- Email: [email protected]
c
Nuclear Physics A486 (198X) 669-686 North-Holland. Amsterdam
STUDY
OF THE
np-+ppn-
REACTION
MOMENTUM T. TSUBOYAMA’,
N. KATAYAMA’,
Received (Rwised
IN THE
RANGE
INCIDENT
NEUTRON
1.0-1.9 GeV/c
F. SAI’
and
S.S. YAMAMOTO
6 August 1987 28 April 19X8)
Abstract: We have studied the np-, ppv- reaction in the incident-momentum range 1.0-1.9 CeV/c using the dp --) pppv reaction in terms of the impulse approximation. The reaction cross sections and the 1 = 0 cross sections were measured. The 1 ==0 cross sections were almost zero except at 1.89 GeVic which indicates the onset of a substantial contribution from the f =O amplitude. The inclusive x angular distribution showed asymmetry’ also at 1.89 GeV/c which was interpreted as an interference between the I = 0 and 1 amplitudes. The -l-production fraction, A angular distributions and j-decay density matrices were measured. These measurements indicate that A-production reaction in our momentum range and that it is induced by pion is substantial in the np-+pprrexchange. Comparison with data from the pp-’ ppv” reaction also confirms the dominance of the nucleon-nucleon f = 1 state in the np-tppn. reaction. :---’ E
1 i
NUCLEAR
!
REACTIONS
‘H(n,prr I = 0, isobar
), E at l-1.9GeV/c; measured production u cotltributions. __-._.___ __I__..
(T, rr(B,i;
deduced
-_..--
1. Introduction The nucleon-nucleon interaction is one of the most fundamental interactions between hadrons. Since the discovery of a structure is the Aa, [ref. I>], a lot of studies have revealed various features of nucleon-nucleon elastic scattering in the intermediate-energy region both theoretically and experimentally. On the other hand the gross features of the inelastic scattering of the exclusive channels are not yet well understood due to the paucity of the experimental data. The aim of this paper is to study the neutron-proton single-pion production reaction np+pp& in the incident neutron momentum range 1.0-1.9 GeV/e, utilizing the KEK 1 m liquidhydrogen bubble exposed to a deuteron beam in the momentum range 2-3.5 GeV/c. a general feature of the reaction np+ pp6 was From the reaction dp+ ppp6 investigated under the impulse approximation. In this momentum range, a thorough study of the proton-proton reactions with an unpolarized proton beam incident on an unpolarized proton target was made ’ Present ’ Present ’ Present Japan.
address: address: address:
National Laboratory for High Energy Physics, Oho-machi, Ibaraki-ken, Japan. Dept. of Physics, State University of New York, Albany, NY, USA. Tokyo Research Laboratory, IBM Japan, Ltd.. Sanbaneho, Chiyoda-ku, Tokyo,
0X75-9474/58/$03.50 @ Elsevier Science Publishers (North-Holland Physics Fublislling Division)
B.V.
670
T Tsuboyama
et al. / np + pp~
by Shimizu ef al. “). They analyzed the pp reactions including single-pion production reactions using the same KEK 1 m liquid hydrogen bubble chamber in the incidentmomentum
range of 0.9-2.0 GeV/ c.
Counter experiments using neutron beams and proton targets were performed by Dzhelepov et al. ‘) at 1.23 GeV/c, Kazarinov et al. “) at 1.22 GeV/c, K~eins~hmidt et al. “) at 1.06, 1.09, 1.12, 1.14, 1.17 and 1.19 GeV/c and Thomas et al. “) at 1.45 GeV/ c. Cochran et al. ‘) obtained proton-deuteron data using a CD, target and a carbon target exposed to a proton beam at 1.38 GeV/c. All these counter experiments measured the inclusive pion angular distributions, which followed the form, da/d(cos
0) = a + b(cos 0)‘.
This shape represents the angular distribution of a single isospin state with an angular momentum 0 or 1, which is a good approximation in the low-momentum region. The total np + ppY cross sections were also obtained from these data. More detailed studies of this reaction were also made using bubble chambers. Liquid-hydrogen bubble chambers were exposed to neutron beams by Handler et al. “) at 0.954 GeVlc and by Abdivaliev et al. “) at 1.250, 1.730 and 2.230 GeV/c. Wideband neutron beams and liquid-hydrogen bubble chambers were used by Alexander et al. “‘) at 1.5-4 GeV/c and Ansorge ef al. “) at I-8 GeV/c. Dakhno et bubble al. “) and Brunt et al. “f measured total cross sections using deuterium-filled chambers exposed to proton beams. They first obtained the pd + ppY total cross section and from it obtained the pn --I pp~- total cross section by correcting for the shadowing effect.
*
Dakhno This
2
2.5
3
total cross sections
Experiment
3.5
Incident deuteron Fig. 1. The dp+pppn-
et at.
4
momentum (GeV/c)
as a function
of incident
momentum.
T.
Tsuho~vama et al. /
2. Experimental
np
671
--) pp
procedure
The KEK 1 m liquid-hydrogen bubble chamber was exposed to a doubly separated secondary beam of deuterons from the KEK 12 GeV proton synchrotron at the following momenta: 2.08, 2.28, 2.49, 2.6%,2.88, 2.96, 3.18,3.38, 3.57 and 3.79 GeV/c. These momenta were determined from the kinematical fit of fully constrained dp + ppprr events. The momentum spread was estimated to be about 1%. The beam contamination by other particles was estimated to be less than 0.5% as described in an earlier publication 14). About 20 000 pictures were taken at each incident momentum. The results of 2-strong events have already been published I”). 4-prong events were scanned for twice. The single-scanning efficiency was about 97% and the double-scanning efficiency was essentially 100%. The beam-flux counting efficiency was also 100%. A total of 7,905 events were found in scan and measured and processed in a standard way. They were fitted to the following kinematical hypotheses: (l)dp+ pppr-, (2)dp+ dpr-n’, (3)dp+ ppnYr+, (4)dp + ppp’rr rrO. An event was categorized as belonging to a particular hypothesis if it fitted this hypothesis with a ,$ probability of greater than O.l”/o. For the rest of the events, we checked the bubble densities of the secondary tracks on the scanning table and determined their final states. About 10% of the events did not fit any hypothesis, and they were identified on the basis of ionization and kinematical information. About 1% of events remained unidentified and were apportioned according to the ratios of the identified events.
Spectator Fig. 2. The momentum
distribution
proton
momentum
(GeV/c)
of the spectator protons at 3.79 GeV/c H&hen wave function.
with the prediction
of the
T. Tsuboyama er al. / np + ppn
672
3. Analysis and results Among
the deuteron-proton
reactions
with the 4-prong
topology,
dp + PPPTis the only single-pion corresponds
production
reaction.
(A)
The 2-4 GeV/ c deuteron-proton
to the l-2 GeV/ c nucleon-nucleon
reaction.
reaction
In the nucleon-nucleon
inelastic reactions in the momentum range l-2 GeV/c, it is well known that the one-pion production reactions dominate the inelastic channels and the contribution from the two-pion production channels gradually increases with momentum. But it amounts at most to 10% of the inelastic channel at 2 GeV/c [ref. ‘)I. Therefore, reaction (A) is expected to be the majority of the 4-prong events in our momentum range. The total cross sections for raction (A) are shown in fig. 1, together with the data of Dakhno et al. I’). In fig. 1 the proton beam momenta of Dakhno et al. ‘?) are represented by their equivalent deuteron beam momenta. Below 3.5 GeV/c, our data agree well with the data obtained by Dakhno et al. I?). The total cross sections and their statistical errors are also shown in columns 2 and 3 of table 1. The data for the reaction, np+ ppn
(B)
are derived from reaction (A) events using the impulse approximation. As the deuteron is a loosely bound state of a neutron and a proton, the high-energy deuteron-proton reaction (A) can be approximated by a quasi-free reaction between the target proton and the constituent neutron in the incident deuteron, the projectile neutron. The momentum distribution of the spectator proton is expected to be that of the proton in the deuteron. In this experiment the spectator proton is defined as the one among the three outgoing protons in the final state which has the smallest momentum
in the rest frame of the incident TARLE
Values of u+_,,,,~,
, u,,,,_~,,~and
vo,,
and their
systematic
u‘lp -pppn
(G&C,
(2P)
(mb)
errors.
deuteron.
The momentum
distribution
1 &r\,L~!.,,,
and
6a‘,;_,,,
are the statistical
and
errc~rs in r,Ip_ppv &T”,” “P+DP”
fi”;“_F”
fl,p-*pp?r
m
(mb)
(mb)
fi~::;+pp;i (mb)
1.04
0.18
0.03
0.19
0.03
0.00
1.14
0.62
0.04
0.67
0.04
0.01
1.25
1.10
0.07
1.19
0.08
0.03
1.34
1.71
0.07
1.8.5
0.08
0.05
~(11 (mb) -0.06 0.22 -0.16 0.19
6a,, 1 (mb) 0.08 0.13 0.22 0.25
1.44
1.99
0.08
2.14
0.09
0.05
0.52
0.27
1.48
2.08
0.08
2.24
0.09
0.05
0.32
0.27
1.59
2.22
0.08
2.38
0.09
0.05
0.17
0.27
1.69
2.48
0.09
2.65
0.10
0.06
0.84
0.29
1.79
2.60
0.09
2.78
0.10
0.06
1.19
0.28
1.89
3.01
0.10
3.23
0.1 I
0.07
2.65
0.29
T. ~~~ib~~~~~nu et al. / np -t
of the spectator together
protons
(dN/dp)
with the momentum
at 3.79 GeV/c
distribution
ppr-
673
is shown
predicted
in fig. 2 as an example
by the H&hen
deuteron
wave
function 15), which is represented by the solid curve. The predicted momentum distribution was normalized to the number of events in the spectator momentum range O-200 MeV/ c. As seen from the figure, in the low spectator momentum region (below 300 MeV/c), the momentum distribution of the spectator protons is well explained by the Hulthen deuteron wave function. In the high spectator momentum region (above 300 MeVie), the difference between data and prediction becomes significant. Quantitatively, about 10% of the spectator protons have momenta greater than 300 MeVie. But the Hulthen deuteron wave function predicts less than 1%. This difference is due to the double scattering and final-state interaction effects. In the subsequent analyses, ail events identified as reaction (A) are analyzed as reaction (B) with a spectator proton, and we did not impose any cut on the momentum of the spectator protons. However, we also analyzed these events with the following events which cut on the spectator momentum P,: P, < 300 MeV/c, to eliminate cannot be explained by the impulse approximation alone. But these events did not show any statistically significant differences in various physical quantities from those obtained by using the entire sample.
x Dakhno 0 Brunt z
1
a Other
2
+ This
Incident
momentum
et
al.
et al. data experiment
tGeY/c)
Fig. 3. The np + ppK total cross sections as a function of incident momentum together with the data of refs. 4-h.*~“,‘31. The smaller error bars indicate the statistical errors and the larger error bars the linear sums of the statistical and systematic errors. The dot-dashed curve is a prediction by VerWest and Arndt I”), and the dashed and solid curves are predictions of the Deck model with and without an I = 0 diharvon by Jauch er ni. ‘“I.
T. Tsuhoyama et
674
al. /
np + pp~
The incident neutron momentum was assumed to be a half of the deuteron momentum. However, its r.m.s. spread was calculated to be about 6-i% using the incident deuteron and spectator proton momenta. To calculate the total cross section for reaction (B) we have made a correction The shadowing effect is usually considered and the fotlowing
approximate
relation
*dp-.ppp?r-
=
to compensate for the shadowing effect. to be mainly due to single pp scattering,
is sometimes -{
unnp-ppx
1 - (1/4n)(
used “f: I/ r’)aFi}
.
If the shadowing effect was neglected, fl+,ppp& would be the same as u_,+,,~~~. However, an elastically scattered proton from the first pp elastic scattering can collide with the spectator neutron to initiate the reaction pns+ pprr-. This sequence factor of reactions simulates the dp + ppp’rr reaction, and the above correction overestimates the shadowing effect. In order to estimate the shadowing effect more realistically we used the following relation between ~dP_PPP~~ and a,,,,,,at an incident neutron momentum p,
do-----=‘o”np+ppa-(P’) da, da
4 x Dakhno 3
t?
+ This
et al.
experiment
1
0
-1
1.0
1.2 Incident
I.4
1.6
momentum
1.8
2.0
(Gev/c)
Fig. 4. vO, as a function of incident momentum. The smaller error bars indicate the statistical errors and the larger error bars the linear sums of the statistical and systematic errors. The dot-dashed curve is a prediction by VerWest and Arndt 191, and the dashed and solid curves are predictions of the Deck model with and without an I = 0 dibaryon by Grein ef af. “).
T
Tsuboynma
675
et al. / np + pprr
(a) 100
loo
80
80
60
60
40
40
yr Q
20
2o
3 c !?
0
0
200
200
Y 150
150
100
100
Lm-
50
0
50
0 OS -1 -0.5
-1-0.5
0 0.5
-1 -0.5
0 0.5 -1 -0.5
0 0.5-l
-0.5
0 Q5
0
1
(b)
$ cn
E
2”
40
40
30
30
20
20
10
10
0
0
60
60
40
40
20
20
0 -1-0.5
0 05
-1 -0.5
0 0.5 -1 -0.5 0 0.5 -1 -0.5
0 45 -1 -0.5
0 0.5
1
0
cos@&f-
Fig. 5. (a) Proton
angular distributions for the reaction np* pprat all momentn. distributions for the reaction np+ pprr- at all momenta.
(b) Pion al~gul,tr
616
al/a0 +?‘C +
0.5
0.0
**+
l
-0.5 t -1.0
1
E....,....,.,..,. 1.2 1.4
1.6
-0.5 1.5
1.8
1.0
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
-as E -I.*,-
1.2
1.4
1.6
1.8
incident Fig. 6. The normalized
coefficients
2
momentum
(GeV/c)
of the Legendre expansions of the proton functions of incident momentum.
angular
distributions
as
where p’ denotes the momentum of the secondary proton which collides with the spectator neutron, a:;(p) the total pp cross section at momentum p, da,,/dfl the pp elastic differential cross section, and (l/r’) is the mean inverse distance squared between the proton and neutron in the deutron, which was taken to be 0.0311 mb-’ was approximated by in our case 16). The value of a,p_PPn (p’) in the integrand I$(p’) below p’ = 1.2 GeV/ c, where ~+,_pppn-(2~‘) for p’> 1.2 GeV/c and by 2u,,_,,, the I =0 contribution is negligible. With this approximation provisional values of F~,,,_~~~ (p) were calculated for all values of p, using the values of p’
1.0 0.5 0.0 al/a0
-0.5 -1.0
. ..I.-
-I-..-....
1
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
incident Fig. 7. The normalized
coefficients
momentum
(Gel//c)
of the Legendre expansions of the pion functions of incident momentum.
angular
distributions
BS
sums of the statistical and systematic errors. The dot-dashed curve is a prediction by Verwest and Arndt “), and the dashed and solid curves are Deck model predictions with and without an I = 0 dibaryon by Jauch et ai. I’)). They are also shown with their statistical and systematic errors in columns 4, 5 and 6 of table 1. Our data are quite consistent with the other data except at 1.89 GeV/c. At 1.89 GeV/c our cross section is larger than the other data. We checked the data at this momentum carefully for any anomaly in the beam condition and the final state identification but found none. Our data also agree with the predictions by VerWest and Arndt I’), and by Jauch ef al. with an I =0 dibaryon I”). According to a model proposed by Rosenfeld IO), nucleon-nucleon -single-pion production cross sections are categorized by the initial and final two-nucleon isospins I and T, denoted as (T{~. In this representation, a,, is obtained by, u 01 = 2~J,,P-pPr
- ~,,-.,,,“.
Using this formula and rr,,P_Ppr ‘1interpolated from the data of ref. ‘1, we obtained rC,, as a function of incident neutron momentum. The errors in the estimation of these cross sections were taken into account to obtain the error in (T(~,. The results are shown in fig. 4 together with the data of Dakhno et al. I’). The smaller error bars indicate the statistical errors and the larger error bars the linear sums of the statistical and systematic errors, which are 26a,,,,,,, . The dot-dashed curve is a prediction by VerWest and Arndt ‘“), and the dashed and solid surves are predictions of the Deck model with and without an I= 0 dibaryon by Grein et al. ‘I). Our data
T. Tsuboyuma et al. / np + pp6
678 n 5 50 s : 40 0
t30 * ; $20 ; 2”
10 0
1.1
1.2
1.3 1.4 (0 eV/c’ 1
.1.5 (GeV/c’) M(PW)
M(PA’)
2.4 (GeV/c’) M(PP)
0 1.6
2.0 2.a (GeV/c*f M(PP)
2.4
Fig. 8. The invariant mass distributions for the prr- system and the pp system from the reaction np+ ppvat 1.48 CieV/c and 1.89 GeV/c. The dotted, dashed and solid curves are the pure phase space, phase space weighted by the Breit-Wigner function to represent d and the results of the fit discussed in the text, respectively.
agree well with the data of Dakhno et al. ‘“1. The values of rtr, and their statistical errors are also shown in columns 7 and 8 of table 1. Fig. 4 indicates that our cross sections are a little larger than the prediction by VerWest et al.I').But their calculation was based on sparse data and the disagreement may not be very serious. Although the Deck model prediction without an I = 0 dibaryon by Grein et al. “) agrees with the experimental data, their prediction with an I = 0 dibaryon completely disagrees with our data, which is in contradiction to the fact that our np+pprrcross sections agreed with the prediction of another Deck model calculation by Jauch et al. 19) with an f -=O dibaryon. This contradiction is due most likely to the inadequacy of the Deck models adopted. The angular distributions of the protons and the Y in the final state of reaction (B) are shown in figs. .5a and 5b. They are simiiar to each other in shape. At lower deuteron incident momenta the distributions are flat. At higher incident momenta, the forward and backward peaks become clear. In order to study the momentum dependences of the angular distributions, we expanded them in terms of Legendre polynomials by the moment method. The
619
Tsuboyama et al. / np + ppK P’I”“r”“l”“I”“i”“1’9 100
-
80
-
60
-
I
o\” 40
-
20
-
0”
E I PP-+PA+
E I
’ ’ ’ 1
I-I,’ ’ 1.2
Incident Fig. 9. The fractions
E
of -l-production
I nP-*PAO
’ ’ ’ ’
’
’
’
1.4
momentum
’
’
’
’
’ ’
1.6
’
’
1.8
’
”
’
’
’
2
4
(GeV/c)
in the reaction np+ ppr momentum.
and pp + pp~~‘(’as functions
of incident
values of the normalized coefficients of the proton and rTT angular distributions are shown in figs. 6 and 7 as functions of incident neutron momentum. From these figures we conclude that the coefficients for the odd-order Legendre polynomials are consistent with being 0, which means that the angular distributions are symmetric around cos 0 = 0. However, at 1.89 GeV/c the angular distribution of the r- is not symmetric. The asymmetry in the angular distribution can arise only when both the I = 0 and I = 1 amplitudes exist. The fact that at the highest incident momentum the negative-pion angular distribution shows an asymmetry seems to indicate the onset of a significant contribution of the I = 0 amplitude in reaction (B) at this momentum. This is consistent with the fact that cr(,, at this momentum is significantly non-zero. We studied A production in reaction (B). First, we estimated the fraction of A0 production in np + pprr at each incident momentum. The fraction of A0 production in reaction (B) is estimated from the distributions of the pn- invariant mass, m(pY) and the proton-proton invariant mass, m(pp). Using a Monte Carlo phase-space program FOWL”), we generated two sets of m(pY) and m(pp) distributions for reaction (B). One set is a pure phase-space distribution, In the other set, each event which was generated by FOWL was weighted by the relativistic Breit-Wigner function 23) for the m(pY) to represent the A resonance. The central value and the width of the Breit- Wigner function were chosen as 1.232 GeV/ c* and 0.1 GeV/ c’. For the m(pp) distribution, this weighting represents the reflection of the A in the
680
40
20
0 125 100 75 50 25 0 -1-0.5
0 0.5 -1 -0.5 0 0.5 -1 -0.5 0 0.5 -1 -0.5 0 0.5 -1-0.5
Fig. 10, The -I-production
angular
distribution
of the reaction
np+
0 0.5
p-1”- ppK at all momenta.
(pr) system. These two sets of invariant mass distributions were fitted to the experimental data by the maximum likelihood method simultaneously. Fig. 8 shows the m(pC) and m(pp) distributions at 1.48 and 1.89 GeV/c. The fitted distributions are indicated by the solid curves, the contributions of pure phase space by the dotted curves and the contributions of the Breit-Wigner distribution by the dashed lines. The values of the fractions of A production are shown in fig. 9 as a function of incident neutron momentum. They are between 25-75s. In our momentum range of 1.0-1.9 GeVfc, the pure phase-space distribution and the phase-space distribution including the if resonance are similar in shape, and in the fitting procedure the correlation between the two distributions is substantial. The correlation is duly included in the estimated errors, which are typically 3%. These are statistical errors obtained from the fitting procedure and are likely to be underestimated. The value of the fraction also varies from momentum to momentum. This is due most likely to the way the fitting process converges and to the simple nature of the model adopted. Thus these fractions should be regarded as rough estimates. In fig. 9 the fractions of the A+ production from the reaction pp-2 pp~” of Shimizu et al. ‘) are also shown. They roughly agree with our data except at around 1.9 GeV/c. From these results, it is concluded the 3 production is substantial in reaction (B). Moreover, the fraction of A is largest at around 1.6-1.8 CeV/c where the central values of the m(pY) distributions are about equal to the mass of the A.
Incident The momentum J-production
MomentUm
dependences
angular distributions.
)
(GeV/c
of the normalized
coetficients
of the Legendre
expansion
of the
Open circles represent the data from the reaction np + p-l” and filled
circles represent the data from the reaction pp + pJ+.
We selected the J sample whose effective mass m(pn ) of one ofthe two final-state protons and the final-state 6 satisfies the following inequality, lnr(pr ) - m(~)l< r(A), where m(J)= 1.232GeV and f-(,4) =O.l GeV. Since there were two pC combinations
for each event, the one whose m(pn
) is closer to the m(J)
was used,
when both pairs satisfied the inequality. The &resonance production angular distribution with respect to the neutron direction at each incident momentum is shown in fig. 10. At high incident momenta the d production angular distributions peaked strongly in the forward and backward direction. It can be interpreted as due to the fact that the momentum transfer from the incident neutron to the 3 is small, and this reaction is dominated by light-particle exchange. In order to study the momentum dependence of the angular distributions, we expanded them in terms of Legendre polynomials by the moment method. The normalized coefficients are plotted in fig, 11 by open circles. At low neutron incident momenta, all coefficients are consistent with 0. At high momenta even-order terms dominate
the reaction, but ~,/a,, is still consistent with 0 within the statistical terms are always consistent with 0. Also in fig. 11 the normalized
accuracy. Odd-order
682
T. Tsuboyavamaet al. / np -+ pp”r-
coefficients which
of the A ’ production
are obtained
angular
by a reanalysis
distributions
from the reaction
of the data of Shimizu
et ai. >)
pp + pprO,
are shown
by
filled circles. They agree well with those of the A” from the reaction np+ pp6. Finally we studied the density matrix of the A in the reaction np+ pA”;rpp?~-. If dibaryons couple strongly to the pion production channels, it is expected that the observables relating to the spin states of the nucleons show some anomalies, The A-decay angular distributions are measured in the helicity frame and GottfriedJackson frame. In the helicity frame the z-axis is parallel to the direction of the A seen in the c.m. of the initial two nucleons. In the Gottfried-Jackson frame, the z-axis is parallel to the direction of the incident nucleon seen in the rest frame of the A. In both frames, the y-axis is chosen to be perpendicular to the A-production plane, and the x-axis is chosen to make a right-handed Cartesian coordinate system. The elements of the density matrix are obtained from the angular distribution using the moments of spherical harmonics, PX = a - 24 Y2”)* I 1 PII =z-P33, Re p31= Re &d Rep,_,
Yd*)
,
= Re (-&Y&“),
where Y,,, represents the spherical harmonics. The elements of the density matrix were obtained as functions of neutron momentum and are shown in figs. 12a and 13a. In the helicity frame, the pJ3 gradually decrease from 0.5 to 0.25 as the incident momentum is increased from 1.1 GeV/c to 1.89 GeV/c, while Re p3, and Re pj_, are always consistent with 0. In the Gottfried-Jackson frame, the p,, dominates the A spin state and the other values are very small. These facts can be interpreted to mean that the reaction np+ PA’+ ppn- is induced by exchange of a spin-0 particle. As discussed previously the exchanged particle that pion exchange dominates this A production and the Gottfried frame, there is no obvious
is not a heavy one. Thus it seems reaction. In both the helicity frame structure which indicates sudden
changes
in the spin states. The values of the density matrix elements PP + PA + + PP”“, obtained by a reanalysis of the data of Shimizu et in figs. I2b and 13b. The similarities between the two reactions in the angular distributions and the density matrix elements indicate charge
independence
for these A-production
of the reaction are shown the behavior of the validity of al. *)
reactions.
4. Conclusions We have systematically studied the np -$ pprr- reaction in the incident-momentum range l-l.9 GeV/c, using the dp+ pppK reaction in the incident deuteron momentum range of 2-3.8 GeV/c. The total cross sections for this reaction were obtained. They agree with the earlier data below 1.7 GeV/c. But our cross section at 1.89 GeV/c is larger than the two adjacent data points obtained by Brunt ef al. IA). The predictions
T. Tsuboyama
et al. / np + pprr
1.00
‘*O”
(a)
0.75
0.75
a50
0.50
425
0.25
0.00
0.00
-0.25
-0.25
-0.50
1 1.25
1.5 1.75
Real
1.00
-0.50
2
P31
050
0.25
0.25
0-W
0.W
-0.25
-0;25
-0.50
1 1.25
1.5 1.75
-0kJ
2
Incident
p3-1
1.5 1.75
2
(GeV/c)
PI1 .
a50
**
++
0.00
++
++
0.25
l*
+t++
+t
0.00 -0.25
~ 1 1.25
1.5 1.75
-0.50
2
Real 33 I
1.00
w5
0.50
0.50
425 0.00
+
+*++
angular
2
RealP3-1
0.00 -0.25
~ 1 1.25
1.5 1.75
matrix
elements
distributions
-0.50
2
Incident 12. The density
1.5 1.75
0.25 *i*+
-0.25 -0.50
~
1 1.25
1.00
0.75
the decay
2
0.75
0.25
Fig.
1 1.25
1.00
0.75 0.50
from
Real
momentum
P33
1.00
-0.50
1.5 1.75
0.75
0.50
-0.25
1 1.25
1.00
a75
(b)
683
as functions
1 1.25
momentum of incident
of the A, (a) from
2
(GeV/c) momentum
the reaction
pp + p&l ’ + pp7r”.
1.5 1.75
np+
in the helicity p-l”+
ppr’
frame
obtained
and (b) the reaction
684
P33 (a)
0.75
0.75
0.X)
0.50
0.23
0.25
?***++*t
0.00
0.00
-0.25
-0.25 -0.90
1.00
~ 1 1.25
1.5 1.75
2
RealPa,
0.75
0.75 OS0
0.25
0.25
0.00
0.00
1 1.25
1.5 1.75
2
-0.50
l.OO
1.00 o.75
as0
oso
a25
0.25
a00
a00
-0.25
-0.25
1.00
1 1.25 Real
1.5 1.75 &
I
2
-050
1.00
w5
a75
O.!iO
OS2
0.25
0.25
0.00
o.oo
-0.25
-0.25
-0.50
-o&o
2
f,+ ** + . * F l
1 1.25
momentum
0.75
1.5 1.75
RfsalPa_,
-0.25
Incident
-0.50
I 1.25
1.00
-0.25
ibl
-0.50
0.50
-0.50
P11
1.00
‘xlo
1.5 1.75
2
(GeV/c)
I 1.25
1.5 1.75
2
Realpg-1
Incident momentum
(GeV/c)
Fig. 13. The density matrix elements as Functions of incident momentum in the Gottfried-Jackson obtained from the decay angular distributions of the &I, (a) from the reaction np+ pA”-t ppvthe reaction pp+ pJ++ ppn”.
frame and (b)
T. Tsuboyama
685
et al. / np + ppF
of a Deck model calculation by Jauch et al. 19) which includes an I = 0 dibaryon agrees with our data. However, our values of Us,, , which were obtained independent of any model, are consistent with zero below 1.7 GeV/c and become substantial only above 1.8 GeV/c. In addition, a Deck model calculation with an I = 0 dibaryon by Grein et al. *I), which is essentially the same as the calculation of Jauch et al. I”), predictions by is in complete disagreement with our go, data. Such contradictory Deck model calculations are most likely due to the inadequacy of the model. We conclude that our data on uO, rule out the existence of any I = 0 dibaryon resonance in the mass range 2.0-2.3 GeV/c’. An indication of the contribution from the I = 0 initial state in this reaction was observed in the angular distribution for the &, which showed an asymmetry at a neutron momentum of 1.89 GeV/c. The fractions of A production in np + pprr were estimated from the pp and pr’ invariant mass distributions. The value of the fraction was 25575% and was largest at around 1.6-1.8 GeV/c. Imposing a cut on the prr invariant mass, we selected the A samples and analyzed these events in terms of the A-production reaction, np+ ~3”. The angular distributions and the spin-density matrix elements of the A were obtained. They do not show any obvious momentum dependence which might result from the existence of a dibaryon state. They are quite consistent with the data for the reaction pp + pA ‘. This fact shows a similarity between the two reactions. We would like to acknowledge the operating crews of the KEK PS, the beam channel group and the 1 m bubble chamber group. We are also grateful to the scanners and measures at University of Tokyo for their painstaking efforts. Thanks are also due to M. Kajita, H. Koiso, Y. Kubota, S. Sakamoto and F. Shimizu who took part in the early stage of this experiment. This work was supported in part under the auspices of the Meson Science Laboratory, a Grant-in-Aid of the Ministry of Education, Science
University of Tokyo, and by and Culture (No. 58540145).
Data analyses for this work were done at the Computer Center and the Meson Science Laboratory of University of Tokyo and at the Computer Center of KEK.
References et 01, Phys.
I)
I.P. Auer
2)
F. Shimiru
3)
V.P. Dzhelepov
4)
Y.M.
Lett.
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B70 (1977)
Phys.
et al., Sov.
Kararinov
A386
Phys.
JETP
er al., Sov. J. Nucl.
5) M. Kleinschmidt
ef a/., 2. Phys.
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571;
Nucl.
23 (19661
Phya. 4 (19671 (1980)
Phys.
A389
(1982)
993 100
253
6) W. Thomas CI al., Phgs. Rev. D24 11981) 1736 7) D.R.F. Cochran et cd.,Phq,. Rev. D6 (1972) 3085 8)
R. Handler,
Phys.
Rev.
Bl38
9) A. Abdivalia
ef al., JINR
IO) G. Alexander
et n/.. Nucl. et al., Nucl. et al., Phys.
II)
R.E. Ansorge
12)
L.C.
Dakhno
13)
D.C.
Brunt
ef al., Phyu.
(1965)
Pi-81-128
1230 (1981)
Phys.
B52 (1973)
221
Phys.
B63 (1973)
93
Lett.
Lett.
B114
(1982)
B26 (1968)
409
317;
Phys.
Rev.
187 (1969)
1856
445
686
T Tsuboyama
et al. / np + ppn
14) N. Katayama et al.,Nucl. Phys. A438 (1985) 685; F. Sai et al, Phys. Rev. Lett. 55 (1985) 2668 15) L. Huhhen and M. Sugawara, Encyclopedia of Physics 39 (1955) 16) D.V. Bugg et nl., Phys. Rev. 146 (1966) 980 17) P. Schwaller et al., CERN 72-13 (1973) 18) B.J. VerWest and R.A. Amdt, Phys. Rev. C25 (1982) 1979 19) W. Jauch, A. Konig and P. Kroll, Phys. Lett. B143 (1984) 509 20) A.H. Rosenfeld, Phys. Rev. 96 (1954) 139 21) W. Grein, A. Konig and P. Kroll, Phys. Lett. B96 (1980) 176 22) F. James, CERN 68-15 (1968) 23) E. Colton et al.,Phys. Rev. D6 (1972) 95
STUDY
OF THE
np-+ppn-
REACTION
MOMENTUM T. TSUBOYAMA’,
N. KATAYAMA’,
Received (Rwised
IN THE
RANGE
INCIDENT
NEUTRON
1.0-1.9 GeV/c
F. SAI’
and
S.S. YAMAMOTO
6 August 1987 28 April 19X8)
Abstract: We have studied the np-, ppv- reaction in the incident-momentum range 1.0-1.9 CeV/c using the dp --) pppv reaction in terms of the impulse approximation. The reaction cross sections and the 1 = 0 cross sections were measured. The 1 ==0 cross sections were almost zero except at 1.89 GeVic which indicates the onset of a substantial contribution from the f =O amplitude. The inclusive x angular distribution showed asymmetry’ also at 1.89 GeV/c which was interpreted as an interference between the I = 0 and 1 amplitudes. The -l-production fraction, A angular distributions and j-decay density matrices were measured. These measurements indicate that A-production reaction in our momentum range and that it is induced by pion is substantial in the np-+pprrexchange. Comparison with data from the pp-’ ppv” reaction also confirms the dominance of the nucleon-nucleon f = 1 state in the np-tppn. reaction. :---’ E
1 i
NUCLEAR
!
REACTIONS
‘H(n,prr I = 0, isobar
), E at l-1.9GeV/c; measured production u cotltributions. __-._.___ __I__..
(T, rr(B,i;
deduced
-_..--
1. Introduction The nucleon-nucleon interaction is one of the most fundamental interactions between hadrons. Since the discovery of a structure is the Aa, [ref. I>], a lot of studies have revealed various features of nucleon-nucleon elastic scattering in the intermediate-energy region both theoretically and experimentally. On the other hand the gross features of the inelastic scattering of the exclusive channels are not yet well understood due to the paucity of the experimental data. The aim of this paper is to study the neutron-proton single-pion production reaction np+pp& in the incident neutron momentum range 1.0-1.9 GeV/e, utilizing the KEK 1 m liquidhydrogen bubble exposed to a deuteron beam in the momentum range 2-3.5 GeV/c. a general feature of the reaction np+ pp6 was From the reaction dp+ ppp6 investigated under the impulse approximation. In this momentum range, a thorough study of the proton-proton reactions with an unpolarized proton beam incident on an unpolarized proton target was made ’ Present ’ Present ’ Present Japan.
address: address: address:
National Laboratory for High Energy Physics, Oho-machi, Ibaraki-ken, Japan. Dept. of Physics, State University of New York, Albany, NY, USA. Tokyo Research Laboratory, IBM Japan, Ltd.. Sanbaneho, Chiyoda-ku, Tokyo,
0X75-9474/58/$03.50 @ Elsevier Science Publishers (North-Holland Physics Fublislling Division)
B.V.
670
T Tsuboyama
et al. / np + pp~
by Shimizu ef al. “). They analyzed the pp reactions including single-pion production reactions using the same KEK 1 m liquid hydrogen bubble chamber in the incidentmomentum
range of 0.9-2.0 GeV/ c.
Counter experiments using neutron beams and proton targets were performed by Dzhelepov et al. ‘) at 1.23 GeV/c, Kazarinov et al. “) at 1.22 GeV/c, K~eins~hmidt et al. “) at 1.06, 1.09, 1.12, 1.14, 1.17 and 1.19 GeV/c and Thomas et al. “) at 1.45 GeV/ c. Cochran et al. ‘) obtained proton-deuteron data using a CD, target and a carbon target exposed to a proton beam at 1.38 GeV/c. All these counter experiments measured the inclusive pion angular distributions, which followed the form, da/d(cos
0) = a + b(cos 0)‘.
This shape represents the angular distribution of a single isospin state with an angular momentum 0 or 1, which is a good approximation in the low-momentum region. The total np + ppY cross sections were also obtained from these data. More detailed studies of this reaction were also made using bubble chambers. Liquid-hydrogen bubble chambers were exposed to neutron beams by Handler et al. “) at 0.954 GeVlc and by Abdivaliev et al. “) at 1.250, 1.730 and 2.230 GeV/c. Wideband neutron beams and liquid-hydrogen bubble chambers were used by Alexander et al. “‘) at 1.5-4 GeV/c and Ansorge ef al. “) at I-8 GeV/c. Dakhno et bubble al. “) and Brunt et al. “f measured total cross sections using deuterium-filled chambers exposed to proton beams. They first obtained the pd + ppY total cross section and from it obtained the pn --I pp~- total cross section by correcting for the shadowing effect.
*
Dakhno This
2
2.5
3
total cross sections
Experiment
3.5
Incident deuteron Fig. 1. The dp+pppn-
et at.
4
momentum (GeV/c)
as a function
of incident
momentum.
T.
Tsuho~vama et al. /
2. Experimental
np
671
--) pp
procedure
The KEK 1 m liquid-hydrogen bubble chamber was exposed to a doubly separated secondary beam of deuterons from the KEK 12 GeV proton synchrotron at the following momenta: 2.08, 2.28, 2.49, 2.6%,2.88, 2.96, 3.18,3.38, 3.57 and 3.79 GeV/c. These momenta were determined from the kinematical fit of fully constrained dp + ppprr events. The momentum spread was estimated to be about 1%. The beam contamination by other particles was estimated to be less than 0.5% as described in an earlier publication 14). About 20 000 pictures were taken at each incident momentum. The results of 2-strong events have already been published I”). 4-prong events were scanned for twice. The single-scanning efficiency was about 97% and the double-scanning efficiency was essentially 100%. The beam-flux counting efficiency was also 100%. A total of 7,905 events were found in scan and measured and processed in a standard way. They were fitted to the following kinematical hypotheses: (l)dp+ pppr-, (2)dp+ dpr-n’, (3)dp+ ppnYr+, (4)dp + ppp’rr rrO. An event was categorized as belonging to a particular hypothesis if it fitted this hypothesis with a ,$ probability of greater than O.l”/o. For the rest of the events, we checked the bubble densities of the secondary tracks on the scanning table and determined their final states. About 10% of the events did not fit any hypothesis, and they were identified on the basis of ionization and kinematical information. About 1% of events remained unidentified and were apportioned according to the ratios of the identified events.
Spectator Fig. 2. The momentum
distribution
proton
momentum
(GeV/c)
of the spectator protons at 3.79 GeV/c H&hen wave function.
with the prediction
of the
T. Tsuboyama er al. / np + ppn
672
3. Analysis and results Among
the deuteron-proton
reactions
with the 4-prong
topology,
dp + PPPTis the only single-pion corresponds
production
reaction.
(A)
The 2-4 GeV/ c deuteron-proton
to the l-2 GeV/ c nucleon-nucleon
reaction.
reaction
In the nucleon-nucleon
inelastic reactions in the momentum range l-2 GeV/c, it is well known that the one-pion production reactions dominate the inelastic channels and the contribution from the two-pion production channels gradually increases with momentum. But it amounts at most to 10% of the inelastic channel at 2 GeV/c [ref. ‘)I. Therefore, reaction (A) is expected to be the majority of the 4-prong events in our momentum range. The total cross sections for raction (A) are shown in fig. 1, together with the data of Dakhno et al. I’). In fig. 1 the proton beam momenta of Dakhno et al. ‘?) are represented by their equivalent deuteron beam momenta. Below 3.5 GeV/c, our data agree well with the data obtained by Dakhno et al. I?). The total cross sections and their statistical errors are also shown in columns 2 and 3 of table 1. The data for the reaction, np+ ppn
(B)
are derived from reaction (A) events using the impulse approximation. As the deuteron is a loosely bound state of a neutron and a proton, the high-energy deuteron-proton reaction (A) can be approximated by a quasi-free reaction between the target proton and the constituent neutron in the incident deuteron, the projectile neutron. The momentum distribution of the spectator proton is expected to be that of the proton in the deuteron. In this experiment the spectator proton is defined as the one among the three outgoing protons in the final state which has the smallest momentum
in the rest frame of the incident TARLE
Values of u+_,,,,~,
, u,,,,_~,,~and
vo,,
and their
systematic
u‘lp -pppn
(G&C,
(2P)
(mb)
errors.
deuteron.
The momentum
distribution
1 &r\,L~!.,,,
and
6a‘,;_,,,
are the statistical
and
errc~rs in r,Ip_ppv &T”,” “P+DP”
fi”;“_F”
fl,p-*pp?r
m
(mb)
(mb)
fi~::;+pp;i (mb)
1.04
0.18
0.03
0.19
0.03
0.00
1.14
0.62
0.04
0.67
0.04
0.01
1.25
1.10
0.07
1.19
0.08
0.03
1.34
1.71
0.07
1.8.5
0.08
0.05
~(11 (mb) -0.06 0.22 -0.16 0.19
6a,, 1 (mb) 0.08 0.13 0.22 0.25
1.44
1.99
0.08
2.14
0.09
0.05
0.52
0.27
1.48
2.08
0.08
2.24
0.09
0.05
0.32
0.27
1.59
2.22
0.08
2.38
0.09
0.05
0.17
0.27
1.69
2.48
0.09
2.65
0.10
0.06
0.84
0.29
1.79
2.60
0.09
2.78
0.10
0.06
1.19
0.28
1.89
3.01
0.10
3.23
0.1 I
0.07
2.65
0.29
T. ~~~ib~~~~~nu et al. / np -t
of the spectator together
protons
(dN/dp)
with the momentum
at 3.79 GeV/c
distribution
ppr-
673
is shown
predicted
in fig. 2 as an example
by the H&hen
deuteron
wave
function 15), which is represented by the solid curve. The predicted momentum distribution was normalized to the number of events in the spectator momentum range O-200 MeV/ c. As seen from the figure, in the low spectator momentum region (below 300 MeV/c), the momentum distribution of the spectator protons is well explained by the Hulthen deuteron wave function. In the high spectator momentum region (above 300 MeVie), the difference between data and prediction becomes significant. Quantitatively, about 10% of the spectator protons have momenta greater than 300 MeVie. But the Hulthen deuteron wave function predicts less than 1%. This difference is due to the double scattering and final-state interaction effects. In the subsequent analyses, ail events identified as reaction (A) are analyzed as reaction (B) with a spectator proton, and we did not impose any cut on the momentum of the spectator protons. However, we also analyzed these events with the following events which cut on the spectator momentum P,: P, < 300 MeV/c, to eliminate cannot be explained by the impulse approximation alone. But these events did not show any statistically significant differences in various physical quantities from those obtained by using the entire sample.
x Dakhno 0 Brunt z
1
a Other
2
+ This
Incident
momentum
et
al.
et al. data experiment
tGeY/c)
Fig. 3. The np + ppK total cross sections as a function of incident momentum together with the data of refs. 4-h.*~“,‘31. The smaller error bars indicate the statistical errors and the larger error bars the linear sums of the statistical and systematic errors. The dot-dashed curve is a prediction by VerWest and Arndt I”), and the dashed and solid curves are predictions of the Deck model with and without an I = 0 diharvon by Jauch er ni. ‘“I.
T. Tsuhoyama et
674
al. /
np + pp~
The incident neutron momentum was assumed to be a half of the deuteron momentum. However, its r.m.s. spread was calculated to be about 6-i% using the incident deuteron and spectator proton momenta. To calculate the total cross section for reaction (B) we have made a correction The shadowing effect is usually considered and the fotlowing
approximate
relation
*dp-.ppp?r-
=
to compensate for the shadowing effect. to be mainly due to single pp scattering,
is sometimes -{
unnp-ppx
1 - (1/4n)(
used “f: I/ r’)aFi}
.
If the shadowing effect was neglected, fl+,ppp& would be the same as u_,+,,~~~. However, an elastically scattered proton from the first pp elastic scattering can collide with the spectator neutron to initiate the reaction pns+ pprr-. This sequence factor of reactions simulates the dp + ppp’rr reaction, and the above correction overestimates the shadowing effect. In order to estimate the shadowing effect more realistically we used the following relation between ~dP_PPP~~ and a,,,,,,at an incident neutron momentum p,
do-----=‘o”np+ppa-(P’) da, da
4 x Dakhno 3
t?
+ This
et al.
experiment
1
0
-1
1.0
1.2 Incident
I.4
1.6
momentum
1.8
2.0
(Gev/c)
Fig. 4. vO, as a function of incident momentum. The smaller error bars indicate the statistical errors and the larger error bars the linear sums of the statistical and systematic errors. The dot-dashed curve is a prediction by VerWest and Arndt 191, and the dashed and solid curves are predictions of the Deck model with and without an I = 0 dibaryon by Grein ef af. “).
T
Tsuboynma
675
et al. / np + pprr
(a) 100
loo
80
80
60
60
40
40
yr Q
20
2o
3 c !?
0
0
200
200
Y 150
150
100
100
Lm-
50
0
50
0 OS -1 -0.5
-1-0.5
0 0.5
-1 -0.5
0 0.5 -1 -0.5
0 0.5-l
-0.5
0 Q5
0
1
(b)
$ cn
E
2”
40
40
30
30
20
20
10
10
0
0
60
60
40
40
20
20
0 -1-0.5
0 05
-1 -0.5
0 0.5 -1 -0.5 0 0.5 -1 -0.5
0 45 -1 -0.5
0 0.5
1
0
cos@&f-
Fig. 5. (a) Proton
angular distributions for the reaction np* pprat all momentn. distributions for the reaction np+ pprr- at all momenta.
(b) Pion al~gul,tr
616
al/a0 +?‘C +
0.5
0.0
**+
l
-0.5 t -1.0
1
E....,....,.,..,. 1.2 1.4
1.6
-0.5 1.5
1.8
1.0
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
-as E -I.*,-
1.2
1.4
1.6
1.8
incident Fig. 6. The normalized
coefficients
2
momentum
(GeV/c)
of the Legendre expansions of the proton functions of incident momentum.
angular
distributions
as
where p’ denotes the momentum of the secondary proton which collides with the spectator neutron, a:;(p) the total pp cross section at momentum p, da,,/dfl the pp elastic differential cross section, and (l/r’) is the mean inverse distance squared between the proton and neutron in the deutron, which was taken to be 0.0311 mb-’ was approximated by in our case 16). The value of a,p_PPn (p’) in the integrand I$(p’) below p’ = 1.2 GeV/ c, where ~+,_pppn-(2~‘) for p’> 1.2 GeV/c and by 2u,,_,,, the I =0 contribution is negligible. With this approximation provisional values of F~,,,_~~~ (p) were calculated for all values of p, using the values of p’
1.0 0.5 0.0 al/a0
-0.5 -1.0
. ..I.-
-I-..-....
1
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
1
1.2
1.4
1.6
1.8
2
incident Fig. 7. The normalized
coefficients
momentum
(Gel//c)
of the Legendre expansions of the pion functions of incident momentum.
angular
distributions
BS
sums of the statistical and systematic errors. The dot-dashed curve is a prediction by Verwest and Arndt “), and the dashed and solid curves are Deck model predictions with and without an I = 0 dibaryon by Jauch et ai. I’)). They are also shown with their statistical and systematic errors in columns 4, 5 and 6 of table 1. Our data are quite consistent with the other data except at 1.89 GeV/c. At 1.89 GeV/c our cross section is larger than the other data. We checked the data at this momentum carefully for any anomaly in the beam condition and the final state identification but found none. Our data also agree with the predictions by VerWest and Arndt I’), and by Jauch ef al. with an I =0 dibaryon I”). According to a model proposed by Rosenfeld IO), nucleon-nucleon -single-pion production cross sections are categorized by the initial and final two-nucleon isospins I and T, denoted as (T{~. In this representation, a,, is obtained by, u 01 = 2~J,,P-pPr
- ~,,-.,,,“.
Using this formula and rr,,P_Ppr ‘1interpolated from the data of ref. ‘1, we obtained rC,, as a function of incident neutron momentum. The errors in the estimation of these cross sections were taken into account to obtain the error in (T(~,. The results are shown in fig. 4 together with the data of Dakhno et al. I’). The smaller error bars indicate the statistical errors and the larger error bars the linear sums of the statistical and systematic errors, which are 26a,,,,,,, . The dot-dashed curve is a prediction by VerWest and Arndt ‘“), and the dashed and solid surves are predictions of the Deck model with and without an I= 0 dibaryon by Grein et al. ‘I). Our data
T. Tsuboyuma et al. / np + pp6
678 n 5 50 s : 40 0
t30 * ; $20 ; 2”
10 0
1.1
1.2
1.3 1.4 (0 eV/c’ 1
.1.5 (GeV/c’) M(PW)
M(PA’)
2.4 (GeV/c’) M(PP)
0 1.6
2.0 2.a (GeV/c*f M(PP)
2.4
Fig. 8. The invariant mass distributions for the prr- system and the pp system from the reaction np+ ppvat 1.48 CieV/c and 1.89 GeV/c. The dotted, dashed and solid curves are the pure phase space, phase space weighted by the Breit-Wigner function to represent d and the results of the fit discussed in the text, respectively.
agree well with the data of Dakhno et al. ‘“1. The values of rtr, and their statistical errors are also shown in columns 7 and 8 of table 1. Fig. 4 indicates that our cross sections are a little larger than the prediction by VerWest et al.I').But their calculation was based on sparse data and the disagreement may not be very serious. Although the Deck model prediction without an I = 0 dibaryon by Grein et al. “) agrees with the experimental data, their prediction with an I = 0 dibaryon completely disagrees with our data, which is in contradiction to the fact that our np+pprrcross sections agreed with the prediction of another Deck model calculation by Jauch et al. 19) with an f -=O dibaryon. This contradiction is due most likely to the inadequacy of the Deck models adopted. The angular distributions of the protons and the Y in the final state of reaction (B) are shown in figs. .5a and 5b. They are simiiar to each other in shape. At lower deuteron incident momenta the distributions are flat. At higher incident momenta, the forward and backward peaks become clear. In order to study the momentum dependences of the angular distributions, we expanded them in terms of Legendre polynomials by the moment method. The
619
Tsuboyama et al. / np + ppK P’I”“r”“l”“I”“i”“1’9 100
-
80
-
60
-
I
o\” 40
-
20
-
0”
E I PP-+PA+
E I
’ ’ ’ 1
I-I,’ ’ 1.2
Incident Fig. 9. The fractions
E
of -l-production
I nP-*PAO
’ ’ ’ ’
’
’
’
1.4
momentum
’
’
’
’
’ ’
1.6
’
’
1.8
’
”
’
’
’
2
4
(GeV/c)
in the reaction np+ ppr momentum.
and pp + pp~~‘(’as functions
of incident
values of the normalized coefficients of the proton and rTT angular distributions are shown in figs. 6 and 7 as functions of incident neutron momentum. From these figures we conclude that the coefficients for the odd-order Legendre polynomials are consistent with being 0, which means that the angular distributions are symmetric around cos 0 = 0. However, at 1.89 GeV/c the angular distribution of the r- is not symmetric. The asymmetry in the angular distribution can arise only when both the I = 0 and I = 1 amplitudes exist. The fact that at the highest incident momentum the negative-pion angular distribution shows an asymmetry seems to indicate the onset of a significant contribution of the I = 0 amplitude in reaction (B) at this momentum. This is consistent with the fact that cr(,, at this momentum is significantly non-zero. We studied A production in reaction (B). First, we estimated the fraction of A0 production in np + pprr at each incident momentum. The fraction of A0 production in reaction (B) is estimated from the distributions of the pn- invariant mass, m(pY) and the proton-proton invariant mass, m(pp). Using a Monte Carlo phase-space program FOWL”), we generated two sets of m(pY) and m(pp) distributions for reaction (B). One set is a pure phase-space distribution, In the other set, each event which was generated by FOWL was weighted by the relativistic Breit-Wigner function 23) for the m(pY) to represent the A resonance. The central value and the width of the Breit- Wigner function were chosen as 1.232 GeV/ c* and 0.1 GeV/ c’. For the m(pp) distribution, this weighting represents the reflection of the A in the
680
40
20
0 125 100 75 50 25 0 -1-0.5
0 0.5 -1 -0.5 0 0.5 -1 -0.5 0 0.5 -1 -0.5 0 0.5 -1-0.5
Fig. 10, The -I-production
angular
distribution
of the reaction
np+
0 0.5
p-1”- ppK at all momenta.
(pr) system. These two sets of invariant mass distributions were fitted to the experimental data by the maximum likelihood method simultaneously. Fig. 8 shows the m(pC) and m(pp) distributions at 1.48 and 1.89 GeV/c. The fitted distributions are indicated by the solid curves, the contributions of pure phase space by the dotted curves and the contributions of the Breit-Wigner distribution by the dashed lines. The values of the fractions of A production are shown in fig. 9 as a function of incident neutron momentum. They are between 25-75s. In our momentum range of 1.0-1.9 GeVfc, the pure phase-space distribution and the phase-space distribution including the if resonance are similar in shape, and in the fitting procedure the correlation between the two distributions is substantial. The correlation is duly included in the estimated errors, which are typically 3%. These are statistical errors obtained from the fitting procedure and are likely to be underestimated. The value of the fraction also varies from momentum to momentum. This is due most likely to the way the fitting process converges and to the simple nature of the model adopted. Thus these fractions should be regarded as rough estimates. In fig. 9 the fractions of the A+ production from the reaction pp-2 pp~” of Shimizu et al. ‘) are also shown. They roughly agree with our data except at around 1.9 GeV/c. From these results, it is concluded the 3 production is substantial in reaction (B). Moreover, the fraction of A is largest at around 1.6-1.8 CeV/c where the central values of the m(pY) distributions are about equal to the mass of the A.
Incident The momentum J-production
MomentUm
dependences
angular distributions.
)
(GeV/c
of the normalized
coetficients
of the Legendre
expansion
of the
Open circles represent the data from the reaction np + p-l” and filled
circles represent the data from the reaction pp + pJ+.
We selected the J sample whose effective mass m(pn ) of one ofthe two final-state protons and the final-state 6 satisfies the following inequality, lnr(pr ) - m(~)l< r(A), where m(J)= 1.232GeV and f-(,4) =O.l GeV. Since there were two pC combinations
for each event, the one whose m(pn
) is closer to the m(J)
was used,
when both pairs satisfied the inequality. The &resonance production angular distribution with respect to the neutron direction at each incident momentum is shown in fig. 10. At high incident momenta the d production angular distributions peaked strongly in the forward and backward direction. It can be interpreted as due to the fact that the momentum transfer from the incident neutron to the 3 is small, and this reaction is dominated by light-particle exchange. In order to study the momentum dependence of the angular distributions, we expanded them in terms of Legendre polynomials by the moment method. The normalized coefficients are plotted in fig, 11 by open circles. At low neutron incident momenta, all coefficients are consistent with 0. At high momenta even-order terms dominate
the reaction, but ~,/a,, is still consistent with 0 within the statistical terms are always consistent with 0. Also in fig. 11 the normalized
accuracy. Odd-order
682
T. Tsuboyavamaet al. / np -+ pp”r-
coefficients which
of the A ’ production
are obtained
angular
by a reanalysis
distributions
from the reaction
of the data of Shimizu
et ai. >)
pp + pprO,
are shown
by
filled circles. They agree well with those of the A” from the reaction np+ pp6. Finally we studied the density matrix of the A in the reaction np+ pA”;rpp?~-. If dibaryons couple strongly to the pion production channels, it is expected that the observables relating to the spin states of the nucleons show some anomalies, The A-decay angular distributions are measured in the helicity frame and GottfriedJackson frame. In the helicity frame the z-axis is parallel to the direction of the A seen in the c.m. of the initial two nucleons. In the Gottfried-Jackson frame, the z-axis is parallel to the direction of the incident nucleon seen in the rest frame of the A. In both frames, the y-axis is chosen to be perpendicular to the A-production plane, and the x-axis is chosen to make a right-handed Cartesian coordinate system. The elements of the density matrix are obtained from the angular distribution using the moments of spherical harmonics, PX = a - 24 Y2”)* I 1 PII =z-P33, Re p31= Re &d Rep,_,
Yd*)
,
= Re (-&Y&“),
where Y,,, represents the spherical harmonics. The elements of the density matrix were obtained as functions of neutron momentum and are shown in figs. 12a and 13a. In the helicity frame, the pJ3 gradually decrease from 0.5 to 0.25 as the incident momentum is increased from 1.1 GeV/c to 1.89 GeV/c, while Re p3, and Re pj_, are always consistent with 0. In the Gottfried-Jackson frame, the p,, dominates the A spin state and the other values are very small. These facts can be interpreted to mean that the reaction np+ PA’+ ppn- is induced by exchange of a spin-0 particle. As discussed previously the exchanged particle that pion exchange dominates this A production and the Gottfried frame, there is no obvious
is not a heavy one. Thus it seems reaction. In both the helicity frame structure which indicates sudden
changes
in the spin states. The values of the density matrix elements PP + PA + + PP”“, obtained by a reanalysis of the data of Shimizu et in figs. I2b and 13b. The similarities between the two reactions in the angular distributions and the density matrix elements indicate charge
independence
for these A-production
of the reaction are shown the behavior of the validity of al. *)
reactions.
4. Conclusions We have systematically studied the np -$ pprr- reaction in the incident-momentum range l-l.9 GeV/c, using the dp+ pppK reaction in the incident deuteron momentum range of 2-3.8 GeV/c. The total cross sections for this reaction were obtained. They agree with the earlier data below 1.7 GeV/c. But our cross section at 1.89 GeV/c is larger than the two adjacent data points obtained by Brunt ef al. IA). The predictions
T. Tsuboyama
et al. / np + pprr
1.00
‘*O”
(a)
0.75
0.75
a50
0.50
425
0.25
0.00
0.00
-0.25
-0.25
-0.50
1 1.25
1.5 1.75
Real
1.00
-0.50
2
P31
050
0.25
0.25
0-W
0.W
-0.25
-0;25
-0.50
1 1.25
1.5 1.75
-0kJ
2
Incident
p3-1
1.5 1.75
2
(GeV/c)
PI1 .
a50
**
++
0.00
++
++
0.25
l*
+t++
+t
0.00 -0.25
~ 1 1.25
1.5 1.75
-0.50
2
Real 33 I
1.00
w5
0.50
0.50
425 0.00
+
+*++
angular
2
RealP3-1
0.00 -0.25
~ 1 1.25
1.5 1.75
matrix
elements
distributions
-0.50
2
Incident 12. The density
1.5 1.75
0.25 *i*+
-0.25 -0.50
~
1 1.25
1.00
0.75
the decay
2
0.75
0.25
Fig.
1 1.25
1.00
0.75 0.50
from
Real
momentum
P33
1.00
-0.50
1.5 1.75
0.75
0.50
-0.25
1 1.25
1.00
a75
(b)
683
as functions
1 1.25
momentum of incident
of the A, (a) from
2
(GeV/c) momentum
the reaction
pp + p&l ’ + pp7r”.
1.5 1.75
np+
in the helicity p-l”+
ppr’
frame
obtained
and (b) the reaction
684
P33 (a)
0.75
0.75
0.X)
0.50
0.23
0.25
?***++*t
0.00
0.00
-0.25
-0.25 -0.90
1.00
~ 1 1.25
1.5 1.75
2
RealPa,
0.75
0.75 OS0
0.25
0.25
0.00
0.00
1 1.25
1.5 1.75
2
-0.50
l.OO
1.00 o.75
as0
oso
a25
0.25
a00
a00
-0.25
-0.25
1.00
1 1.25 Real
1.5 1.75 &
I
2
-050
1.00
w5
a75
O.!iO
OS2
0.25
0.25
0.00
o.oo
-0.25
-0.25
-0.50
-o&o
2
f,+ ** + . * F l
1 1.25
momentum
0.75
1.5 1.75
RfsalPa_,
-0.25
Incident
-0.50
I 1.25
1.00
-0.25
ibl
-0.50
0.50
-0.50
P11
1.00
‘xlo
1.5 1.75
2
(GeV/c)
I 1.25
1.5 1.75
2
Realpg-1
Incident momentum
(GeV/c)
Fig. 13. The density matrix elements as Functions of incident momentum in the Gottfried-Jackson obtained from the decay angular distributions of the &I, (a) from the reaction np+ pA”-t ppvthe reaction pp+ pJ++ ppn”.
frame and (b)
T. Tsuboyama
685
et al. / np + ppF
of a Deck model calculation by Jauch et al. 19) which includes an I = 0 dibaryon agrees with our data. However, our values of Us,, , which were obtained independent of any model, are consistent with zero below 1.7 GeV/c and become substantial only above 1.8 GeV/c. In addition, a Deck model calculation with an I = 0 dibaryon by Grein et al. *I), which is essentially the same as the calculation of Jauch et al. I”), predictions by is in complete disagreement with our go, data. Such contradictory Deck model calculations are most likely due to the inadequacy of the model. We conclude that our data on uO, rule out the existence of any I = 0 dibaryon resonance in the mass range 2.0-2.3 GeV/c’. An indication of the contribution from the I = 0 initial state in this reaction was observed in the angular distribution for the &, which showed an asymmetry at a neutron momentum of 1.89 GeV/c. The fractions of A production in np + pprr were estimated from the pp and pr’ invariant mass distributions. The value of the fraction was 25575% and was largest at around 1.6-1.8 GeV/c. Imposing a cut on the prr invariant mass, we selected the A samples and analyzed these events in terms of the A-production reaction, np+ ~3”. The angular distributions and the spin-density matrix elements of the A were obtained. They do not show any obvious momentum dependence which might result from the existence of a dibaryon state. They are quite consistent with the data for the reaction pp + pA ‘. This fact shows a similarity between the two reactions. We would like to acknowledge the operating crews of the KEK PS, the beam channel group and the 1 m bubble chamber group. We are also grateful to the scanners and measures at University of Tokyo for their painstaking efforts. Thanks are also due to M. Kajita, H. Koiso, Y. Kubota, S. Sakamoto and F. Shimizu who took part in the early stage of this experiment. This work was supported in part under the auspices of the Meson Science Laboratory, a Grant-in-Aid of the Ministry of Education, Science
University of Tokyo, and by and Culture (No. 58540145).
Data analyses for this work were done at the Computer Center and the Meson Science Laboratory of University of Tokyo and at the Computer Center of KEK.
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