high-energy physics

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Maybe even more surprisesin neutrinos!