東北大学機関リポジトリTOUR

Study of νd→μ-pps and νd→μ-Δ++(1232)ns

using the BNL 7-foot deuterium-filled bubble

chamber

著者

Kitagaki T., Yuta H., Tanaka S., Yamaguchi

A., Abe K., Hasegawa K., Tamai K., Sagawa

H., Akatsuka K., Furuno K., Tamae K.,

Higuchi M., Sato M., Kahn S. A., Murtagh

M. J., Palmer R. B., Samios N. P., Tanaka

M.

journal or

publication title

Physical Review. D

volume

42

number

5

page range

1331-1338

year

1990

URL

http://hdl.handle.net/10097/53660

doi: 10.1103/PhysRevD.42.1331

PHYSICAL REVIEW

0

VOLUME 42, NUMBER 5 1SEPTEMBER 1990

Study

of

vd

=1M

pp,

and

vd

=p

5,

++(1232)n,

using the

BNL

7-foot

deuterium-filled

bubble

chamber

T.

Kitagaki,

H.

Yuta,

S.

Tanaka,

A.

Yamaguchi,

K.

Abe,

K.

Hasegawa,

K.

Tamai, *

H.

Sagawa, *

K.

Akatsuka,

K.

Furuno, and

K.

Tamae

Tohoku University, Sendai, Japan

M.

Higuchi and

M.

Sato

Tohoku Gakuin University, Sendai, Japan

S. A.

Kahn,

M.

J.

Murtagh,

R.

B.

Palmer, N.

P.

Samios, and

M.

Tanaka

Brookhaven National Laboratory, Upton,

¹w

York 11973

(Received 8january 1990)

The weak nucleon axial-vector

(F~)

and vector (F&) form factors are determined from the momentum-transfer-squared (Q )distributions using 2538p, p and 1384_p

b++

events. The data

were obtained from 1800000pictures taken in the BNL7-foot deuterium-filled bubble chamber

ex-posed to awide-band neutrino beam with a mean energy

E

=1.

6GeV. In the framework ofthe conventional V

—

A theory with standard assumptions, the value obtained from the _p p events for the axial-vector mass

M„

in the pure dipole parameterization is 1.070+oo45 GeV and from the

p

5++

events is 1.28+0loGeV. These results are in good agreement with an earlier measurement

from this experiment and other recent results. The reaction mechanisms for both processes are compared and found to be very similar. A two-parameter fitfor the quasielastic reaction, using di-pole forms for F& and

F„,

yields

M„=0.

97+oi& GeV and MV=0.89+007GeV, which is in good

agreement with the conserved-vector-current value ofMv

=0.

84GeV. Possible deviations from the standard assumptions are also discussed.

I.

INTRODUCTION

The weak and electromagnetic structure

of

the nucleon has been studied both theoretically and experimentally for many years. The vector form factor

F

v(Q ), which

has been successfully explored in high-energy elastic elec-tron scattering, is well described by a dipole form factor

A,

(Q

)/(1+Q

/Mv)

with a vector mass

Mz

and a

correction factor A,(Q )to correct for a few-percent

devi-ation from a pure dipole form factor.

The weak nucleon structure has been investigated in

several experiments using both quasielastic neutrino scattering v„n

~p

p,

' and the

6

+ production reac-tion,

_v~~jM

5++.

Both the vector

(Fv)

and the axial-vector

(F„)

form factors can be measured using ei-ther neutrino quasielastic scattering or

5++

production reaction in deuterium bubble-chamber experiments. The form factor

F~

is usually parametrized in terms

of

the axial-vector mass

(M„)

and determined using the V

—

A

theory with the standard assumptions

of

conserved vec-tor current (CVC), an absence

of

second-class currents, and time-reversal invariance. While there have been a number

of

studies

of

Mz using the

_p

_{p reaction} from light-liquid bubble chambers, only one other study using

6++(1232)

production in D2has been reported. '

In this paper the final results

of

a detailed study

of

the quasielatic reaction

v

+d~p

+p+p

and the

6++

reaction

v„+d~@

+b,

++(1232)+n,

, (2)

where

_p,

and n, are the spectator proton and neutron re-spectively, are presented. The data were taken with the 7-foot deuterium-filled bubble chamber exposed

to

the wide-band neutrino beam at the Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory. The primary objective

of

this study was to determine the axial-vector mass

_(M„)

using the dipole form

of

F„and

to compare the mass values obtained from the two reac-tions. Parametrizations

of

F„other

than the convention-al dipole form are considered and the standard assump-tions used in extracting

M„are

tested. In the determina-tion

_{of M~,}

the effects

of

the deuteron should be taken into account. Since theoretical calculations for the deute-ron effects are only available for reaction (1), caution must be taken in comparing the values

of M„determined

from the two processes. The results

of

a comparison

of

the two reaction mechanisms are presented. In

Sec.

II

details

of

the experiment are presented while in

Sec.

III

the procedures used in the form factor analysis are dis-cussed. The results

of

the various analyses are discussed

in

Sec.

IV and the conclusions from this study are de-tailed in Sec. V.

1332

T.

KITAGAKI etal. 42

II.

EXPERIMENTAL PROCEDURE 0,

400

The data were obtained from a total

of

1

800000

pic-tures taken in the 7-foot deuterium-filled bubble chamber exposed to a wide-band neutrino beam with a mean

ener-gy

of 1.

6 GeV from the Alternating Gradient

Synchro-tron at Brookhaven National Laboratory. The final data samples for reactions (1)and (2)are obtained from all ex-posures

of

the chamber and the sample for reaction (1)is approximately twice the size

of

that used in an earlier analysis. ' Details

of

the experiment and a full descrip-tion

of

the chamber have been given elsewhere. '

The film was scanned for neutral-induced interactions with more than one visible charged track.

Approximate-ly

32% of

the film was rescanned, yielding scanning eSciencies

of

0.90+0.

01,

0.95+0.

01,

and

0.

93+0.

01 for the two-, three-, and all-prong event topologies, respec-tively. Each event was measured and processed through the geometry progr am TvGp and the kinematic-fitting program sQUAw, and then examined by physicists.

Neutrino charged-current events were selected by im-posing the following requirements: (1)the magnitude

of

the total visible momentum vector must be greater than 150 MeV/c; (2) the angle between the total visible

momentum vector and the neutrino-beam direction must be less than 50',and (3) at least one

of

the negative tracks must either leave the chamber without interacting, or stop in aplate with a range consistent with amuon inter-pretation, or decay into an electron. The initial data set contained approximately

8100

charged-current and 800 neutral-current event candidates inside a restricted

fidu-cial volume

of

4 m

.

The candidates for the reactions

v„1~@,

pp, and v„d

~p

pm+n, were selected using

three-constraint fitting and particle identification.

If

the spectator nucleon was not measured, an initial value

of

0245

MeV/e for each component

of

the spectator momentum

(P„,

P,

P,

) was assigned in the fit. A total

of

2684

_p

_pp, and

_{1610 p}

pm+n, events were obtained

with a

_y

fit probability greater than l%%uo and with the

particle identification consistent with the track mass hy-pothesis in the successful fit.

If

an event fit to two reac-tion hypotheses, the hypothesis with a larger

_g

probabil-ity was accepted. In Table

I

the data used forthe present analysis are summarized.

Events in reaction (1)with low-momentum recoil pro-tons and slow spectator protons would appear in the film

as one-prong events and would be lost at the scanning stage. However, it is possible

to

estimate the effect

of

this problem on the subsequent analysis. Figure 1(a) shows

200— w 0.2 P (GeV)

0.

4

0

~

g4

t00-cl_w

50-Wh Wb ww

0

I

z

lo-w O 0.

8-(c)

I i

05

I.O 02 (Gg+2) l.5 .

0

FIG.

1. (a) The spectator-proton momentum distribution

with the prediction from the Hulthen wave function. The shad-ed and the unshaded areas correspond to the measured and the

Atted spectator momenta for quasielastic

v„d~p

pp, events.

(b) The event detection efficiency as a function of

Q'.

(c)The average scanning efficiencies with the event detection efficiency (solid circle) and without the event detection efficiency (open

circle).

the spectator proton momentum distribution for reaction

(1).

The shaded region in this figure denotes measured spectator protons where the spectator isdefined

to

be the slower

of

the two measured protons. The unshaded area corresponds to the two-prong events in which the mo-menta for the invisible spectator protons are obtained from the kinematic fit. The curve represents the predic-tion from the Hulthen wave function and it describes the data adequately except for

I',

)

200 MeV/c, where the re-scattering effects in deuterium become apparent. The

TABLE

I.

Summary ofevents.

Reaction vd~|M pps Observed 2684 0.5(E (6.0 GeV 2544

Q'&3.

0 GeV (0.

1&Q'&3.

0 GeV') 2538 (2310)

vd~p

pn n 1.08(M(mp) + 1.40 GeV 1610 1547 1385 1384 (1232)

42 STUDY OF

vd~p

pp, AND

vd~p

200

iso

-I O O

IOO--50 .

— LLI

0

0

I I I 0.I 0.2 0.

3

0.4 0.5 P (GeV)

FIG.

2. The fitted spectator-neutron momentum distribution for the

5+

events.

proton detection efficiency is then the ratio

of

observed spectators topredicted spectators from the distribution

of

Fig.

1(a), where one assumes that the proton detection for

P,

)

200 MeV/c is

100%.

Using this proton detection to-gether with Monte Carlo

—

generated events for reaction (1),itis possible to calculate an event detection probabili-ty (i.e.,

)

2 prongs visible on the scanning table) as a function

of

Q

.

The resulting curve shown in

Fig.

1(b)

in-dicates, as expected, that the losses due to missing 1-prong events are at very low _Q and for values

of

Q

)

0.

08 (GeV/c) no correction is required. The effect

of

the loss

of

1-prong events on the scanning efficiency as a_{function Q} is clearly visible in

Fig.

1(c). In addition to these experimental problems, the low-Q region is also most sensitive to nuclear corrections and to Fermi motion corrections. Consequently, in the maximum-likelihood analysis

of

_{the Q distribution} todetermine the form factors, only the region Q

)

0.

10 (GeV/c) isused.

A potentially important experimental problem for the study

of

the

6+

reaction isthat the spectator neutron is

not measurable. Since the kinematic fitting procedure constrains spectators to relatively low momenta, this im-plies a cutoff in the neutron spectator momentum. This can be seen by comparing the neutron-spectator momen-tum distribution (Fig. 2) for the b,

++

reaction with the previously discussed proton-spectator momentum distri-bution

[Fig.

1(a)]for the quasielastic scattering where the measured high-energy tail isapparent. One way toassess the impact

of

this limitation is toconsider the sensitivity

of

the quasielastic results toacut onthe spectator-proton momentum. As isdiscussed below there is no evidence

of

a significant change in the value

of M„determined

from the quasielastic scattering

if

only events with

P,

&50 MeV/c are used. Consequently, one might not expect the

5++

_{reaction results to be sensitive}

_to

the loss

of

high-momentum spectators.

The number

of

selected quasielatic events in the neutri-no energy range

0.

5(E„(6.

0

GeV and

0.

1(Q2(3.

0

(GeV/c) is

2310.

The primary background comes from the reaction

v„d~p

p~

p, .

This background was

es-timated to be

—

5%

using three-constraint fit

v„d~p

pm+n, events. The overall correction factor was found to be

1.

11+0.

04 including the one-prong correction

of

2.

3%

estimated from the event detection efficiency shown in

Fig.

1(b). Table II(a) details the corrections for the

_v„d~@

_pp, reaction.

It

should be noted that these corrections only affect the total number

of

quasielastics in the data and they do not affect the shape

of

the _Q distribution in the region

of

interest.

Figure 3 shows the per+-mass

[M(pm+)]

distri. bution for the

_p

p~+

state. The curve is the result

of

the best

fit tothe distribution using a relativistic Breit-Wigner

res-TABLE

II.

Corrections for the vd

~

_p pp, and vd

~

_p pm.+_{n, reactions.}

Correction Correction factor

Scanning efficiency Measuring efficiency One-prong correction proability cut Background vd

~p

p&ps vd

~vp&

ps (a) vd

~p

pp, g4 gs 1.092+0.025 1.038+0.030 1.023 1.010 0.948+0.008 0.998+0.001 Total correction _g,XgzXg3 Xg4XgsXg6 1.110+0.040 Scanning efficiency Measuring efficience

y'

probability cut H2 contamination in D~

Loss offast neutron spectator Background

vd~p

pm' 7Tn, vd~vpm m n (b)

vd~p

pn+n, gl gz g4 gs 1.092+0.037 1.038+0.040 1.010 0.870+0.020 1.220+0.010 0.977+0.008 0.998+0.001 Total correction _{gl Xg~}Xg3Xg4Xgs Xg6Xg7 1.123+0.059

1334 T. KITAGAKI etal. 42 f I I I ( I I I i ] I 1 I I ( I I I I ( I I t I I l l I I I I ) I I I i ~ O IOO-O O (A

so-Z'. QJ LLI P. 0 I i

»

i I i

»

i I I I.2 I.4 I.6 I.S 2 M(pm-+) (Gev)

FIG.

3. The effective-mass distribution for the _p pm+n, events.

500—

IOO

50

0

O

O

M

2

IOO 5O Ld IO 5

(a)

I ~ I

(b}

.07GeV . 28GeV-.14GeV-.

onance form with a three-body phase-space background. The phase-space _component obtained from the fit was less than

1%.

The number

of

selected )M

5++

events

with the pm.+ mass

of 1.

08

&M(pn.

+)

1.

40 GeV, neu-tron energy

0.

5&

E„&

6.

0

GeV and

0.

1&Q2&

3.0

(GeV/c) is 1232. The primary background comes from the reactions

_v„d~p

pm+n, m and

v„d~v~n+m

n,

and from a

(13+2)%

H2 contamination in the deuteri-um. ' There isalso a systematic event 1oss from the kine-matic fitting due to fast neutron spectators and the scanning-measuring ineSciency. The overall correction factor was estimated to be

1.

123+0.

059 and is described

in detail in Ref.

4.

Table II(b) lists the corrections for the vd

~p

p~+n,

reaction. Again, these corrections do not affect the _Q distribution in the region

of

interest.

Figures 4(a) and 4(b) show the neutrino-energy

_(E,

)

distributions for the quasielastic and

6++

production re-actions. Both distributions peak at approximately

1.

2

GeV. Figures 5(a) and 5(b) show the

momentum-0

I I I I I I l I I I I l I 'EwI I 2 Q (GeV )

FIG.

5. The Q' distribution for (a) the quasielastic and (b)

the

6++

production reactions. The curves are the theoretical predictions obtained from least-squares fits with the fitted

M„

values for the Q' &3.0 (GeV/c) .

III.

FORM-FACTOR ANALYSIS

transfer-squared (Q-") distributions for reactions (1) and (2). The scanning and measuring efficiencies are included

in these distributions as well as the correction for the one-prong event loss for reaction (1)shown in

Fig.

1(b). The curves in

Fig.

5are the theoretical predictions which

will be discussed in

Sec. IV.

400—

e)

200—

O V) I-

₀

200—

LIJ I

00—

0

l

0

2 4

E„(GeV)

F„(g

)= —

1.

254/(1+Q

/M„)

(3)

To

extract the weak nucleon form factors from reac-tions (1) and (2), the experimental data are fit to the theoretical predictions using maximum-likelihood method. Denoting the hadronic mass

M(pn.

+)as

8',

the

predictions

of

the cross sections, dcr

/dg

and d

o/dg W,

are formulated from the standard V

—

A

theory with the following assumptions: (i) time-reversal invariance and charge symmetry, (ii) partial conservation

of

vector-current, and (iii) conservation

of

vector current (CVC). The vector form factor

Fz(g

)istaken tobe the dipole form

Fv(g

)=A,

_(g

_)/(1+g

/M~)

where

MV=0.

84 GeV, and A,

(g

) is a correction factor

ac-counting forsmall deviations from apure dipole form ob-tained from electron scattering data. ' Under these as-sumptions, the axial-vector form factor is the only

un-known. A _{complete description}

of

the cross sections may be found elsewhere.

"'

In quasielastic scattering, the axial-vector form factor

F„(g

)isconventionally parametrized by a dipole form:

FIG.

4. The E„distribut&on for (a) the quasielastic and (b)

the

5++

production reactions.

where M~ is the axial-vector mass. The maximum-likelihood function

L

~ used in this analysis is given by

vd~p

pp,

vd~p

5++{1232)n, USING.

. .

1335 R (Q;)der/dQ; N

f,

'

R

(Q')(der/dg')dg'

Qmin

c;(0)[1+a(g

/(b,

+Q

)]

F;"(

)=

(i

=3,

4,

5),

(1+Q /M„)

(5)

where c;(0),

a;,

b; are the model-dependent axial-vector

form-factor parameters determined for the Adler

mod-el:"

c3(0)

=0,

c4(0)

= —

0.

3,

c~(0)

=

l.

2,

a3=b3=0,

a4=a5

= —

1.21, b4=b5

=2.

0

. The likelihood function

L

in this case isdefined as

L

(MA) d

crldg

dW Q W

f

IIIRx

f

ms 2 P _2)d Qmin min co(Q, ) (6) where N is the total number

of

events in the Q range from

_Q;„

to

Q,

_„,

R (Q;) is the correction factor' for

the free-neutron cross section due to the effects

of

the Pauli exclusion principle and deuteron binding and co(g; )

isan event weight based on the scanning efficiency. There are several theoretical models'

'

' for

5++

production which are based on the hypotheses outlined above. Detailed comparisons

'

of

these predictions to other experimental data have shown that the Adler mod-el' best desc'ribes the data. In this analysis the Adler model as developed by Schreiner et

al.

' is used. The axial-vector form factors are parametrized as

for the dipole form in the Q range

0.

1 _Q

~

3.0

(GeV/c) . This value is more than 4 standard deviations from the equality M~

=M&=0.

84 GeV. The curve in

Fig.

5(a) is the prediction with

M„=1.

07 GeV fitted to the distribution for _Q

(3.

0

(GeV/c) . There is a good agreement with the data forall Q

.

Since there is no theoretical basis for the assumption

of

a dipole form, we have also fit to a quark model with axial-vector-meson dominance {QM-AVMD) suggested by Sehgal

F„(g

)=F„(0)(1+Q

/M„)

Xexp[

—

—,

'Q

R

/(1+Q

/4M&)],

where R

=6

GeV and

M

isthe proton mass. The re-sult

of

the fit is

M„=

1.

37+0.

13GeV forQM-AVMD.

It

is interesting to note that this value is consistent with the mass

of

the

a,

(1260) meson' with a full width

of 330

MeV, though the mass value is quite sensitive to the form used for

F„(Q

).

A simple monopole form for

_F„(Q

)isexcluded at the

level

of

5 standard deviations based on the likelihood-function analysis.

By fitting both

M„and

M~ simultaneously to dipole forms, one can test the CVC prediction

of

M&=0.

84 GeV. Figure 6shows the one-standard-deviation contour plot

of L

~ _in

_(Mr,

_{MA ) space. This fit yields}

M„=0.

97+o

&& GeV and My

=0.

89+@'7 GeV, in

agree-ment with the value

of

Mv=0.

84GeV.'

The present results are consistent with a previous re-sult

of

this experiment' as well as the results from other experiments. ' _{These various results are summarized in}

Table

III

for the single-parameter fits and in Table IVfor the two-parameter fits. All the errors quoted correspond to a change in the corresponding likelihood functions by

0.

5units.

In this analysis the deuterium-target effects are taken into account by applying the correction factor' R (Q )

where

8';„and

8',

_„are

taken to be

1.

08 and

1.

4 GeV, respectively.

To

compare the

M„values

from reactions (1) and (2), we have used events with

0.

1&Q~

~

3.0

(GeV/c) for both reactions. Maximum-likelihood fits to the data with the dipole axial-vector form factors have been performed for reactions (1)and (2), and the results are given in the next section.

+

OP o.

e-(3

X

IV. RESULTS

A. The quasielastic reaction v„d

~

p pp, 0.8 I.O l.2

Mq

=

1~070 _o(~q GeV (7)

With the standard assumptions and

MV=0.

84GeV, a one-parameter fittothe data yields

MA (GeV)

FIG.

6. The one-standard-deviation contour plot of

L~

in

(M&,

M„)

space. The open circle isthe point obtained from the one parameter fit.

1336

T.

KITAGAKI etal. 42

TABLE

III.

Axial-vector mass

M„

in the dipole form factor from

v+

H,/D2 experiments.

E.

(Gev) 0.5-6.0 0.

3-6.

0 0.15—3.0 5.0-200 Raw events 2544 1138 1737 362 M~ (GeV) (a)

v+n

~p

_p 1070+oo~ 1.07+0.05 1.00+0.05 1.05—_0.&6 Reference This expt.

This expt., BNL 1981 (Ref. 1)

ANL 1982 (Ref. 2) Fermilab 1983(Ref. 3) 0.5-6.0 0.5-6.0 5.0—₁₀₀ 5.0-200 0.5-6.0 1385 672 138 551 871 (b)

v+p-q-a++

128+0.08 1.14+0.014 1.25+0.15 0.85+0.10 0.98+0.06 This expt.

This expt. (P,&50MeV) Fermilab 1978 (Ref. 5)

BEBC 1980 (Ref. 6)

ANL 1982 (Refs. '7,₈₎

for the free-neutron cross section, which iscalculated us-ing the impulse approximation with the Hulthen wave

function for the deuteron. A number

of

other theoretical calculations

of

these deuteron effects have been made

us-ing various deuteron wave functions with and without final-state interactions, or using different methods such as the closure approximation or the elementary-particle-model approach. ' ' _{The numerical results are all}

com-parable and they all indicate that the deuteron effects are important only for _Q

(0.

1 (GeV/c) .

To

investigate a possible deviation from the pure dipole form factor, the

M„values

from the maximization

of

the likelihood function are plotted as a function

of

the _Q cut in

Fig.

7(a). The arrow in

Fig.

7(a) indicates the lower limit

Q;„=0.

1 (GeV/c) used to obtain the value

M

„=

1.

07 GeV (the dashed line).

For

Q;„~

0.

06 (GeV/c) the value

of

M„obtained

is insensitive to the actual

Q~;„used.

However for lower

Q;„

there isan

in-dication

of

a change in the

M„obtained.

This may in

large part be due simply tothe difficulty

of

correction for losses in low-Q (single-prong) events or it could refiect problems in correcting for deuteron effects.

The effects

of

the deuteron binding are known to be

very strong at Q

=0

and they reduce the deuteron cross section by

40%.

To

study this effect further,

Fig.

7(b) shows the

M„distribution

as a function

of

the

_Q;„cut

for events with spectator-proton momentum

P,

&50 MeV/c. Events with low

P,

are likely to be less affected

by the deuteron effects. Again there is an indication that the

M„value

rises for very low

Q;„cuts.

However, the likelihood fit for events with

P,

&50 MeV yields

M„=1.

07+0.

07 GeV for

Q;„=0.

1 (GeV/c) . This is

identical tothe value

of

M„obtained

forall the events ir-respective

of

their spectator momentum. These studies suggest that for

Q;„&0.

1 (GeV/c) the deuteron

correc-tions are small and adequate and also that the results ob-tained are not sensitive to the spectator momentum dis-tribution.

B.

The reaction v„d

~p

LL++n, l.4— l.

2-y lO—

(a)

0.8—

0.

6-l.

4-

(b}

ps

iz-(

AE l.

o—

&5OMeV

Using the dipole axial-vector form factors given in

Eq.

(5) and the likelihood function

L

defined in

Eq.

(6), a maximum-likelihood fit was performed for the 1232

p

b,

++

events with

0.

1

+Q

3.0

(GeV/c) . Since the

correction R (Q ) for quasielastic scattering is only significant in the small-Q region

_[Q

(0.

1 (GeV/c)

_],

only the Q region from

0.

1 to 3(GeV/c)~ is used for the

TABLEIV. Axial-vector mass M~ and vector mass Mv from the two-parameter fitfor reaction

v+n

~p

p.

08-Mv Reference O.l 0.2 0 97+0.14 1.04+0.14 0.80+0.10 0.72+O' 20 089+0'07 0.86+0.07 0.

96+0.

04 0.

90+0.

05 This expt.

This expt., BNL 1981 (Ref. 1)

ANL 1982 (Ref. 2)

Fermilab 1983{Ref.3}

Qmin (Gey )

FIG.

7. The axial-vector mass

M„as

a function of

_Q;„

for the quasielastic events (a) without P, cut and, (b) with P,

(50

MeV/c. The dashed lines correspond to

M„=

1.07GeV.

42 STUDY OFvd _{+p pp,} AND vd +p 6++(1232)n, USING.

. .

1337 l.

6-1 I I I i I I I f

(a)

I.2— I,O—

fitin reaction (2). The likelihood fittothe data yields

M~

=1.

28+ GeV

.

This result is more than one standard deviation larger than that obtained from reaction (1). The axial-vector meson mass

M„

isexpected tobe the same forboth reac-tions (1)and (2).

Figure 8(a) shows the dependence

of

the fitted

M„on

the

Q;„cut.

As was true in the case

of

the quasielastic

process, the value

of

M„

is stable for values

of

Qm;„+0.

06 (GeV/c) and there is an indication

of

an

in-crease in

_M„

if

a lower

Q;„

isused. As was pointed out earlier the kinematic fitting procedure restricts the spec-tator neutrons to relatively low momentum. This can clearly be seen by comparing the spectator neutron distri-bution in Fig. 2 with the corresponding spectator-proton distribution for the quasielastic channel

[Fig.

1(a)],where the high-energy tail from the measured spectator proton is significant. In the quasielastic analysis there was no evidence that the value to Mz was sensitive to the momentum range

of

spectator momenta. A maximum-likelihood analysis using only the

6++

events with

P,

(n)&50 MeV/c in the _Q range

0.

1&_Q &

3.0

(GeV/c) yields

M„=1.

14+0.

14 GeV. This value is

lower but consistent with the fit using all the

b++

events. The

Q;„dependence

of

_M„

for the events with

P,

(n)&50 MeV/c isshown in

Fig.

8(b). Again the values are consistent for

Q;„~0.

06

(GeV/c) but the mean does tend to be lower than in the case when all events are used.

The curves in

Fig.

5(b) are the theoretical predictions

with

M„=1.

28 GeV (solid) and

M„=

1.

14GeV (dashed) obtained from the least-squared fit to the data for Q &

3.

0

(GeV/c)

.

Good agreement is observed between that data and the predictions for Q

~0.

2 (GeV/c)

.

The

I.

o—

CL I Z' ++ 0.

5—

Cl Z,'

0

0

I I I 2 4

E„(GeV)

difference between the two curves becomes larger for higher Q and amounts to

=15%

at Q

=2

(GeV/c),

but

the difference isnot statistically significant. C. Comparison ofthe

_p

_pand

_p

6,++channels

In the naive quark picture the quasielastic and

6++

production reactions are similar toeach other. By

denot-ing

8'+,

u, and d as the positively charged weak boson and the up and down quarks, respectively, these process-esare

W++d

~

u and u

+

(du )

~p

for the

_p

_{p reaction,}

and

W++d~u

and

u+(uu)~b,

++

for the

6++

pro-duction reaction. The only difference between the quasi-elastic and the

5++

production reactions is the recom-bination

of

the recoiled u quark with different diquark states, resulting in different spin and isospin final states.

To

compare these two reactions, the ratios

of

the 2544 quasielastic events and the 1385

6++

events with the corrections listed in Table

II

are used. Figure 9 shows

the

E„distribution

of

the ratio

N(p

b,

++)/N(p

p)

where N stands for the number

of

events. The curves are the ratios

of

the corresponding predictions with

M„=1.

28 GeV (solid) and

M„=1.

14GeV (dashed) for the b,

++

reaction and Mz

=1.

07 GeV for the quasielastic reactions, respectively. The dashed curve with

M„=1.

14

FIG.

9, The

E

distribution for the ratio of N(p

5++)/N(p

p). The curves are the ratios ofthe

corre-sponding predictions with M&

=

1.28 GeV (solid) and

M„=

1.14 GeV (dashed) for the

5++

reaction.

O (3~

08-I I.

4-

"

) 2 Il il I.O— 0.8—

(b)

I I I I Ps +5OMeV l.

0—

CL I Z,' +

0.

5

0

Qmin2 (Gev2) 0.2

0

0

FIG.

8. The axial-vector mass m

„as

a function of

_Q;„

for the

5++

events (a)without P, cut, and (b) with P,

(50

MeV/c.

The solid and dashed lines correspond to M

„=

1.28 and M&

=

1.14 GeV, respectively.

Q {GeV )

FIG.

IO. fhe Q'- _{distribution for the ratio of}

N(_p

6+

+)/N (_{p p).} The solid and dashed curves correspond tothe same ratios as stated inFig.9.

1338

T.

KITAGAKI etal. 42

GeV describes the data well except for the points with

E

&2.

3 GeV where the data points lie above the curve by slightly more than one standard deviation. The solid curve with M~

=1.

28 GeV does not describe the data as well.

Figure 10 shows the _Q distribution

of

the ratio X(lJ.

6++)/N(p

p).

The solid and dashed curves cor-respond to the same ratios as described in

Fig.

9.

The dashed-dotted line isthe average ratio

of

0.

55. Again, the dashed curve describes the data well compared to the solid curve for Q

(0.

8

(GeV/c),

but deviations became apparent for _Q

)

0.

8 (GeV/c)

.

The dashed-dotted line

generally describes the data well for the whole range

of

Q

.

The

y

values per degree

of

freedom are

0.

59,

1.

12, and

1.

61 for the dashed-dotted, dashed, and solid lines, respectively. These results slightly favor the constant ra-tio which suggests that the Q dependence for the b,

++

production reaction is similar to the neutrino quasielastic reaction in spite

of

the different hadronic spin and isospin

final states.

V. CONCLUSION

The quasielastic reaction v n

—

+p, _p and the b,

++

pro-duction reaction

_v~~p

b have been investigated to study the weak nucleon structure.

For

the quasielastic reaction, the conventional form-factor analysis yielded

the axial-vector mass Mg

=1.

070

0'O45 GeV for the di-pole form and

M(QM-AVMD)=1.

37+0.

13GeV for the quark model with axial-vector-meson dominance. Using dipole form factors, a two-parameter fit gave M~

=0.

97+O'„GeV

and

M&=0.

89+OO7 GeV, in good agreement with the CVChypothesis. These results are in

agreement with other recent neutrino results. A dipole axial-vector form factor

F„(Q

)adequately describes the

data in the fitted region

[0.

1 _Q

3.0

(GeV/c)

].

While

there is some evidence that the Gt is not adequate in the lower-Q region it is unclear, given the experimental un-certainties in this region,

if

this deviation is significant.

A likelihood fit

to

the

6++

channel yields

M~

=1.28+o

&0GeV which is consistent with, but a little

over

1.

5 standard deviations, higher than the value

of

M„determined

from the quasielastic reaction. In this

5++

_analysis no deuteron corrections were applied and the kinematic fitting could not accommodate fast neutron spectators. While the conclusions from the quasielastic analysis are that the analysis is not sensitive to either

of

these restrictions for the Q and

E„ranges

used the value

of

_M„

from the

5++

analysis does drop to

M„=

l.

14+0.

14GeV

if

only events with very slow spec-tators are used.

Finally, acomparison

of

the quasielastic and

6++

pro-duction reactions indicates very similar Q and

E„behav-ior. In both cases the theoretical ratio using

M„=1.

14 GeV from the

6++

reaction is preferred. However, the results

of

the

_y

fits forthe _Q dependence favor constant ratio, suggesting a similar _Q dependence for the quasi-elastic and

6++

production reactions in spite

of

the different hadronic spin and isospin final states.

ACKNOWLEDGMENTS

We are grateful tothe AGS staff, the operation crew

of

the

BNL

7-foot bubble chamber,

F.

M.

Simes who helped

in the data processing, and to the scanning and

measur-ing personnel at

BNL,

Tohoku University, and Tohoku Gakuin University for their dedicated work. This research was supported by the

U.S.

-Japan Cooperative Program in High Energy Physics under the Japanese Ministry

of

Education, Science, and Culture and the

U.S.

Department

of

Energy under Contract No.

DE-AC02-76CH00016.

'Present address: KEK,Ibaraki, Japan.

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