El

E2

E3

E4

E5

Fl

F2

F3

F4

F5

F6

F7

F8

F9

F10

Fll

F12

F13

F14

F15

G. Ebel et. &, Springer Tract in Modern Physics 55, Springer Verlag, Berlin 1970.

L. Egart, Nuovo Cimento 2, 954, 1963.

M. Elitzur and A. Pais, Rockefeller University Preprint NYO-4204-14, 1971.

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Gl

G2

G3

G4

G5

G6

G7

G8

G9

G10

Gil

G12

G13

G14

G15

G16

G17

G18

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11

12

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J2

53

54

J5

J6

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K5

K6

K7

K8

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K15

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LlO

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2

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L15

L16

L17

L18

L19

L20

L21

L22

L23

L24

L25

Ml

M2

M3

M4

M5

M6

M7

M8

M9

Ml0

Ml1

A. D. Liberman et. al., Phys. Rev. Lett. 22, 663, 1969.

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01

Pl

P2

P3

P4

P5

P6

P7

P8

P9

PlO

Pll

P12

P13

P14

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Sll

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Tl

T2

T3

T4

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W2

w3

w4

W5

W6

w7

W8

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Yl

Y2

Y3

Y4

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- 164 -

Table

1

Tests

of

som

e hy

poth

eses

ab

out

weak

int

erac

tions

.

Hypo

thes

is

9 ef

f -

Ji’

2 co

mpo

nent

ne

utrin

o th

eory

Cons

erva

tion

of l

epto

n nu

mbe

rs

I Le

andL

P

z ul I

Best

evide

nce

from

de

cay

proc

esse

s

Fits

all

obse

rved

de

cays

Fits

all

obse

rved

de

cays

Fits

all

obse

rved

de

cays

( at!+

& < 2

x 1o

-8 >

Poss

ible

tests

in

neut

rino

reac

tions

E,

and

c$ de

pend

ence

of

cro

ss

sec-

tio

ns

(2.1

0)

Prob

abilit

y of

pro

ducin

g rig

ht-

(left-

) ha

nded

lep

ton

(ant

ilept

on)

- m

2 (2

.12)

(The

we

aker

hy

poth

esis

that

Lp

+ L

e an

d th

e sig

n of

(-D

Le

are

cons

erve

d +

dete

ctable

ie

adm

ixtur

e fro

m

/J de

cay

in

v be

ams

(see

pa

7

)

Abse

nce

of n

eutra

l cu

rrent

s

Unive

rsali

ty of

e a

nd /

J int

er-

actio

ns

Fits

all

obse

rved

de

cays

< 1.9x

10

Fits

all

obse

rved

de

cays

u(v

P +

v P)

p

<0.1

2*0.

06

Wpn

-+

1-0

)

Com

paris

on

of I

;L(~

~)

with

~~

(3~)

ini

tiate

d re

actio

ns

-

Table

1

(con

t’d.

) -

2

Fits

all

obse

rved

de

cays

7-y

I-+ P-

P K+

K”

$p

- j.i+

A (K

”+yii

o)

(y=O

if

AY ,

< 1)

,

etc.

(see

Ta

ble

2)

AY=A

QifA

Y=*l

Fits

all

obse

rved

de

cays

vp

n+

p-C+

vpp +

/i-c

+7r+

A AY

=-A

&Ay=

aQy

2 10

% i

n KY

3

vpn

-+ p

-p

(K”+

yliio)

(y

’=O

if AY

= A

Q) ,

etc.

(see

Ta

ble

2)

AI=1

2if

AY=f

l I

Tests

in

Ki3

deca

y’wo

rk

to i

lO%

and

man

y ot

her

relat

ions

Q, I

I (E

qs.

2.14

-2.1

7)

AI=1

if

AY=O

Un

teste

d u(

v p-

N*

74

ZZ

4 u(

v I-1

n -+

N*+

p-)

3

and

othe

r re

lation

s (p

. 39

)

Char

ge

sym

met

ry

cond

ition

for

AY =

0 c

urre

nt

Lack

of

mirr

or

sym

met

ry

in nu

clear

p

deca

y is

evide

nce

again

st th

is (u

nless

du

e to

iso

spin

violat

ion)

Stru

cture

fu

nctio

ns

for

mirr

or

5n

proc

esse

s re

lated

by

Wyp

=Wi

, 3P

wi

=

Wr”

(A

Y=O)

-

obvio

us

relat

ions

(e.g

.) be

twee

n ov

d an

d cE

d.

Abse

nce

of s

econ

d cla

ss

curre

nts

(=

char

ge

sym

met

ry

cond

ition

if T

cons

erve

d)

Lack

of

mirr

or

sym

met

ry

of

ft va

lues

requ

ires

2nd

class

cu

rrent

s if

CFT

holds

(u

nless

du

e to

iso

spin

violat

ion)

Fixe

s re

lative

ph

ases

of

qua

sielas

tic

form

fa

ctors

Table

1

(con

t’d.

) -

3

cvc

Isotri

plet

curre

nt

v v

gp =

gp

Limits

nu

mbe

r of

ind

epen

dent

ve

ctor

form

fa

ctors

. No

par

ity

violat

ion

when

8 Vl

=0

Wea

k m

agne

tism

pr

edict

ed

to r

t 20%

Ve

ctor

form

fa

ctors

giv

en

by

r(7r+

-, @

e+v

$ =

(0.9

5 f

0.07

) x

theo

ry

) ele

ctrop

rodu

ction

PCAC

Go

ldber

ger-T

reim

an

relat

ion

work

s to

-

10%

uv

(e,

=0)

CK o;

r cc

“A

2 31

,

Curre

nt

algeb

ra

Adler

-Weis

sber

ger

relat

ion

work

s I Ad

ler

sum

ru

les

(2.2

4 an

d 2.

25)

to - 5

%

I se

e Ta

bles

7 an

d 8

T vio

lation

l-W

; -+

7r 7

r +

-) ?

2 x’

1o-3

f-(

KL--+

all

) Tr

ansv

erse

po

lariza

tion

of l

epto

n or

ba

ryon

in

quas

i-elas

tic

proc

ess.

r(K”L

-+

r+1

-v)

Tran

sver

se

polar

izatio

n of

lep

ton

#1

when

ha

dron

s un

obse

rved

.

UK;

--*A+

?)

Table 2

Reactions allowed by charge conservation but forbidden by the

AY = 0, f 1 rule and the AY = A& rule for AY = 1 transitions.

Each box represents a reaction. The boxes representing reactions with

the same initial state are grouped into rectangles, the initial state being

inscribed in the upper right hand corner. The final state consists of the

appropriate lepton and a baryon and a meson chosen from the corresponding

position in the left hand column and the top row respectively. (The column

headed vat. represents reactions with a single baryoii in the final state).

X- indicates that the reaction has AY >\ 2 \

0 - indicates that the reaction has AY = 1 and AY # AQ

The same results obtain, of course, -if the pseudoscalar mesons are everywhere

replaced by the corresponding vector mesons.

- 168 -

Table 2

- 169 -

Table

3

VW

Char

acte

ristic

s of

Dim

uon

Even

ts.

plk

is th

e co

mpo

nent

of

the

p*

mom

entu

m

p* p

erpe

ndicu

lar

to t

he

direc

tion

of t

he

incide

nt

v O

p 1* =p

, sin

Op

* (th

e pI

give

n fo

r th

e tri

lepto

n pr

oces

s dis

agre

es

with

th

at

obta

ined

by o

ther

au

thor

s -

see

t:e

text)

.

Proc

ess

g+

P I- I

I eP

+ *l-

i- pP

+

Trile

pton

(c

oher

ent)

1 O-

50

MeV

/

O-50

,M

eV

1 Sm

all

1 Sm

all

/ Sm

all

W p

rodu

ction

I

‘v M

w/2

O-10

0 M

eV/c

1 La

rge

/ Sm

all

(inco

here

nt)

I I

1 I

z 0 Ba

ckgr

ound

I

from

sin

gle

300

- 50

0 M

edium

Sm

all

7r pr

oduc

tion

Back

grou

nd

Small

fro

m

mult

iple

1 m

300

1

Small

1

to

r pr

oduc

tion

I Lar

ge

pP-

--EV

Mod

erat

e

Rem

arks

p119

ep

k ar

e m

ultipl

e sc

atte

ring

limite

d

>;EV

>+Ev

Table 4

Errors expected from a Y experiment at ANL with 1018 incident protons D3 .

Dipole formulae were assumed for FA, Fi and Ft parametrized by M A’

MV and WM respectively. 5 is the strength of the weak magnetism term Fc ,

as in the text.

- 171 -

Table

4

Unkn

owns

MA

NEUT

RINO

AN

TINE

UTRI

NO

Flux

Un

know

n Fl

ux

10%

Fl

ux

Exac

t Fl

ux

Unkn

own

Flux

10

%

Flux

Ex

act

78

51

35

85

83

82

MA

293

221

198

97

84

82

Mv

881

,553

47

7 18

2 11

7 10

5

748

5.2

494

3.3

416

2. 7

158

108

100

1. 0

0.

6 0.

6

MA

389

302

246

’ M

v 89

2 58

0 48

7

WM

14

0 11

5 10

0

219

184

179

293

258

248

200

177

172

MV

999

583

489

I s W

M

149

135

130

I

237

188

182

387

300

281

2.9

2.2

2.1

264

247

245

Table 5

Isobar coupling constants for ?/n-p -N.““+ in various models - adopted from B20. The static model results are essentially the same as Berman and Veltmans’. The multipole content of these form factors may be obtained using the formulae in Adler’s A6 Appendix 5.

Berman and Veltman

Salin Bij tebier Adler**

V c3 2.0” 2.0 2.0 1.85

CV 4 0 0 0 -0.89

0 0 0 0

cA 3 0 0 0 0

4 cA 0 2.7 2.9 to 3.6 -0.35

5 cA -1.2 0”“” - 1.2 - 1.2

* Corrected (see p. 90 ). - **

Approximate equivalent values deduced by Bij tebier. ***

This model violates PCAC which gives Ci = -1.2.

- 173 -

Table 6

t channel quantum numbers for weak and electromagnetic structure functions. Pl

Structure Functions

WYP 1 , 2 + WTn2 I

W* - wyn 1,2 1,2

VP WY;2 + wl,2

W;H2 ) - wF2

VP w;p -I- w3

vn wlP - w3

(-lJJP

l-

+

+

+

+

(-lJJC IG Regge Trajectory

0+

1-

0+

1+

0-

1-

P,fo,f’

0 A2

P,fo,f’

P

A1

- 174 -

Table 7

Quark model sum rules for AY=O reactions in the scaling region (assuming scale invariance).

s g (F; - F;‘) = 2

- J dw ,2

(FgP + Fin) = 6 Peculiar to the quark model. G18 (R.H.S.=2 in Sakata and Fermi-Yang models.)

Sum rules from commutators of currents and their time derivations in models with renormalizable interactions -

Sum rules from commutators of currents

Comments

A5 The Adler sum rule. models.

True in all reputable

Bjorken’s ‘fbackwardl’ sum rule. B22 True in all models in which the elementary fields have spin l/2.

2 Fy, v, 5 = wFy’ VY iJ 1 2

V,V F5

= 2 F;”

v, v F4 =0

12(Fyp - FTn) = FiP - F;” Peculiar to the quark model. L18, L20

(FTP + F;“)

L

Callan-Cross relation. C6, Cl8 Depends on the elementary fields having spin l/2.

- follows from 2 F1= cciF2 and kinemati- cal inequalities.

asymptotic chiral symmetry. L20

(12 + 4 in Sakata or Fermi-Yang models.)

Peculiar to the quark model. L18, L20

(4 equality with $ + 2 in Sakata or Fermi-

Yang model. )

- 175 -

Table 8

Quark model sum rules for AY=l reactions in the scaling region (assuming scale invariance).

Sum rules from commutators of currents

J +$ (f; - f;) = <3Y +213>

2 f

3 (fp - f;) = (3Y + 213>

(W

W2)

-f ,2 3 dw (f’ + f;) = (4B - Y +213> (Glf9

Sum rules from commutators of currents and their time derivatives in models with renormalizable interactions

(G18, L20)

v,F = f4 O ( L20)

FYp 3 F”P ‘n= 2-- 4

F; F; F”P FVP Uii=2f4 , y+++

-

uA + UK = 9 (FyP + F;‘7 - $ (Fy + F;‘)

5 - F3

vn + F;’ 4

the fi are given by (L19, L20)

f;p = uA+u-, P f3”P = 2 (Up - Uh) f+Jp+ux, f? = Z(U;,-up)

f; = uA+uE, f;” = 2 (UE - U-J f~=UnfUx, fp = 2(Ux-Un)

1. e., the fi are determined by the Fi and (e.g.) qP-frP (in the parton model the Ui are the distribution functions for the quarks).

- 176 -

Table

9

Theo

retic

al to

tal

cros

s se

ction

s fo

r W

pro

ducti

on

(B43

) fo

r M

W=1

0 Ge

V in

units

of

10

-38

cm2

. c(

p),

cr(n

) de

note

th

e cr

oss

secti

on

for

scat

terin

g of

f pr

oton

s an

d ne

utro

ns

with

a

dipole

fo

rm

facto

r. u’

(p)

and

o’(n

) de

note

th

e co

rresp

ondin

g cr

oss

secti

ons

with

th

e ex

clusio

n pr

incipl

e an

d Fe

rmi

mot

ion

includ

ed.

crine

l de

note

s th

e “i

nelas

tic”

cros

s se

ction

. ac

(Ne)

/lO,

ac(F

e)/2

6,

and

ac(U

)/92

deno

te

the

cohe

rent

cr

oss

secti

ons

per

prot

on

from

ne

on,

iron,

an

d ur

anium

nu

clei

with

Fe

rmi

form

fa

ctors

. Th

e to

tal

cros

s se

ction

ca

n be

calc

ulate

d by

com

bining

th

ese

num

bers

ac

cord

ing

to

Eq.

3.13

4.

Sim

ilar

table

s ar

e giv

en

in B4

3 fo

r M

W=5

GeV

and

M

W=1

5 Ge

V.

K U(P)

u(

n)

U’(P

) u’

09

U. m

e1

yJNe

)/lO

uc(F

e)/2

6

ypJv

g2

O(P)

u(

n)

U’(P

) u’

(n)

u ine

l uc

(Ne)

/10

u,(F

e)/2

6

UC W

/92

-1

0 -!-

1

El

= 10

0 Ge

V _E

l =

200

GeV

0.09

23

0.09

91

0.10

7 0.

0405

0.

0436

0.

0471

0.

175

0.18

8 0.

204

0.07

90

0.07

90

0.08

58

0.03

87

0.04

45

0.05

14

-El

= 40

0 Ge

V

21.8

4.

38

18.7

3.

90

13.5

1.

61

0.66

4

0.52

8

23.9

27

.3

4.94

5.

88

20.6

23

.7

4.42

5.

30

16.0

20

.2

1.67

1.

73

0.69

0 0.

721

0.54

8 0.

572

-1 4.37

1.

41

4.85

1.

50

2.29

7.41

x

1o-3

6.

64

x 1O

-3

3.15

x 10

-3

74.0

81

.4

96.4

8.

45

9.44

12

.1

50.0

55

.4

67.3

7.

05

7.89

10

.3

50.6

59

.0

79.6

75

.8

80.5

86

.8

103

109

116

75.0

78

.5

82.3

0 4.76

1.

55

5.28

1.

66

2.68

7.67

x

1O-3

6.

90

x 1O

-3

3.25

x

1O-3

_E

l =

1000

GeV

+l 5.26

1.

74

5.86

1.

87

3.25

7.

97

x 1o

-3

7.21

x

1O-3

3.

36

x 1O

-3

Table 10

Yield of events in lo6 pictures

Assume: lo6 pictures at 2 x 10 13 protons/pulse

500 BeV protons

Horn focusing

vflux 1 -=- v flux 3

Reaction

Total

vn-, p-p

- $ vndp nn

h - p+C-

15 m3 H2- 15 m3 D2-

0.5 x lo6 1.0 x lo6

1.4x lo4

1.8 x lo4 1.8 x lo4

4.8 x lo3

200

70

- 200 - 1300

70 400

130 800

10 m3 Ne

6 x lo6

1 x lo5

1.2 x lo5

3.2~ lo5

- 178 -

Table 11

W and four-fermion search in neon

Assume: lo6 pictures at 2 X 1013 protons/pulse

500 BeV protons

Horn focusing

Reaction Events in 10 m3 Ne

vp Ne ---) Ne p-e+v e

vp Ne -+ Ne p-p+v P

100

50

v Ne+p-W+

Mw= 5

8

10

12

14

16‘

2.5 x lo5

2.5 x lo4

5.5 x lo3

1.2 x lo3

250

50

- 179 -

Reaction

Total

vn-,p-p

vn -+ j~-pnO

vn-b Penn+

vp - /A-pn*

Table 12

Cross sections used in compiling Tables 10 and 11.

crincm 2

0.8 Ev X 1O-38

0.7 x 1o-38

0.24 x 1O-38

0.32 x 1O-38 l

0.88 x 1o-38

3 x 1o-4o

1 x 10-40 1

2 x 1o-4o

vNe - Nep-e+v

vNe --) Nep-p+v

- -I- VP-+/J PW

1o-42 - 10-40

_ 10-Q - 10-40

-

lo-42 - 10-36

Adler X 2 because of CERN experiments

Cabbibo and Chilton corrected

by Cabbibo

(depends on MA)

Coherent on Neon

depending on Mw and E V

- 180 -

Figure Captions

1.

2.

3.

4.

5.

6.

Approximate neutrino event rates as a function of time (taken from P15 and

updated slightly). In the interests of clarity the expected results of improve-

ments planned for Brookhaven (- loo/hour) and Argonne (- 20/hour) in 1973

have not been included. Although it will use an iron target (so that the scale

of this figure does not really apply) we have included the event rate expected

in the first experiments planned for NAL for comparison (in this experiment

it is planned to introduce the liquid H2 store as a target at some stage; this

should yield - 4 events/hour).

Production of neutrino beams at proton accelerators (schematic!).

Neutrino fluxes obtainable at various accelerators in 1973. ‘lo (Perfect

focusing assumed. Hagedorn-Ranft Hl predictions used for T/K yields for

Ep > 70 GeV; Sanford-Wang s2 used for Ep < 70 GeV. Experimental data used

for SLAC. The number of interacting protons corresponds to lo5 incident

protons on the target assumed. The flux was averaged over a detector with

radius 1.8 m. )

Predicted neutrinospectra for a variety of incident energies at NAL. Cl0

(Assuming 450m decay length, 1000 m. shielding, 1.35 m radius detector,

Hagedorn-Ranft production model HI and perfect focusing. )

v/v spectra for a possible NAL beam operating at 200 GeV primary proton

energy. K3 (Assuming 600m. decay length, 300m. shielding and 2.5 m.

target - m. f. p. = 0.9m. )

ve flux from Ki3 and p+ decay expected in the NAL V~ beam shown in

figure 5. K3

- 181 -

I!

7. Spectra in the NAL *~monoenergetic’~ beam - schematic ( 8 is the angle

the neutrino makes with the primary n/K beam).

8. The coherent cross section to order G2a2 with a target nucleus A = 56 C28 for

a) vpZ - p”- e+veZ

b) v~Z - p-p+vpz - + c) veZ - e e v Z

P full lines - exact (numerical) calculation

dashed lines - asymptotic formulae (see text)

ao = G2a2Z2m2 = 3.03 x 10-44Z2cm2. P

(the dipole form factor given in the text was used).

9. Numerical results to order G2cu2 for the coherent process vclZ - p- e+veZ

for various nuclei. C28

full lines - nuclear form factor in text

dashed lines - F(q2) = exp(q2Ri/10) _

o. as in figure 8. (Similar curves are given in C28 for v~Z - ,u-~+v~Z -

see also figure 8. )

10. Cross sections for the quasielastic process in the conventional theory with

m = 0 and dipole forms

- (1- 0.7Lv2)

1,2 L12 for the form factors FA and FV (the dotted line is the limit for a,, and Ok

as E- m).

11. Differential cross section for the quasielastic process; as in figure 10 with

0.73 Gev2 - 0.71 Gev? D3

12. Contributions of the structure functions “Al*, “B*’ and ‘rC’l to the differ-

ential cross section for the quasielastic process (P9 quoted in D3) where

u= PfAfl + “B”(s-u) + “c”(s-u)~] /E2.

- 182 -

13.

14.

15.

16.

17.

18.

19.

20.

Simulated experiment at the AGS (Brookhaven)(PS quoted in D3). The model

input is the same as in figures 11 and 12.

Average transverse polarizations in quasielastic neutrino scattering as a

function of the neutrino energy. D4

a) Bound of O(a) contribution of the elastic intermediate state.

b) Bound of O(a) contribution of the inelastic intermediate states.

c) Predictions of Cabibbo’s theory of T violation (see text for a discussion of the form factors used).

labels: p polarization of proton in vn - p-p

n polarization of neutron in Vp -c p+n

P polarization of muon in Vp - p+n.

Exclusion factors defined in text for C 12 Bll .

Exclusion factors defined in text for Fe 56 Bll .

Ratio of deuteron to neutron cross sections in the quasielastic process for

Ev >> 1 obtained using a Hulthen wave function in the closure approximation. B33

Results of the Argonne experiment for quasielastic events on an iron target. K15

The upper and lower solid curves are the experimenters theoretical results for

a free neutron and for the Fermi gas model. The three dashed curves were

obtainedBll from the free neutron curve using 1) symmetric Fermi gas; 2)

asymmetric Fermi gas; 3). shell model (5 = cross section per neutron).

Same experiment and solid curves as figure 18. 3) is as in figure 18. 4) is

curve 3) increased by 3OYc (the experimenters regard their absolute flux as

uncertain to this degree).

Results of the CERN spark chamber experiment H5 for events with Ev > 1.4 GeV

and cos6 ,111 > 0.8:

- 183 -

21.

22.

23.

24.

25.

26.

27.

28.

inelastic + elastic (MA= 0.84 GeV)

- - - - inelastic + elastic (MA = 0.5 GeV)

-.-.-. inelastic contamination.

Results of the CERN bubble chamber experiment for the elastic cross section Es45

as a function of the visible energy (Evis).

Q2 distribution of quasielastic events in the CERN bubble chamber experimentB45

0 experimental values.

0 7r ’ contribution

theoretical curve for MA = 0.7 GeV.

Total cross section for vp - &.L+ as a function of the antineutrino energy in the

Cabibbo theory. The same q2 dependence was taken for all form factors. w9

Total cross section for vn - Z-p+ (otherwise as for figure 23). wg

Polarizations in I AY I = 1 antineutrino reactions at Ev = 0.5 GeV (in a double-

pole approximation with six form factors)‘and a comparison AY = 0 curve M4

1. Vp - p+n

2. vp-P+A

3. ‘;;p-/.&+ZO

4. Fn -p%-

(This figure and figure 26 are reproduced by permission of John Wiley and

Sons, Inc.)

Polarizations as in figure 25 except Ev = 5 GeV. M4

Berman-Veltman angles (defined in the N* rest frame).

Total pion production cross section in Adler’s model with W < 1.39 BeV, by a

neutrino incident on a target consisting of ip + &n. Curve (a) - Born

approximation plus resonant multipoles; curve (b) - full model, including

- 184 -

dispersion integral corrections to the small partial waves; curve (c) - full

model, multiplied by the electroproduction experiment/theory ratio R(k2).

The values of Mi are in (BeV) 2 A6 .

29. Total pion production cross section in Adler’s model with Wls 1.39 GeV by

antineutrinos incident on CF3Br. The values of Mi are in Ge v2 . Theoretical

curves calculated from the Born approximation plus resonant multipole

model. A6 Experimental points from Y4. The same experiment gave a

neutrino cross section compatible with Adler’s model with Mi in the range

0.71 to 2 GeV2 (a N (0.6 f 0.2) x 10-38cm2/nucleon - see reference Y4 or

Adler’s figure 25. In a later experiment on C3H8 .B46 the events originating

on free protons were selected; this (presumably) more reliable procedure

gave a much larger result - see figure 35).

30. da for single pion production in Adler’s model A6

dQ2 using the Born

approximation plus resonant multipoles all multiplied by the experiment/theory

ratio for electroproduction. The theoretical curves are normalized to the

number of events. (The data is from the CERN CF3Br experiment - see the

discussion in the previous figure caption. )

31. Differential cross section for vn - N*+p- for each form factor taken one at a

time as Fi = 1 ( l-q2/b2p

with b = 850 MeV. A12 Dashed curves - n = 1;

solid curves - n = 2. The form factors are those defined by Albright and Liu Al2

(see the appendix).

32. Total cross sections corresponding to figure 31. Al2

33. q2 and M2(np) distributions for @-7r’p) events with Evis > 1 GeV originating on

free protons in’ the CERN C3H8 experiment. B46

34. Distributions in the Berman and Veltman angles (figure 27) for events with

- 185 -

35.

1.3 < I < 1.9 GeV2 and sin2f < 0.1 (same experiment as figure 33). B46

Cross section for vp - p’n+p (same experiment as figures 33 and 34 B46 ).

36.

The errors shown are purely statistical. Systematic errors are f 20%.

The Q2 - v plane for neutrino scattering.

I. Elastic scattering: Q2 = 2v

37.

II. Threshold for 7r production: Q2 =2v-2Mmn-Mt

III. Line of fixed missing mass M*: Q2 = 2v + M2 - M*2.

Total neutrino-nucleon cross section as a function of neutrino energy E. The

freon cross sections have been multiplied by 1.35 to normalize them to the

propane cross sections for Ev > 2 GeV. The errors shown are statistical

only. B47

38.

39.

Plot of Q2 versus the neutrino energy. MlO, Ml1

Form of the distributions in y = v/ME for three ranges of neutrino energy.

The dotted lines in the first and last bin indicate the raw data before making

small corrections for the exclusion principle in elastic events and for the E

dependent coefficient in Eq. (3.67) so that (3.74) applies M1oy M11. (The labels

F 1 = F3 = 0, etc. really mean that the integrals over these quantities are

equal, weighted as in (3.74)).

40. Fits to the ratios A and B (Eq. 3.118) for all the data with E > 1 GeV. Ml1 The

broad hatched area is the physical region allowed by the positivity conditions

(3.77). The ellipse is the likelyhood contour corresponding to one standard

deviation from the best fit. A and B together determine

r = (U vn + avp)/(u~p + avp ) and lines of constant r are shown (see the text for

a discussion of the significance of these results).

41. Fraction F of “clean’~ events with an identified proton (momentum

- 186 -

2 Ml0 5 0.8 GeV/c) plotted against q . II Clean” events have net secondary

charge Q = 0 or + 1 and do not contain more than one identified nucleon

(indicating that the nucleus did not necessarily break up).

42. Average pion mu1 tip1 ic i ty in Yfcleanfl events (see caption to figure 41) plotted

against log v . Ml0 The authors of the paper from which this figure is taken Ml0

caution that because of uncertainties due to the fact that the target is a nucleus

(so that, e.g., the selection of 11 clean” events biases against large multi-

plicity) it is only possible to conclude that 5 increases slowly with v. In

spite of this we give this figure because it shows the only data now available.

43. The forward neutrino cross section averaged over free neutrons and protons.

(a) The inelastic cross section according to Adler’s theorem using an=35 mb

for missing mass W > 2.13 Mp and a resonance formula for W < 2.13 M . P

(b) The contribution to the inelastic cross section from W < 2.13 Mp. (c)

The elastic cross section. BiO

44. The differential cross section for the forward process in the resonance region

for a neutrino energy 4Mp (upper curve) and the result (lower curve) of multi-

plying by the square of the modulus of the shadow factor, the potential V being

computed in a modified forward scattering approximation. W is the invariant

mass of the final hadron system. B10

45. The inelastic differential cross section da/dcos6 in our model averaged over

free neutrons and protons and over the CERN neutrino spectrum. The muon

energy was required to be > 1.2 GeV. The longitudinal contribution (which is

liable to shadowing) and the transverse contribution (which is not) are shown

separately. The horizontal scale is related to cos0 by case = l.O- 0.00095 x. BlO

- 187 -

46.

47.

48.

49.

50.

51.

52.

53.

Cross sections for vN - JL- W+N with N = proton/neutron, MW = 7 Gev,

K = 0, * 1 and dipole form factors. B43

*I Elastic” cross section (up - ,u- W’p), as in figure 46 with K = 0, and

I1 inelastic II cross section (v p - p- W+ + . . . ). B43

Incoherent total cross sections for W production off protons and neutrons

without allowing for the Pauli principle or the Fermi motion (i. e. , the free

nucleon cross section (T(P) of table 9 is plotted; we refer to the table for an

illustration of the influence of nuclear effects which would not change the

qualitative features of this figure) and the coherent cross section per nucleon

in typical cases. MW- - 8 GeV, K = 0. B43

Plot of the fraction of p-‘s with energy greater than a specific E * P- ill VP - /A-w+p. Solid curves. .s= 5 GeV. Dashed curves: MW = 10 GeV

(K = 0 in both cases). B44 _

The angular distribution of the /A- with respect to the neutrino direction in B44

VP - /W+p (K = 0).

Plot of cv = ainel, (x,y) + aw against x and Ev for MW = 7 GeV. The cross

sections are for Pb 208 C23 .

Scatter plot of M versus cos e /JP

TV : x freon (1963-1964); propane (1967);

the continuous curve is the expected elastic distribution. B45

Ideograms, his tograms, and least squares fitted means for the M dis- P=

tribution for events giving one possible single muon-pion combination in the

1967 neutrino experiment. a. Total distribution for 217 v events and 12 v

events, the latter also shown separately (34 v events are off scale). The

inset shows the mass distribution of the seven A0 obtained in the experiment.

b. Distribution for 106 v events and 6 ‘i; events remaining after selecting out

- 188 -

events with 1.125 i M* < 1.350 GeV (21 v events are off scale). c. Ideograms

of all v events and all ‘G events in the region of M P

= 0.425 GeV. The

weighted means and their standard errors are shown for all the largest groups

of three or more consecutive values of M ~~ with a confidence level 1 50%.

The two groups indicated are: WM (17~ ) = 0.423 f 0.002 GeV; WM(4F) =

0.424 f 0,003 GeV. Rl

54. Anti-neutrino cross section ratios for Yf cqmpared to N* production. w9 Here

- 189 -

c-l a I -Q-

-:,,. ., ,.. .., ,..v........P

- -I 2

___--------

- - -.

I I

I I

I M

KJ-

r-Q c\I

0 -i

‘: I

0 0

0 -0 -

0 - 0

0 0

- -

- -

_ -

i .

- -

X 0 CL: a a 4

W-IOH

/N0313nN 33Uzl

NO 3lVtl

lN3A3 ONltllnN

318lSSOd

_ _. _.--.

1 T-i

c:’ -. ,

.

,.

.

DECAY TUNNEL SHIELDING

CYTRAf’TFn I , q I TARGET AND , EXPERIMENT

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