"THE NEUTRINO" BY M A MARKOV, PROF OF PHYSICS, JOINT INSTITUTE OF NUCLEAR RESEARCH, DUBNA.

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• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80T00246A025300270001-1
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• Original Classification: C
• Document Page Count: 238
• Document Creation Date: December 23, 2016
• Document Release Date: September 16, 2013
• Sequence Number: 1
• Publication Date: February 24, 1964
• Content Type: REPORT

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CENTRAL 1NTE1 tiocrAcr. AGE11CY
This material contains infortnatialt affecting rhe National Defense of the United States within M. meaning ot t i,nage Laws, Title
18, U.S.C. secs. 793 and 794. Me trGnsmissicn or revelation Of which in any manner to an unauthorized pt ,,rohibited by low.
CONFIDENTIAL
50X1
COUNTRY USSR
REPORT
? SUBJECT "The Neutrino" by M A Plexkov, Prof of DATE DISTR.
Physics, Joint Institute of Nuclear Research,
Dibna. NO. PAGES
REFERENCES
DATE OF
INFO.
PLACE &
DATE ACQ.
24 Feb 64
1
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THIS IS UNEVALUATED INFORMATION
5
4
3
2
!STATE
a monograph titled "The
Neutrino" written and t.:axislated from the Russian language by M A Markov,
Prof of Physics at the Joint Institute of Nuclear Research at Dubna, USSR.
The paper is a survey essentially confined. to Neutrino flux processes. Some
Problems of weak interactions involving neutrino physics are also dealt with.
-End-
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V;
A
O6IED,1HEHHH171 IlliCTMTYT SWEPHbIX HCCJIE,a0BAHHA
JIABOPATOPHR TEOPETWIECKOPI 01,1314K14
M.A.Markov
THE NEUTRINO
ji1y6aa 1963
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?
M. A.Marko v
. THE NEUTRINO
1*.
,lay6ma 1963
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Contents
? Preface_
. 5
. . ,, ? , , . .. ?
Introduction . .
1. Peculiarity of Four-Fermion Interactions
?
8
2. Dynamically Deformable Formfactors
25
3. ve ? Two Types of Dirac Fields .............. ........ ...................... ..........
.............
36
4. Intermediate Boson
5. Possibilities for Neutrino Experiments on High-Energy Accelerators
62
6. Possibilities for Neutrino Experiments in Cosmic Rays
99
Intermediate Boson
110
Resonance Anti-Neutrino Scattering
120
7. Neutrino-Lepton Interactions
.131
8. Weak Interactions of the (an) (an) and (aa) (aa) Type
.141
9. Is the Neutrino Aspect of Weak Interactions Hopeless?
150
10. (ev)(ev) - Interaction
165
11. Can Weak Interactions Show Macroscopically ?
174
12. Natural Neutrino Fluxes
The Sun
?
185
The Earth
192
Cosmic Rays .
198
13. Cosmological Problems
200
"Neutrino Sea" .
208
14. Prospects of Neutrino Physics
Colliding Beams 220
?
References ..... . 226
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Pref ace
This survey is essentially confined to neutrino, flux
processes,Some problems of weak interactions involving neu-
trino physics are also dealt with.
There has been growing evidence of the importance of
neutrino processes in nature.New and varied neutrino effects
are being discovered.
There are good grounds to believe that the solution
of many astrophysical problems depends on the advance of
neutrino physics.It is not impossible that neutrino processes
are of essential importance in cosmology and cosmogony.
Neutrino astronomy is not perhaps a matter of a
far-away future.
Experimental results in high energy neutrino physics
may prove decisive in constructing the future theory of elem-
entary particles.This will require adequate data on the be-
haviour of neutrino processes at very high energies.
Some of these data can in principle be obtained on
accelerators and in cosmic ray experiments.Finally,the acceler-
ators of the decade to come--colliding beams and Competing
accelerators of enormous intensities affording very high
experimental accuracies--will probably culminate the pro-
grammes and accomplish the targets of neutrino physics
holding our imagination today.
The Author
Acknowledgements.The author is indebted to I.k.Zhe-
leznykh,G.T.Zatsepin,A.A.Komar,V.A.Kuzmin and lipiert Van Hieu.
for stimulating remarks and N.Asanov for the preparation
of the preprint.
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?
Introduction
The discovery of the neutrino,a particle so striking
in many respects,was neither spectacular nor dramatic.As a
matter of fact,it cannot even be associated with any defin?
ite date.
The neutrino was being discovered on and off for
nearly a quarter of a century.
4 Contemporary reminiscences seem to Show that the
neutrino was first introduced as a hypothetical particle by
W.Faulil) (1931).
The hypothesis originated from the consideration
of conservation laws in the analysis of s/3 ?decay effects
of different complex nuclei2).
It was with caution.and hesitation that the neutrino
was admitted 'to the holy Precincts of the elementary particles:
there were years of doubt as to Whether it was a real particle
or a quantitatively conceptualized disappearance of energy
and angular momentum in different reactions.
Finally,Reines and Cowa0) showed that the neutrino
can be absorbed' and not only emitted.Thus,once'a "semi?particle
(capable of 'onlybeing "emitted") the neutrino became -a full
fledged member of the community of "elementary" particles.
In other words, just like all "elementary" particles
the neutrino is described by the four?dimensional vector of
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energy momentum and angular momenta.Possessing semi-integral
spin momentum,the neutrino belongs to the class of fermions
along with the electron,muon and baryon:.
The consensus of opinion tends to regard the rest
mass of the neutrino as vanishing.'1)
At any rate the experimental value of the neutrino .
eigen mass is given by the quantity tille4(1/2500./I75 where
Pne is the electron mass.
The theory of -decay and the theory of weak in-
teractions was in general pioneered by Fermi5) (1934).The
theory of weak interactions was constructed as a theory of
interactions between electron-neutrino and proton-neutron
fields on the pattern of electrodynamics.
The four-vector,a mathematical analogue of the
vector field of electrodynamics,was constructed out of
electron-neutrino .functions while a new constant (Cr ) in-
dicated the smallness of the interaction of the new field
with the nucleons.
The theory underwent a long process of immanent de-
velopment.Initially,a more thorough study of the inherent
possibilities of the theory led to deviations from the
electromagnetic pattern.
There were attempts,for example,to bring into play
higher field derivatives, on the one hand,and electron-neutrino
fields in the non-vector form, on the other. ft appeared that
4.
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not only the vector field ( NT ),but also the scalar ( ),
pseudoscaiar ( ),pseudovector ( A ) or tensor ( 97 )
fields could be constructed out of electron-neutrino spinor
functions.
The deamon of physics rebelled against the imaginary
narrowness of the electrodynamic prototype and it was hoped
that nature would accept the new alternatives.Nature,hoWever,
proved to be less imaginative or perhaps harder to please.
The higher derivatives in weak interactions were
soon abandoned. (1937) on the insistence of experiments.
As for the other non-vector variants of the theory,
it seemed for a while that the nature had been coaxed by
theorists into accepting the tensor and scalar variants
of interaction.
Yet quite recently (1957) the theory of .13 -decay
returned to its electrodynamic prototype807).
The comeback was so sweeping that it game rise to
the suspicion that vector interactions were at work in nature
in general and hence to the trend to "vectorizen physics8).
For all its affinity to electrodynamics the theory
of weak interactions has so far preserved that peculiarity
' which it received at Fermi's hands: the postulating of the
interaction of four feradons localized at any one space-time
point.Thus there arises an essentially new class of interac-
tions quite unlike anything known in electrodynamics or
meson field theory (the problems of renormalization,the
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character of divergences,the character of the cross section
energy dependences,etc.).
Some physicists,dissatisfied with this Peculiarity,
are working tor the unification of all types of interactions
(the idea of an intermediate vector meson).0thers expect
that it is precisely this peculiarity that will help them
'to surmount the nOtorious fundamental difficulties of the
. current field theory by imparting'a fundamental meaning to
thetour-fermion interaction.
It is to be hoped that the dilemma will be solved
within a few years and the theoreticians will thus have
less ambiguous experimental indications of new possibili-
ties for constructing the elementary particle theory.
Neutrino experiments loom prominently in the expected so-
lution of the problem.
1. Peculiarity of Four-Fermion Interactions
In accordance with the well-known neutron -decay
processee,the interaction Lagrangian describing the decay,
can be written as the products of nucleon and lepton cur-
rents6'7)
=
/ ? /11e ?
Ce (4,6
A
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where
le 5--e-otr4 (i.e6)5?
(2)
(3)
ZP is the operator of the production of a particle or the
annihilEctzlon of an antiparticle, If is that of the annihi-
lation of a particle or the production of the antiparticle,
?
04= rrity is a vector,
_KO= lit100 18 a pseudovector,
od,
= (1.40 2: 0.01) 10-49 erg cm3, (4)
and Gr.- is a specific constant governing the weak interac-
tions.
If we introduce the muon current
= d
(5)
the Lagrangian in the same form (1) with the same intera\.ction
_constant
c'e (4"1.4e
(6)
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describes well the muon decay (}4 .tp
)?
. time
The life/of the muon is here meant:
theor =
(2.26 I 0.04) 10-6 sec,
_6
? 0.02) 10 sec.
exp
Hence the natural impulse to write the Lagrangian
=
0.71)04.
(7)
describing the weak muon-nucleon interaction and in general
universalize the weak interaction of four fermions
=
(8)
where 1 and are the currents of the form (2),(3),
(5), etc. composed of Fermion functions.
Hbwever,the attempt to universalize the interaction
in the general form (8) proves to be too ambitious.In this
form it appears to include many possibilities which are not
effected in reality (decays of the type 14 e-te4
decays with a change of the strange number more than by unity,
etc.).
Hence the need,in a sense unpleasant,for devising
different forms of forbiddenness which are not justified in-
trinsically and quite often are sheer acts of violence with
10
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respect to formalism.The situation is made none the better
by scientific opinion having in recent. years recognized and
accepted the universal application of some rules which can
by no means be claimed to have originated as a result of
exhaustive experimental research.Sometimes these rules
sound rather like invocations
The rule lAsq = 1: in the decay of particles the strange?
ness cannot change by more than unity.
The rule ,:161=AS4 : this rule regulates the variation
of the electrical charge and strange number.
The rule A7'=1/2: this rule regulates the variation of
isobaric spin in weak decays.
In other words,a broad universal theory of weak inter?
actions is only in the making now.
Returning to the analysis of the peculiarities of
four-fermion interactions,the dimension of the weak interac?
tion constant is worth noticing,viz.,
7.3.6-17 cm (9)
The difficulties of the current theory of the elem?
entary particles are often associated with the absence in
the theory of the fundamental length which would essentially
1,
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modify interactions at small distances.
Inside the current theory (electrodynamics, meson
field theory) there are no intrinsic limitations of the
applicability of the space-time description: the theory is
of meaning for any parameters of the collision of elementary
particles.
In this respect four-fermion interactions exemplify
a theory incorporating a new world constant of the dimension
of length: the fundamental length 4 regulating the in-
teraction.
The formalism of four-fermion interactions itself
contains a restriction of its applicabiliV.Namely,for.the
collision parameters e,,5- et, the theory in its current
form proves inacceptable and has to be essentially modified.
Weak four-fermion interactions are known to lee& to
the cross sections for effects with quadratic energy depend-
ence in the centre-of-mass system of the colliding particles
6---
(10)
Viewed in terms of the current theory,the cross sec-
tion (10) is correct up to 101 eV in the c.m.s. .It is
1,0e 1/4'V
The unitarity condition is fulfilled only if E f(2..t:) ?
i.e.,if TA:
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The conventional perturbation theory is known to be
unitary only accurately to higher approximations. In electro-
dynamics this circumstance leads to no difficulties since
the cross sections themselves as a rule decrease or prac-
tically do not,inerease with energy. In the four-fermion-
interaction the cross sections rapidly increase with energy
and therefore the conventional perturbation theoryinon-uni-
tarian in each given order does not apply.
Consequently,at higher energies it is necessary to
114Y'44444,-.)
use the SP-matrix-1-0-2eayley form
where
or
4:5%
, and
The form of r is given by Schwinger (Phys.Rev. 74(1948)439).
In this form,for each K the AP -matrix is unitary.
The covariant radiation damping theory was then
elaborated by J.Pirenne (Phys.Rev. 86 (1952) 395).
Calculated by means, of the urinary -matrix, the
cross sections of the four-fermion interactions prove to
be decreasing with energy at higher-than-critical energies
(6;k2-> 1 ).The problem reduces to the following:are there
13
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other circumstances which would decrease the cross sections
of the four-fermion interactions at lower energies (when
< 1) when the radiation damping effect is still in-
essential, and what is the nature of these factors if they
do not arise naturally in the framework of only the
theory of weak interactions?
14
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implied that perturbation theory via which the cross section
(10) is obtained does not hold for E ) 1011 eV since the
cross sections given by the higher approximations of the
theory begin to compare with, and for high energies be larger
than,the cross sections described by the lower approxima-
tions of perturbation theory.The critical energy value in
question lies somewhere near the value E =3.1011 eV.
This circumstance is connected with the fact that the form-
alism of the four-fermion interaction theory'contains the
fundamental length dimension constant, and the dimensionless
expansion parameter in the series obtained by perturbation
theory is,roughly speaking,the ratio of the impact parameter
to the given fundamental length (4) .
The increase of effectiveness of weak interactions
with the energy of colliding particles has been experiment-
ally confirmed in various decay effects up to the energies
of the order of tens of millions eV.,
The study of the effects of direct interactions of
high energy neutrinos with nucleons confirms the further in-
crease of the-corresponding cross sections with the neutrino
energy.lhe latest experimental data61) have been brought to
energies r../ 1 GeV.
There are many important considerations which impel
us to seek an answer to the question of how weak interactions
behave at still higher energies of the particles.
15
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At very high energies the intensity. of weak interac-
tions could in principle compare with that of strong inter-
actions,which would result in a quite peculiar situation in
'this field.
At extremely high (from the viewpoint of modern con-
cepts) energies weak interactions could become comparable
with electromagnetic, and; for example, the conversion of a
photon and electron into a muon and. two neutrinos could
compete with the Compton effect.9)
Bor the estimates? of an extremely relativistic case
the cross section of the effect 411.e _v. 4-JJ 1.1
of the 'forml?)
6-c
_ /,,
41r Y "
rn
/"-
is
(12)
where Fp is'the photon energy in the c.m.s.
It is clear from eq.(12) that the cross section
increases somewhat more rapidly than .
On the other hand, the Compton effect cross section
decreases approximately as
2
For energies 6 250 GelT we have in the c.m.s.
16 .
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Way back at the dawn of physics of weak interactions
W.Heisenberg drew attention in several papers11) to the
special role of the lengtalparameter ( eo ) in the four-
fermion interaction and to the possible peculiarity of
physics of weak interactions at very high energies. In par-
ticular he pointed to the possibility of a peculiar situa-
tion at very high energies in the multiple particle produc-
tion effects.
Four-fermion interactions are known to lead to inter-
particle forces for which a strong dependence on the distance
is characteristic.
Thus thep -field (electron-neutrino field) gives
the potential between nucleons at rest (eg.,a proton and
.
neutron) in the form12)
(14)
-
At distances ?1013' cm these forces are very weak
because of the smallness of the weak interaction constant
in the coefficient of eq.(14),but at Shorter distances close
to the weak interaction range ( ?0.7.10716 cm ) these forces
could be enormous on the scale of the known forces.
There have been proposals to regard bosons13Lfor
site
exampleos compound particles,pions as systems of a nucleon
and antinUcleon and -mesons as systems of nucleons, anti-
hyperons and antinucleons14 -16).
17
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The formation of systems with such enormous mass
defects requires very strong forces acting at snail inter-_
particle distances.Four-fermion interactions meet these
requirements. It is precisely four-ferMion weak interactions
have been used in the concrete attempts to construct the
models of compolleparticles15'17-I9).
, The success or failure of such attempts again depends
on our knowledge of the behaviour of weak interactions at
small distances,at distances close to the fundamental length
of weak interactions. In the concrete calculations of compound
particles it was assumed that weak four-fermion interactions
cut off just at the distances ,,-0.7.10-16 cm.Under this
assumption it is possible to obtain,in what is known as
chain approximation summing a class of Feynman graphs,a num-
ber of results showing that such suggestions are not unreason-
able and deserve s further more rigorous analysis.
Not only bosons ,pions and K -mesons could in prin-
ciple prove compogrparticles,but such fermions like muons
and electrons could also represent systems made up of an odd
=Ober of baryons and-antibaryons20,21) bound by four-fermion
interactions increasing so powerfully at small distances.
- It is well known,for example,that the nuclear forces
give the largest mass defect in the system of four nucleons
C. .L--particle).
It is .not? impossible that such systems, more condensed
in this sense are muons, electrons and even photons and
18
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neutrinos20'21).
Tentative estimates show that, obtained with the aid
of weak interactions,the pions as systems of nucleons and
antinucleons interact,in turn,with nucleons whose effective
constant is of the order of unity.In other words,strong in-
teractions (nuclear fields) can,from this point of view,be
interpreted as the result of "weak interactions".
This curious outcome deserves in itself more thorough
studies by more elaborate methods.However,this unquestionably
attractive possibility can be realized only if the above en-
ergy dependence in the weak interaction cross sections per-
sists nearly up to the critical value -/3.1011 eV in the c.m.s.
In other words,the development and substamtiation of
this set of interesting problems also require data on the
behaviour of four-fermdon interactions in the region of very
high energies.
One Can well extend the list of fundamental problems
the solution of which depends on the answer to this question:
how far doea the growth of weak interactions with energy go?
The electromagnetic part of the proper electron en-
ergy,for example, is known to diverge logarithmically. It is
only for length far smaller than the electron'gravitation
radius ,( tr?,..10-58 cm) that the electromagnetic proper mass
of the electron becomes equal to its experimental value.
On the other hand,weak four-fermion interactions,
e.g.,interactions involved in the transition of an electron
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into a muon and back e -t)44.1.1419 e ,yield the exper-
imental value of the electron mass already at distances close
to g
Thus,four-fermion interactions involving,in particular,
neutrinos could be fundamental in the theory of the elementary
particles themselves.
Finally,the entire range of these problems could be
fornulated in more general terms.
The main fundamental difficulty of modern field theory
con7ists in that for several major quantities such as the
proper particle mass or particle charges the theory leads
to expressions given by divergent integrals in the region of
high energies (or small lengths).
One gets the impression that the appearance in the
theory of any fundamental length at which the interactions
would cut off might lead to the bona fide theory of elementary
particles.Cne of the candidatures to the role of this universal
length is the length of weak interactions.,
The competing length has so far been assumed to be
the length connected with the proper energy of the nucleon;
(1s)
At first glance there seems to exist a decisive argum-
ent in favour of the nucleon length.The fact is that for lengths
smaller than e the above integrals to which strong interac-
tions lead would give unreasonably large values for the masses
20
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A
of baryons and their specific charges.
It should be borne in mind,howsver,that the last
argument is meaningful only when the strong field quanta
( r- and 14; -mesons) are treated as elementary,point ones.
If,however,the matter is viewed in terms of the complex struc-
ture of these particles,the sizes of the systems representing
yy-- and g -mesons could figure as lengths natural for the
given class of interactions and cutting off the corresponding
divergent integrals Where necessary .
It should be emphasised that a universal length close in
its value to the nucleon length would Cut off all the diverg-
ent integrals of weak and electromagnetic interactions at too
large distances.lhat is meant here is that the corresponding
contributions to,say,the proper energy of particles would prove
insignificant as compared with the experimental masses: this
would mean that the electron and union masses would have no
field origin,for example.
The above considerations also intensify the interest
in high energy neutrino physics characteristic of physics
today in general.
Unfortunately,the energies of the order 10'1 eV (in
the c.m.s.) will not be accessible at least in the next few
years.Such energies could be obtained with colliding electron-
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electron and electron-positron beams with particle energies
-104 67 in each beam.
This possibility is unlikely to become a reality
in the near future.Therefore it is worthwhile for the time
being to try to get answers to these questions in a less
direct way.
One of such indirect ways is connected with the
consideration of the higher effects of the perturbation
theory for weak interactions. In the calculation of these
effects in intermediate state the 'modern mathematical form-
alism allows the possibility of any large momenta close to
the critical ( I.:, Ye ).
The magnitudes of many of these effects essentially
depend on the maximum momenta allowed in the intermediate ?
state.Thus,comparison of the theoretical and experimental
values for the effects of this kind can in principle yield
valuable data on the allowable magnitudes of the limiting
momentum.
Several effects23-25) have been analyzed from this
point of view22).The angllysis leads to several new fundamental
problems of the theory of weak interactions which also await
their experimental verification.
One of the effects of this kind is the conversion
of a union into an electron in union-proton scattering. This
process is described by a Feynman graph of the type
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The ratio of the probability of this effect to that
of the lower approximation (..)4 )7,7` ) is given by
the expre s sion24 )
2 y
677(/44:P-?1/-4 &max (is)
?
t.4.7/9 /7))) is.5TY
At present ratio (16) is limited,according to experim-
ental data,by the value26)
< (!)
X
In the gross estimate (It) ) the effects of the first
and. second orders begin to compare ( ) approximately
for momenta
The experimental ratio of these cross sections,consid-
erably less than unity ( ) indicates that the intermediate
momenta in the effect jr+p e-* p cut off at the maximum
.momenta which .are perhaps fractions of the critical ones.
Unf ortunately, the effect under discussion' has not
23
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been detected experimentally and so far only its upper limit
is experimentally given.
It is desirable to make ratio (/7 ) more accurate
in further exPeriments.It Should be borne in mind,however,
that ratio (16 ) depends on the momentum ( k ) in fourth
power and the experiment should be improved in accuracy at
least by two orders in order to decrease the quantity K
ItIELX
only by a factor of 3.
Obviously, in the fUture theory there must arise certain
circumstances cutting off the growth of four-fermion interac-
tions at some msyillinm momenta,but the physics of the nearest
future will have to determine within what limits the magni-
tude of this
max lies and what mechanism is responsible
for the weakening of the interactions when this energy region
is approached.
The analysis of experimental and theoretical data
on the cross sections 6i and 61: would warrant the con-
clusion that k max 4. Kcrit if it were certain that the
processik-4p-41,ipte-is not forbidden in general by some
attendant circumstances.
Such circumstances may arise in a theory assuming
the existence of,say,two kinds of neutrinos,the existence
of an intermediate boson,and,specially for the given effect,
the possible role of the formfactors of strong interactions.
.All aspects of these possibilities require wide exper-
2 4
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imental research in high energy neutrino physics. Of course,
weak interactions can in principle be invest4gated in
and )4 e collisions as well.But'the participation of these
particles in the pattern of other stronger interactions gives
rise to a great variety of effects, and against the background
of these it is difficult to isolate the rare events due to
weak interactions.
? The neutrino is a unique particle in this Sense?it
interacts with other.particles via weak interactions only.
TherefOre,the high' penetrating power of the neutrino makes .
it possible to absorb in large shielding layers the admixtures
of all other kinds of radiation in the neutrino flux and elim-
inate in toto the undesirable background of the effects due '
to other kinds of interactions.
2. Dynamically Deformable Formfactsra
At present there are certain grounds to believe that
the neutrino-nucleon interaction cuts off at the electro-
Or rather the process ,0161 +.24- corresponding to
the first non-vanishing approximation of perturbation theory
:for the weak interaction.
magnetic nucleon radius,i.e.,at a considerably larger distance
than the critical weak interaction length.But this is still
OR
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a hypothesis to be checked experimentally.
It can be visualized how strong interactions are
at all capable of smearing out the source of weak interac-
tions.For the vector part of the Hamiltonian of weak interac-
tions the same picture can be drawn more convincingly.
Indeed,the electromagnetic formfactor of the nucleon
(Hofstadter30)) weakens correspondingly the interactions of
electromagnetic fields with nucleons. The weak vector interac-
tion can formally be treated as a kind of "weak electromagne-
tism".Assuming that the equation of continuity for the corre-
sponding currents is fulfilled we can conclude that the Hof-
stadter formfactor,which gives the distribution of the elec-
trical charge of the nucleon,is also a formfactor at least
for the vector part of the weak interactions.
The situation with the A -interaction (axial-vector
interaction) is much more complicated.The above analogies do
not hold here.True,in this case as well there are considers,-
tions according to which the behaviour of the matrix elements
of the -interaction becomes, in the limit of very high
energies,identical,in a sense,with the 17 -interaction.
However,it is unknown at what energies the differences be-
tween the V -and A-interactions are actually (in this
sense) erased.
.Finally,it is possible that what we have in reality
is a more coLl14cated case.Perhaps,the vector interaction
is indeed cut off by the Hofstadter formfactor,while the
26
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axial-vector interaction still continues its increase over
a considerable energy interval.This possibility has its
attractive aspects.But in this case the effects of the
P e--type must be suppressed by some other mech-
anism.
The idea of the cut-off of weak interactions by the
formfactors of baryons produced as a result of strong inter-
actions has gained wide recognition very easily27-29),Its
popularity,however,does not correspond to its tenability.
If the experimental data on the existence of the Hofstadter
formfactor are used in the argument,it Should be borne in .
mind that the experimental data refer to relatively small
momentum transfers30),viz., 41,1 Xrrirer,i.e.,the cor-
responding lengths are no smaller than the nucleon length
( e ??2.10-14 cm),It is not impossible that farther
vi .4
on the electrical formfactor turns to a constant,for example:
At any rate the extrapolation of the experimental
? Hofstadter formf actor expression for arbitrarily small
lengths is still unwarranted.
It is worthwhile to emphasise the fact that the
popular contention about the cutting-off role of strong in-
teractions in elastic nucleon-neutrino processes tends to.
a kind Of universality without weighty theoretical and
I.e.,to the spread onto inelastic processes,virtual
a,
-states for which 2- .
P
07
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experimental grounds. If the problem is discussed in a purely
theoretical aspect,taking into account the role of strong
interactions in electromagnetic processes and weak effects
actually leads to the appearance in the matrix elements of
some factors dependant on the momenta transferred to the
nucleon /36Lit' these factors could always play the role
of formfactors suppressing large momentum transfers,in
\particular the large momenta of the virtual states,this
would mean the absence of the notorious difficulties with
divergences in electromagnetic and weak fields.That would
be an inference of fundamental importance if it were just.
Some vague grounds (or rather hopes) for such a
possibility have been discussed in literature31).
It is well known that the phenomenological ("rigid")
formf actor cannot be introduced in moaern theory without
violating such fundamental properties as causality and
unitarity.
Actually,however,this is the question of formfactors
which arise automatically in relativistically invariant and
unitary theoxy: by definition they must be free from the
defects of the rigid phenomenological formf actor.
In other words,these "natural" formfactors must, in
contrast to the "rigid" ones,be deformable so that the
finiteness of the propagation of the signal over the form-
factor region be conserved and,thus the causal description
of modern theory be conserved as well.
28
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A special term: "dynamically deformable formfactor"
has been introduced31) to distinguish such a desirable
natural formfactor from its defective rigid counterpart.
But so far the dynamically deformable formfactor is merely
a terminological expression of hopes.
No case of the dynamically deformable fon:doctor
has been constructed phenomenologically.Such a "non-rigid"
system of charges acts as cutting-off formfactor only for
small momentum transfers,or rather when elastic scattering
cases are specially selected.It has become habitual to con-
nect the visualizable concepts of the nucleon structure with
the formfactors of nucleons arising in elastic electron-
nucleon scattering. In this case as well it is perhaps more
correct to stress merely the peculiarity of the given kind
of elastic process .
stic processes in-large
nsfers must to
un tarity: inelas
str g interac
the ncrease the incident particle
the astic attering c annel.It is
the to al attering cro section i
forwar Sc ttering of whi small
charac r stic.For the tot cro
tam n extent be a mani
cess channels due t
mentu.m
est t ion o
,in p tic
ons and.
arising in increa
:
ing num ers
? rgy must supeil e?s
t accidentA t at
connected wi h elas
omentum transfe s are
section,the "ela ic fo
bus seems in
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Rather,the visua/izable concepts of the origin of
the particle sizes because of the "smearing-out" of nucleons
due to strong interactions are justified in the non-relativ-
istic region when the formfactor in the p -representation
depends on the spatial part of the momentum vector.
The electron cloud of the hydrogen atom furnishes
a certain illustration of the dynamically deformable form-
factor. In the non-relativistic region for very slow electrons
incident on the hydrogen atom,the electron cloud of the atom,
becomirg somewhat deformed,acts as an actually distributed
charge.
Purthermore,the electromagnetic proper energy of the
bound electron can be calnulated,taking into account the
possibilities for its transition to any discrete levels,
and this energy will even prove finite.However,taking into
account any possible deformation of the electron cloud,viz.,
taking into account the possibility of the transition to the
continuous spectrum (inelastic process),returns the problem
to the divergent integrals.
The absence of the observed effecti4-+p p 4- e-
would seem a strong argument in favour of the existence of
the nucleon formfactor capable of cutting off the momenta
of virtual states as well. At this stage it is perhaps not
even very essential whether the formfactor appears naturally,
as a result of strong interactions,or a new, essentially dif-
ferent theory will be required for the introduction of such
f ormfactors. in the light of what has been said above,this
30
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amounts to the same. Or rather we cannot in the frame of the
conventional theory describe consistently such a situation
even if it exists.
Thus the problem is whether we should believe that
precisely =2 situation has already arisen. in the experim-
enti-tp e- or the interpretation of it cannot
be regarded unambiguous.
Unfortunately, it mast be admitted that the latter
is the.case.No unambiguous inference on the existence of
the folmfactor can be drawn only on the basis of the absence
of the effect .
If the effect/4.-+p -?p+ did axist,but with
small probability on the basis of which the corresponding
Kmax could be calculated,this would essentially narrow
the arbitrariness of the interpretation.Especially if k
.coincided with the corresponding quantity for the Hastadter
nucleon.Unfortunately,the accuracy of the experiment26) has
to be increased by 5 or 6 orders to have the possibility of
registering the latter effect if it exists.
The fact is that it is not only the/-p p e-
effect proves to be forbidden.For some reason or other a
whole string of effects is not realized.though each of them
should have been observed if the formulation of weak inter-
actions in the form (e ) has any general meaning.
31
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some of the forbidden reactions do not contain
strongly interacting particles at all.Thus,the reactions
244 e++ y
and `t. e++e-t a+ which can by
no means be suppressed by the formfactors due to strong inter-
actions are not observed.The idea of looking for some common
causes for the entire set of the knOwn cases of forbiddenness
might seem more natural.
The conversion of a muon into electrons (./14 e
can be forbidden in the first order Of perturbation theory
by assuming that there are no "neutral" currents in Lagrangian
( g ).This hypothesis was put forward in ref ?67) as a cer-
tain contention generalizing the experimental data on weak in-
teractions without any thorough theoretical grounds.
But even these violations over the theory of weak
interactions prove insufficient.Effects of the type.), 15e
'may,bypasaing the forbiddenness thus established, arise in
the higher approximations of the perturbation theory22).
.In the lowest non-vanishing approximation the graph
of the,_)se process is of the form
Fig.2
or
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4
Fig.3
? rough
A gross estimate of the probability for the effect
by the graph24) of fig.2 yields for the ratio of the effects
of the second and first order an expression of the same type
as ( 16 )
W (At, 3e)
W -0 evc)7
,?????
2.4',Q),
A more detailed estimate of the effect32) leads to
the relation
2, y - fo
Ic eena
.Z.r6 ir F5fI mf.
The experimental value of this relation is known accurately
to within33)
33
('9)
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Comparing eq.( 18?) and eq( t' ) we ought to tate
kmax 4" GeV. (2D)
From the same point of view the conceivable possi-
bility for the decay of a anon into an electron and
quantum given by the graphs of fig.4
Fig.4
seems also interesting.The estimate of the contribution of
these graphs to the probability for the d/# -# decoy
leads to the expression24)
(tA)
where 4 is the fine structure constant and )14 is the
anon mass.A more accurate estimate of the same effect given
by Ioffe25) (if his arguments about the a priori smallness
of the contribution of some graphs are accepted) is expressed
by the relation
,A
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Wete
= Weorti
t
eLotilcj,?, [en ntexi
oraX /77 t'
cAFC ?
The latest experimental data give34)
AL