Present and future experiments on neutrino masses and mixing

Petr Vogel, Caltech

1. Recent triumphs. Where are we?2. Planned refinements. Looking for symmetries and possible CP symmetry violation.3. Are neutrinos Majorana particles? How can we tell? And how light neutrinos really are?

Heraeus Summer School, Dresden, Aug. 29 - Sept 7, 2005

Note: Throughout references are used sparingly(my apologies to those not quoted properly)

Summaries of the field, with references, can be found at e.g.1) APS Multidivisional Neutrino Study /www.aps.org/neutrino/2) Neutrino Telescopes, Venice 2005 /axpd24.pd.infn.it/conference2005/talks/Venezia_talks.htm3) Neutrino 2004, Paris, June 14-19 /neutrino2004.in2p3.fr/

There are many review papers, again with apologies let me quote our own, R.D.McKeown and P.Vogel, Phys.Rep.394,315(2004)

First lesson: Quantum mechanics works! (or in other words, phases matter)

In the standard electroweak model neutrinos are massless and the lepton flavors are exactly conserved. Formally this is a consequence of the

absence of the right-handed weak singlet components. Neutrino masses do not arise even through loop effects.

Charged lepton and neutrino fields form doublets in SU(2)L:

Lets assume that this is not so, and that neutrinos are massive, and thatthe above flavor eigenstates are coherent superpositions of states withdefinite masses, socalled mass eigenstates.

Thus

And the states i propagate as plane waves, for E>>mi (common phase is skipped)

The flavor is no longerconserved, and thetransition amplitude is

Transition probability is an oscillating function of the distance

When only two flavors (and mass eigenstates) exist, thereis only one mass square difference m2 and only one mixingparameter The oscillation probability is then

and the characteristic oscillation length is

,

.

For three neutrino flavors there are 3 mixing angles

one Dirac phase and two Majorana phases The mixing matrix (often called PMNS or MNS) is then written as

Obviously, there are no oscillations when m2=0, or or

By observing oscillations one can then determine(at least in principle) the corresponding fundamental parameters:• Two mass squared differences m21

2, m312

a) Three mixing angles

c) CP violating phase • Majorana CP violating phases which affect only processes that violate total L)

We will see shortly what has been done so farin that respect, and what remains to be done.

But first we should, however, discuss what happens when neutrinos propagate in matter.

In matter neutrinos of all flavors interact equally with theelectrons and quarks by the Z exchange, but only e interactwith electrons by the W exchange. Thus, an additional phaseappears

and a corresponding matter oscillation length

To see what happens, one has to solve the correspondingequations of motion which for 2 flavors is of the form

Schematic illustration of the survival probability of e created at thesolar center. The labels are sin22 values.

Note the possiblesuppression of Pin particularfor small This is the famousMSW effect.

Second lesson: Neutrino oscillations are real. We are lucky enough that the oscillation parameters are such, that this is possible.

Even though we know that there are (at least) three flavorsall observations up to now can be analysed in the two flavorcontext (we will see shortly why this is so) .

Interestingly, oscillation phenomena were found`by accident’, in experiments designed to observesomething else, and with `natural’ sources ofneutrinos. (Remember Becquerel’s discovery ofradioactivity or Anderson’s discovery of the muon.)

Atmospheric neutrinos: Angle and the mass difference m31

2 ~ m322.

Cosmic ray protons and nuclei interact with the nitrogen and oxygenin the upper atmosphere, and produce (dominantly) pions.These, in turn, decay, Most of the muons also decay,and one thus expects the ratio of e events to be ~2. Also, bydetermining the zenith angle of the incoming neutrinos, one canstudy the path length dependence of the results.

Atmospheric neutrinos were observed in a number of detectors,most of which were built to study proton decay. Most of themcan distinguish between and e like events (but not between and

Illustration of the relation between the zenith angle and flight path (from V. Barger et al.)

upgoing downgoing

S-K I: 1489 live-days, 100 yr MC,15,000 neutrino events

Recent Atmospheric Sector MeasurementsZenith angle distributions showing disappearance

M. Vagins, EPS/HEPP2005

Red MC no osc.Green MC with oscillations

upgoing downgoing

S-K II: 627 live-days

M. Vagins, EPS/HEPP2005

Recent Atmospheric Sector MeasurementsZenith angle distributions showing disappearance

What does it mean?

Clearly, the flux is less than expectations, in particular for the upwardgoing neutrinos, while the e flux is in agreement.This finding is also supported (was preceded) by the determination of the`double ratio’ (e)exp/ (e)MC ~ 0.6.Fits suggest that and are essentially maximally mixed, i.e. sin2

and that |m312|~|m32

2| = 2.4-0.6+0.5 x10-3eV2

(note that for such m2 and E ~ 1 GeV, Losc ~ 1000 km, correspondingapproximately to cosanthropic principle’?). `disappearance’ has been confirmed by the K2K accelerator experiment(260 km distance) where 107 events were observed (151 expected)(Aliu et al, Phys.Rev.Lett. 94,081802(2005))

Atmospheric neutrino results, with nearly maximal and with e ~2are insensitive to the mixing between e and other flavor (i.e. to .This is so, because in such situation the and e fluxes are almostequal, and therefore unaffected by oscillations.

Solar and reactor neutrinos:Angle and mass difference m21

2

Predicted (SSM)solar e spectrum.thresholds of theVarious experimentsare indicated.

Results of different experiments (as ratios to SSM) ordered accordingto their their thresholds. Filled circles - exp. Data. Open circles - bestfit to oscillations.

Schematic illustration of the survival probability of e created at thesolar center. The labels are sin22 values.

pp 7Be

8B

Measured charged current (CC), neutral current (NC) and elastic scattering(ES) from SNO, together with the SSM prediction.

The only way one can interpret the solar neutrino results isby invoking the idea of neutrino oscillations enhanced by thematter effects.Even though only the 8B neutrinos (~10-4 fraction of the totalsolar e flux) has been observed in `live’ experiments, it isimpossible to explain the findings by some hypotheticalflaws in the solar model.Moreover, the suppression factor ~1/3, can be understood onlyif the matter effects play a decisive role.Interpreting the results as oscillations, we arrive at the followingparameters: m21

2 ~ 10-4 eV2, sin2~ 0.31 (large but not maximal).Note that the matter effects depend on the sign of m2, hencewe know that m2 > m1. The decisive confirmation of the oscillation hypothesis involving

e and e comes from the reactor experiment KamLAND.

In fact, solar neutrinos (from 8B decay observed in SK andSNO) actually “do not oscillate”. They areborn as the heavier eigenstate and propagate like

that all the way to a detector.The fact that the oscillation parameters derived fromthe solar eand reactor e agree is a sign of not only

CPT invariance but test the whole concept of vacuumand matter oscillations.

Two comments:

Since solar density, and e energies, are fixed, it isfortuitous that the parameter m21

2~ 10-4 eV2 > 0is such that we can observe the rich phenomenaof matter oscillations. (Another example of`anthropic principle’ ?)

Nuclear reactors produce e isotropically in the -decay of neutron-rich fission fragments. A typical 3 GW power reactor produces ~6x1020 e/s.A convenient way of detecting reactor e is by using the relatively largeand well understood cross section of the inverse neutron decay,e + p -> n + e+, and its correlated signal.

An example for 12 tons detector0.8 km from a 12 GWth powerreactor.

So far all reactorexperiments reliedon the known e

spectrum, and measuredthe signal at a givendistance L. Since theenergies are fixed,the distance L definesthe sensitivity regionfor m2.

From Araki et al. (KamLAND coll.) Phys. Rev. Lett. 94, 081801 (2005)

One can see that not only is the total rate less than expected,but there is evidence for spectrum distortion that allows oneto determine m21

2 = 7.9-0.5+0.6x10-5 eV2 in agreement, but more

accurate, than the solar result.

• `interferometry’ probes flavor non-diagonal processes

For example, when traveling through matter:

(for ’s, we can treat bulk matter as just a potential term!)

Simple approach:

Reactor Solar

E 2-10 MeV 0.1-15 MeV

L 150 km 1.5 x 108 km

MSW No Yes

Anti-e e

Only(?) Standard Model couplings predict that these 2 experimental regimes

will see the same effect

KamLAND+SNO: Testing the Model

KamLAND, PRL 94, 2005

What about the mixing angle

We have argued that the determination of the e component of atmospheric neutrino flux does not give very useful informationon the angle . The most natural way of determining thatangle is to look for the e disappearance (or appearance) atdistances corresponding to m2

atmos.

Two such experiments with reactor antineutrinos, CHOOZ andPalo Verde were done in late nineties when it was unclear whetherthe atmospheric neutrinos involve or e.The characteristic distance is ~ km, and no effect was seen.Hence these result constrain from above to rather small

value.

-3eV2

Constraints on fromthe Chooz and PaloVerde reactorexperiments. Theregion to the rightof the curvesis excluded.Note that the maximumsin213 value dependson the so far poorlydetermined m31

2 value.

Global fits givesin213= 0.9-0.9

+2.3x10-2

at 95% CL, consistentwith vanishing

Preliminary conclusions:1) The existence of neutrino mass and mixing has been convincingly established. Lepton flavor is not conserved. A window to physics beyond the

SM has been opened.2) Assuming that only 3 flavor and mass eigenstates play a role (careful, we will comment on this

shortly), the elements of the mixing matrix and the mass squared differences have been determined (albeit some with rather large error bars).1) The mixing matrix is, surprisingly, unlike the CKM matrix for quarks, which is `nearly’

diagonal. In contrast, the neutrino mixing matrix has two

large mixing angles. The neutrino masses are very small compared to the charged fermions, and their

pattern is also different.2) Note, however, that there appear to be two small parameters, m2

sol/m2atm ~ 1/30 and sin2213

0.09.

€

≤

The neutrino sector is really strange….

(entries evaluated for Ue3 = 0.1,near the middle of allowed range)

The neutrino sector is really strange….

Three-flavor fit of oscillation parameters (Fogli et al. hep-ph/0506083, errors 95%CL)

m212 = 7.92-0.71

+0.71 x 10-5 eV2

m312 = 2.4-0.62

+0.50 x 10-3 eV2

sin212=0.314-0.047+0.057 (substantially less than 0.5)

sin2 = 0.44-0.10+0.18 (compatible with 0.5)

sin2= 0.9-0.9+2.3 x 10-2 (compatible with 0.0)

LSND – fly in the ointment

L = 30 m, E= 20-50 MeV, “decay at rest spectrum”

Oscillations -> e, 87.9 +- 22.4 +- 6.0 events,oscillation probability 0.264 +- 0.067 +- 0.45 %

Most of the parameter range excluded by reactorand KARMEN experiments, but a sliver with0.2 < m2 < 10 eV2 remains.

Requires existence of sterile neutrinos !!!

At present tested by Mini-BOONE at Fermilab, waitand see……(until late 2005 at least, probably even later)

Third lesson: Not everything is simple, or

Decay at rest spectra:

monoenergetice+ + e + `Michel spectra’ are produced less and do notdecay weakly, instead they forma pionic atom and are absorbedby strong interaction.Thus e are missing

But we know that there are only 3 `active’ neutrinos. If indeed (at least)one light `sterile’ neutrino exists, all bets are off. Thus, we shall wait(eagerly) for the MiniBoone result, and reserve judgment for now.

Numerous attempts tofit all existing data(including LSND) inschemes 3+1 or 2+2etc. are `disfavored’,i.e. the fit is not too good.

e [|Uei|2] [|Ui|2] [|Ui|2]

Normal Inverted

m2atm

(Mass)2

m2sol}

m2atm

m2sol}

or

sin213

sin213

The spectrum, showing its approximate flavor content, is

So, here is once more what we know (dismissing LSND for now):

Slide by B. Kayser

So what are the remaining issues?

a) Qualitative: What is the sign of m2atm?

Is the angle nonvanishing, or can one hope

to observe CP violation of leptons? Are neutrinos Majorana particles, or, is

the total lepton number conserved? What is the absolute mass scale? Are there other surprises?b) Quantitative: Measure the magnitude of Is exactly 450 ? ( symmetry) Measure m2

atm more accurately.

We will discuss black issues in the second lecture,and purple issues in the third lecture.