neutrino properties and tests of symmetries · neutrino 2004 andr´e de gouvˆea, northwestern...

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


“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)



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)



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.



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



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.



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).



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



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).



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,

• . . .



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?

• . . .



TESTS OF CPT-INVARIANCE

and/or LORENTZ-INVARIANCE

“Abandon Every Hope,

Ye Who Enters”

(Apologies to A. Rodin)



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!



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).



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!)



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]



(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.



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 →



[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



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)



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]



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?)



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 ⇒

• ?



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]



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?



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


Maybe our next “change of picture” will look something like this: EXCITING!

⇒

⇒

⇒

⇒

⇒

⇒

“new” SM ?!

(with apologies to P. Picasso)(with apologies to D. Velasquez)


neutrino properties and tests of symmetries · neutrino 2004 andr´e de gouvˆea, northwestern...

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