Nuclear Physicx B (Proc. Suppl.) 28A (192)153-155North-Holland

NEUTRIN® MIXING AND FUTURE ACCELERAT®R NEUTRIN® EXPERIMENTS

S.M. BILENKY

Joint Institute for Nuclear Research, Dubna, USSR and Department de Fisica Teôrica, Universitat de Valencia,46100 Burjassot (Valencia) Spain.

The problemofneutrino masses and mixingis arealchal-

lenge of to-days neutrino physics . üp to now the "deficit"

of the solar neutrino flux that was discovered b;~ Davis et.al. ~ and confirmed by Kamiokande II collaboration2 gives

as an indication in favour of nonzero neutrino masses and

mixing . No evidence for neutrino mixing has been obtained

in experiments searching for oscillations with neutrinos from

accelerators and _eactors3. The possible reason is that neu-

trino masses are too small to produce any sizable effects

in the experiments with terrestrial neutrinos . We will put

forward here the (more optimistic) point of view that the

reason for that can be traced ~u the presence of a hierarchy

of neutrino masses as well as strength of couplings between

lepton familiesOur starting point will be usual assumption that flavour

neutrino fields v~L (d = e, ~,, T) are given by

v!L =~UléviLv

where v, is the field of neutrino with mass m. ; (Dirac or

Majorana) and U is an unitary miring matrix . We assume

further that there are three massive neutrinos, and neutrino

masses are submitted to the following hierarchy

mi « ml «m; s

(2)

and m, and ml are very small, so that m2 - mi could

be relevant for the explanation of solar neutrino data (say,

10-7eVz < (m2 - mi) < 10-~~eVl).

For the probability of transition v~ -; vj~ (h ~ l) in a

beam of terrestrial neutrinos with momentum p" we have in

this case

zp(v~ --, v~,) = 2A(vi -~ v~~)(1 - cos~2PR ),

0920-à5632/92/$05 .ß ®1992 - Elsevier Science Publishers B.i~

All rights reserved .

where ßm2 = m;-m~ . m -m~, Ris the distance betw~nneutrino saurce and detector and

A(v~ -' v~~) = 4lUt~sIl~Uts~x

is the amplitude of~scillation~ v~ = v~~ .A few remarks are in order. Ifa hierarchy (3) is realized

in nature in this case:1. The probabilities for the transition between differenttypes of neutrinos are characterized by the same Om2.2. The amplitudes of oscillations are determined only by thematrix elements U~ 3 connecting the charged leptons to theheaviest neutrino v,~;, which belong ., io the third family.3. The values ~Utsl2 satisfy the unitarity constraint

Now in analogy with the situation in the quark sector wewill assume that there exists some hierarchy of the strengthof couplings between lepton families . It is clear from (2) and(3) that only two types of such an hierarchy are relevant forexperiments with terrestrial neutrinos:

(Urall « (Ih,s Î t K IUraI2,

~~patl « ~ll,.al~ « ~L'rai l.

(71

The first type of hierarchy is analogous to the hierarchy

in the quark sector . we will call it "natural" hierarchy. Thesecond type of hierarchy, we will call "unnatural" . Due t:.

unitary constraint (4) in both cases we have

G'(~L®~~~~L(~L~Û

(that means the "mass" of yr is practically equal to ms).

It is clear from (2), (5) and (7) that in the case of "natu-

ral" hierarchy the amplitude of oscillations v. ;-.t v, will be

the largest one

A(v,, -+ vr) = 4Id10 :;I2 .

For the amplitude ofoscillations vC ;F:-- il, we have

A(v, -,, vr) = zA(v,, -" vr),

(10)

where x = iiJO i

« 1. The amplitude ofoscillations v,,

v,.is determined by amplitudes of oscillations v,. = yr and

vit `- yr

A(v, - vj = 1A(v, --+ vr)A(vl+ --+ vr)

(11 )

and A(v,, -+ v,) is the smallest amplitude. Thus in the caseof natural hierarchy we have

P(v,,-Yr)»P(v, --+vr)»P(VM-+yj . (12)

A(ve -+ v,.) ^_- 3.10-7.

In the case of "unnatural" hierarchy (6) the largest am-plitude of oscillations will be the amplitude of oscillationsv, = vr .

A(v, --, vr ) .� 41U,;11 2 .

(15)

For the amplitudes of other oscillations we have

A(v,, --, vr) = 1 A(v,, -. vr)

(x » 1),x

&M. Bilenky /Neutrino mixingandfuture accelerator neutrino experiments

A(v,, - " v,.) = 1A(v,, -+ vr)A(v, -+ vr ) .

(16)

So in the case of unnatural hierarchy we have

P(v~-vr)»P(-P-v,)»P(v,, --.) . (17)

It is clear that from the point of view of hierarchies dis-cussed above the experiments that were proposed at CERN6and Fermilab 7 to search for v,, = yr oscillations with ahigh sensibility to the mixing angle are very interesting andpromising (such experiments were discussed and strongly ad-vocated in ref./ . Notice that in the case of U ^_- VCKnt, ef-fects ofoscillations will be seen in this experiments if Om2 >3eV2.

Our final remarks will be related to Simpson neutrino .̀From the experiments in which a positive indications infavour of the existence of neutrino with the mass 17 KeVwas obtained it follows that

v,. --* vr :

P(v,. --+ vr) ^_" 2.10-2 .

(21)

Up to now we implicitely assumed that 17 KeV neutrinois a Dirac particle. If it is Majorana particle we must takeinto account limitations imposed by experiments searchingfor neutrinoless double A-decay. Let us notice that for pro-posed in" Majorana neutrino mass spectrum with two lightand two heavy neutrinos (that could accomodate all data)we have in general

As an example of the "natural" hierarchy (6)sider the case' in which neutrino mixing matrixwith Cabibbo-Kobayashi-Maskawa matrix

let as con-coincides

IU,31 ' -- 10-2 . (18)

An upper bound on IU,,31 2 could be obtained from exist-ing experimental upper bounds"" :

U = Vctcnt . (13)P(v,, -+ v,.) < 1.7.10-7, P(v,, --+ vr ) < 2.10-2 . (19)

We have in this caseWe have

A(v,, ~ vr ) = (1 .0 f0.2) 10-2 ,IU,, :,I 1 < 10-3 and IUr:11 2 . ^-' 1 -f- 0( 10-2 ) (20)

A(v,. - vr) ^_" 10`, (14)A comparison of (17) and (18) shows that we have the

case of "unnatural" hierarchy. With the help of (3), (4), (17)and (19) it is possible to predict the probability oftransition

P(v,. -4 vr ) < 2.10-2 .

(22)

So information on the transition yr -. vT could be veryimportant both from the point of view of possible hierar-chy in the lepton sector and from the point of view of theproblem of neutrino with mass 17 KeV. The experiment 12

with tagged produced in K3-decays provide a possi-bility to reach (1-2) % sensitivity in searching for yr --" v,.

transition.

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155

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