12
PHYSICAL REVIEW D VOLUME 44. NUMBER 7 1 OCTOBER 1991 Measurement of y rays from antiproton-deuteriumannihilation at rest M. Chiba,e T. ~ujitani,* J. Iwah~ri,~.*, M. Ka~aguti,~ M. ~oba~ashi,~ S. ~ u r o k a w a , ~ Y. ~a~ashima,d T. 0mori,*,' S. ~ u ~ i r n o t o , ~ M. ~akasaki,~ F. Takeut~hi,~ Y. yamaguchi,* and H. ~ oshida~'~ aFaculty of Engineering, Fukui University, Fukui, Fukui, 910 Japan "National Laboratory for High Energy Physics (KEK), Tsukuba, Ibaraki 305, Japan CFaculty of Science, Kyoto Sangyo University, Kita, Kyoto, 603 Japan dPhysics Department, Osaka University, Toyonaka, Osaka, 560 Japan ePhysics Department, Tokyo Metropolitan University, Hachioji, Tokyo 192-03, Japan (Fukui-KEK-Kyoto Sangyo-Osaka-Tokyo Metropolitan Collaboration) (Received 7 March 1991) Using modularized NaI(T1) detectors, we have carried out a high-statistics measurement of inclusive y-ray spectra from jid annihilation at rest separately for each charge multiplicity of the final state. We have not seen, at statistical significance above 40, any monochromatic y-ray peaks, which may be as- signed to baryonium production pp or jin + yB or to RNN bound-state production jid + y (RNN). The 4u upper limit for baryonium production per annihilation varied between lo-' and lop4 depending on baryonium mass of 1700 to 600 MeV/c2 and on the charge multiplicity. At (2-3)u levels, however, five peaks were observed and three of them are located at the same position with the similar (2-3)u peaks observed in pp + y B and jip +rroB. I. INTRODUCTION In previous papers [I ,2], we described our experiment searching for narrow y or ro lines from pp annihilation at rest in a liquid-H2 target. The primary physics aim of the experiment was the search for baryonia below the antinucleon-nucleon (NN) threshold; we denote a proton or a neutron as N throughout the present paper. We ob- tained a four-standard-deviation (40) upper limit of ( 1.2-0.2) X [I] for the yield (i.e., the branching ra- tio) of pp 5p yB (here B denotes an antidiquark-diquark baryonium or an NN bound state) depending on the y-ray energy of 80-938 MeV, and a 40 upper limit of lo-'- [2] for pp -+--tao~ depending on the rro energy of 150-900 MeV. Both Angelopoulos et al. [3] and Adiels et al. [4] also gave a negative result on baryonia below the threshold at similar sensitivities as in our experiment. Any of the three experiments mentioned above did not confirm the three candidates for baryonia reported before [5] with branching ratios as large as lop3. With the same experimental setup as for the pp annihi- lation experiment [1,2], we have also carried out a high- statistics measurement of inclusive y-ray spectra from pd annihilation at rest separately for each charge multiplici- ty. The first physics aim of the present measurement is the search for baryonia arising from pn annihilation. Should isovector baryonia exist, they may be more clearly ob- served in the Jin system than in pp. In addition to the larger population of the isovector state, another advan- tage of using the pn initial state is that the G-parity con- servation in pn + yB is less restrictive than C-parity con- servation in pp-yB. For example, quantum numbers JPC, If - f or B are allowed only from the 's, state of Jip under the S-state dominance hypothesis, while they are allowed from both 's, and 3 ~ 1 states of pn. Although B's with JPC=O+- , I + - , 2'- (via El transition), l p + (M 1 ), etc., are inhibited from pp, they are allowed from pn . Only a few experiments have been reported on narrow (Jin ) states below the threshold. A narrow (pn ) state at 1795 M~V/C' with the width l-58 ~eV/c~ and 1~(~~~)=1+(1--, 2+- , 3--, etc.) was suggested by Gray et al. [6] with a branching ratio of the order of from a measurement of the recoil-proton momen- tum spectrum in pd+(jin)p with a bubble chamber. Amsler et al. [7], however, did not confirm the above state from a missing-mass spectrum obtained with a nu- cleon time-of-flight spectrometer. They gave a 40 upper limit of 3 X for the branching ratio B(pd -NB ) in a mass range of M, = 1650- 1930 M~V/C' for B. They also measured photon spectra searching for narrow states iri pd -NB y and obtained a 4c7 upper limit of 2X lo-'. Recently, a few candidates of ) quasinuclear states have been suggested (X( 1110) with I~(J~~)=O+(O'+ 1, xO( 1480) with 0+(2+ +), etc. [a]) from measurement of exclusive channels in pd annihilation at rest. Although 1933 @ 1991 The American Physical Society

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Page 1: rays from antiproton-deuterium annihilation at rest

PHYSICAL REVIEW D VOLUME 44. NUMBER 7 1 OCTOBER 1991

Measurement of y rays from antiproton-deuterium annihilation at rest

M. Chiba,e T. ~uj i tani ,* J. I w a h ~ r i , ~ . * , M. K a ~ a g u t i , ~ M. ~ o b a ~ a s h i , ~ S. ~ u r o k a w a , ~ Y. ~ a ~ a s h i m a , d T. 0mori,*,' S. ~ u ~ i r n o t o , ~ M. ~ a k a s a k i , ~ F. T a k e u t ~ h i , ~

Y. yamaguchi,* and H. ~ o s h i d a ~ ' ~ aFaculty of Engineering, Fukui University, Fukui, Fukui, 910 Japan

"National Laboratory for High Energy Physics (KEK), Tsukuba, Ibaraki 305, Japan CFaculty of Science, Kyoto Sangyo University, Kita, Kyoto, 603 Japan dPhysics Department, Osaka University, Toyonaka, Osaka, 560 Japan

ePhysics Department, Tokyo Metropolitan University, Hachioji, Tokyo 192-03, Japan (Fukui-KEK-Kyoto Sangyo-Osaka-Tokyo Metropolitan Collaboration)

(Received 7 March 1991)

Using modularized NaI(T1) detectors, we have carried out a high-statistics measurement of inclusive y-ray spectra from jid annihilation at rest separately for each charge multiplicity of the final state. We have not seen, at statistical significance above 40, any monochromatic y-ray peaks, which may be as- signed to baryonium production pp or jin + yB or to RNN bound-state production jid + y ( R N N ) . The 4u upper limit for baryonium production per annihilation varied between lo-' and lop4 depending on baryonium mass of 1700 to 600 MeV/c2 and on the charge multiplicity. At (2-3)u levels, however, five peaks were observed and three of them are located at the same position with the similar (2-3)u peaks observed in pp + y B and jip +rroB.

I. INTRODUCTION

In previous papers [ I ,2], we described our experiment searching for narrow y or ro lines from pp annihilation at rest in a liquid-H2 target. The primary physics aim of the experiment was the search for baryonia below the antinucleon-nucleon ( N N ) threshold; we denote a proton or a neutron as N throughout the present paper. We ob- tained a four-standard-deviation (40) upper limit of ( 1.2-0.2) X [I] for the yield (i.e., the branching ra- tio) of pp 5p y B (here B denotes an antidiquark-diquark baryonium or an NN bound state) depending on the y-ray energy of 80-938 MeV, and a 40 upper limit of lo-'- [2] for pp - + - - t a o ~ depending on the rro energy of 150-900 MeV.

Both Angelopoulos et al. [3] and Adiels et al. [4] also gave a negative result on baryonia below the threshold at similar sensitivities as in our experiment. Any of the three experiments mentioned above did not confirm the three candidates for baryonia reported before [5] with branching ratios as large as lop3.

With the same experimental setup as for the pp annihi- lation experiment [1,2], we have also carried out a high- statistics measurement of inclusive y-ray spectra from p d annihilation at rest separately for each charge multiplici- ty.

The first physics aim of the present measurement is the search for baryonia arising from pn annihilation. Should isovector baryonia exist, they may be more clearly ob-

served in the Jin system than in pp. In addition to the larger population of the isovector state, another advan- tage of using the pn initial state is that the G-parity con- servation in pn + y B is less restrictive than C-parity con- servation in pp-yB. For example, quantum numbers JPC, I f - f or B are allowed only from the 's, state of Jip under the S-state dominance hypothesis, while they are allowed from both 's, and 3 ~ 1 states of pn. Although B's with J P C = O + - , I + - , 2'- (via E l transition), l p + ( M 1 ), etc., are inhibited from pp, they are allowed from pn .

Only a few experiments have been reported on narrow (Jin ) states below the threshold. A narrow (pn ) state at 1795 M ~ V / C ' with the width l -58 ~ e V / c ~ and 1 ~ ( ~ ~ ~ ) = 1 + ( 1 - - , 2 + - , 3--, etc.) was suggested by Gray et al. [6] with a branching ratio of the order of

from a measurement of the recoil-proton momen- tum spectrum in pd+( j in)p with a bubble chamber. Amsler et al. [7], however, did not confirm the above state from a missing-mass spectrum obtained with a nu- cleon time-of-flight spectrometer. They gave a 4 0 upper limit of 3 X for the branching ratio B(pd -NB ) in a mass range of M, = 1650- 1930 M ~ V / C ' for B. They also measured photon spectra searching for narrow states iri p d -NB y and obtained a 4c7 upper limit of 2 X lo-'.

Recently, a few candidates of ) quasinuclear states have been suggested ( X ( 11 10) with I ~ ( J ~ ~ ) = O + ( O ' + 1, xO( 1480) with 0+(2+ +), etc. [a]) from measurement of exclusive channels in pd annihilation at rest. Although

1933 @ 1991 The American Physical Society

Page 2: rays from antiproton-deuterium annihilation at rest

1934 M. CHIBA et al. 44

their detection in inclusive y-ray or 77-O spectra should not be straightforward because of their large widths (as large as or larger than several tens of M~v/c , ) , there exists an increasing interest in the study o fpd annihilation at rest.

The second aim is the search for baryonia from jip in jd. The motivation for this search came from the posi- tive signals of narrow y-ray peaks observed by Adiels et al. [9] in p 4 ~ e annihilation at rest. They observed two narrow peaks in the y-ray spectrum at 161.9 and 203.0 MeV at statistical significance higher than 4 a , and suggested that baryonia might be produced in nuclei more copiously than in hydrogen.

While p annihilation in liquid H, is dominated by the initial atomic S state with a small contamination of P state (roughly 20% [lo]), p annihilation in liquid 4 ~ e seems to be dominated by the ( n , L ) = 2 P state [ l l ] . Baryonia may become stable by the centrifugal barrier between antinucleon and nucleon in potential models, or between antidiquark and diquark in quarkonium models. Such stabilized baryonia may be more easily produced when the initial orbital angular momentum of the annihi- lating p nucleus is large.

Although there is not yet any clear direct experimental information on the initial atomic state of the annihilating pd system, there are some reasons to expect that the amount of P state should be much larger than in pp an- nihilation. This is intuitively understood by comparing pp and p d atoms with respect to the nuclear radius R,,,( A)=1 .3A1l3 fm and the Bohr radius of PA atom given by

where n is the principal quantum number and y is the re- duced mass of p and the nucleus A. The Bohr radius for n = l is smaller for jid (43.2 fm) than for pp (57.6 fm), while the nuclear radius is larger for p d (about 4 fm) than for pp (about 1.3 fm). Consequently, the overlap of an- tiproton and nucleus wave functions in the n = 2 state ( 2 s and 2P) should be larger in p d than in pp.

Large contribution of L L 1 pd atomic states can also be understood from an intuitive consideration on the or- bital angular momentum of antiprotonic atoms. Since the annihilating antiproton will be most dominantly lo- calized at the nuclear surface, it will acquire a kinetic en- ergy in the Coulomb potential, which corresponds to a momentum [9] in the laboratory system of

When annihilation occurs, the impact parameter should be between 0 and R,( A) . Hence, the quantity defined by

may give a rough measure for the orbital angular momen- tum of the annihilating jiA system. Substituting Eq. (2) into Eq. (31, we get

which is 0.21, 0.43, and 0.43 for pp, pd, and jJ 4 ~ e atoms, respectively. Similar magnitudes of L o for both p d and ji 4 ~ e suggest that L 1 1 initial atomic states may also be important in pd annihilation as in ji 4 ~ e [9].

Also, when the jid system is taken as an annihilating pp plus a neutron, the relatively energetic neutron can carry away a finite angular momentum, thus leaving the jip sys- tem in a nonzero angular-momentum state.

The above consideration on the orbital angular momentum of annihilating pd is supported by the experi- mental observation of pd annihilation at rest into two pions by Gray et al. [12] and by Sun et al. [13]; both ex- periments have shown that the orbital angular momen- tum of jiN is equal to or larger than 1 for most of the an- nihilation.

The third aim is the search for jipn bound states, which have been predicted in nuclear potential models [14]. Though Dal'karov et al. [14] predicted many ( N N N ) bound states, narrow ones with a width less than 50 MeV should lie close to the threshold (three times the nucleon mass) with the binding energy less than -30 MeV. Since our present experiment could measure y rays above 10 MeV, we could detect some of the bound states if they should exist. The inclusive y -ray spectra from jid annihi- lation at rest, obtained in the present experiment, is more than an order of magnitude higher in statistics than those [15] reported before.

11. EXPERIMENT AND DATA REDUCTION

The experimental setup was essentially the same as de- scribed in [I] except filling liquid D, instead of liquid H, into the target cell of 14 cm (in diameterlX23 cm (length). Deuterium runs were taken after having comp- leted hydrogen runs.

A secondary antiproton beam at 580 MeV/c from the KEK 12-GeV Proton Synchrotron was made to stop in- side the target cell. The emitted y rays were measured with a modularized NaI(T1) calorimeter (with 96 modules assembled into a half barrel) covering an effective acceptance of 22% of 477- sr. The charged parti- cles were tracked with cylindrical as well as flat multiwire proportional chambers (MWPC's). Data taking was car- ried out under a triggering condition of (i) a slow antipro- ton being incident on the liquid-D, cell and (ii) one or two y rays falling on the NaI.

For 1.92 X 10' triggered events in total, various cuts [1,2] were first applied with respect to hardware errors in readout and in tracking of the degraded antiproton. Re- quiring then in vertex reconstruction that (i) the vertex should not be located outside the target cell wall by more than 1 cm either radially or longitudinally and that (ii) the rms distance from the vertex to the charged tracks should be less than 1 cm, we obtained 7.32 X lo6 events. y rays were identified by energy deposits in NaI and ab- sence of signal in the scintillator hodoscope and in the MWPC in front of the hit NaI modules. Applying a cluster-finding logic [I], and requiring that the shower leakage into the scintillating glass surrounding the NaI modules should be less than 10% of the y-ray energy, we finally obtained the total number of y rays above 10 MeV, N y , of 6.70 X lo6.

Page 3: rays from antiproton-deuterium annihilation at rest

MEASUREMENT O F y RAYS FROM ANTIPROTON-DEUTERIUM . . . 1935

111. ANALYSIS AND RESULT

A. Inclusive y -ray spectra

The obtained inclusive y-ray spectra are presented in Fig. 1 for each charge multiplicity, Nch, as well as for the sum over Nch. The number of y rays in each spectrum is 2 . 3 1 ~ 1 0 ~ for Nch=O, 6 . 9 1 ~ 1 0 ~ for N c h = l , 1 . 9 9 ~ 1 0 ~ for NCh=2 , 1 .88x1o6for Nch=3, 1 .31x106for Nch=4 , 4 . 5 4 ~ lo5 for NCh=5, 1 . 2 2 ~ lo5 for NChz6, and 2.67 X lo4 for Nch L 7.

Table I gives the number of events registered in the y - ray spectra for each charge multiplicity. The ratio of pp to pn annihilations, a /( 1 -a ), has been measured in bubble-chamber experiments. Taking an average of four experimental data of 1 .31f 0.03 [16], 1.33f0.07 [17] and 1 .45f 0.07 [18], 1 .34f 0.03 [19], we obtain

Since, as shown later, the detection efficiency should be approximately the same both for jip and pn events, the present pd events should consist of 4.18X lo6 pp and 3.14X lo6 pn annihilations. Using the charge- multiplicity distribution of pp events obtained in our ex- periment [2] with a liquid-H, target, we can subtract pp from pd to deduce the amount of pn events for each charge multiplicity; the result is also given in Table I. Events with even charge multiplicities in pn annihilation may arise from (i) inefficiency in track reconstruction (about 10% per track) and (ii) conversion of y rays into e + e - pairs (about 6% per y ray) in and close to the tar- get cell.

B. Narrow peaks in y-ray spectra

Each y-ray spectrum, presented in Fig. 1, was fitted with a polynomial background plus narrow Gaussian peaks by using the program MINUIT [20] in a similar way as in [I]. In order to reduce the fitting parameters, we have divided the whole energy range (30-980 MeV) into four with ample overlap between adjacent regions. The order of the polynomial between 2 and 4, mostly 3, was sufficient to give good fits.

In order to search for peaks with the intrinsic width much narrower than the instrumental one, the width of the peaks was restricted to be within + 0 % , -30% above the instrumental one which was corrected for smearing of y energy due to the Fermi motion, etc. The asymmetric limits of +0%, -30% were chosen since the instrumen- tal resolution [I] (before correction) was, for safety, overestimated rather than underestimated. The correct- ed instrumental width [in the full width at half maximum (FWHM)] for the y energy E can be written as

AE/E=[ (AE/E)?+(AE/E) ;

+(AE/E);]O.~ (in F W H M ) .

TABLE I. Number of pd annihilation events registered in the y-ray spectra of Fig. 1 is given for each charge multiplicity N,,. It is also divided into pp and pn annihilation by assuming pd an- nihilation as the sum of quasifree reactions of p;D and p annihi- lations (see the text).

Nc h Fd FP lin (measured) (deduced) (deduced)

Total 7.32X lo6 4.18X lo6 ( 100%) 3.14X 10' ( 100%)

b % 0 - 1 ~ 3 E v e n t s 1 Bin

Y ENERGY (MeV )

FIG. 1. Inclusive y-ray spectra from pd annihilation at rest for each charge multiplicity as well as for their sum. Bars on the data points give the statistical error ( l o ). Number of events per 4.16-MeV bin is given at an appropriate position on each spectrum to show the vertical scale.

Page 4: rays from antiproton-deuterium annihilation at rest

1936 M. CHIBA et al. - 44

where q- is the momentum of the annihilating F N in the PN

laboratory system, qF is the Fermi momentum (see the Appendix) of the nucleon in deuterium, and M N is the nucleon rest mass. The first term comes from the purely instrumental width [I], the second one from the Doppler smearing due to the Fermi motion, and the last one from the shift of the y energy due to the change in the p N rest mass. The estimation of the second term is given in the Appendix. The third term can be derived as follows: when we designate the nucleon momentum due to Fermi motion as q, the spectator nucleon and the p N system carry away kinetic energies of approximately q 2 / 2 ~ , and q 2 / 4 ~ , , respectively. As a result, the p N rest mass scatters by

event by event. Then the ambiguity of the y energy is ap- proximately equal to A(M(FN)) , when the y energy is much smaller than MAT, and decreases with the increasing y energy. We assume that the elementary process of baryonium production in F N annihilation should not prefer any specific values of q as far as q is small. Then the distribution of q which is effective in baryonium pro- duction can be simply calculated from the deuterium wave function. A numerical calculation with the Hulthen wave function for deuterium shows that about 75% of nucleons should have q L q , ( = 104 MeV/c, see the Appendix). Since the FWHM of Gaussian distribu- tion corresponds to 75% lying within it, we may take q l q , to estimate the effect on the FWHM resolution AE /E. The above consideration leads to the third term of Eq. (6). We actually neglected this term because it is much smaller than the first term as far as E is as large as 100 MeV or larger.

The modified instrumental resolution of Eq. (6) is plot- ted in Fig. 2. The FWHM resolution of 12% at 100 MeV and 7.9% at 900 MeV should be compared with 1170 at 100 MeV arid 6.470 at 900 MeV, respectively, obtained without the Doppler smearing.

Above 600 MeV, we have observed several peaks [21] which can be assigned to the two-meson annihilation of pp or p n + n - O ~ with .rro mistaken as a single y ray. Misidentification of TO-yy as a single y ray was possi- ble at high energies because of limited spatial resolution 121. Except for the two-meson annihilation peaks and the so-called Panofsky y-ray peak at 129 MeV, no narrow peak was seen between 80 and 938 MeV with statistical significance above 40. Only five narrow peaks at 2 to 3u levels were obtained with the parameters given in Table 11. The fit between 200 and 600 MeV is, after subtraction of the polynomial background, presented in Fig. 3 for the sum over the charge multiplicity, and in Fig. 4 for each charge multiplicity, separately.

The baryonium mass, calculated for the initial p N with the rest mass of 2MN, is also given in Table 11. Since the p N rest mass in pd annihilation at rest is by AMB = B + 3 q 2 / 4 ~ , (here, B - 2.23 MeV, the binding energy of deuterium) below the threshold (2M,,,), the correct baryonium mass should be less than the value given in the table by AM, at the maximum (the case with

the y energy much less than MN). Although the shift of AMB scatters event by event, the center of the distribu- tion corresponds to q with the largest phase-space densi- ty. Referring to the Appendix, this condition reads q 2 / ~ ( q ) / 2 = m a x i m u m and occurs at q -43 MeV/c for the Hulthen wave function. Substituting this value of q into AMB, we obtain AMB=2.23+ 1.41 =3.64 MeV. Since this value is as small as or smaller than the ambi- guity of baryonium mass due to the fitting error, we neglect it below.

C. Yields of peaks

The yield of Fd + yBN, with N, a spectator proton or neutron or of Fd -yB with B an NNN bound state was calculated in a similar way as for Bp + y B [I]. The yield Y per p d annihilation is given by the number of mono- chromatic y rays, i.e., the peak area A above the back- ground, divided by the number of annihilations NF corrected for the detection efficiency r lB(E) of y rays with the energy E as

Here < is equal to a ( =0.571), 1 -a, and 1 when B can be produced only in Fp, only in pn, and both in pp and Fn annihilations, respectively. The last case of < is possible because the charge state of B was not measured very pre- cisely. < is also unity for p d -yB with B an NNN bound state.

I

5 5 x 5 Array (injection dong axis) [?I

0.02 ----- Whole Array (Uniform injection +software c u t s ) (11

b' ENERGY : E (MeV)

FIG. 2. The solid curve gives the modified energy resolution of the NaI calorimeter given by Eq. (6 ) . Uniform injection of y rays on NaI and application of software cuts including the clus- ter logics are assumed. The resolution without the Doppler smearing, etc. (dotted curve), and that of a 5 X 5 array of NaI modules for y-ray injection along the central axis of the array (dash-dotted curve) are also shown for comparison.

Page 5: rays from antiproton-deuterium annihilation at rest

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.8(3

.6,1

)

Posi

tion

(MeV

) 57

1.3+

6.2

582.

8+6.

1 55

7.1+

8.8

576.

1+4.

0 Y

ield

(K

T3)

0.69

+0.

31

0.17

+0.

08

0.21

+0.

10

M5

= 11

67±7

St

atis

tical

sig

nifi

canc

e 2.

3a

2.0a

2.

1a

Wid

th a

(M

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17.8

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14

.5 (

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)

Page 6: rays from antiproton-deuterium annihilation at rest

M. CHIBA et al.

I " " "

S u m of ALL Prongs -

r , , l 1 8 , , I , , , , , . , , , ,

100 200 300 300 400 500 600

Y ENERGY (MeV) Y ENERGY (MeV)

FIG. 3. The fitted result of the inclusive y-ray spectra (see Fig. 1) below 600 MeV is shown for the sum over the charge- multiplicity after subtraction of the polynomial background.

Generally speaking, q B ( E ) should depend on the decay stop inside the target. Although the spectator neutron scheme of B as well as on the spectator nucleon. First we may come out, the kinetic energy is much less than the consider a quasifree process of j7d + yBN,. Since the threshold (10 MeV) for y-ray (or neutrals) detection. So, Fermi momentum in deuterium is as small as 104 MeV/c the detection efficiency of y rays should hardly be (see the Appendix), the spectator proton should mostly affected. Approximately, therefore, q B ( E ) should not de-

7 ENERGY (Me*!) 7 SNERGY (l4eV) 7 ENERG* (MeV)

FIG. 4. The fitted result of the inclusive y-ray spectra (see Fig. 1) below 600 MeV is shown for each charge multiplicity after sub- traction of the polynomial background.

Page 7: rays from antiproton-deuterium annihilation at rest

44 - MEASUREMENT OF y RAYS FROM ANTIPROTON-DEUTERIUM . . . 1939

pend on the spectator nucleon. Since we do not know the where p ( E ) is the number density of y rays per pp annihi- decay scheme of B, we assume that its decay branching lation discussed in [I] . Since qAv can be calculated once ratios into various channels are the same as in pp annihi- the charge and y multiplicities in the final state are given, lation at rest. Then vB(E) can be taken the same as in pp the above relation leads to an approximate equality of annihilation at rest discussed in [I].

The situation is a little different for p d + y B with vp(E)=v,(E )=v(E) , (12)

B = PNN. In the decay where v(E) is the detection efficiency of y rays in pp an-

B-(mesons from NN)+N , (9) nihilation at rest given in [I]. Substituting Eqs. ( l o ) - ( 12) into Eq. (8), we obtain a

the nucleon may have enough energy to come out of the simple equation: target, leading to a decrease in vB. The decrease amounts to 0.015 in vB per charged track or per y ray (or Y = K ( E ) A / ( g N , ) (1 3)

a neutral which mimics a y ray) as typically seen in Fig. with 23 of [I], corresponding to about 10% of ve. Since we do not know about the decay of the VN system in Eq. (9 ) , K ( E ) = J p ( ~ l ) v ( ~ l ) d ~ f / v B ( ~ ) , we again assume that the decay branching ratios into various channels should be the same as in pp annihilation. which is of the same form as in pp annihilation [ I ] except

~h~~ v B ( ~ ) for p d + y ~ with B =VNN can be taken the for the presence of 6. K ( E ) is the effective multiplicity of

same as the vB(E) for pp annihilation at rest [I] within y rays per p d (or pp or pn) annihilation and is taken to be

an ambiguity of 10%. From the above consideration, we approximate vB(E) in Eq. (8) to be equal to the vB(E) in pp annihilation at rest given in [I].

As Np in Eq. (8) is proportional to the number of y - rays in the inclusive y -ray spectrum (6.70 X lo6 ), we ob- tain, by taking p d annihilation as the sum of quasifree pp and pn annihilations, another relation:

Here p ,v(E ' )dE ' with N =p, n is the number of y rays (mostly coming from TO) with the energy between E' and E ' f d E ' per p N annihilation, and vN is the detection efficiency of y rays produced in p N annihilation.

According to the statistical models, for example, one by Orfanidis and Rittenberg [22], the charge multiplicity (mainly T') as well as the y multiplicity (nearly twice the no multiplicity) should be almost independent of pp or pn annihilation. This prediction is consistent with the ex- perimental data listed in Table 111. Then we may have an approximation of

K =4.45 (14)

within a systematic ambiguity of i 2 0 % [I]. We have calculated the yield according to Eq. (13) with

K given by Eq. (14). The obtained yields are given in Table I1 for the peaks with statistical significance higher than 2 a .

The most prominent peak comes from the Panofsky y rays at 129 MeV. Its yield of 2.3 X per p d annihila- tion is roughly consistent with an estimation (4 .2X which is derived by multiplying the following three num- bers: the n multiplicity of 1.78 per jid annihilation [from a of Eq. (5) and the n - multiplicity of 1.57 per p7a and of 2.07 per pn annihilation as seen in Table 1111, the branch- ing ratio B (.rr-d -+ y nn ) =0.25 [26,27], and the average probability that a a- meson should stop in the liquid D,=0.94% corresponding to the pion range of 7 cm in deuterium. The last number was deduced from the T-

momentum distribution calculated by a Monte Carlo simulation [ I ] for pp annihilation. Since the T- momen- tum distribution should depend on the model of pd an- nihilation mechanism, the last number may suffer from some ambiguity.

Except for the Panofsky y-ray peak, we have seen five narrow peaks at photon energies of E- 175, 328, 356,

TABLE 111. Charge-multiplicity M + + M - , and y multiplicity M y in pp, pn, and pd annihilation at rest.

M + + M - Mv Reference

PP 3.2110.12 3.46t0.38 N. Horwitz et al. (1959) [23] 2.99k0.08 T. Kalogeropoulos et al. (1980) [19] 3.22 3.93 G. Backenstoss et al. (1983) [24]

V. Barnes (1964) [I61 A. Bettini et al. (1967) [18] T . Kalogeropoulos et al. (1980) [19]

pd 3.23k0.18 3.6t0.5 N . Horwitz et al. (1959) [23] 3.04 3.77t0.08 T. Kalogeropoulos et al. (1974) [25] 3.06310.09 T. Kalogeropoulos et al. (1980) [19]

Page 8: rays from antiproton-deuterium annihilation at rest

1940 M. CHIBA et al 44

470, and 576 MeV with statistical significance of 2 to 3a levels. The yields of these peaks are plotted in Fig. 5. The solid curves give the 4a upper limit; it corresponds to four times the rms statistical fluctuation of the back­ground y rays, which are registered in an energy span of ± [modified instrumental F W H M given by Eq. (6)]. Al­though a few more peaks have been observed above 600 MeV in the y-ray spectra, they are not shown in Fig. 5 since, as already described in the last paragraph of Sec. I l l B, all of them could be assigned to monochromatic ir° peaks coming from pp or pn annihilation into TT°M with M one of known mesons.

In the low-energy region below 180 MeV, precision fitting was carried out by using an experimental

MASS of NNN (MeV/c2) 2800 2600 2400 2200 2000 1800

i i i i i i i 1 l i l L

MASS of B (MeV/c2)

Y ENERGY (MeV)

FIG. 5. The 4<r upper limit for the yield of narrow peaks (baryonia or NN bound states) is plotted with solid curves. Solid points show narrow peaks seen at 2 to 3<r levels. Solid and open arrows give the positions (except for the Panofsky peak at 129 MeV) where 2 to 3a signals were observed in pp annihila­tion at rest into yX and TT°X, respectively [1,2], with yields larger than 2X 10~4 per annihilation.

Panofsky-peak spectrum instead of a Gaussian shape. We did this before in the analysis of y-ray spectra from pp annihilation [1] because the Panofsky 7-ray spectrum, i.e., the spectrum of y rays coming from annihilation of low-energy secondary n~ on proton, has a complicated structure consisting of a monochromatic peak at 129 MeV plus a broad peak between 55 and 83 MeV.

In pd annihilation, the y rays arising from capture of secondary n~ by another deuterium should be localized dominantly around 129 MeV [26-28] corresponding to radiative capture of 7r~ (7r~d-^ynn) with a far smaller amount of charge exchange (7r~d-^7r°nn-^yynn) which will produce a nearly box-type spectrum between 62 and 74 MeV. Consequently, the y-ray spectrum from TT~ capture should be much simpler in deuterium than in hydrogen. Actually, however, contamination of neutrons could make the apparent "y-ray" spectrum complicated. Neutrons arising from ir~d at rest into nn (B — 15% [26,27]) and ynn (B-25% [26,27]) were mistaken as y rays on Na l because no separation between y rays and neutrons was made. The former could mimic y rays with energies less than 68 MeV and the latter as small as 9 MeV.

Figure 6 shows the "y-ray" spectrum from TT~d an­nihilation at rest obtained in the present setup and with essentially the same data reduction procedure as for pd annihilation. The beam was changed from 580-MeV/c antiprotons to 167 MeV/c TT~ SO that TT~ should stop around the target center. The y-ray spectrum has a sharp peak around 129 MeV and an additional peak around 25 MeV with a broad tail toward higher energies. The latter structure may come from neutrons produced in ir~d^ynn and 7r~d-^nn. Although the kinetic ener­gy of neutrons should be smaller than 68 MeV (in 7r~d-^nn) for stopping ir~, neutrons from in-flight reac­tions should have higher energies. A small structure be­tween 50 and 80 MeV may be interpreted in terms of the

p~ T 1 1 1 j 1—~i 1 1 r—1 1 1 1 1 r

[ r f d at Rest

6 0 0 0 h ,"iii '•',

CQ L

>̂ 4000[— z: \-LU > \-LLI

2000 U

I L_-.1_J___0__L__I_L__L ._L._.J_L_, , L__L_ 0 50 100 150

ENERGY DEPOSIT of NEUTRALS (MeV)

FIG. 6. An energy-deposit spectrum of y rays and neutrons in the Nal detector for TT~ capture in deuterium.

Page 9: rays from antiproton-deuterium annihilation at rest

MEASUREMENT OF y RAYS FROM ANTIPROTON-DEUTERIUM . . . 1941

box-shape y-ray spectrum between 55 and 83 M e V from -

n capture by contaminating hydrogen atoms, i.e., n p p -non with no- y y. T h e amount of y rays between 55 and 83 M e V above the smooth background curve was about 4% of the y rays in the 129-MeV peak. Using the Panofsky ratio

[29] and t h e branching ratio B (T-d --t y n n )=0 .25 [26,27], we find tha t t h e observed amount can be inter- preted by contamination of H, in liquid D2 by 0.9% (in moll. T h e above-mentioned s tructure may also include a small amount of photons coming from n-d -nOnn with no-yy.

W e have reanalyzed the y-ray spectra from pd annihi- lation in t h e low-energy region of 30-180 MeV, using a high-statistics "y-ray" spectrum from n- capture by deuterium instead of a simple Gaussian. Each y-ray spectrum was fitted with the s u m of a polynomial back- ground of order 3-4, t h e experimental y-ray spectrum from n capture by deuterium, and any additional narrow Gaussians. T h e fitted result is presented in Figs. 7 and 8 after subtraction of the background. W e have not ob- served any other new narrow peaks.

IV. SUMMARY AND DISCUSSION

W e have carried out a high-statistics measurement of inclusive y-ray spectra in Fd annihilation a t rest. Fitting t h e spectra with a polynomial background plus narrow Gaussian peaks, we have not observed any mono- chromatic y-ray peaks which may be assigned to baryoni- u m production P N - y B ( N = p or n ) o r NNN bound- s tate production pd - y (NNN) a t statistical significance above 40. T h e 4 a upper limit for the baryonium produc- tion per annihilation is plotted in Fig. 5; it varies between

Residue Sum of ALL Prongs

E 1 ; 1 : I I i 1 i t ; ' I

Original Spectrum i

Y ENERGY (MeV)

FIG. 7. A fit to the inclusive y-ray spectrum summed over the charge multiplicity in the energy range of 40-200 MeV: original spectrum on the bottom and the residue after subtrac- tion of the polynomial background on the top. An experimental spectrum for rr-d-ynn, rronn was used in fitting (see the text).

TABLE IV. Comparison of five y peaks observed in the present experiment at 2-3u levels with the corresponding y or .rro peaks observed before in pp annihilation at rest. The peak position gives the y or -rO energy at the peak. The mass of B in the reaction pd-yBN, was deduced from the y energy by as- suming pN+yB with the initial pN at the threshold 2M,. Since the initial pN is actually below the threshold, the correct mass of B should be less than the value given in the table by 3.6 MeV at the max- imum (see the text). -

Reaction pd-yBNs ~ P + Y B pp - aOB assumed present expt. [I] [21

Peak position (MeV) 174.5t 1.8 156.4i-2.4 (mass of B in MeV) (M, = 1693t2) ( M B = 1 7 1 3 i 3 )

Peak position (MeV) 328.2i5.3 319.6k2.9 (mass of B in MeV) (MB=1512+7) (MB 1524+4)

Peak position (MeV) 355.8k2.3 355.9k7.0 362.2k2.3 (mass of B in MeV) (Me = 1479+5) (M,=1478k 9 ) (M, = 1483k5)

Peak position (MeV) 470.2i3.3 467.5t5.4 465.9+8.0 (mass of B in MeV) (M,= 1325k5) ( M , = 132958) (MR=1338+11)

Peak position (MeV) 576.1i4.0 560.3i6.3 562.2f 3.1 (mass of B in MeV) (MB=1167t7) (MB=1191k10) (MB = 1197t6) -- -

Page 10: rays from antiproton-deuterium annihilation at rest

1942 M. CHIBA et al. 44

L+!-.L&-~ 50 100 150 200

Y ENERGY (MeV1

5 m

4WO

3WO

2 Prongs

lLmO

Y ENERGY (MeV)

5 Prongs IT'-++

I-- . -.-A 50 100 150 203 %'o" I ~ O . 1;0. . 2&

Y ENERGY (MeV) Y ENERGY ( M a 1

FIG. 8. A fit to the inclusive y-ray spectrum in the energy range 40-200 MeV for each charge multiplicity separately. Original spectra are shown on the right-hand side and the residue on the left-hand side. The other items are the same as in Fig. 7.

and l o p 4 depending on the baryonium mass and the Professor H. Hirabayashi, and Professor K. Nakai for charge multiplicity. supporting the present work, and to the staff of the com-

The above result indicates, within the sensitivity given puter center of K E K for giving valuable help during the in Fig. 5 and above the y energy of 40 MeV, the follow- analysis. ing: (i) absence of narrow baryonia produced in pn + yB, (ii) absence of baryonia in pp + y B even for pp in the or- bital P state, and (iii) absence of (HNN ) bound states in APPENDIX: DOPPLER SMEARING OF y ENERGIES frd-y ( R N N ) .

Five narrow peaks were observed at 2 to 3 0 levels at photon energies of 175 MeV (the corresponding B mass, MB = 1693 M ~ V / C ~ when frd - yBN, is assumed), 328 MeV (MB=1512 M ~ v / c ~ ) , 356 MeV (MB=1479 Mev/c2), 470 MeV (MB = 1325 M ~ v / c ~ ) , and 576 MeV ( MB = 1 167 M ~ V / C 2 ) . Three of the above five peaks, ex- cept for the 175- and 328-MeV ones, are located close to the 2-30 peaks which we have observed in pp annihilation at rest to yX [I] (the position given in Fig. 5 with solid arrows) and in pp annihilation at rest to T O X [2] (open ar- rows). Although the coincidence of the peak positions between the frp and frd annihilations seems remarkable (see Table IV), it is difficult to draw a definite conclusion at the present stage, since the significance of the peaks observed is not large. A search for narrow y lines with an order-of-magnitude higher statistics could give a definite conclusion.

ACKNOWLEDGMENTS

1. Momentum of annihilatingpN system in the laboratory system

Antiproton annihilation in deuterium occurs from fTN ( N = p or n ) moving in the laboratory system. One of the contributions to the momentum of the frN system comes from the momentum q of the Fermi motion of each nu- cleon in deuterium. Another contribution comes from the kinetic energy of antiprotons acquired from the po- tential energy when the antiproton annihilates at the nu- clear surface. The corresponding momentum of the an- tiproton is given by qF in Eq. (2). The deuterium carries the opposite momentum. Because only one of the two nucleons of the deuterium interacts with p, it carries - ?qP. 1 AS a result, the momentum of the frN system is iq, in the laboratory system. By summing the above two contributions, the total momentum of the annihilating p N system in the laboratory system is

The authors express their deep thanks to Professor T. Nishikawa, Professor S. Ozaki, Professor H . Sugawara,

Page 11: rays from antiproton-deuterium annihilation at rest

44 MEASUREMENT OF y RAYS FRI 3M ANTIPROTON-DEUTERIUM . . . 1943

2. Estimation of the Fermi momentum g~

The deuterium wave function is given, apart from a normalization factor, by

where r=rp -r, is the relative position vector of the two nucleons, and u ( r ) and w ( r ) are the radial wave func- tions of the S and D waves, respectively. Since the amount of the D wave is as small as 6-7 % [30], the rela- tive momentum between proton and neutron may be determined almost completely by the S wave. The momentum ( q ) distribution of the proton or neutron is given by \II(q)12dq, where V ( q ) is the Fourier transform of \y(r ) and is reduced, apart from normalization, to

When the Hulthen wave function [3 11

is used, we obtain

\ I I ( q ) = ( q 2 + f f 2 ) - ' - ( q 2 + ~ 2 ) - 1 .

Here,

for the deuterium binding energy B =2.225 MeV [31] and /3 is numerically estimated to be

[32] from nucleon-nucleon scattering data at low ener- gies.

Since qF is given by the rms value of q, we obtain

3. Doppler smearing

The annihilating jiN system is moving with respect to the laboratory system with a velocity of

Since q is represented by q,, which is much larger than qp /2 ( - 10.6 MeV/c) in deuterium, the approximate magnitude of /3, is qF/(2MN )=0.055.

The photon energy k in the laboratory system is different from the corresponding quantity k * in the center-of-mass system of jiN, depending on the Fermi motion along the direction of the boost. We obtain a re- lation

k-k*-fiG(k*.qpN)/qpN=k*-(k*.qFN)/2MN , (A10)

neglecting the higher-order terms in DG. Since the direc- tion of qFN is distributed uniform with respect to the pho- ton vector, the rms value of (k*.qF,v) is k*qFN/V'3. Then we obtain

- u 0, N . - d

E ,Gaussian Fit b C - g 0.5- 2 0- u rzl

a -

FIG. 9. \ ~ ( ( q ) / ' dq, dq,, the two-dimensional integral of the Hulthen wave function squared for deuterium (see the text) is shown in comparison with the best fit by a Gaussian shape with 0 = 38 MeV/c.

which directly gives Eq. (6). Approximating q by qF in qFN of Eq. (Al l and neglecting i q F compared with qF, we

get a ( k ) / k -qF1/(2MN) , (A121

where qFII=qF/g? is the Fermi momentum along the photon vector.

4. Effect of Doppler smearing on the instrumental y -energy resolution

In the search for narrow peaks in the inclusive y-ray spectra, we used for simplicity the Gaussian shape for the peaks. In this approximation, Doppler smearing of the y energy is also taken to be of a Gaussian shape. Since the smearing is related to the Fermi momentum along the photon vector according to Eq. (A12), we should use for qFll its effective value qFl,(eff), which can be obtained by approximating the Fermi momentum distribution along the photon vector by a Gaussian function as

For the Hulthen wave function of Eq. (A5), the left-hand term becomes, apart from a constant factor,

with A = a 2 + q 2 and B =f12+q2. The best fit over the re- gion of k =0- 150 MeV/c is obtained with q,(eff)= 38 MeV/c (see Fig. 9). This value does not vary by more than 1% even if the fitted region is extended up to 200 MeV/c. Substituting the above value of qFll(eff) into qFll of Eq. (A12), we finally obtain

Although the Gaussian approximation should cause an underestimate of the yield of narrow y-ray peaks, its amount should be much less than 10% from the difference between the areas below the J" j- I \v( q 11 2d 'q, - - curve and below its Gaussian fit.

Page 12: rays from antiproton-deuterium annihilation at rest

1944 M. CHIBA et al. - 44

* ~ r e s e n t address: Kochi Medical School, Nankoku, Kochi, 783 Japan.

+present address: KEK, National Laboratory for High En- ergy Physics, Tsukuba, 305 Japan.

$present address: Naruto University of Education, Naruto, Tokushima, 772 Japan.

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[9] L. Adiels et al . , Phys. Lett. 138B, 235 (1984). [lo] L. Adiels et al . , Z. Phys. C 35, 15 (1987). M. Chiba et al . ,

Phys. Rev. D 38, 2021 (1988). [ l l ] H. Poth et al . , Phys. Lett. 76B, 523 (1978). [12] L. Gray et al . , Phys. Rev. Lett. 30, 1091 (1973). [13] C. R. Sun et al . , Phys. Rev. D 14, 1188 (1971). [14] 0. D. Dal'karov et al . , Yad. Fiz. 17, 1321 (1973) [Sov. J.

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(1975). [16] V. Barnes, in Pion and Kaon Production in Antiproton-

Neutron Annihilation at Rest, Proceedings of the 12th In- ternational Conference on High Energy Physics, Dubna, U.S.S.R., 1964, edited by Ya. A. Smorodinskii et al. (Aromizdat, Moscow, 1966), p. 764.

[17] W. Chinowsky et al . , Nuovo Cimento 43, 684 (1966). [18] A. Bettini et al . , Nuovo Cimento A 47, 642 (1967). [19] T. K. Kalogeropoulos et al . , Phys. Rev. D 22, 2585 (1980). [20] F. James and M. Roos, Comput. Phys. Commun. 10, 343

(1975). [21] The result on the observed y-ray peaks above 600 MeV

due to two-meson annihilation will be presented elsewhere together with the result on the inclusive rro spectra (under analysis) from pd annihilation at rest.

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(1974). [26] P. K. Kloeppel, Nuovo Cimento 34, 11 (1964). [27] J. W. Ryan, Phys. Rev. 130, 1554 (1963). [28] R. MacDonald et al . , Phys. Rev. Lett. 38,746 (1977). [29] T. Spuller et al., Phys. Lett. 67B, 479 (1977). [30] See, for example, M. A. Preston and R. K. Bhaduri, Struc-

ture of Nucleus (Addison-Wesley, Reading, MA, 1975). [31] See, for example, M. L. Goldberger and K . M. Watson,

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