Fortschritte der Physik / Progress of Physics: Band 30, Heft 11/12 [Reprint 2021 ed.] 9783112591048, 9783112591031

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FORTSCHRITTE DER PHYSIK H E R A U S G E G E B E N IM AUFTRAGE D E R P H Y S I K A L I S C H E N

GESELLSCHAFT

DER DEUTSCHEN DEMOKRATISCHEN

REPUBLIK

VON F. K A S C H L U H N , A. LÖSCHE, R. R I T S C H L U M ) R. R O M P E

H E F T 11/12 • 1982 . B A N D 30

A K A D E M I E

ISSN 0015 - 8208

- V E R L A G

•

B E R L I N

Fortschr. Phys., Berlin 30 (1982) 11/12, 5 8 3 - 6 5 1

EVP 2 0 , - M

31728

BEZUGSMÖGLICHKEITEN Bestellungen sind zu richten — in der DDR an eine Buchhandlung oder an den AKADEMIE-VERLAG, DDR-1086 Berlin, Leipziger Straße 3—4 — im sozialistischen Ausland an eine Buchhandlung für fremdsprachige Literatur oder an den zuständigen Postzeitungsvertrieb — in der BRD und Berlin (West) an eine Buchhandlung oder an die Auslieferungsstelle KUNST UND WISSEN, Erich Bieber OHG, D-7000 Stuttgart 1, Wilhelmstraße 4—6 — in den übrigen westeuropäischen LSndern an eine Buchhandlung oder an die Auslieferungsstelle KUNST UND WISSEN, Erich Bieber GmbH, CH-8008 Zürich, Dufourstraße 51 — im übrigen Ausland an den Internationalen Buch- und Zeitschriftenhandel; den Buchexport, Volkseigener Außenhandelsbetrieb der Deutschen Demokratischen Republik, DDR-7010 Leipzig, Postfach 160; oder an den AKADEMIE-VERLAG, DDR-1086 Berlin, Leipziger Straße 3 - 4 Zeitschrift „Fortschritte der Physik" Herausgeber: Prof. Dr. Frank Kaschluhn, Prof. Dr. Artnr Lösche, Prof. Dr. Rudolf Bitsehl f, Prof. Dr. Bobert Bompe, im Auftrag der Physikalischen Gesellschaft der Deutschen Demokratischen Bepublik. Verlag: Akademie-Verlag, DDB-1088 Berlin, Leipziger Straße 3 - 4 ; Fernruf: 2230221 und 2236229; Telex-Nr.: 114420; Bank: Staatsbank der DDE, Berlin, Konto-Nr.: 6836-26-20712. Chefredakteur: Dr. Lutz Bothkirch. Anschrift der Bedaktion: Sektion Physik der Humboldt-Universität zu Berlin, DDB-1040 Berlin, Hessische Straße 2. Veröffentlicht unter der Lizenznummer 1324 des Presseamtes beim Vorsitzenden des Ministerrates der Deutschen Demokratischen Bepublik. Gesamtherstellung: VBB Druckhaus „Maxim Gorki", DDE-7400 Altenburg, Carl-von-Ossietzky-Straße 30/31. Erscheinungsweise: Die Zeitschrift „Fortschritte der Physik" erscheint monatlich: Die 12 Hefte eineB Jahres bilden einen Band. Bezugspreis Je Band 180,- M zuzüglich Versandspesen (Preis für die DDE: 120,- M). Preis je Heft 1 5 , - M (Preis für die DDE: 1 0 , - M). Bestellnummer dieses Heftes: 1027/30/11/12. © 1982 by Akademie-Verlag Berlin. Printed in the German Democratic Bepublici AN (EDV) 57618

Fortschritte der Physik 30 (1982) 11/12, 583-632

Neutral Currents and P-Odd Effects in Processes with Participation of Leptons S . M. BILENKY

Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, Dubna,

USSR

S . I . BILENKAYA

Laboratory for Nuclear Problems, Joint Institute for Nuclear Research, Dubna, USSR . and G . B . MOTZ

Sektion Physik der Humboldt-Universität zu Berlin, Berlin, GDR

Content I. Introduction

584

II. Neutral current of the standard SU(2) x i7(l) theory of Glashow, Weinberg and Salam 585 III. jP-odd asymmetry in deep inelastic scattering of longitudinally polarized leptons by nucleons 3.1. General expression for the P-odd asymmetry 3.2. P-odd asymmetry in deep inelastic scattering of polarized leptons by nucleons (parton approximation) 3.3. SLAC experiment on measurement of the P-odd asymmetry in deep inelastic scattering of polarized electrons by deuterons IV. P-odd asymmetry in elastic scattering of polarized leptons by nucleons

597 597 607 611 614

V. Neutral current contributions into the cross sections of the processes e+ + e~ -»- e+ + e~ and e + + e - - > ¡x++ (x. : 622 VI. Conclusions

630

Abstract The present article is a detailed review on P-odd effects in deep-inelastic and elastic scattering of polarized leptons on nucleons. The contribution from neutral currents into the cross sections of processes e+ + e - -»• Z+ + = e, (JL) for the case of unpolarized initial particles is also considered. 1

Zeitschrift „Fortscnritte der Physik", Bd. 30, Heft 11/12

584

S. M. BILENKY, S. I . BILENKAYA and G. B . MOTZ

I. Introduction The discovery of the parity violating weak interaction between electrons and nucleons in Novosibirsk [J] and Stanford [2] is one of the most outstanding achievements of particle physics. 1 ) The data obtained in these experiments are in agreement with the SU(2) x U(l) gauge theory of electroweak interactions of G L A S H O W - W E I N B E R G - S A L A M [4, 5]. The value of the parameter sin2 6W (6W is the Weinberg angle) extracted from these data agrees with that, obtained from neutrino experiments. Recently, the first experiments on the measurement of the neutral current contribution into the cross section of the leptonic processes e + + e" ¡x+ 4and e + + e" - > e + + e" have been done with the e + — e - colliding beams at P E T R A . The experimental data obtained also agree with the Glashow-Weinberg-Salam theory. I t is obvious, however, that the investigation of the neutral current induced effects in both lepton-nucleon and purely leptonic processes will be continued. I t is important to improve the accuracy of measurements, to enlarge the kinematical region and also to investigate the neutral current effects in new processes. Having mainly in mind these future experiments we will consider in this review in detail: 1. The P-odd effects in deep inelastic scattering of longitudinal]y polarized leptons and antileptons by unpolarized nucleons. 2. The P-odd effects in the elastic scattering of polarized leptons by unpolarized nucleons. 3. The contribution of neutral currents into the cross sections of the processes e + -(- e" -»• e + -j- e" and e + + e" —> + • I t will be shown in sect. I l l , that the contribution of the vector part of the neutral hadronic current into the P-odd asymmetry of the deep inelastic scattering of polarized leptons by nucleons is given (within a few percent accuracy) by the parton model. Using only the transformation properties of the neutral current in the Glashow-WeinbergSalam theory, we obtain in this section a relation connecting the P-odd asymmetry with the cross sections of deep inelastic neutrino-nucleon processes (charged and neutral currents) and the cross section of deep inelastic lepton-nucleon scattering. Further in sect. I l l a relation is given between the P-odd asymmetries in deep inelastic scattering of leptons and antileptons by nucleons (A_ and A+) and the cross sections of deep inelastic neutrino-nucleon and lepton-nucleon processes. This relation is independent of the value of the parameter sin2 6 t v . Experimental verification of this relation would enable to test the Glashow-Weinberg-Salam theory (in the following: the standard theory of the electroweak interaction) without assumptions on strong interaction dynamics. A general formula, connecting the parameter sin2 dw with the asymmetries A_ and A+ and other experimentally measurable quantities will be also given in section I I I . Sect. I V contains a detailed calculation of the P-odd asymmetry in the elastic scattering of polarized leptons by nucleons. If one assumes the validity of the standard theory of the electroweak interaction then the P-odd asymmetry in this process is determined by the electromagnetic formfactors of proton and neutron, by the axial formfactor of the nucleon and by the parameter sin 2 6 W . The information on the proton formfactors, obtained from the elastic e—p scattering, is rather detailed. The electromagnetic formfactors of the neutron are much less known than those of the proton. The sensitivity of Already in 1 9 5 9 ZEL'DOVJLCH [3] suggested to search for P-odd effects in polarized lepton scattering on nucleons and in atomic transitions. The effects expected were determined [3] to a correct order of magnitude.

Neutral Currents

585

the P-odd asymmetry in the elastic e—p scattering to the parame triza tion of the electromagnetic formfactors of the neutron and the axial formfactor of the nucleón is analysed in sect. IV. In sect. V the cross sections of the processes e + + e" ->• e + + e~ and e + + e~ - » fj.+ + are calculated in the lowest order of electromagnetic and weak interactions for unpolarized initial particles. At the accelerators P E T R A and P E P values of q2 are reached unattainable till now (q2 ~ 1000 GeV 2 ). At such values of q2 the contribution of the interference between electromagnetic and weak amplitudes into the cross sections reaches 1 0 % and doubtlessly will be measured with good accuracy in future experiments. In the second introductory section the SU(2) x U(l) gauge theory of Glashow-Weinberg-Salam is shortly reviewed. The expression for the neutral current of this theory is derived. II. Neutral current of the standard SU(2)

X [7(1)theory of Glashow-Weinberg-Salam

All currently available experimental data on neutral currents are described [6] within the unified gauge theory of weak and electromagnetic interactions of Glashow-Weinberg Salam. In this introductory section we will obtain the expression for the neutral current of this theory. The standard theory of the electroweak interactions is built up in accordance with the local SU(2) X 17(1) invariance of the Lagrangian for massless fields. Then the gauge invariance is spontaneously broken, and leptons, quarks and intermediate bosons acquire masses. We will consider the standard case of three neutrinos (ve, v^, vT), three charged leptons (e, (j., t ) and six quarks (u, c, t, d, s, b)2). The free field Lagrangian of massless lepton and quark fields is 3 )

= -IvlLyadarlL/=

£

iy.8.1-

i = e f [x.T

e,[jL,T

E

q'y„daq'.

(2.1)

q = d,s,...t

Any spinor field can be represented as y=if>L + V>R,

where

VL=—ö—V'

(2.2)

Vr =—Ö—y

(2-3)

are the left and right helicity projections of the field y>, respectively. With eq. (2.2) taken into account, the free field Lagrangian i° 0 becomes

•fa = ~E

VaLV* daVaL — E iRy«dalR— E i = e,ti,T q = d,s,...i

a = e,t*,T, 1,2.3

(2.4)

(¡RY«d«qR-

Here Z = e,[x, t , (2.5)

^H/)'-) Note, that the experimental data in favour of existence of the ¿-quark are still lacking. Also there is no direct experimental evidence for the existence of vT. 3) We use the Pauli metric with x = (x, ix ). The Dirac equation has the form (y., d + m) y> = 0, 0 a ya are hermitian matrices, obeying the anticommutation relations y„yp + ypy„ — 2S«p; y = yiy>y.,y4;

(.9„ = e/dz.).

586

S. M. BILENKY, S. I . BELENKAYA a n d G. B. MOTZ

The standard theory of the electroweak interactions is based upon the assumption t h a t ipaL(a = e, (j., x, 1, 2, 3) form doublets of the SU(2) group and that the right-handed components of lepton and quark fields are singlets (lR and qR) of this group. if 0 is obviously invariant under .the global SU(2) transformations (2-6) lR'{x) = lR(x),

(?R'(X))' =

qR'{x).

(A = const, Tj — Pauli matrices). Local SU(2) invariance (i.e. the A; in (2.6) are functions of x) can be assured provided both leptons and quarks interact with vector particles, the fields of which form a triplet of the 8U(2) group. The Glashow-Weinberg-Salam theory is based upon the assumption, that the gauge invariant interaction between leptons, quarks and vector bosons is minimal. Such an interaction is introduced [7] with the help of the following replacement in j f 0 : d*V>aL

- ig j

tA^j ipaL.

(2.7)

Here g is a dimensionless constant. F r o m (2.4) and (2.7) the following interaction L a grangian of the fundamental fermions (leptons and quarks) and vector bosons is obtained = igiAa,

(2.8)

where the current j„k (k = 1, 2, 3) is given b y the expression Uk = E ValY* 4 " JkVaL • a "

(2.9)

Now we single out the interaction lagrangian of fermions and charged vector bosons. W e have: = *f

[j^Al-*

+

+ igjMa*,

(2.10)

where i.1±a=i.1±ija%,

Ai±«=Ai±iAa*.

Using (2.5) and (2.10) we find iJ+} Here

= 2/„1+i2 = 2 Z WaiVa a " U = 2 [uL%dL'

+ ir2) y>aL =

£

viya( l +

Yi)

I + ja.

(2.11)

/ = e,n,T

+ cL'yasL'

+ iL'yabL'}.

(2.12)

T h e first term in (2.11) is the charged leptonic current of the standard theory and as we will see in the following, ja is the charged hadronic current of this theory. The expression (2.10) can be rewritten as follows -*7 =

7. ( + ) W. + h.c.J + igjM.*,

where TIR

w.

=

AA 1

IAJ*

f2

is the field operator of charged vector bosons.

(2.13)

587

Neutral Currents

The Glashow-Weinberg-Salam theory is a unified theory of weak and electromagnetic interactions. The first term of the L a g r a n g i a n d e s c r i b e s the interaction of leptons and quarks with charged intermediate vector bosons, the second one describes the interaction of leptons and quarks with the neutral vector particles. Obviously, the second term of the expression (2.13) cannot be identified with the Lagrangian of the electromagnetic interaction. For the unification of weak and electromagnetic interactions the symmetry group has to be extended. The standard theory of electroweak interactions is based on the gauge group S U( 2) X U( 1). Let us consider the expression for the electromagnetic current of leptons and quarks ;'«em = £ ( - 1 ) hJ + I e#'yaq'. f I

(2.14)

Here eq is the charge of the ^-quark (in units of the proton charge). Using the Gell-MannNishijima formula:

(/ 3 is the third projection of weak isospin, Y is the hypercharge), it is easy to show that hem=h3 + j h

(2-15)

Y

with jaa being the third component of the isovector ja and UY = E YLIWILY^IL + t L

¡=1

YLqyiLyaVlL

+ £ YmiRyJR L

• + £ YRqqR'yaqR' Q

(2.16)

is the current of hypercharge. In equation (2.16) YLl =0 7

+ (-l) =

-1,

(2.17)

_ i + / _ I \ _ I 3/ 3

are the hypercharges of the doublets f¡L(l = e, ¡a, r) y)iL(i = 1, 2, 3), respectively, and Yri = 2( —1) = —2, YRq = 2e„

(2.18)

are the hypercharges of the singlets I and qR, respectively. We require the Lagrangian of the system considered to be invariant to the direct product of the local weak group SU(2) and the local E7( 1) group of the weak hypercharge. Such an in variance takes place provided that the following replacements in the free field Lagrangian of the leptons and quarks will be performed: OFOL

> (d* ~ ig Y rA„ - ig' Y YLaB.j ipaL, 8JR

(d. ~ iq' j

daqR -> {d* — ig' j

YRlB„J lR, YRqB^j qR .

(2.19)

588

S. M. B i l e n k y , S. I. B i l e n k a y a a n d G. B. Motz i

Here Ba is the gauge field of the hypercharge group and g' is a dimensionless constant. Thus we have arrived at the following Lagrangian of the minimal SU(2) xU(l) invariant interaction

I j = igjaA« + ig' j nYBa,

(2.20)

where the currents j * and / / are given by the expressions (2.9) and (2.16), respectively. Using now eqs. (2.13) and (2.15) we rewrite the interaction Lagrangian (2.20) as follows

where

¿7» = igjMJ + ig'(Um - U3) Ba

(2.22)

is the interaction Lagrangian of leptons, quarks and neutral vector bosons. We have = *1 ¥ T 7

l

h3 I ,

W

-g

•A3 2

+ g'

,

g

2

2

ig + g'

^

I

+ igVmB„ .

(2.23)

Further, instead of the fields A„3 and Ba we introduce

Z.=

, -A»ig2 + g'2

v

=Ba, ig + g'2 2

(2.24)

v

A* + , =Ba. ' I f + g'2 ' Ig2 + g' Consequently

A/ = -=J±= za + - J = A Ig2 + g'2 Ig2 + g'2 ig2 + g'2

a

, (2.25)

ig2 + g'2

For the interaction Lagrangian of fermions and neutral vector bosons we find, with the help of (2.23) —(2.25), the following expression .¡V =

i ig2g'2

(f.* \

9+9

uA za + % 1 = == / yg2 + g2

•

(2.26)

If the constants g and g' are related to the charge e by:

99' ig2 + g'2

(2.27) ,

then the last term of (2.26) becomes the Lagrangian of the electromagnetic interactions {A* is, accordingly, the operator of the electromagnetic field). The first term of the Lagrangian (2.26) describes the interaction of leptons and quarks with neutral intermediate bosons.

589

Neutral Currents

Now we define the angle 0W (the Weinberg angle) as — = tan 6 W . g

(2.28)

Inserting (2.28) into (2.27) we find that (2.29) Further, we have g" ig2

+ g'2

(2.30)

ig2 + g'2 = Finally, using (2.30) we arrive at the following total interaction Lagrangian describing the interactions of the fundamental fermions with the gauge vector bosons Xi = (i \ 2]/2

wa + h.o)

/

+ i

2cos0„,

+ iej™Aa.

(2.31)

Here = 2 j * - 2 sin2 B w j* m

(2.32)

is the neutral current. Thus in the standard theory of the electro weak interaction the neutral weak current • contains only one parameter, the Weinberg angle sin2 dw. The first term of the expression (2.32) is the third component of an isovector, the "plus" component of which is the charged current. The second term in (2.32) originates from the unification of weak and electromagnetic interactions. Up to now we have considered the case of massless fields. In the following we will briefly discuss the Higgs mechanism of mass generation [7], which belongs to the bases of the standard theory. We will assume that the leptons, quarks and intermediate bosons interact with scalar Higgs particles and require the corresponding interaction Lagrangian to be locally invariant under the SU(2) x ?7(1) gauge transformation. Later on the gauge invariance will be spontaneously broken. As a result leptons, quarks and both charged and neutral intermediate bosons acquire masses. Assume that the fields of the Higgs particles form a doublet of the group SU(2) [5]: (2.33)

a

where @+(x) and 0o(x) are the fields of charged and neutral particles, respectively (0O* =j= 0O). The Lagrangian for the field (x)l

(2.37)

where dk(x) and ip{x) are real functions of x. The phase factor e i ( 1 ' 2 ) r 9 ( a : ) has no physical meaning and can be omitted (it can be absorbed by a gauge transformation). Consequently, we have for the function 0(x) *(*)=(

M .

(2.38)

Using (2.35) and (2.38) it is easy to show, that the Hamiltonian of the system considered has a minimum at (UH Thus, to the minimum of the energy there correspond the values

Let us choose

and introduce instead of ip(x) the function -L

x

(

x ) = w

(2.42)

(x)--^v

which is" idefined so that y — 0 at the minimum of the energy. Thus, we obtain

n Choosing (2.41) we have spontaneously broken the original symmetry of the Lagrangian. Let us show now that as a result the charged and neutral intermediate bosons become massive. Using (2.34), (2.36) and (2.43) weobtainfor that part of the Lagrangian describing the field %{x) and its interaction with the vector bosons the following expression j g2(tAa) (rAa) + 1 g'*BaBa + 2 jgg'(rAa)

Ba 0 — V (2.44)

4

) The hypercharge of a doublet is equal to the sum of the charges of upper and lower components.

Neutral Currents

591

0 is given by eq. (2.43)). Further it is obvious that 7

(rA.) (Til.) = A. A. = 2W.W. +

AM*3,

(2.45)

-0+0A*,

0+(r A.) 0 = where 1/2

is the field operator of the charged vector particles (Wa = l/|/2 (A,1 + iAa2)). (2.24), (2.35), (2.44) and (2.45) we get = ~Y8'X

8

°X ~ \

Using

- j V t e + a®)'.

(*> + X?

(2.46) From this for the masses of the charged and neutral intermediate bosons we find

(2.47) 2

2

™z =j(g

+

2

g' )v*.

Introducing the Weinberg angle (see eq. (2.28)) we obtain from (2.47) m 2

_ g2 + g'2 _ ,

.

m

w2

Such a relation between mz2, m w 2 and cos2 8W arises provided the Higgs fields form a doublet. Note that the existing neutral current data are consistent with (2.48). After spontaneous symmetry breaking not only the intermediate bosons but also the leptons and quarks acquire masses. Let us consider the Higgs mechanism of quark mass generation. The simplest Yukawa interaction between quarks and Higgs bosons which is invariant under the group $£7(2) x ?7( 1), is of the form r

=

Z f i i G ' ^ R * + h.c., i = l q = d,s,b

(2.49)

where G'iq are complex constants. Since the hypercharges of the doublets ipiL and 0 have the values 1/3 and 1, respectively, the hypercharge of the singlet qn has to be equal to —2/3 (Accordingly, only the d^, sR' and bn' enter into (2.49)). It is obvious, that after the spontaneous symmetry breaking from (2.49) only the mass terms of the quarks with charge —1/3 are singled out. The Lagrangian !f is not the most general SU(2) X U(l) invariant interaction Lagrangian of the Yukawa type. Together with the doublet 0 we can also introduce another doublet 0=u20*. (2.50) Obviously, the hypercharge of the doublet 0 is equal to —1. Using 0 the following 8U{2) X 17(1) invariant interaction Lagrangian for quarks and Higgs bosons can be

592

S . M . B I L E N K Y , S . I . B I L E N K A Y A a n d G . B . MOTZ

constructed i" = - E E ¿=1 q=

+ h.o.

u,c,t

(2.51)

From (2.43) and (2.50) we find (2.52) Now we insert (2.43) and (2.52) into (2.49) and (2.51). We-obtain I =1'

+ 1" = -nL'M.nnR' - (v + x) - pL'MppR' - (v + z) + h.c. v v

(2.53)

Here (2.54) and Mn and Mp are complex 3 x 3 matrices. The matrices Mn and Mp can always be diagonalized by biunitary transformations: Mn = VL+mnVR,

Mp = UL+mpUR

(2.55)

the m„ and mp being diagonal matrices with positive elements ((m„) > 0, (mp)u > 0, i = 1, 2, 3), VL-R and ULiR are unitary matrices. Inserting (2.55) into (2.5.3) we get 1 {v Jf = —nmnn •— Here

n = nL + nR, nL = VLnL', PL

=

ULpL',

yv) — pmvp — (v + %). p =

pL+pR,

nR = VRnR', pR =

(2.56)

URPH

(2.57) .

We write (2.58) From (2.56) and (2.58) we get the standard expression for the quark mass term of the Lagrangian = -E mm (2-59) q = d,s,...t

(mg is the mass of the q quark). Similarly also the lepton mass term 'of the Lagrangian arises as a consequence of the spontaneous symmetry breakdown. Now we turn to the expression (2.32) for the neutral current. Consider the quark neutral current . j j = 2 f y)iLya i z3VtL - 2 sin2 0,,/,""* ¡=i ^

(2.60)

593

Neutral Currents

where ;'£,em;h is the electromagnetic current of quarks. With (2.5) and (2.54) we find 3

E

VIIV**3

q — eR(q) =

3 i n 2

d,s,b.

w•

8

The effective Hamiltonian for the neutral current induced processes is obtained from (2.66) and (2.76) as follows = £ f?(7'«V + U zu z \2

+ UV

+ 2//// + 2j.'jj+.2j j j j ) .

(2.85)

The first term in eq. (2.85) describes the interaction between neutrinos. The information available on this interaction is most poor. F r o m the experimental d a t a one can conclude t h a t ,[20] F m < 3 • 10*G (2.86) where F v v is the effective v—v interaction constant. The second term of the Hamiltonian (2.85) contributes to the effects of parity violation in hadronic processes. Such effects are experimentally observed [11]. Their detailed analysis is, however, complicated b y the necessary quantitative account of strong interactions [12].

596

S. M. B i l e n k y , S. I. B i l e n k a y a a n d G. B. Motz

The most successful investigations of neutral current phenomena are connected with the investigation of processes described by the third, fourth and sixth terms of the Hamiltonian (2.85). The Hamiltonian = 2

ojjj/

(2.87)

governs the processes involving neutrinos and hadrons. The following processes of this type have been investigated experimentally

V(v„) + p -5- V^v,*) + P, (2.88)

+N

+

+

The most detailed data exist on the inclusive processes \12] V(v^) + N

Vpi(vn) + X.

Treatment of the processes (2.88) enables to get an information on the structure of the neutral hadronic current. All available experimental data are in agreement with the standard theory of electroweak interaction [6]. Processes involving neutrinos and charged leptons are due to the interaction Hamiltonian J? = 2Q-^rU'jJ.

(2.89)

The following processes have been studied experimentally ve + e - » ve + e,

v^vn) + e -> v , ^ ) + e.

(2.90)

The cross sections of the processes (2.90) are substantially smaller than those of (2.88). This makes their investigation very difficult. Note that the existing data are in agreement with the Glashow-Weinberg-Salam theory [23]. Knowledge about the neutral current interaction *

= 2 e i .

l

u '

(2.91)

can be obtained by studying processes which involve charged leptons and hadrons. The main contribution to the matrix elements of such processes is given by the electromagnetic interaction. Extremely subtle experiments were necessary to single out the contribution of neutral currents."Namely, one investigated the effects of parity violation in leptonnucleon processes due to the interference between the electromagnetic and weak amplitudes of these processes. We will consider in detail the P-odd effects in the deep inelastic scattering of polarized leptons by nucleons (section III). The Novosibirsk experiments [2] measuring the parity violation effects in atomic transitions and the SLAC experiments [2] measuring the P-odd asymmetry in the deep inelastic scattering of polarized electrons by deuterons have played the decisive role in the determination of the neutral current structure. After

597

Neutral Currents

ture these experiments have been performed, the possibility appeared to determine uniquely all of the coefficients characterizing the neutral current. I t has been shown [14] that this unique solution is in agreement with the Glashow-Weinberg-Salam theory. In section I V we will calculate the neutral current induced P-odd asymmetry in the elastic scattering of polarized électrons by protons. Experiments to measure this asymmetry are planned at present in various laboratories [25]. In sec. V we shall discuss the leptonic processes e + + e"

+ (J.",

e + + e"

e + + e~.

(2.92)

The matrix elements of these processes get a contribution from the third term of the Hamiltonian (2.85). We consider effects arising from the interference of the electromagnetic and weak amplitudes. The first measurements of these effects have been performed recently [16\ in experiments with e + — e~ colliding beams.

III. P-odd asymmetry in deep inelastic scattering of longitudinally polarized leptons by nucléons 3.1. General expression for the P-odd asymmetry Consider the processes of deep inelastic scattering of longitudinally polarized leptons (antileptons) by unpolarized nucléons l~{l+).+

N ->l~{l+)

+ N,

-

(3.1)

{I = e, fx). The cross section has the following general form dak = do0{l

+ ?.A),

(3.2)

where X is the longitudinal polarization of incident leptons, and da0 is the cross section of unpolarized particles. The quantities da0 and A depend only upon kinematical invariants. Thus the term linear in X (pseudoscalar) can enter into the cross section only if together with the contribution of the electromagnetic interaction also the weak interaction contributes to the amplitude of the process. The asymmetry A appears due to the interference between the electromagnetic and weak amplitudes. The main contribution into the asymmetry is given by the diagrams shown in Fig. 1.

Fig. 1. Diagrams of the process I + N ->• I + X a) diagram with one-photon exchange between the lepton and hadron vertices b) diagram with Z-boson exchange

598

S . M . B I L E N K Y , S . I . B I L E N K A Y A a n d G . B . MOTZ

At presently available energies q2 mz2(q and mz are the momentum and the mass of the Z boson, respectively). Neglecting q2 versus mz2 in the Z-boson propagator we get the effective interaction Hamiltonian of charged leptons and quarks Jf = 24"

£

j/2 i = e,|x

lya{gv

+ giVi)

IjJ.

(3.3)

Here is the hadronic neutral current, gv and gA are constants (in the standard theory gr =-1/2+ 2 sin 2 6W, gA = - 1 / 2 ) . In this section we derive the general expressions for the P-odd asymmetries. At the beginning no assumptions will be made about the neutral hadronic current except its V, A structure. From (3.3) we obtain the following matrix element for the deep inelastic scattering process of leptons (antileptons) on nucleons -