Volume ZEB, number 7 PHYSICS LETTERS 20 January 1969 NEUTRINO ASTRONOMY AND LEPTON CHARGE V. GRIBOV * and B. PONTECORVO Joint Institute for Nuclear Research, L?ubna, USSR Received 20 December 1968 It is shown that lepton nonconservation might lead to a decrease in the Ember of detectable solar neutrinos of VeZ VP oscillations, similar to K o Z K” oscillations. Equations are at the earth surface, because such oscillations for the case when there exist only four neutrino states. presented describing fidence level of about 70% one finds respectively Recently there became known the results of the beautiful experiment of Davis et al. [l], in the following upper limits for the corresponding constants zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA f 1, f 2, f 3 which deep underground a search was made of interaction phenomenologi- tally responsible for such processes [e.g.12]. sun neutrinos. Using a spectrometer proportional counter f [2,3] to detect 37A produced in the reaction fl/G < 0.02; 2/G < 0.15; 0.005, f$G < v + 37Cl + 37A + e- [3,4], (which is expected to where G = lO-5/M 2 take place in 390000 litres of C2C14 ), Davis et P is the Fermi weak interaction al. so far were not able to detect solar neutrinos. constant. It was shown by them that the neutrino flux at the In a period of development of physics in which earth from 8B decay ivlthe sun [5] is smaller such quantum numbers as P, PC were found to C, . This limit is definitely than 2 x lo6 cmW2 set be not good, it is natural to question the exact smaller than the theoretical predictions [6,‘7]. validity of any symmetry [e.g. 131. The relative- ly high upper limits for f 1, f 2, f 3 However, various astrophysics and nuclear show that there is once more plenty of room for a violated con- physics uncertainties do not allow to draw the conclusion that we are faced with a catastrophic servation law and suggest the lepton charge(s) as discrepancy [7]. The purpose of this note is to the first candidate(s) for the nonconserved quan- emphasize again that the result of sun neutrino tum number(s). experiments are related not only to the above In previous publications [8,14] there was shown mentioned uncertainties but also, and in a marked that lepton nonconservation leads to the possibili- way, to properties which are so far unknown [8] ty of ostiillations in vacuum between various of the neutrino as an elementary particle. The neutrino states, and, generally speaking, acts in question at issue is: are (is) lepton charges the sense of decreasing the number of detectable (charge) conserved exactly ?. The question which, solar neutrinos with respect to the number ex- as we shall see, is relevant to neutrino astro- pected theoretically under ttie assumption that nomy, is certainly not far-fetched from an ele- lepton charges are strictly conserved. mentary particle physics point of view. As a This effect, which incidentally would be in the matter of fact the most significant and recent right direction if the necessity should definitely experiments on lepton conservation give upper arise of accounting for unexpectedly small values limits for the constants of hypothetical interac- of detected solar neutrinos is due to the fact that tions nonconverving lepton charge which are in the presence of oscillations, part of the neu- surprisingly large. trinos are sterile, that is practically unobserv- The most accurate information can be obtained able. It turns out that the study of solar neutrino from the experiments, in which a search was oscillations is the most sensitive way of investi- made for the processes 48Ca -+ 48Ti + e- + e- [9], gating the question of lepton charge conservation. v/J + P -+ cc+ + n [lo], 1_1+ -+ e+ + y [ll]. At a con- In ref. 8 possible oscillations ve 2 iTe, vpZ$, v,Zvj$ have been discussed. In view * Leningrad of applications to neutrino astronomy we would Physical-Technical Institute Leningrad, USSR. like to point out here that the first two types of 493
Volume 28B, number 7 PHYSICS LETTERS 20 January 1969 oscillations should not be considered if it is re- In this case the (V-A) lepton current, to which quired that in nature there are only four neutrino weak processes are due, can be written as usual states. In order to study the oscillations for this case, (5) we shall consider in approximation zero (V-A theory) four neutrino states with mass zero, which The mass difference between Majorana neu- are described by two two-component spinors ve trinos described by ‘pl and ‘p2 leads to the oscil- and v~. In such approximation it is convenient to lations v vi (in the usual notations e=Vp, $2 think of two exactly conserved lepton charges Fe 2 pp). If at the time t = 0, one electron neu- (muon and electron charges). trino is generated, the probability of observing Lepton nonconservation leads to virtual or real it at the time t is _ n transitions between the above mentioned neutrino states. All the possible transitions may be des- cribed with the help of an interaction Lagrangian where m_ = me-, - mpp; + Herm. conjug. where v’ = 3C is the charge conjugated spinor. For the charge conjugated spinors there was adopted the notation v’ instead of i; to avoid con- and P is the neutrino momentum. fusion with p. It should be emphasized that the oscillations Below for simplicity it will be assumed that take place only if rn,p and at least one of the are real values, i.e. CP-inva- values me8 and zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA mpp are different from zero. In meii,mpn,mep riance is assumed. Otherwise, the formulae be- the absence of oscillations there are two possibi- come somewhat more complicated and in the lities. If m,p = 0, then 5 = 0 and there exist two present note we shall not give them for the gen- Majorana neutrinos (without oscillations). If eral case. Interaction (1) can be easily diagona- rnee = mpp = 0, but mep # 0, it is natural to at- lized. The diagonal states are: tribute an opposite sign of the lepton charge (only one ! ) to charged leptons of equal electrical charge (ve + v;, + sin qv, + ‘pl = cos 5 vi) (say, e- and p-) [15] and to consider, (instead of (2) the degenerated states cp 1 and ‘~2 = y5’p2 with the ‘pz =sin5 (v,+v~)-c0~5(v~+v;1) mass m = mep), ,the state,s with a definite lepton where charge Ic/ = ve + v@, t,b = ve + VP (this is the four- 2 meii component neutrino theory with parity nonconser- tg25 = meg-mpp * vation [ 161). If meR and one of the values m,g, mpp are These states correspond to two Majorana neutri- different from zero, i.e. if oscillations take place, nos (i.e. four states when the spin orientation is a very attractive case arises when me -,,mCL p << In such a case taken into account) with the masses ml and m2 CC m,p. 2_ m1,2=$[meE+ml*Gi (meE-mpp)2+4mep] (3) (if m2 < 0, the real state with the positive mass and the oscillations are entirely similar to the Ko + -0 - m2 is ‘pi = y592). ,- K oscillations, (~1 and ~2 being analogous The two component spinors ve and vfi now are to Kf and K$ According to (6) the oscillation not describing anymore particles with zero mass amplitude in this case is the largest possible one. but must be expressed in terms of four-compo- The two @ spin states, vleft and Vright are ap- nent Majorana spinors ~1 and (~2 proximately the same as the obeervable “pheno- menological” particles ve and ,vj (or &), simi- Ve = $ (1 + y5)[ql c0S 5 + ‘p2 sin (1 larly Gleft * VP and i);ight N ve E Te. A very (4) simple picture of neutrino oscillations, similar vti =a (1 + Yg)[‘PIsinI - ~2cosC;] to the K O Z K” oscillations arises also if mee- 494
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