Neutrino 2004 Andre de Gouvea, Northwestern University
Neutrino Properties andTests of Symmetries
Andre de Gouvea
Northwestern University
XXI International Conference on Neutrino Physics and Astrophysics
14–19 June 2004, College de France, Paris
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
“old” SM
“new” SM
— — — — — — — — — — — — — — — — — — — — —
Massless Neutrinos:
• gauged SU(3)c × SU(2)L × U(1)Y
• global U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ
• No “leptonic” CP -invariance violation
Massive Neutrinos:
• gauged SU(3)c × SU(2)L × U(1)Y
• global U(1)B (×U(1)L)
• Leptonic CP -invariance violated (?)
(?) ⇒ to be determined experimentally!
(with apologies to C. Monet)
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
There are two “minimal” guesses for the New Standard Model Lagrangian:
(a) L = Lold SM − λij LiHLjH2M + h.c.
• mν = λv2
M– Tiny neutrino masses: M � v ⇒ mν � m`,q ,
• Higher Dimensional Operator – SM no longer works above scale M ,
• Neutrinos are Majorana Fermions – lepton number violated
(b) L = Lold SM + iNi/∂Ni − λαiLαHNi + H.c.
• mν = λv – neutrino masses require λ < 10−11
• Renormalizable Lagrangian – like the old SM
• New degrees of freedom – standard model gauge singlets N
• Neutrinos are Dirac Fermions – lepton number conserved — WHY?
Neither (a) nor (b) yield other observable new physical effects, except forthe faith of lepton number violation YES/NO. [⇒ see talks on 0νββ]
—
(L = lepton doublets, H = Higgs doublet, λ = dimensionless couplings, M = “seesaw” scale)
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
However, the fact that neutrinos have mass and given the unprecedentedabundance of neutrino data we are in position to probe whether neutrinoare endowed with other “unexpected” properties, including,
• a magnetic moment; [⇒ see talk by Wong]
• a finite lifetime;
and whether the leptonic sector respects a variety of fundamentalsymmetries, including
• CP, T invariance; [⇒ see talk by Petcov]
• Lorentz invariance;
• CPT invariance.
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
NEUTRINO MAGNETIC MOMENTS
Now that neutrinos have mass, they are “allowed” to have a nonzeromagnetic moment µν .
The nature of µν will depend on whether the neutrino is its ownantiparticle:
Lm.m. = µijν (νiσµννjF
µν) + H.c.,
µijν = −µji
ν , i, j = 1, 2, 3 → Majorana Magnetic Moment
or
Lm.m. = µijν (νiσµνNFµν) + H.c.,
i, j = 1, 2, 3 → Dirac Magnetic Moment
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
In either version of the new SM, µ is really small:
µ ≤ 3eGF
8√
2π2mν = 3× 10−20µB
( mν
10−1 eV
); µB =
e
2me
Bounds come from a variety of sources and constrain different linearcombination of elements of µ. ⇒ next talk
• νee− → νβ (νβ) e−, ∀β (β = e, µ, τ) TEXONO, MUNU reactor expt’s,
SuperK solar
• searches for electron antineutrinos from the Sun (νe →(m.m.) νβ →(osc) νe)~B in the Sun?, how well oscillation parameters are known?(KamLAND!) ⇒ posters
• astrophysics red giants, SN1987A, . . .
⇒ µν < 1.5× 10−10µB (PDG accepted bound);
also O(10−[12÷11]) bounds from astrophysics and solar neutrinos.
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
Generic new, electroweak-scale physics effects yield much larger neutrinomagnetic moments. E.g.,
µ ∼ eλ2
Mnewmf f = e, µ, τ, . . .
Searches for neutrino magnetic moments constrain the new physics scale(M) and coupling (λ) like searches for new physics in the charged-leptonsector: µ → eγ, (g − 2)µ, muon and electron electric dipole moments, etc.After all, they all come from the same effective operator!
One can place bounds on (or find “evidence” for)
• SUSY,
• large extra dimensions (νee− →
∑kk νkke
−),
• . . . (the usual suspects).
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
THE NEUTRINO LIFETIME
Now that neutrinos have mass, the heavier neutrino mass eigenstates areunstable and will eventually decay into the lightest mass eigenstates plusX. In the new SM, X are photons and other light (anti)neutrinos.
νi → νjγ is governed by the same type of operators as magnetic moments,
and expectations for τ are absurdly long: τ > 1038 years, for mν ∼ 1 eV
(GIM suppressed).
Other new SM induced decays are also rare beyond all reason:
τν→3ν > 1039 years
Constraints on µ severely constrain neutrino lifetimes already e.g.,
τ > 5× 1011
(10−10µB
µν
)2
years mν ∼ 1 eV
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
Similar to magnetic moments, observable neutrino decays are a sign forphysics beyond the new SM. The new physics effects are either of the“bread and butter” 1/Mnew-type, or involve the presence of very light, yetto be observed degrees of freedom (say, (quasi-)massless (pseudo)scalars,like “Majorons”).
Experimental bounds are very dependent on the decay mode (and thekinematics of the decay) and vary from the billion of years scale (boundson UV light) to the hundreds of microseconds scale (model independentbounds from the sun).
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
Best model independent bound comes from solar neutrinos. In order todisentangle the oscillation effects from the decay effects we profit from acombination of solar and KamLAND data. It is easy to see that theconstraints are very mild [e.g., Beacom+Bell 2002]:
γτ > 500 s ⇒ τ > 500 sm
E∼ 10−4 s
( m
eV
) (5 MeV
E
)Much better (many orders of magnitude) constraints are expected
• high energy cosmic neutrinos at Ice-Cube (e.g., large violations of1:1:1 flavor ratios [Beacom et al. 2003] with dependency on mixingparameters),
• relic supernova neutrinos [Fogli et al. 2004] ⇒ poster,
• . . .
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
TESTS of CP-INVARIANCE and T-INVARIANCE ⇒Petcov
Given that there are three lepton families and that the neutrinos havedistinguishable masses, CP-invariance violation and T-invariance violationare expected in the new SM. They can be probed by
• P (να → νβ)× P (να → νβ), “Dirac” CP-violation; beware of matter effects;
requires |Ue3|2 6= 0
• P (να → νβ)× P (νβ → να), “Dirac” T-violation; “no” matter effects on
Earth-based experiments; requires |Ue3|2 6= 0
• Rate for 0νββ, CP-even effect, sensitive to Majorana CP-odd phases; can
we really observed the effect of the phases?
• CP-odd observables in L-violating processes; “Majorana” CP-violation; we
can’t measure this in the real world! [AdG, Kayser, Mohapatra 2002]
• Leptogenesis; Other “Majorana” CP-violation; how do we learn about this?
• . . .
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
TESTS OF CPT-INVARIANCE
and/or LORENTZ-INVARIANCE
“Abandon Every Hope,
Ye Who Enters”
(Apologies to A. Rodin)
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
TESTS OF LORENTZ-INVARIANCE VIOLATION
Violation of Lorentz-invariance would lead to a modified neutrinodispersion relation (E2 − |~p|2 6= m2) in a CPT-invariant or violating way.
Modified dispersion relations for the neutrino lead to deviations from thecharacteristic L/E–oscillatory behavior, which means that precisionoscillation measurements can set unprecedented bounds on such effects!
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
One example ⇒ see poster
Spontaneous breaking of Lorentz invariance [Coleman+Glashow 1997,Colladay+Kostelecky 1997, Barger et al. 1998, also Bahcall, Barger,Marfatia 2002, AdG 2002]
LCPTV ⊃ Aijµ νiγ
µνj + Bµν νσµνν + H.c. + . . .
where Aµ is interpreted as having a vacuum expectation value in the“time” direction Aµ
ij = (Vij/2,~0), (in the reference frame where weperform experiments), Bµν can have a vev in some ij direction, etc...
In the limit E, |~P | � m,V ,
E = |~p|+ m2
2|~p|± V
2This looks just like matter effects!
± refers to neutrinos/antineutrinos → CPT violation (Does NOT fitLSND + ATM + SOL).
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
We can use intuition of matter effects to understand what is going on (Vij
are “ether” potentials). E.g., two-flavor “ether” oscillations
Pex = sin2 θeff sin2(
∆eff2 L
)∆eff =
√(∆ cos 2θ − V )2 + (∆ sin 2θ + Vex)2
∆eff sin 2θeff = ∆ sin 2θ + Vex
∆eff cos 2θeff = ∆ cos 2θ − Vex
where ∆ = ∆m2/(2E), V = 2(Vee − Vxx), and for antineutrinosVij → −Vij
⇒ neutrinos and antineutrinos have different effective mixing angles(which are energy dependent), and the L/E oscillatory behavior isviolated!)
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
One can probe these “ether effects” through several oscillationmeasurements. Order of magnitude estimates bounds are easy to estimate∆m2/(2E) > Vij (conservative!, read “certainly bigger/less than”):
• Atmospheric: Vµτ,µµ,ττ < 10−3 eV2/GeV→ < 10−21 GeV ⇒ poster
• Solar + KamLAND: Veµ,eτ < 10−6 eV2/MeV→ < 10−21 GeV
This is a MUCH richer phenomenon. There are even studies of whetheryou can explain all the neutrino data with Lorentz invariance violation(and no neutrino masses)! Keep in mind that there are MANY freeparameter you can tune. [Kostelecky+Mewes, 2003]
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
(SPECIFIC) TEST OF CPT-INVARIANCE: mν = mν?
Different masses for neutrinos and antineutrinos were postulated as apotential solution to the LSND anomaly (and also helped address a smallproblem with SN1987A data) in Murayama+Yanagida (2001), and furtherpursued in Barenboim et al.(2001–2003).
Currently, this form of CPT-violating solution to all neutrino puzzles plusLSND (and only active (anti)neutrinos) is experimentally disfavored
• KamLAND and solar data “agree” (∆m2sol = ∆m2
Kam)
• ∆m2atm � ∆m2
LSND
+ Given that there is no evidence for CPT violation, these (and other)“precision neutrino oscillation experiments” allows one to bind how muchCPT can be violated in the neutrino sector.
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
Atmospheric
Atmospheric, LSND
SolarKamLAND
Neutrinos Antineutrinos
m 1
m 3
m
m
m
3
2
1
m 2
[Gonzalez-Garcia+Maltoni (2003)]
SuperK atmospheric data exclude
values of ∆m213 required to address
the LSND anomaly at 3σ
3.6σ →
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
[Gonzalez-Garcia+Maltoni (2003)]
Assuming CPT-invariance, we can bind CPT-violating observables
∆(∆m2) ≡ |∆m2 −∆m2| ∆(sin2 θ) ≡ | sin2 θ − sin2 θ|
⇒ [see Kearns, “δ”]
∆(∆m213) < 1.9× 10−2 eV2 ∆ sin2 θ23 < 0.5
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
Solar and KamLAND data, interpreted in terms of two-flavor neutrino
oscillations, agree!!!!! This is a remarkable achievement of Physics.
)2 (
eV2
m∆
-510
-410
θ 2tan
-110 1 10
KamLAND
95% C.L.
99% C.L.
99.73% C.L.
KamLAND best fit
Solar
95% C.L.
99% C.L.
99.73% C.L.
solar best fit
θ 2tan
0.2 0.3 0.4 0.5 0.6 0.7 0.8
)2 (
eV2
m∆
KamLAND+Solar fluxes
95% C.L.
99% C.L.
99.73% C.L.
global best fit-510×4
-510×6
-510×8
-410×1
-410×1.2
⇒ ⇒ ⇒ ⇒“new SM” assumed (including CPT-invariance)
Gratta, KamLAND (2004)
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
10-5
10-4
10-3
10-1
1 10
∆m2 (
eV2 )
tan2θ
KamLAND versus Solar Data
⇐ Could they have disagreed?
⇒ 9 × “old” KamLANDsample (9×162 ton-years)
Contours are agreement at 90%,95%,99%, and 3σ confidence level
Things Could Have Gotten
Much More “Interesting”...
Kam
(? best fit point of LMA)
Kam[AdG+Pena-Garay, to appear]
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
Assuming CPT-Invariance, we can bind CPT-violating observables
∆(∆m2) < 1.2× 10−4 eV2
From solar data!
∆(sin2 θ) < 0.7
will not improve much – matter efffects donot matter!
⇓
)2 (
eV2
m∆
-510
-410
θ 2tan
-110 1 10
KamLAND
95% C.L.
99% C.L.
99.73% C.L.
KamLAND best fit
Solar
95% C.L.
99% C.L.
99.73% C.L.
solar best fit
θ 2tan
0.2 0.3 0.4 0.5 0.6 0.7 0.8
)2 (
eV2
m∆
KamLAND+Solar fluxes
95% C.L.
99% C.L.
99.73% C.L.
global best fit-510×4
-510×6
-510×8
-410×1
-410×1.2
Gratta, KamLAND (2004)
⇑Dark-side mirror
∆(sin2 θ) = | cos 2θ|?
(θ + θ = π/2?)
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
In order to address whether CPT-invariance is “maximally violated” inthe solar mixing we need:
• Antineutrinos
• Matter effects
Possible experiments include
• Supernova neutrinos ⇒ Pνe' cos2 θ; can it really be done?
• Very long baseline νe ↔ νµ,e searches with frequency ∆m2Kam ⇒
• ?
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
00.10.20.30.40.50.60.70.80.9
1
0.1 0.2 0.3 0.4
L=2540km∆m
_ 2=(7.0-7.6)x10-5eV2
sin2θ-=0.68-0.74
sin2θ-=0.26-0.32
E(GeV)
1-P(
ν_
e→ν_
e)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.1 0.2 0.3 0.4
L=730km
∆m_ 2=(7.0-7.6)x10-5eV2
sin2θ-=0.68-0.74
sin2θ-=0.26-0.32
E(GeV)
1-P(
ν_
e→ν_
e)
“KamLAND” LBL Oscillations
(Ue3 = 0)
PRELIMINARY!
• low energies
• very long baselines
• antineutrinos
⇓
Small statistics, hard to detect,
large backgrounds,. . .
BNL-setup, β-beams, NuFact ?
[AdG+Pena-Garay, to appear]
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
In summary (some tests of CPT-invariance)
• “Order one” CPT-violating observables are allowed: improvementsexpected from more “precision neutrino data” (which we expect to geta hold of in the next several years!)
• ∆(∆m212) ≡ ∆(m2
2)−∆(m21) – Need to ignore “conspiracies” in order
to interpret bound
• cf. with |m2(K0 −m2(K0))| < 0.25 eV2 – neutrino bounds muchbetter? This is a “model dependent” question.
• Binding CPT-violating leptonic mixing angles may be very challenging– Is this another job for (next-)next-generation LBL experiments?
June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
CONCLUSIONS
• In the new SM (old SM plus neutrino masses) “other” observable neutrino
properties are NOT expected, and one can only verify whether CP -invariance,
T -invariance and L-number are conserved. All three are naıvely expected to be
violated.
• Nonetheless, massive neutrinos plus precision neutrino data allow one to look for
new new-physics. Neutrino experiments are “weaker” but “unique” relatives of
charged-lepton experiments like the search for rare muon processes (e.g., µ→ eγ),
charged-lepton electric dipole moments, and deviations of the anomalous magnetic
moment from SM predictions.
• Finally, neutrinos serve as narrow but very deep, unique probes of
“Earth-shattering” effects, that if observed would require a long and hard revision
of some of the fundamental principles of Physics. This is a consequece of the
“quantum interferometry” nature of the oscillation phenomena. Keep in mind that
these may have allowed a peek at a very large energy scale, Mseesaw > 1010 GeV!
⇒June 16, 2004 Neutrino Properties and Symmetries
Neutrino 2004 Andre de Gouvea, Northwestern University
Maybe our next “change of picture” will look something like this: EXCITING!
⇒
⇒
⇒
⇒
⇒
⇒
“new” SM ?!
(with apologies to P. Picasso)(with apologies to D. Velasquez)
June 16, 2004 Neutrino Properties and Symmetries