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
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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
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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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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
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Kamiokande-II
• SN1987A in Large Magellanic Cloud
• ~150,000 light years away
• Burst of neutrino events at Kamiokande-II and IMB
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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.
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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)
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SN1987A neutrino burstdoesn’t like LSND
HM, Yanagida
Posc<90% Posc<35%
Sterile Neutrinos
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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 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)
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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)
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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)
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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
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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
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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)
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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
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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
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KamLAND
• Reactor anti-neutrino experiment
• KamLAND will exclude or verify LMA definitively
• But if CPT violated, KamLAND won’t confirm neutrino oscillation
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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
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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
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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)
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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!