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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


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SLIDE 1

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

  • f detectable

solar neutrinos at the earth surface, because

  • f VeZ VP oscillations,

similar to K

  • Z K” oscillations.

Equations are presented describing

such oscillations for the case when there exist only four neutrino states. Recently there became known the results of fidence level of about 70%

  • ne finds respectively

the beautiful experiment

  • f Davis et al. [l],

in the following upper limits for the corresponding which deep underground a search was made of interaction constants zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

f 1, f 2, f 3

phenomenologi- sun neutrinos. tally responsible for such processes [e.g.12]. Using a spectrometer proportional counter [2,3] to detect 37A produced in the reaction v + 37Cl + 37A + e- [3,4], (which is expected to take place in 390000 litres of C2C14 ), Davis et

  • al. so far were not able to detect solar neutrinos.

It was shown by them that the neutrino flux at the earth from 8B decay ivlthe sun [5] is smaller than 2 x lo6 cmW2 set

. This limit is definitely

smaller than the theoretical predictions [6,‘7]. However, various astrophysics and nuclear physics uncertainties do not allow to draw the conclusion that we are faced with a catastrophic discrepancy [7]. The purpose of this note is to emphasize again that the result of sun neutrino experiments are related not only to the above mentioned uncertainties but also, and in a marked way, to properties which are so far unknown [8]

  • f the neutrino as an elementary

particle. The question at issue is: are (is) lepton charges (charge) conserved exactly ?. The question which, as we shall see, is relevant to neutrino astro- nomy, is certainly not far-fetched from an ele- mentary particle physics point of view. As a matter of fact the most significant and recent experiments

  • n lepton conservation

give upper limits for the constants

  • f hypothetical

interac- tions nonconverving lepton charge which are surprisingly large. fl/G < 0.02;

f

2/G < 0.15;

f$G <

0.005, where G = lO-5/M 2 constant. P is the Fermi weak interaction In a period of development

  • f physics

in which such quantum numbers as P,

C, PC were found to

be not good, it is natural to question the exact validity of any symmetry [e.g. 131. The relative- ly high upper limits for f

1, f 2, f 3

show that there is once more plenty of room for a violated con- servation law and suggest the lepton charge(s) as the first candidate(s) for the nonconserved quan- tum number(s). In previous publications [8,14] there was shown that lepton nonconservation leads to the possibili- ty of ostiillations in vacuum between various neutrino states, and, generally speaking, acts in the sense of decreasing the number of detectable solar neutrinos with respect to the number ex- pected theoretically under ttie assumption that lepton charges are strictly conserved. The most accurate information can be obtained from the experiments, in which a search was made for the processes 48Ca -+ 48Ti + e- + e- [9], v/J + P -+ cc+ + n [lo], 1_1+

  • + e+ + y [ll].

At a con- * Leningrad

Physical-Technical Institute Leningrad, USSR.

This effect, which incidentally would be in the right direction if the necessity should definitely arise of accounting for unexpectedly small values

  • f detected solar neutrinos

is due to the fact that in the presence

  • f oscillations,

part of the neu- trinos are sterile, that is practically unobserv- able. It turns out that the study of solar neutrino

  • scillations

is the most sensitive way of investi- gating the question of lepton charge conservation. In ref. 8 possible

  • scillations

ve 2 iTe, vpZ$, v,Zvj$ have been discussed. In view

  • f applications

to neutrino astronomy we would like to point out here that the first two types of 493

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SLIDE 2

Volume 28B, number 7 PHYSICS LETTERS 20 January 1969

  • scillations

should not be considered if it is re- quired that in nature there are only four neutrino states. In order to study the oscillations for this case, we shall consider in approximation zero (V-A theory) four neutrino states with mass zero, which are described by two two-component spinors ve and v~. In such approximation it is convenient to think of two exactly conserved lepton charges (muon and electron charges). Lepton nonconservation leads to virtual or real transitions between the above mentioned neutrino

  • states. All the possible transitions may be des-

cribed with the help of an interaction Lagrangian + 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- fusion with p. Below for simplicity it will be assumed that meii,mpn,mep are real values, i.e. CP-inva- riance is assumed. Otherwise, the formulae be- come somewhat more complicated and in the present note we shall not give them for the gen- eral case. Interaction (1) can be easily diagona-

  • lized. The diagonal states are:

‘pl = cos 5

(ve + v;,

+

sin qv, +

vi)

‘pz =sin5 (v,+v~)-c0~5(v~+v;1) where tg25 = 2 meii meg-mpp *

(2)

These states correspond to two Majorana neutri- nos (i.e. four states when the spin orientation is taken into account) with the masses ml and m2 2_ m1,2=$[meE+ml*Gi (meE-mpp)2+4mep] (3) (if m2 < 0, the real state with the positive mass

  • m2 is ‘pi = y592).

The two component spinors ve and vfi now are not describing anymore particles with zero mass but must be expressed in terms of four-compo- nent Majorana spinors ~1 and (~2 Ve = $ (1 + y5)[ql c0S 5 + ‘p2 sin (1 vti =a (1 + Yg)[‘PIsinI

  • ~2cosC;]

(4) In this case the (V-A) lepton current, to which weak processes are due, can be written as usual (5) The mass difference between Majorana neu- trinos described by ‘pl and ‘p2 leads to the oscil- lations v e=Vp, $2 vi (in the usual notations Fe 2 pp). If at the time t = 0, one electron neu- trino is generated, the probability of observing it at the time t is _ n where m_ = me-, - mpp; and P is the neutrino momentum. It should be emphasized that the oscillations take place only if rn,p and at least one of the values me8 and zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

mpp are different from zero. In

the absence of oscillations there are two possibi-

  • lities. If m,p = 0, then 5 = 0 and there exist two

Majorana neutrinos (without oscillations). If rnee = mpp = 0, but mep # 0, it is natural to at- tribute an opposite sign of the lepton charge (only

  • ne ! ) to charged leptons of equal electrical charge

(say, e- and p-) [15] and to consider, (instead of the degenerated states cp 1 and ‘~2 = y5’p2 with the mass m = mep), ,the state,s with a definite lepton charge Ic/ = ve + v@,

t,b = ve + VP (this is the four-

component neutrino theory with parity nonconser- vation [ 161). If meR and one of the values m,g, mpp are different from zero, i.e. if oscillations take place, a very attractive case arises when me -,,mCL

p << CC m,p. In such a case

and the oscillations are entirely similar to the Ko + -0 ,- K oscillations, (~1 and ~2 being analogous to Kf and K$ According to (6) the oscillation amplitude in this case is the largest possible one. The two @ spin states, vleft and Vright are ap- proximately the same as the obeervable “pheno- menological” particles ve and ,vj (or &), simi- larly Gleft * VP and i);ight N ve E

  • Te. A very

simple picture of neutrino oscillations, similar to the K O Z K” oscillations arises also if mee-

494

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SLIDE 3

Volume 28B, number 7 PHYSICS and mclp are no longer small in comparison with mep, but are equal (m ee-= zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

m pj7) in other words

if there is a p-e symmetry. In such a case 5 = = an and relations (7) are exact. In ref. 8 and also in unpublished work of Kobzarev and Okun there was discussed mainly the possibility that the neutrino oscillations are due to the so called milliweak interaction [17] which, in addition to PC, would violate lepton charge conservation as well. The oscillations might be also induced by a (first order) superweak interaction changing the lepton charge by two units [18]. This interaction reminds

  • f the Wolfenstein

[19] superweak inter- actions, changing the strangeness by two units and might be closely related to it. Let us remark here that the “sterility”

  • f the

neutral leptons generated, say, as a result of ve Z V~ oscillations is not absolute (as it would be in the case of the oscillations [8] ve 2 Fe, VP +

  • ) r@ corresponding

to the existence

  • f more

than four neutrino states) and in the case of solar neutrinos arises simply from the fact that low energy Ve transform mainly into zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

vp which

cannot interact with matter (their energy is smaller than the muon mass). Unfortunately, nothing can be said about the mass values m ee; m@,

mep and about the OS-

cillation length l/A, (see 6), even if they were connected to a definite “etiquette” (milliweak, superweak), as the cut off energy is unknown. Returning now to neutrino astrophysics, we are going to consider

  • nly the simple cases

mee, mctp << m,F or me5 = mpLp, when the OS- cillations are similar to the oscillations in the Ko meson beams. What can be said about the oscillation length? In reactor experiments the existence

  • f an oscil-

lation smaller than the lengths involved in the problem (the diameter

  • f the reactor

and the dis- tance detector-reactor,

  • f the order of a few

metres) would lead to a decrease by a factor two in the number of active particles reaching the detector since the number of sterile particles is equal to the number of active particles (Ye) at large distances. Such a circumstance would have the effect that the cross section for the reaction Ve + P - n + e+, measured in the experiment

  • f

Nezrik and Reines [20] would have been two times smaller than the cross section expected for exact two-component neutrinos. Since there is no such a discrepancy, it can be stated that reactor ex- periments exclude oscillations with a length smaller than a few meters. From the point of view of observing neutrino

  • scillations,

the ideal object is the sun. If the

References _ R. Davis, D. Harmer and K. Hoffman, Phys. Rev.

1.

2. 3. 4. 5. Letters 20 (1968) 1205.

  • B. Pontecorvo, Helv. Phys. Acta 23 Suppl. III (1950)

97;

  • B. Pontecorvo,
  • D. Kirkwood and G. Hanna, Phys.
  • Rev. 75 (1949) 982.
  • R. Davis.
  • Phvs. Rev. Letters

12 (1964) 303.

  • B. Pontecorvb,
  • Chalk. River Rep&t
  • 6. D. (1946) 205.
  • W. Fowler,

Astrophys.

  • J. 127 (1958) 551;
  • J. Bahcall,
  • W. Fowler,
  • I. Iben and R. Sears,

Astro-

  • phys. J. 137 (1963) 344.

LETTERS 20 January 1969

  • scillation

length is much smaller than the radius

  • f the sun region effectively

generating neutrino (say,

  • ne tenth of the sun radius R,,
  • r about

0.1 X 106 km for Ve from 8B) it will be impossible to observe

  • scillations

because

  • f the smearing

effect. At the earth surface the only effect con- sists in the following: the flux of observable neutrino must be two times smaller than the total sun neutrino flux. As it was pointed out by I. Pomeranchuk, if the

  • scillation

length of solar neutrinos is compar- able with or larger than the radius of the sun region which generates neutrinos but smaller than the earth-sun distance, there might arise time variations

  • f the intensity of detectable

neutrinos of the earth surface. These variations are connected with the fact that the sun-earth distance varies with time. In order to observe the oscillations mentioned above it is necessary to make measurements

  • ver relative

distances (times), comparable with the oscillation length (period). If the oscillation length is of the order

  • f 0.1 R, = 0.1 x 106 km, there will arise time

variations) in the intensity of detectable neutri- nos with the period of the order of days. If the

  • scillation

length is of the order zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

  • f 5 X 106 km

(the difference in the semi-axis

  • f the earth orbit),

variations will arise with periods

  • f the order of

a hundred days. Summarizing, the presence

  • f neutrino oscil-

lations leads to a decrease

  • f the detectable

neutrino intensity by a factor 6. This factor will be 2, if the oscillation length is smaller than the radius of the sun region effectively generating neutrinos. Otherwise, equal to 2 will be the value baver. averaged over time variations. If the oscillation length is comparable with the earth-sun distance, the variations are not observable, but 6 could turn out to be much larger than 2 (of course, the statement is true if a detector

  • f more or less

monoenergetic neutrinos is assumed). In conclusion we wish to express

  • ur warm

gratitude to I. Kobzarev,

  • L. Okun, B. Ioffe,
  • A. Mukhin for critical

a.nd illuminating discussions.

495

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SLIDE 4

Volume 28B, number 7 PHYSICS LETTERS 20 January 1969 6. 7. 8. 9. 10. 11. 12. 13.

  • J. Bahcall,
  • N. Bahcall,
  • W. Fowler

and G. Sharir,

  • Phys. Letters

26B (1968) 1.

  • J. Bahcall,
  • N. Bahcall and G. Sharir,
  • Phys. Rev.

Letters 20 (1968) 1209.

  • B. Pontecorvo,
  • J. Expl. Theoret. Phys. 53 (1967)

1717.

  • R. Bardin,
  • P. Gollon,
  • J. Ullman and C. Wu, Phys.

Letters 26B (1967) 112.

  • J. Bienlein et al.,
  • Phys. Letters

13 (1964) 80;

  • G. Bernardini,
  • Int. Conf. on High energy phys. ,

Dubna 2 (1964) 48.

  • S. Parker,
  • H. Anderson

and C. Reg, Phys. Rev. 133B (1964) 768.

  • B. Pontecorvo,

Uspekhi Fiz. Nauk 95 (1968) 503.

  • L. Okun, School of Theoretical

and experimental physics, Nor Amberd,

  • 1966. Ed. of Acad. of

Armenian SSR.

  • 14. B. Pontecorvo,
  • Zh. EXD. i Teor. Fiz. 34 (1958) 247.
  • 15. Ya. Zeldovich,’

Doklad‘Akad. Nauk 86 (1952) 505;

  • E. Konopinski

and I-I. Mshmoud.

  • Phvs. Rev. 92

(1953) 1045.

  • 16. I. Kawakami,
  • Prog. Theor. Phvs. 19 (1958) 459;
  • E. Lipmanov,
  • J. Exp. i Teor. Fiz. 37 (1959) 1054;
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3 (1963) 21.

  • 17. L. B. Okun and C. Rubbia,

Talk given at the Heidel- berg Int. Conf. on Elementary Particles, 1967.

  • 18. B. Pontecorvo,
  • Phys. Letters

26B (1968) 630.

  • 19. L. Wolfenstein,
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13 (1964) 562.

  • 20. F. Nezrik and F. Reines,
  • Phys. Rev. 142 (1966) 852.

*****

496