Neutrino Physics III Hitoshi Murayama University of Pisa February 26, 2003
Neutrino Physics III
Hitoshi MurayamaUniversity of PisaFebruary 26, 2003
2
Outline
• Three Generations• LSND• Implications of Neutrino Mass• Why do we exist?• Models of flavor• Conclusions
Three Generations
4
MNS matrix
• Standard parameterization of Maki-Nakagawa-Sakata matrix for 3 generations
UMNS =Ue1 Ue2 Ue3Uμ1 Uμ2 Uμ3Uτ1 Uτ2 Uτ3
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
=1
c23 s23−s23 c23
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
c13 s13e−iδ
1−s13e
iδ c13
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
c12 s12−s12 c12
1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
atmospheric ??? solar
5
Three-generation
• Solar & atmospheric oscillations easily accommodated within three generations
• sin2223 near maximal, m2atm ~ 310–3eV2
• sin2212 large, m2solar ~ 510–5eV2
• sin2213 < 0.05 from CHOOZ, Palo Verde
• Because of small sin2213, solar & atmospheric oscillations almost decouple
• Need to know sin2213,
and mass hierarchy
6
Raised More Questions
• Why do neutrinos have mass at all?
• Why so small?• We have seen mass
differences. What are the masses?
~m/15eV• Do we need a fourth
neutrino?• Are neutrinos and anti-
neutrinos the same? • How do we extend the Standard Model to incorporate massive neutrinos?
7
3-flavor mixing
• If m1 and m2 not very different, it reduces to the 2-flavor problem
€
τ μ ,t =Uτ 1* Uμ1 e−im1
2t /2 p
+Uτ 2* Uμ 2 e−im2
2t /2 p +Uτ 3* Uμ 3 e−im3
2t /2 p
≅ Uτ 1* Uμ1 +Uτ 2
* Uμ 2( )e−im1
2t /2 p +Uτ 3* Uμ 3 e−im3
2t / 2 p
= −Uτ 3* Uμ 3e−im1
2t /2 p +Uτ 3* Uμ 3 e−im3
2t /2 p
= eiφ sinθ −e−im12t / 2 p + e−im3
2t /2 p ⎛ ⎝ ⎜
⎞ ⎠ ⎟
8
When is 3-flavor important?
€
τ μ ,t2
= Uτi*UμiUτjUμj
* e−i mi
2 − m j2
( )t / 2 p
i, j∑
= −2ℜe Uτi*UμiUτjUμj
*( ) sin2 mi
2 − m j2
4 pi, j∑ t
+ ℑm Uτi*UμiUτjUμj
*( ) sin
mi2 − m j
2
2 pi, j∑ t
When all masses significantly differentAnti-neutrinos: UU*, the last term flips signPossible CP violation
9
CP Violation
• Possible only if:– m12
2, s12 large enough (LMA)
– 13 large enough
P(νe → νμ)−P(νe → νμ) =16s12c12s13c132 s23c23
sinδsin Δm122
4EL
⎛ ⎝ ⎜
⎞ ⎠ ⎟ sin Δm13
2
4EL
⎛ ⎝ ⎜
⎞ ⎠ ⎟ sin Δm23
2
4EL
⎛ ⎝ ⎜
⎞ ⎠ ⎟
10
11
LSND
12
ν μν e?
ν ep→ e+n
μ+→ e+νeν μ
p→ π +
π+→ μ+νμ
13
3.3 Signal
• Excess positron events over calculated BG
P(ν μ → ν e)=(0.264±0.067±0.045)%
14
Mini-BooNE
• LSND unconfirmed• Neutrino beam from
Fermilab booster• Settles the issue of
LSND evidence• Started data taking the
summer 2002
15
LSND Affects SN1987A neutrino burst
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
• LSND parameters cause complete MSW conversion ofeμ if light side (e lighter)eμ if dark side (e heavier)
• Either mass spectrum disfavored
_
_ _
16
LSND Affects SN1987A neutrino burst
HM, Yanagida
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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 neutrinoNew type of neutrino with no
weak interaction
• 3+1 or 2+2 spectrum?
18
Sterile Neutrino getting tight
• 3+1 spectrum: sin22LSND=4|U4e|2|U4μ|2
– |U4μ|2 can’t be big because of CDHS, SK U/D
– |U4e|2 can’t be big because of Bugey– Marginally allowed
• 2+2 spectrum: past fits preferred– Atmospheric mostly μτ
– Solar mostly es (or vice versa)
– Now pretty much ruled out(Barger et al, Giunti et al, Gonzalez-Garcia et al, Strumia, Maltoni et al)
19
WMAPMaltoni, Schwetz, Tortola, Vallehep-ph/0209368
20
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)(Barenboim, Lykken, et al)
Best fit to data before KamLAND (Strumia)
21
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.
• Not a great fit (Strumia)
• New CPT violation:
22
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-local Hamiltonian? (HM, Yanagida)– Brane world? (Barenboim, Borissov, Lykken, Smirnov)– Dipole Field Theory? (Bergman, Dasgupta, Ganor, Karczmarek, Rajesh)
23
Implications on Experiments
• Mini-BooNE experiment will not see oscillation in neutrino mode, but will in anti-neutrino mode
• Because KamLAND is consistent with LMA, atmospheric neutrino oscillation relies on m2
LSND ~ eV2 (not a great fit)
• Katrin may see endpoint spectrum distortion in t3He+e–+e
We’ll see!
_
24
Maybe even more surprisesin neutrinos!
25
Mass Spectrum
What do we do now?
26
Two ways to go
(1) Dirac Neutrinos:– There are new
particles, right-handed neutrinos, after all
– Why haven’t we seen them?
– Right-handed neutrino must be very very weakly coupled
– Why?
27
Extra Dimension
• All charged particles are on a 3-brane• Right-handed neutrinos SM gauge singlet
Can propagate in the “bulk”• Makes neutrino mass small
(Arkani-Hamed, Dimopoulos, Dvali, March-Russell;Dienes, Dudas, Gherghetta)
• Barbieri-Strumia: SN1987A constraint“Warped” extra dimension (Grossman, Neubert)
• Or SUSY breaking(Arkani-Hamed, Hall, HM, Smith, Weiner;
Arkani-Hamed, Kaplan, HM, Nomura)
€
d 4θ S*
M (LHu N∫ )
28
Two ways to go
(2) Majorana Neutrinos:– There are no new light
particles– What if I pass a
neutrino and look back?
– Must be right-handed anti-neutrinos
– No fundamental distinction between neutrinos and anti-neutrinos!
29
Seesaw Mechanism
• Why is neutrino mass so small?• Need right-handed neutrinos to generate
neutrino mass
νL νR( )mD
mD
⎛ ⎝ ⎜
⎞ ⎠ ⎟
νLνR
⎛ ⎝ ⎜
⎞ ⎠ ⎟ νL νR( )
mDmD M
⎛ ⎝ ⎜
⎞ ⎠ ⎟
νLνR
⎛ ⎝ ⎜
⎞ ⎠ ⎟ mν =mD
2
M<<mD
To obtain m3~(m2atm)1/2, mD~mt, M3~1015GeV (GUT!)
, but R SM neutral
30
Grand Unification
• electromagnetic, weak, and strong forces have very different strengths
• But their strengths become the same at 1016 GeV if supersymmetry
• To obtain m3~(m2
atm)1/2, mD~mt
M3~1015GeV!Neutrino mass may be probing unification:
Einstein’s dream
M3
Why do we exist?Matter Anti-matter Asymmetry
32
Big-Bang NucleosynthesisCosmic Microwave Background
η =nBnγ
= 4.7−0.8+1.0( )×10−10
5.0±0.5( )×10−10
(Thuan, Izatov)
(Burles, Nollett, Turner)
WMAP
33
Matter and Anti-MatterEarly Universe
10,000,000,001 10,000,000,000
Matter Anti-matter
34
Matter and Anti-MatterCurrent Universe
The Great Annihilation
1
us
Matter Anti-matter
35
Sakharov’s Conditionsfor Baryogenesis
• Necessary requirements for baryogenesis:– Baryon number violation– CP violation– Non-equilibrium (B>0) > (B<0)
• Possible new consequences in– Proton decay– CP violation
36
Original GUT Baryogenesis
• GUT necessarily breaks B. • A GUT-scale particle X decays out-of-equilibrium
with direct CP violation
• Now direct CP violation observed: ’!
• But keeps B–L0 “anomaly washout”• Also monopole problem
B(X → q) ≠B(X → q)
B(K0 → π+π−) ≠B(K0 → π+π−)
37
Electroweak Anomaly
• Actually, SM converts L to B.– In Early Universe (T >
200GeV), W/Z are massless and fluctuate in W/Z plasma
– Energy levels for left-handed quarks/leptons fluctuate correspon-dingly
L=Q=Q=Q=B=1 B–L)=0
38
Two Main Directions
• BL0 gets washed out at T>TEW~174GeV• Electroweak Baryogenesis (Kuzmin, Rubakov, Shaposhnikov)
– Start with B=L=0– First-order phase transition non-equilibrium– Try to create BL0
• Leptogenesis (Fukugita, Yanagida)
– Create L0 somehow from L-violation– Anomaly partially converts L to B
39
Leptogenesis
• You generate Lepton Asymmetry first.• Generate L from the direct CP violation in right-handed
neutrino decay
• L gets converted to B via EW anomaly More matter than anti-matter We have survived “The Great Annihilation”
Γ(N1→ νiH)−Γ(N1 → νiH)∝ Im(h1jh1khlk* hlj
*)
40
Does Leptogenesis Work?
• Much more details worked out(Buchmüller, Plümacher; Pilaftsis)
• ~1010 GeV R OK• Some tension with supersymmetry because
of unwanted gravitino overproduction• Ways around: coherent oscillation of right-
handed sneutrino (HM, Yanagida+Hamaguchi)
41
Does Leptogenesis Work?
• Some tension with supersymmetry:– unwanted gravitino
overproduction– gravitino decay
dissociates light nuclei– destroys the success of
Big-Bang Nucleosynthesis
– Need TRH<109 GeV(Kawasaki, Kohri, Moroi)
42
Leptogenesis Works!
• Coherent oscillation of right-handed sneutrino (Bose-Einstein condensate) (HM, Yanagida+Hamaguchi)
– Inflation ends with a large sneutrino amplitude
– Starts oscillation – dominates the Universe– Its decay produces asymmetry– Consistent with observed
oscillation pattern– isocurvature perturbation at
WMAP? (Moroi, HM)nBs
~εTdecay
M1~ nB
s⎛ ⎝ ⎜ ⎞
⎠ ⎟ obs
Tdecay
106GeVargh132
h332
43
Can we prove it experimentally?
• We studied this question at Snowmass2001 (Ellis, Gavela, Kayser, HM, Chang)
– Unfortunately, no: it is difficult to reconstruct relevant CP-violating phases from neutrino data
• But: we will probably believe it if– 0 found– CP violation found in neutrino oscillation– EW baryogenesis ruled out
Archeological evidences
Models of Flavor
45
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
46
Fermion Mass Relationin SU(5)
• down- and lepton-Yukawa couplings come from the same SU(5) operator 10 5* H
• Fermion mass relationmb= mτ, ms = mμ, md = me @MGUT Reality:mb≈ mτ, 3ms ≈ mμ, md ≈ 3me @MGUT
• Not bad! (small correction compared to inter-generational splitting ~20–200)
47
Broken Flavor Symmetry
• Flavor symmetry broken by a VEV ~0.02• SU(5)-like:
– 10(Q, uR, eR) (+2, +1, 0)
– 5*(L, dR) (+1, +1, +1)
– mu:mc:mt ~ md2:ms
2:mb2
~ me2:mμ
2:mτ2 ~4: 2 :1
Mu ~ε4 ε3 ε2
ε3 ε2 εε2 ε 1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ,Md~
ε3 ε3 ε3
ε2 ε2 ε2
ε ε ε
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ,Ml~
ε3 ε2 εε2 ε2 εε3 ε2 ε
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
48
Not bad!
• mb~ mτ, ms ~ mμ, md ~ me @MGUT
• mu:mc:mt ~ md2:ms
2:mb2
~ me2:mμ
2:mτ2
49
New Data from Neutrinos
• Neutrinos are already providing significant new information about flavor symmetries
• If 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 smallbig big bigbig big big
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
νeνμντ
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
Δmsolar2
Δmatm2 ~0.01– 0.2
50
Is There A StructureIn Neutrino Masses & Mixings?
• Monte Carlo random complex 33 matrices with seesaw mechanism
(Hall, HM, Weiner; Haba, HM)
51
Anarchy
• No particular structure in neutrino mass matrix– All three angles large– CP violation O(1)– Ratio of two mass splittings just right for LMA
• Three out of four distributions OK– Reasonable Underlying symmetries don’t distinguish 3 neutrinos.
52
13 in Anarchy
• 13 cannot be too small if anarchy
• How often can “large” angle fluctuate down to the CHOOZ limit?
• Kolmogorov–Smirnov test: 12%
• sin2 213>0.004 (3)• If so, CP violation
observable at long baseline experiment
53
Anarchy is Peaceful
• Anarchy (Miriam-Webster): “A utopian society of individuals who enjoy complete freedom without government”
• Peaceful ideology that neutrinos work together based on their good will
• Predicts large mixings, LMA, large CP violation• sin2213 just below the bound• Ideal for VLBL experiments• Wants globalization!
54
Program:More flavor parameters
• Squarks, sleptons also come with mass matrices• Off-diagonal elements violate flavor: suppressed by flavor symmetries
• Look for flavor violation due to SUSY loops• Then look for patterns to identify symmetries
Repeat Gell-Mann–Okubo!• Need to know SUSY masses
M ˜ Q 2 ~M ˜ L
2 ~1 ε ε2
ε 1 εε2 ε 1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
55
To Figure It Out…
• Models differ in flavor quantum number assignments
• Need data on sin2213, solar neutrinos, CP violation, B-physics, LFV, EWSB, proton decay
• Archaeology• We will learn insight on origin of flavor by
studying as many fossils as possible– cf. CMBR in cosmology
56
More Fossils:Lepton Flavor Violation
• Neutrino oscillation lepton family number is not conserved!– Any tests using charged leptons?– Top quark unified with leptons– Slepton masses split in up- or neutrino-basis– Causes lepton-flavor violation (Barbieri, Hall)
– predict B(τμ), B(μe), μe at interesting (or too-large) levels
57
Barbieri, Hall, Strumia
58
More Fossils:Quark Flavor Violation
• Now also large mixing between τ and μ
– (τ, bR) and (μ , sR) unified in SU(5)
– Doesn’t show up in CKM matrix
– But can show up among squarks
– CP violation in Bs mixing (BsJ )
– Addt’l CP violation in penguin bs (Bd Ks)
(Chang, Masiero, HM)
Conclusions
60
Conclusions
• Historic era in neutrino physics• Oscillation in atmospheric neutrino: an unexpected
discovery, strong evidence for neutrino mass• Decades-long problem in solar neutrinos now being
resolved• A lot more to learn in the near future• Interesting connections to cosmology, astrophysics• We’d like to know how to build the new Standard
Model!