Antiproton-proton annihilation at rest in H2 gas into π+ π− π0

Z. Phys. C - Particles and Fields 46, 191-202 (1990) fgr Physik C

and FL-:L4ds �9 Springer-Verlag 1990

Antiproton-proton annihilation at rest in H2 gas into n + r-1r ~

I. Annihilation from S states

A S T E R I X Co l l abora t ion

B. May, K.D. D u c h 1, M. Heel 2, H. Kal inowsky , F. Kayse r 3, E. Klempt , J. Reifenr6ther , O. Schreiber 4, P. Weidenauer , M. Ziegler s Institut f/Jr Physik, Johannes-Gutenberg-Universit/it, D-6500 Mainz, Federal Republic of Germany

D. Bailey 6, S. Barlag 7, J.M. Butler 8, U. Gastaldi a, R. Landua a, C. Sabev CERN, CH-1211 Gen+ve, Switzerland

W. Dahme 9, F. Feld-Dahme lo, U. Schaefer 11, W.R. Wodrich 1,a Sektion Physik, D-8000 Miinchen, Federal Republic of Germany

J.C. Bizot, B. Delcourt, J. Jeanjean, H. Nguyen Laboratoire de l'Acc616rateur Lin6aire, Universit~ de Paris-Sud, F-91405 Orsay, France

E.G. Auld, D.A. Axen, K.L. Erdman, B. Howard, R. Howard, B.L. White Department of Physics, University of British Columbia, Vancouver, B.C., Canada V6T2A6

S. Ahmad, M. Comyn, G.M. Marshall TRIUMF, Vancouver, B.C., Canada V6T 2A3

G. Beer, L.P. Rober tson Department of Physics, University of Victoria, Victoria, B.C., Canada V8W 2Y2

M. Botlo 12, C. Laa 13, H. Vonach Institut fiir Kernphysik, Universitfit Wien, A-1090Wien, Austria

C. Amsler, M. Doser 14, j. Riedlberger, U. Straumann a, P. Tru61 Physik Institut der Universit/it Ziirich, CH-8001 Ztirich, Switerland

Received 21 August 1989; in revised form 21 November 1989

Present addresses: 1 Schott Glaswerke, 6500 Mainz/Wiesbaden, FRG 2 Boehringer, 6507 Ingelheim, FRG 3 Volkshochschule, 6450 Hanau, FRG 4 AT + T, 8000 Miinchen, FRG s GEI, 6100 Darmstadt, FRG 6 University of Toronto, Ontario, Canada M5S 1AT 7 Max-Planck-Institut, 8000 Mfinchen, FRG 8 FNAL, Batavia, IL-60510, USA 9 LeCroy Research Systems, 1211 Gen6ve, Switzerland

lo AMESA, Techn., 1219 Gen6ve, Switzerland 11 DLR, 7000 Stuttgart, FRG lz (]sterreichische Akademie der Wissenschaften, 1050 Wien, Aus- tria 13 Voest Alpine, 1050 Wien, Austria 14 KEK, Tsukuba 305, Japan

" Part of this work was done while at Universitfit Mainz

Abstract. Annihilation of antiprotonic hydrogen atoms into n + n - n ~ is studied by stopping antiprotons from L E A R in hydrogen gas. Two data samples were taken. In the first data sample events were collected independently of the cascade of the/~p a tom; in the second sample only those events are selected for which a low-energy X-ray is observed in coincidence with the final state. The latter data sample contains a large fraction of events in which a radiative transition to the 2 P level of the /~p a tom was followed by annihilation. The former data contain comparable fractions of annihilation from S and P states. By subtraction of the P wave contribution annihilation from S states can be studied. The spin-parity analysis of the n + n - n o Dalitz plot shows that/Sp annihilation from S waves proceeds dominantly via product ion

192

of p mesons from the spin-triplet isospin-singlet state of the i0p atom. Strong interference with a background amplitude or an amplitude for p(1600) production is needed to obtain a satisfactory description of the data. The production off2 mesons is weak.

1 Introduction

Antiproton-proton annihilation at rest into mesons is often considered as an ideal tool to study the dynamics of quarks in the confinement region. Considerable theoretical effort has therefore been devoted to obtain a quantitative understanding of the measured branching ratios. We refer here only to the most recent work [i-9], earlier work is quoted in these papers. Most of these analyses were made with the hope that annihilation might be understood in terms of simple leading dia- grams, and that an effective quark-gluon operator appli- cable in the confinement region could be derived from the data.

Unfortunately, data from different experiments are often inconsistent, making definite conclusions rather difficult. The last analysis of CERN bubble chamber data on i0p annihilation into ~+z~-zr ~ had found that this process is dominated by p ~ as intermediate state with clear preference for isoscalar initial states [10]. The p--. z~ ~ decay angular distribution showed that antiprotons stopping in liquid H2 annihilate from/Sp states with zero angular momentum. Earlier analyses had shown, however, strong contributions from isovector initial states [11, 12]. A new analysis based on a large data sample seems therefore desirable. In this and in the subsequent paper we report on the reaction

p p --, ~+ ~ - r~ ~ (1)

by stopping antiprotons in H2 gas at normal temperature and pressure (NTP).

Antiprotons stopping in H2 form antiprotonic hydrogen atoms. Their cascade is the result of a subtle balance of density-dependent and -independent processes: Collisions between iOp atom and H2 molecules lead to intense electric fields and to a fast reshuffling of states with different angular momenta; the/Sp atom may deexcite by ejecting - via external Auger effect - one of the electrons of a H2 molecule. These processes compete with radiative transitions and annihilation from S wave and P wave orbitals. Annihilations from D states are expected not to contribute [13]. In liquid H2, more than 90% of all antiprotons annihilate already from S states with high principal quantum numbers n [14-16] and radiative transitions are not observable [17, 18]. In H2 gas at NTP there is a chance of radiative transitions [19], and the fractions of S wave and P wave annihilation become comparable [-20]. The determination of this ratio is a result of this paper. Observable radiative transitions populate mostly the atomic 2P levels. Their hadronic width is larger by a factor of 100 than their radiative width [-21-24]. Detecting the X-rays of the Balmer series

allows therefore to tag annihilations from 2 P states of antiprotonic hydrogen. For the present analysis we use two sets of data on i0p annihilation in Ha gas at NTP. In one set of data events were recorded independently of the details of the /~p atomic cascade, in the other data set a X-ray enhancing trigger was used. The latter data set was then scanned for tow-energy X-rays. Thus we arrived at two data sets in which the ratio of S wave to P wave annihilation is approximately 1:1 and 1:10, respectively. Thus separate studies can be made of annihilation from S states and from P states. In this paper we present data selection, analysis method and the results on antiproton-proton annihilation into ~+ ~-rc ~ from S states; annihilation from P states in discussed in an accompanying paper [25].

The outline of this paper is as follows: In Sect. 2 we give a brief description of the apparatus and of the data sets which have been taken. The selection of events and their classification into different data sets is described in Sect. 3. Subsequently (Sect. 4) we present the basic experimental results. The analysis method is based on the Zemach formalism which is outlined in Sect. 5. The final results of the analysis are then presented (Sect. 6), and a summary of the results is given.

2 Apparatus and data taking

The ASTERIX detector (Fig. 1) and its performance is described in detail in a technical paper [27]. Here we summarize only those features of the detector which are necessary to understand the present analysis.

Antiprotons of 105 MeV/c momentum from LEAR stop in the center of a hydrogen gas target at normal temperature and pressure. The stop distribution has a longitudinal spread of ~r~=12.5 cm and a transverse spread of a~y-- 5.4 cm. The distribution is nearly com- pletely contained in the hydrogen target, which has 76 cm in length and 16 cm in diameter.

The target is surrounded by a X-ray drift chamber (XDC) with flash-analog-to-digital readout [28]. Target and XDC are separated by a thin (6 gm) mylar foil. The XDC serves to detect X-rays emitted in the cascade of the i0p atom and to measure the X-ray energy. The ion- isation loss of charged particles provides the innermost space points (3 or 4 wire hits per track) for track reconstruction. X-rays convert locally and only one wire is hit. The hardware trigger "one wire with detected charge and the two adjacent wires without charge" is used to enhance the fraction of data on tape with X-rays. This condition is called one-gap trigger [29].

Seven cylindrical multiwire proportional chambers (MWPC's): (C1, C2, Q1, Q2, P1, Q3, P2) surrounded the XDC. P 1 and P2 had anode readout only, the other chambers had inner and outer helical cathode strips/ wires allowing reconstruction of the tracks in all three dimensions. The assembly of target, XDC and MWPC's is mounted inside of a solenoidal magnet providing a homogeneous magnetic field of 0.8 T. Tracks reaching Q3 have a minimum track length of 0.8 m. The tracks have a momentum resolution of

/ / /

/ /

Z

/ / z

/

r

193

Fig. 1. Side and front views of the ASTERIX spectrometer. (1) H 2 gas target, (2) X-ray drift chamber, (3) lead converter, (4) cylindrical MWPC, (5) coil, (6) yoke and (7) planar MWPC

o-p = [-(0.042 p)2 + 0.0232] 1/2, p in GeV/c. P

(2)

The solid angle subtended by Q 3 is f2 = 0.5.4 ~. Photons are converted in a lead foil of 0.9 radiation

length in front of Q 3 or in lead foils at both endplates of the solenoidal magnet. The latter foils are sandwiched by three MWPC's, one in front of the lead foil to identify charged particles, two behind of it for reconstructing photons. These planar chambers had cathode readout on both sides of the anode plane. Only the position of the photon impact point is measured.

The data used in this analysis were obtained by re- quiring an antiproton stop in the target defined by plas- tic scintillators, and two hits in chambers C1, C2, Q2 and P 1. One missing hit and one noise hit was allowed for one of the chambers. The presence of a X-ray candi- date was also required for part of the data. 1.38.106 events were taken without and 2.13.106 events with X- ray enhancing trigger. We refer to these data sets as /5-GAS data and /5-one-gap data resp. The p-one-gap data are scanned for events containing a low-energy X- ray. The resulting data set is called/5-LX-data.

3 Event selection

The events are reconstructed with the ASTERIX reconstruction program. Events with two tracks of opposite charge and no additional track element were selected. The XDC covers a solid angle of 95% ; this requirement

therefore rejects nearly all contributions from four-prong annihilations, which passed the trigger since the tracks left the detector before reaching C1 and C2. Further we ask for "good-quali ty" tracks: A Z 2 cut on track quality removes tracks for which a noise hit in one of the chambers was associated with the track, or tracks with a decaying particle etc. Further we require both tracks to reach the Q3 chamber. This cut restricts the solid angle and introduces a momentum cut-off at 100 MeV/c. But the remaining tracks have the optimum momentum resolution obtainable with the ASTERIX detector. These cuts lead to data samples of /~-GAS events and/5-one-gap events. We refer to these data samples as two-prong data. Collinear re+re - and K + K -

events are identified by a geometrical collinearity cut. Collinear tracks are defined by

p + ' p - - < -0 .998 (3)

Ip+llp-I where p +, p_ are the momenta of the positive and negative particle, respectively. This cut separates ~z + re-~o events and collinear events with nearly no mutual contamination. The absolute branching ratios for /5p

rc + ~-rc ~ are derived from a comparison of the fre- quencies of pp ~ ~z + ~ - zc ~ and pp --* ~ + ~- annihilations.

Figure 2 shows the missing mass squared distribution of the /5-GAS data sample after rejection of collinear events. Peaks due to annihilations into rc + ~ - ~o, re+ re- t/, and z~ + zc-co with q, o) decaying into neutral particles

194

3 .10

7-( o

"q co

.10 7 6 5 4 3 2 1

0 20 40 60 {~o lO0 probability ~§ [%1

0.0 ~ - - J ~ ' \ ~ ' \ \ I , , , , - 0 . 4 O. 0.4 0.8 1.2 1,6 2.

[CeV2/c 4] m iss ing moss 2

Fig. 2. Missing mass squared distribution of events with 2 good tracks of charged particles but without collinear events (Tr + 7r-). The shaded area contains events with a probability for 7r + 7r-7r ~ > 10%. The probability distribution is shown as inset

3 ,10

I La 2.

1.6 Argon-Fluorescence

1.2

0.8_1 ~. j L

0 . 4 ~

O. O. 5. 10. 15. 20. [keV]

X-roy energy Fig. 3. The energy distribution of the X-rays

are clearly visible. The events were submitted to a kinematical fit to the rc + re-rc ~ hypothesis. There are 67036 events passing the fit with a probability of more than 1%. The data sample still contains a sizable contribution of/~p annihilation into rc + re- re~ ~ and ~+ re- r/ events. Therefore only events satisfying the n + It-rc ~ hypothesis with a probability greater than 10% were retained for further analysis (hatched area in Fig. 2). The probability

distribution for these events is shown as an insert. From this distribution and from the acceptance of Monte Carlo 7r + re- rc~ ~ and rc + n - t /events by the kinematical fit we estimate the background to be (5.2_+ 2.6)% of this event sample. In the p-one-gap data sample we require low- energy X-rays passing standard pulse shape cuts as ex- plained in [21]. 28% of the i0-one-gap events satisfy these criteria. Figure 3 shows the energy spectrum of X-rays in coincidence with the final state 7z+Tr-Tr ~ The peak at low energies is due to X-rays of the/~p atom feeding the 2 P levels and due to a (4+ 1)% contamination by argon fluorescence. The continuous background arises from inner Bremsstrahlung which is emitted in the annihilation process [30]. We have calculated its energy spectrum event by event following the method described by Schaefer et al. [31]. The calculated spectrum is shown in Fig. 3 as solid line. We find a (11.5-+ 0.7)% contribution of inner Bremsstrahlung to the X-ray energy spectrum below 4 keV. The cut a 4 keV defines our final event sample. In this sample the fraction of true L X-rays is

fLx = (84.5 __+ 1.2)%. (4)

We note that for this data sample the fraction of rc+~r-Tr~ ~ or ~r+rc-t/ events is 8+_4%. This number is estimated using the same method as for the full data sample.

4 E x p e r i m e n t a l r e s u l t s

4.1 Absolute branching ratios

The absolute branching ratios for iOp ~ zr + re- rc ~ for both data sets are derived from a comparison of the number of rc + zr- ~o and zr + n - events in our data samples. The absolute branching ratios for iOp -o ~+ zc- has been determined from the same data sets, the results were reported in [20].

The branching ratios are derived from the equation

+ DE(1r+ rc-)N(~r+ n - 7r ~ ) BR(Tr + To- 7r~ = BR(Tr 7r-) ~ N(~T ~ z ~ (5)

where N(Tr + ~-), N(Tr + ~r-n a) are the number of 7c + g - and ~r + 7c-7r ~ events passing the cuts described below, and DE(~+~-)/DE(Tr+Tr-Tr ~ is the ratio of detection efficieneies for these two reactions.

The ~+ ~- r r ~ events are defined by cuts described in Sect. 3; here we use in addition a cut on the decay plane of the ~c + ~ - g o events. We require that the inter- cept between the decay plane and the chamber Q 3 forms a complete ellipse. This decay plane cut leads to a nearly uniform acceptance of 7r+~-g ~ events over the Dalitz plot. Therefore the influence of the internal dynamics on the absolute branching ratio is minimized. The decay plane cut leads to 19647 f -GAS events and 7753 j6-LX events.

The number of 7r + ~ - events is determined by fitting the momentum distribution of collinear events, defined by (3). The numbers are 7310 for the f -GAS data and

195

7%

6%

1" ~ 5%

0 4%

D

22 c~ 2%

oo

AD

+ ~-,~-" in liquid H2

~ -LX-Da ta

00. 01.2 01.4 . -0.61 01.8 f

pure S-wave pure P-wave Contribution of P-wove annihilation

Fig. 4. Absolute BR depending on P wave contribution

> 2.8

9. 2 . 4

~: 2. &

1.6

1.2

0 . 8

0.4

0. O. 0 . 8 1.6 2 .4

(~'~~ tCev ~l Dalitzplot

Fig. 5. The Dalitz plot of/~-GAS events

3380 for the/%LX data. The absolute branching ratios for/~p ~ zc + ~- for these two data sets have been determined by Doser et al. [20].

BRoAs(~ + ~ - ) = (4.30-+ 0.14). 10 -3 /5-GAS

BRLx(zC + zc-)= (4.70-+ 0.40)" 10 -3 /~-LX. (5)

The geometrical acceptance for collinear events and ~z § ~- ~o events restricted by the decay plane cut is rather different. We have simulated both processes by Monte Carlo and find a ratio of detection efficiencies of

DE(re + re-) DE(~ + ~- 72o) =4.5 _+0.3 (7)

From (5)-(7) we find

BR~hs(rC + ~- 7t~ = (5.20__+ 0.35) �9 10 -2 0-GAS

BRLX(~ + ~- 7:~ _+0.50). 10 -2 /~-LX. (8)

These numbers are used to determine the corresponding branching ratio for annihilation from P states. In H 2 gas fp(gas)=(52.8_+4.9)% of all annihilations proceed via P states [20] ; in coincidence with a low-energy X-ray the fraction of P wave annihilation increases to

fp(X-ray) = fLx(1 - K) + (1 --fLX) fe (gas)

=(91.8 -I- 1.0)% (9)

with K = ~,d/Ftot = 0.010-t- 0.005 as ratio of the radiative to total width of the 2P state of the/~p atom [21-24] and fLx defined in (4). In liquid H 2 the branching ratio for /~p~n+zc -~ ~ was determined to be (6.9_+0.9)% [-103: and the fraction of P wave annihilation in liquid H 2 to be (8.6_+ 1.1)% [20]. From these numbers the absolute branching ratio for/~p ~ ~+ ~- ~z ~ as a function of the P wave contribution can be derived (Fig. 4). The extrapolation to 100% S or P wave annihilation leads to the values

BRs (n + r~- s ~ = (6.6 4- 0.8)%

BRv(n + n - ~o)= (4.5 __ 0.6)%. (lo)

4.2 Main features

Figure 5 shows the Dalitz plot of reaction (1) for/~-GAS events. In this plot every event is characterized by the squared invariant mass of the n + n o and re-n ~ subsys- tem. For further convenience we define the Dalitz plot variables X, Y by

X = (E'+ + E~)) 2 - (p'+ + p~)2 __ (2 M p - EL)2 _ p,_Z (11)

I 2 t 2 I2 Y-- (EL + E~) 2 -- (p'_ + Po) = (2 M p - E +) - p +

where p'+, _ o are the measured momenta of the positive, negative and neutral pion, resp., and E ' + _ o their total energies; Mp is the proton mass. Hence X, Y are Dalitz plot variables referring to the measured variables. We also define the decay momenta q'+,-,0 in the re-n ~ ~o~+, ~+ zc- rest systems. The true momenta p, q are known, of course, only for Monte Carlo generated events. These will be used to calculate transition amplitudes; the Monte Carlo Dalitz plots are generated us ing the momenta p', q' resulting from the analysis chain.

The invariant mass spectra of the charged and neutral dipions are presented in Fig. 6. There are clear accu- mulations of events in the p(770) bands and the fz (1270) band. The f2(1270) band exhibits strong enhancements at the edges of the Dalitz plot indicating strong align- ment of the f2(1270). At high ~+ ~- invariant masses a third resonance is seen, which we call AX(1565). It is produced from P states of the pp atoms only and will hence be discussed in the accompanying paper [-25]. Its observation has also been reported elsewhere [26].

The acceptance of the detector in different regions of the Dalitz plot has been studied by Monte Carlo simulations. Figure 7 shows lines of equal acceptance. The acceptance is largest for high ~+ zc- invariant masses

196

3 , lo 1.75

1.5

1.25 1.

0.75 0.5 0.25 0.

Q ) IIIIII i ~ Jl p + ( 7 7 0 )

II

i r I II I

I llllll [IlllI~llllllI I ii I i.,i I I II'l ulrllllllll i i inIIi I [ i iiiiiiiiiiiiiiii

IFIIIIIIIIIIIIIIII [ llllll ,,,i "L"i =i,

0,2 0.6 I. 1.4 1.8 [GeV]

inv. mOSS ( l r ~ ~

700800 b) o IijIi1r

600 l ip (770) III ~1 5o0 ~ II I It ~ IIIIiid, IIl~llllllt II

~ 'd ,,It '1111 '

400 ~1 qlllll~, ItlII'P' IIii .300 II II"ll II Ill

200 III IIIIIIIIIIIIIll II 1 O0 .;,; ,,, ,i

00.2 0.6 1', 1:4 1.8 [OeV] inv moss (~+~-)

Fig. 6a, b. The invariant mass distributions

,10

1.2 1.

0.8

0,6

0.4

0,2

0.

pO f2 ~'~ Illl I \,,, i I I

I it I l t l II II I Iit111t111

!

-o17; & ' 055 cos~

decoy angle p+

400 f IIt p- p* I 300[ if %111 200 I II III I I I

I III 1 O 0 f l I I I i i i1% Ii i i

O' -0,75 0. 0.75 cos~

b d e c o y ong le pO

35o4~176 iiii P" III t P"I 3oo3S~ iiiii1(~ ,c 300 I I I I II 250 II t 25o tl t111 ttll I ii I 2oo 200150 150 I, tlltll IIIII

100 100 ii I i I 50 50 ;

0 . . . . . . . 0 -0.75 0. 0.75 -0,75 0. 0.75 cos~ cos~

c decoy angle f2 d decoy angle AX

Fig. 8 a-d. The angular distributions

2.8

2.4

2.0

1.6

1.2

0.8

> O

E

0.4

0 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8

m~.~o[Gev~/~q Fig. 7. The acceptance plot

for which the ~ + and re- are back to back. The acceptance falls off slowly for lower r~ +re- invariant masses. The acceptance vanishes at the two edges of the Dalitz plot for which one charged and the neutral pion are emitted back to back and for which the second charged pion is very soft. The decay angular distributions of the neutral and charged p (770) and of the f2 (1270) are shown in Fig. 8. The slope in Fig. 8 a is due to the lower acceptance in the p~ region. Cuts of M+_F/2 have been applied to define the resonances. The p~ decay angular distribution exhibits two prominent peaks, these are reflections from the other two charge states of the p(770); otherwise the distribution can approximately be described by a l + a sin20 distribution. The constant

term has to be associated with annihilation from P states, the sin 2 0 part with annihilation from S states. The same observations can be made on the p + (770) decay angular distribution. But here the reflection of the f2(1270) band is seen in addition. The angular distribution of the f2 (1270) seems to follow an 1 + b cos20 distribution with superimposed reflections from the p + (770) bands.

The angular distributions and the relative production rates for production of charged and neutral mesons re- flect the contributions of different jPC initial states of the/~p atom. A Dalitz plot analysis is made to determine these contributions.

5 Analysis method

5.1 Introduction

The experimental Dalitz plot (Fig. 5) is described by a model in which each iOp atomic state annihilates into the rc + ~- rc ~ final state via a sum of interfering transition amplitudes. In S states only two of the four initial states of antiprotonic hydrogen with defined values for total angu!ar momentum J, for parity P, charge conjugation C, and isospin I annihilate into three pions: these are the IG(jPc)=0-(1 - - ) and the 1-(0 -+) state. The G- parity is G=(--1)L+S+I=--I for a three-pion state, hence for S states either spin or isospin must be even, the other one odd. In the following we characterize the /~p atomic state by its jpc quantum numbers. Its I ~ com- ponent - even though well defined - is not explicitly specified.

The transition amplitude for annihilation of a /~p state into three pions is given by

Table 1. Zemach amplitudes and angular distributions

197

pp Atomic state Final state Angular Isospin of Spectr.; I G (jpc) momenta dipion

(1; L) (T; T3)

Clebsch-Gordan coefficients a

Zemach tensors ZT, T3, l

Angular distribution

1So; l-(0- +) (n + n-)sn ~ (0; 0) (0; 0)

(n• lr~ w- (1; 1) (1; ! l )

(Tr + n-)o~ ~ (2; 2) (0; 0)

3S~; 0-(1- -) (nn)en (1; 1) (1; 1, O, -1)

1

- �89 - 1 ) 1

~6 (1, 1, 1)

1

q'p

(%" Po) 2 -- �89 I% [2 I Po 12

qxp

1

cos 2 O

(cos 2 O-�89

s in 2 0

a The pions are ordered in the sequence ~+ n-n ~ or a cyclic permutation

AsPc(p, q)= ~ br, r~Zs~,r, r3,z(P, q)Fr, ra,l(q) T, T3

(12)

p and q are the true momenta in the laboratory system or dipion system, resp. T, T3 characterizes the isospin state of the dipion, br,r3 is the product of Clebsch Gor- dan coefficients for the isospin decomposition of the pp atom into pion and dipion, and of the dipion into two pions. Z is the spin-parity function constructed according to the method developed by Zemach 1-32]. The dynamics of the process is described by the function F. For resonances F is given by a Breit-Wigner amplitude.

5.2 Zemach amplitudes

In the Zemach method the decay momentum q of the dipion in its rest frame is used to construct a tensor describing the intrinsic angular momentum of the dipion. The tensor is 1 for l = 0, q for l = 1 and the dyadic product q | for l= 2. The relative angular momentum state between pion and dipion is described by the/~p decay momentum p. Tensor algebra is used to construct out of these two tensors a tensor describing the initial state of the/~p atom.

In Table 1 the decay modes, angular momenta, Ze- roach tensors, and angular distributions are given for both S states of the/~p atom.

5.3 Breit-Wigner amplitudes

The presence of intermediate resonances in the three pion final state leads to an enhancement of the probability for certain nn invariant masses which are usually described by a Breit-Wigner function. This enhancement can be considered from two different point of views: Watson [33] developed the final state interaction model. He assumed that the three pions are produced according to a three-body phase space distribution. The n n scatter- ing cross section of a pair of two pions in a particular partial wave can be large in comparison to an area defined by the primary interaction volume, at least in the energy range under consideration. Then the nn cross section dominates the production cross section, and an

enhancement factor for the three pion phase space can be derived. Jackson [34] and Pisut and Roos [35] as- sume that the three pion final state is arrived at in two stages: first a n n resonance is produced, second the rcn resonance decays into two pions. Both views lead to the same result: the three body phase space amplitude has to be multiplied by

( q f r(m)~ (m~ - m E) - imo r(m)" (13)

Note that Zemach tensors take into account the centrifugal barrier factors for both the primary annihilation into pion and resonance and for the decay of the resonance. The width of the resonance contains a centrifugal barrier factor as well. The width is given by

/ q\21+l p(m) F(m)=F~ ) p(mo)" (14)

Different functions p(m) are used in the literature [10, 34]. We find no significant differences and use p (m) = 1/m.

5.4 Monte Carlo simulations

The detector acceptance and response, the influence of the event reconstruction programs and of all cuts defin- ing the data sample are taken into account by Monte Carlo simulations. First, three-pion events are generated using the CERN phase space program FOWL (GEN- BOO) [-36].

These events are sent through the Monte-Carlo AS- TERIX detector. Chamber inefficiencies and noise rates of the MWPC's were taken into account; they were determined from the experimental data for groups of 16 electronic channels. The measured performance of the XDC was used to generate space points in this chamber. The events went through the same pattern recognition and event reconstruction program as real data. The Monte Carlo data were kinematically fitted to the n+~-n ~ hypothesis, and the cuts discussed in Sect. 3 were applied. The resulting Dalitz plot is referred to as

198

phase space Dalitz plot PSDP(X, Y). The acceptance plot of Fig. 7 is based on this Dalitz plot.

If only one amplitude contributes to annihilation from a given jvc initial state into three pions, its contribution to the Monte Carlo Dalitz plot density is given by

Ds~c(X ' y) = x 2 [AsPc (p, q)[2. PSDP(X, Y) (15)

x 2 represents the contribution of the f i e initial state to the n + n - n o final state. We emphasize again that the Dalitz plot variables X, Y are calculated from the reconstructed momenta (12) while the amplitude is calculated using the generated momenta. Every event of the Phase- Space Dalitz Plot is multiplied with the squared transition amplitude as a weight factor. For two interfering amplitudes the Dalitz plot density is given by

DsP~(X,~)

= [xl A (p, q) + x2 e i~~ B(p, q)[2. PSDP (X, Y)

= x 2 [A(p, q)[2- PSDP(X, Y)

+ x 2 [B(p, q)]2.PSDP(X, Y)

+ 2 x l x2 cos go1,2 Re {A(p, q). B* (p, q)}. PSDP(X, Y)

+2x~ x2 sin goa,2 Im {A (p, q).B* (p, q)). PSDP(X, Y) 4

= ~ zjlA~(p, q)]2.PSDP(X, Y) (16) j = l

with z l = x 2, z : = x 2, z3=2xlxacosgol,2, z4 = 2 x l x2 sin go1,2. The amplitudes Aj(p, q) are defined by this equation. Hence four Dalitz plots need to be generated, A 2, B 2 and the real and imaginary part of their interference. The amplitudes A and B are normalized by

j" IA(p, q)12 d X d Y = 1 (17)

~ lB(p, q)le d X d Y = l.

This normalization automatically gives the normalization of the two interference terms. The four Dalitz plots enter the final fit with three real parameters, x~, x2 and the phase gol.2. In case of n interfering amplitudes the number of Dalitz plots is n 2 and the number of parameters 2 n - 1.

5.5 Fitting procedure

The experimental Dalitz plot of Fig. 5 is described by a sum of Monte Carlo Dalitz plots simulating annihilation from iOp S states and by two experimental Dalitz plots, one representing annihilation from/~p P states the other one representing the background contribution. The Dalitz plot observed in coincidence with a low-energy X-ray is called LXDP (X, Y). The L X-ray Dalitz plot is analyzed in the subsequent paper [25], here it enters as a phenomenological Dalitz plot only used to parame- terize the contribution from P wave annihilation. The background Dalitz plot BGDP(X, Y) is derived from real events with low (1-10%) probability under the

n + n - n ~ hypothesis. These events have a missing mass squared (MM 2) which is hardly compatible with the squared pion mass m2o. For events with MM2> m2o the contamination with bffckground is large, events with M M2<m2o have nearly no background. Hence a background Dalitz plot can be constructed by subtraction. The background Dalitz plot shows no significant struc- ture; it has most entries for low n+n- invariant masses (recoiling against a fast neutral system), and for events in which one charged pion is fast and one charged pion is slow.

The fractional contributions of the experimental Da- litz plots LXDP and BGDP and of the Monte Carlo Dalitz plots describing annihilation from S waves are obtained as follows: Experimental and Monte Carlo Da- litz plots are folded around the first diagonal and divided into 0.1 x 0.1 GeV2/c 4 cells. Cells of the experimental Da- litz plots having more than 5 entries are used for the fit. The folding improves the statistics per cell for the X 2 fit, a test of charge symmetry of the experimental Dalitz plot gives 22/N v = 249/269.

The numbers of entries per cell in the experimental Dalitz plot is

ni = S EDP(X ,Y )dXdY . (18) cel l ( i )

The mean acceptance per cell is obtained by integration over the phase space Dalitz plot:

pi = ~ P S D P ( X , Y ) d X d Y (19) cel l ( i )

We normalize Monte Carlo Dalitz Plots by dividing the number of entries in the cell i by the total number of Monte Carlo data points Ptot = 156077 and multiplying with the number of experimental data points Ntot = 52224. The contribution of a jPC initial state to one cell is then calculated by

tl 2

dlPC(z)= Y. zj I [A~Pc(p, q) l 2 J t o t j= 1 ce l l ( i )

�9 PSDP (X, Y) dX d Y (20)

The integration over dX d Y corresponds to a summation over all entries falling into the cell i. The n 2 real numbers zj are functions of 2 n - 1 variables Xx .... ,x,, go 1,2 .... , go a,, characterizing annihilation of the f fc initial state via n interfering amplitudes. The zj depend, of course, on the quantum numbers of the initial state

dlpC(z)=.jPc, jPc j c, ai (zl ,.. . ,z,2 }. (21)

All assumptions on the dynamics of the annihilation process are contained in the theoretical Dalitz plot with entries

t i = ~' f, .~ d s~'~ (z) (22) j P C

where fj~e denotes the fractional contribution of the pp atomic state jec to n + n - n ~ annihilations. The squared

199

Table 2. Amplitudes used to describe i0p ~ ~+ ~- ~o from S states

/Sp Atomic state Amplitude Comment Spectr.; IG (jPc)

1So; 1-(0- +) A1 = x l . 1 Phase space Az--xz .{BW(p+)(q+ . p_ ) -BW(p- ) (q_ .p+)} e ~,~ p -+ (770)~z ~

A3 = x3' BW (fz) {(%" Po) 2 - �89 I 2 [Po 12 } ei~~ f2 (1270) n ~

A4 = x4' {BW(p +)(q + x p_) + BW(p~ x Po)+ BW(p-)(q_ x p+)} p(770) n

A s = x s" {q+ x p_ + % x P o + q - x p+} e ~',~ Phase space

A6: x6-{BW(p +')(q+ x p_) + BW(p~ • Po)+ BW(p-')(q_ x p+)} e '~,,o p(1600) n (A 5 and A 6 alternatively)

3S1; 0 - ( 1 - - )

errors m (18) and (19) are given by the number of entries 2 2 a,, = hi, ap, = Pi resp. The squared errors in (22) have to

be calculated from the number of entries in the accep- O-2 -2/_ tance Dalitz plot, Pi. They are given by t, = ~i/~'i-

The background Dalitz plot and the L X-ray Dalitz plot are also normalized to the number of events in the experimental Dalitz plot, Not. The entries of these Dalitz plots are called bi and li, resp., with errors O-b, and %. Hence a )~2 for the comparison of experimental and theoretical Dalitz plot can be defined by

)~2 ~i (hi-- ti-- b i - li) 2 = 2 _~a2 . . F 2 2"

�9 o-hi o-b~ -F O-I~ (23)

6 Results and discussion

6.1 Fit results

We have performed a fit to the experimental Dalitz plot (Fig. 5) by using the same parameters to describe annihilation from S state (Table 2), which were used by Foster et al. [10]. In addition, two experimental Dalitz plots were offered to the fit: the Dalitz plot observed in coincidence with low-energy X-rays of the i0p atom and the background Dalitz plot (see Sects. 3 and 5.5). Tables 3 and 5 list the results of this fit, a comparison of data and fit is shown in Fig. 9. A z2/Nv=344/273 was ob-

Table 3. Fit results: global contributions

S wave (38.0_+2.1)% Background (S wave) (2.6 + 1.3)% LX data (59.4 _+ 1.7)%

tained. The deviation Dalitz plot shows no significant structures apart from the following effects: at cos 0 = + 1, and the p(770) peaks are not fully described. This slight discrepancy can also been seen in the data of [10]. We have no explanation for these two (very small) effects.

The background is fitted to a contribution of (6.4 +_ 3.2)% of the S wave data, fully compatible with the estimate of (5.2 _+ 2.6)% derived from the kinematical fit (Sect. 3).

6.2 The ratio of S versus P wave annihilation

The/5-LX-data contain (8 +_ 4)% background. After subtraction of the S and P wave background, fs=(41.0 +2.6)% of the re+re-re ~ events are S wave, and fL = (59.0 + 2.6)% are in coincidence with a low-energy X- ray of the/Sp atom. In coincidence with an X-ray most annihilations occur from P states, but a small fraction is still due to annihilation from S states. The fraction of S wave annihilation for antiprotons stopping in H2 gas and annihilating into ~ + re- rc ~ at NTP can be determined by use of the formula

fs+KfLxfL qa~-- fs+fLxfr . (24)

where K = F~aa/F~ot is the ratio of radiative to total width of the 2P states of/Sp atoms [21-24], and fLx=0.845 the fraction of true L X-rays in the spectrum of low- energy X-rays. From these numbers we find

q3~ = (45.7 + 3.4)% (25)

~t3~ refers to the z~ + re-rc ~ final state. In order to determine the overall fraction of S wave annihilation we have

Table 4. Comparison of 1S o and 3S1 contributions to n + n - n ~ for different experiments

/Sp Atomic state Spectr.; iG(jPc) Relative branching ratio (rel. to n + n - n ~

[11] [12] [-10] This work

1So; 1-(0 -+) 50+12 45+5 15.7+2.6 13.1+3.3 3S 1 ; 0 - (1 - - ) 50 __+ 12 55 + 5 84.3 + 2.6 86.9 +__ 3.3

200

Table 5. Results of S wave amplitude analysis

/~p Atomic state Spectr.; la(J Pc) Amplitude/phase

This work Foster et al. [1o]

1So; 1 - ( 0 - +) x l : Phase space 0.29_+0.06 xz:p+(770)n z- 0.12+0.03 x3: fz(1270) n ~ 0.18+0.02 q)1,2 1.72-+0.33 qh,3 1.22-+0.24

aS 1; 0 - (1 - -) x4: p (770) n 126 + 0.04 xs: Phase space 0.60-+0.04 (/94, 5 0.95 _+ 0.05

0.35 _ 0.06 <0.15 0.19_+0.02

0.93 _+ 0.21

1.26_+ 0.03 0 .66_ 0.05 1.00 4- 0.03

Branch. ratio This work

0.083 4- 0.029 0.014_+ 0.006 0.033 ___ 0.008

0.709 _+ 0.043 0.161 _+0.017

3 . 10

1.75

1.5

1.25

1.

0.75

0.5

0.25

O, - 0 .2 0.6 1.

inv. m o s s

1.4 1.8 [GeV] (~o)

*10

1.2

1.

0.8

0.6

0.4

0.2

O. -0% ' & %55 cos9 •

decoy angle p

450 t I 4OO

350 0 3OO

25O 20O 150

100 5O 0

- 0 . 7 5 O, 0.75 cos~

decoy angle pO

Fig.9. Comparison of data and fit

800

700

600

500

400

300

200

100

0 0.2

400

350

300

250

200

150

100

50

0

0.6 1.

inv. mOSS

320

280

240

200

160

120

80

40

0 - 0 . 7 5 O, 0.75

cos9 decay angle f2

1.4 1.8

[GeVI (~+,<)

A, - 0 . 7 5 O, 0.75

cos9 decay angle AX

to account for the different branching ratios for /~p n + n - n ~ from S and P states:

r/3" = (36.4 • 5.2)% % - q3 ~ + (1 - %.). BRs/BRe

(26)

with BRs and BRe given in (10)). This number is com- pared in Table 6 to other determinations of this quantity by our collaboration using other final states. The result found in this analysis is just compatible with the results obtained by using annihilations into K / ( final states [20]. The latter determinations are more direct ones, and therefore we do not average the results.

6.3 Par t ia l waves

The contributions of the 3S t and the 1S o initial states - as determined in the four experiments [10-12, this

Table 6. Fractions of S wave in/~p annihilation at rest in H2 gas at NTP

Final state S wave Ref.

rc + n - 0.315 _+ 0.237 [20a] K + K - 0.512 +_ 0.067 [20 a] K ~ K ~ 0.436 _4- 0.077 [20 b]

Average: 0.472 4- 0.049 1-20 b]

zc + n - n ~ 0.364+0.052 this work

work] - are given in Table 4. The two earlier results are inconsistent with the results obtained by [10] and our results. In [11], the number of events was 605 only prohibiting detailed systematic studies. In [12] a cut on the missing mass square may have led to kinematical biases as discussed in [10]. In [10] the same fraction

201

of 3S 1 and 1S o annihilations were found as in this experiment. Table 5 presents the results of the partial wave analysis and a comparison with the results of [10]. The agreement is very good: all amplitudes and phases are reproduced within the quoted errors. This leads us to believe that systematic biases were present in the analyses presented in [11, 12], and that those results should not be used for comparisons with theoretical models of pp annihilations. The contribution of the 1So state to n + n - n o is small, production of f2(1270) mesons rather weak. Annihilation into p n from the ~S o state is also weak but observed as a 3 a effect. The most prominent contribution is annihilation of the 3S~ state into p n with large interferences with a background amplitude.

The presence of large interference effects excludes the determination of meaningful branching ratios corresponding to individual amplitudes. For convenience we define branching ratios in the presence of n interfering amplitudes Xi by

B R ( k ) = ~ fj.~

Z i=1

(27)

neglecting all interference terms. These branching ratios are also listed in Table 5.

6.4 Introduction of a p(1600) amplitude

The strong interference between a p (770) amplitude and a background amplitude with the same quantum numbers seems to contradict the concept of the final state interaction model of Watson [33]. We have therefore replaced the phase space amplitude with an amplitude describing the production of a radial excitation of the p(770). We have used the following values:

Mp(16oo ) = 1600 M e V / c 2

~p(1600)= 300 M e V / c 2.

The same concept had been used before by Besliu [37]. The Z 2 of the fit )~2/NF=385/273 is slightly worse

in comparison of the fit of Sect. 6.1 but the )~2 difference is not large enough to reject this model. No adjustment has been made of mass and width of the p'(1600). The results of the fit are presented in Table 7. The results on the branching ratios for resonance production depend only weakly on the model chosen to describe the annihilation process.

In the meantime, there are new assumptions about the radial exitations of the p(770). There are now two candidates at ~ I450 MeV/c 2 and ~ I700 MeV/c 2. Both would overlapp and their common spectra would not be distinguishable from those of phase space distributions.

7 Summary

We have studied antiproton-proton annihilation into n + ~z-Tc ~ at rest in H2 gas at NTP. Annihilation pro-

Table 7. Results of the ampl{tude analysis with p(1600) instead of phase space amplitude out of 3S x

/~p Atomic state Amplitude/phase Branch. ratio Spectr.;/G(jPC)

1So; 1-(0 -+) xl: Phase space 0.34_+0.03 0.117_+0.018 x2; p-+ (770)~z ~ 0.11_+0.03 0.013_+0.006 xa: f2(1270)~ ~ 0.19_+0.02 0.034_+0.005 ~o1,2 1.86_+0.29 - (cO1, 3 1.46_+0.18 --

3S1; 0 - ( 1 - -) x4: p (770) ~z 0.98 _+0.03 0.768 _+0.041 x6: p(1600) ~ 0.29___0.02 0.068_+0.007 ~o4,6 -0.68_+0.14 -

ceeded from levels of/~p atoms which are formed when antiprotons come to rest in the target. The strong interaction allows annihilation from atomic S and from atomic P states.

We have collected two data sets: one data set was recorded independently of the cascade of the/Sp atom. In this data set 52.8_+4.9% annihilate from P states of the pp atom and 47.2_+4.9% from S states. For the second data sample only events were accepted in which a low-energy X-ray of the i0p atom was detected in coincidence with the n + n - n ~ final state. In this data sample the fraction of P wave annihilation is (91.8_+ 1.0)%. The two data sets allow the analysis of/~p annihilation from S states and from P states.

This paper reports on determination of the absolute branching ratios of lop into n + n-rr ~ from S wave and P wave and on results of a partial wave analysis of annihilation from S states. The only ingredients needed to describe the data are production of p(770) and f2(1270) mesons and background amplitudes. As background phase space amplitudes or amplitudes describing p (1600) production can be used. Different assumptions on the background lead, however, only to small changes in the amplitudes and phases describing annihilation via resonance formation.

Annihilation from S states had been studied in bubble chambers; the results of this experiment are in very good agreement with the results obtained in the last analysis of bubble chamber data. It should be empha- sized that the problems of the two experiments are rather different: in the bubble chamber experiment 3% of all events were due to annihilation in flight; the background due to rc + n-re~ ~ or n + n-t / events was estimated to 14_+3% and assumed to populate uniformly the n+rc - rr ~ Dalitz plot. Only 3838 events were used for the analysis. In this experiment totaly 120000 events were used and the background was smaller by more than a factor of two. However, the subtraction of two data sets led to statistical errors, which are very similar to those obtained in the bubble chamber experiment. We confirmed the bubble chamber results and demonstrate in this way, that we understand the detector rather well and that the detector is described by our Monto Carlo simulations at a high level of accuracy. This is an impor- tant aspect for the discussion of the new resonance pro-

202

duced in ann ih i l a t ions of the P levels of an t ip ro ton ic hydrogen atoms. This resonance is discussed in the subsequent paper.

Acknowledgements. We appreciate the support of Prof. ~. ZupaniG i~, and the continuous encouragement and active participation of Dr. R. Armenteros. The support of the LEAR staff during the runs is gratefully acknowledged. This work was supported in part by the Deutsches Bundesministerium fiir Forschung und Technologie, the French Institut National de Physique Nucl6aire et de Physique des Particules, the Schweizer Nationalfonds, the Osterreichischer Nationalfonds and the Natural Sciences and Engineering Research Council of Canada. It is part of the PhD thesis of B. May.

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Antiproton-proton annihilation at rest in H2 gas into π+ π− π0

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