Observations of atoms consisting of π+ and π− mesons

Physics Letters B 308 (1993) 200-206 North-Holland

PHYSICS LETTERS B

Observation of atoms consisting of

÷ and

- mesons

L.G. Afanasyev, A.S. C h v y r o v , O.E. G o r c h a k o v , M.A. Ivanov, V.V. K a r p u k h i n , A.V. K o l o m y i c h e n k o , V.I. K o m a r o v , V.V. Kruglov, A.V. K u p t s o v , L.L. N e m e n o v , M.V. Nikitin, Zh.P. Pustylnik Laboratory of Nuclear Problems, Jomt Instttute for Nuclear Research, Head Post Office, P 0 Box 79, 101000 Moscow, Russtan Federation

A.V. Kulikov, S.V. Trusov, V.V. Y a z k o v Instttute for Nuclear Physws, Dubna Branch, Moscow State Untverstty, 141980 Dubna, Russtan Federatzon

G.G. Mkrtchyan Yerevan Phystcal Instztute, Erevan, Armema

and A.P. K u r o v lnstttute for Htgh Energy Phystcs, Serpukhov, 142284 Protvmo, Moscow regton, Russtan Federation Received 27 March 1993 Editor: L Montanet

In the experiment 272+_49 atoms consisting o f n + and ~r- mesons were observed The atoms were produced in a Ta target by 70 GeV protons and ~r+ and n - mesons were detected from the atom break-up m the same target.

1. Introduction

In all processes with emission of opposite charge particles production of Coulomb bound states (atoms) is possible. Production of n + n - atoms (and of other hadronic atoms) in inclusive processes was considered and a method of their observation and lifetime measurement was proposed [ 1 ]. The atoms are produced in S-states with the cross section da~

dPA -- (27r)3

I ~(0)

12 d6r°

dp~ dp~ '

(1)

wherepA, EA and MA a r e the momentum, energy and mass of the n +~r- atom (A2~) in the lab system, respectively, [~(O)12=p3/ztn 3 is the atomic wave function squared at the ortgin with the principal quantum number n and the orbital momentum l= 0, PB is the Bohr m o m e n t u m in A2n, dtTo/dpldp2 is the 200

double inclusive production cross section for n + n pairs from short lived sources without taking into account n + n - Coulomb interaction in the final state, Pl andp2 are the n + and n - momenta in the lab system. The momenta of n + and n - mesons obey the relatxonp~ =P2 = ½PA-The A2~ are produced in atomic states with different principal quantum numbers n and are distributed according to n - 3 : W l = 8 3 % , W 2 = 10.4%, W 3 = 3 . 1 % , W n > . 4 = 3 . 5 % . The lifetime zn of A2n with the principal

quantum number n and l = 0 is determined by the charge-exchange process zc+~t---,zc°Tr° and may be written through the S-wave zur scattering lengths ao and a2 with isospin values 0 and 2 [ 2 ]:

z~- 9

(ao--aE)El~Jn(O)] 2 ,

where Am=MA--2mno,

(2)

m#o is t h e 7 r ° - m e s o n m a s s Elsevier Science Publishers B.V.

V o l u m e 308, n u m b e r 1,2

PHYSICS LETTERS B

and/~ 15 the A 2 n reduced mass. The lifetime dependence on n is d e t e r m i n e d by the value o f ] ~un(0)[z and from ( 2 ) one obtains zn = zl" n 3. It follows from ( 2 ) that the z~ m e a s u r e m e n t with 10% precision would allow to d e t e r m i n e Ia o - a21 in a m o d e l i n d e p e n d e n t way with 5% precision. In chlral p e r t u r b a t i o n theory [ 3 - 5 ] one finds [4] ao-- (0.20_+ 0.01 )m~ -1 , a 2 = ( - 0 . 0 4 2 - + 0 . 0 0 2 ) m ~ -1 • Inserting these values in ( 2 ) q can be calculated: z~= ( 3 . 7 + 0 . 3 ) × l 0 -15s.

2 4 J u n e 1993

orget CoL ~0 ~

¥ ~

~

MS --4

. , " 7j---. ............. - ~ = =-. . . .=. . z. . .-. ._--Z . . . . '.-'_"--"-', v.,. . .. .. .. .. .. . . . .

I ~t-

a)

A

MC

2. A2,~ detection method and setup description In the present p a p e r we describe the e x p e r i m e n t o f the observation o f n + n - a t o m s carried out at the 70 G e V p r o t o n synchrotron ( U - 7 0 ) at Serpukhov. Pionlc a t o m s a n d n + n - pairs ( " f r e e " pairs) were p r o d u c e d in a 8 ~tm thick t a n t a l u m target ( " t h i c k " target) inserted into the internal p r o t o n beam. The a t o m s can either annihilate into n ° n ° pairs or break up ( i o n i z e ) into n + n - pairs ( " a t o m i c " pairs) inside the same target. The " f r e e " a n d " a t o m i c " pairs get into the 40 m tong v a c u u m channel (the acceptance is 3 . 8 × 10 - s sr) at 8.4 ° to the p r o t o n b e a m a n d are detected by the setup in the 0.8-2.4 G e V / c pion mom e n t u m interval. The n u m b e r o f " a t o m i c " pairs depends on the atom lifetime z, the break-up cross section and the target thickness. Assuming Zl = 3.7 × 10-15 s the annihilation length o f A2, in the 1S-state at y = 10 is 11 p m a n d the A2, m e a n free path in Ta is 6 ~tm independent o f the y-factor for y > 6. In th~s e x p e r i m e n t 8 atoms on average were generated per 10 ~ p - T a mteracUons into the setup acceptance a n d ~ 40% o f the a t o m s broke up in the target into " a t o m i c " pairs detected by the setup. The checking measurements were carried out with a 1.4 p m thick t a n t a l u m target ( " t h i n " target), where only ~ 10% o f the atoms broke up.

PIons in " a t o m i c " pairs have small relative mom e n t a Q < 3 M e V / c , a n d therefore a p p r o x i m a t e l y equal energies E + ~ E _ in the lab system and a small opening angle O1,2 ~ 6 / y mrad. The e x p e r i m e n t a l setup shown in fig. 1 has a relative m o m e n t u m resolution o f about 1 M e V / c . The channel is connected to the accelerator v a c u u m pipe w~thout any p a r t i t i o n a n d is shielded against the ac-

Fig. 1 E x p e r i m e n t a l s e t u p ( a ) c h a n n e l s c h e m e : p - i n t e r n a l p r o t o n b e a m , T a r g e t - t a r g e t m e c h a m s m , Col - c o l h m a t o r , M S m a g n e t i c shield, ( b ) m a g n e t a n d d e t e c t o r s M - p o l e s o f spectrometer magnet, VC - vacuum chamber, DC - drift chambers, H - s c i n t i l l a t i o n h o d o s c o p e s , S, S u - s c i n t i l l a t i o n c o u n t e r s , C gas Cherenkov counters, Absorber - cast-iron absorber, MC monitor counters

celerator and Earth magnetic fields. The channel ends with a v a c u u m c h a m b e r placed between the spect r o m e t e r magnet poles (B = 0.85 T ). Charged particles were detected by the telescopes T1 and T2. The track coordinates were m e a s u r e d by drift chambers. The time interval between detector hits in T1 and T2 was measured by scintillation hodoscopes. Electrons and positrons were rejected by gas Cherenkov counters, and muons by scintillation counters placed b e h i n d absorbers. Besides n mesons other charged hadrons were also detected. M o n i t o r ing o f the p r o t o n - t a r g e t mteracttons was carried out by y-flux measurements. The n u m b e r o f p r o t o n - t a r get interactions was 7 × 108 per 0.7 s spill, and the detector counting rate ~ 105 per spill. The first level trigger was f o r m e d by the coincidence signal ( H I S I C I S u l ) . (H2S2C2S,u2) (see fig. 1 ). A specml processor selected tracks having small angles to the channel axis in a vertical plane and a vertical coordinate difference I Y~ - Y2 [ -4<80 mm. The n u m b e r o f events per spill written to magnetic tape was about 90. The total statistics contains 1.3X 10 v events using " t h i c k " and " t h i n " targets. The measurements and simulation allowed to obtain the setup resolution on the m o m e n t u m % / p = 0 . 0 0 8 , on the vertical plane angle o f deviation from the target d F e c t l o n %i = %2 = 1.2 m r a d and on 201

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PHYSICS LETTERS B

the angle between particles at the magnet entrance tro~,2= 0.1 mrad. Also were obtained the distributions of "atomic" pairs on the Q projections to the P=P~ +P2 direction (QL) and to the plane perpendicular t o p (Qx). The distributions of the QL and of the QT components Qx and Qr are Gaussian-like and have the standard deviations a ~ = l . 3 MeV/c, aox=aQy=0.60 MeV/c for the "thick" target and a ~ = l . 3 MeV/c, aQx=ao,.=0.44 MeV/c for the "thin" target. The momentum resolution and all standard deviations are averaged in 0.8-2.4 GeV/c pion momentum range.

3. Data processing At data processing the space reconstruction of events was fulfilled. The corrections on the residual magnetic field in the channel and on the horizontal component of the spectrometer magnet field were taken into account. The particle momenta and the track coordinates at the magnet entrance were calculated under the assumption that the particles came from the target. The angles ~yl and fay2 in TI and T2 between the track projections and the direction towards the target were also determined. The FWHM of the ~0yI and ~0v2distributions for particles coming from the target is 2.5× 10 - 3 rad (fig. 2) in accordance with s~mulation. Pairs originating in the target

24 June 1993

were selected by applying a cut ~y~<3.5 × 10 - 3 rad, where tpy= (2 ~0y,+~2) 1/2, and by some other requirements. The selected events are distributed in the time difference tu between hits of the hodoscopes as shown in fig. 3. The distribution contains a true coincidence peak (a = 0.8 ns ) and a uniform background from accidental coincidences. The intervals Aft = A t 3 = 8.0 ns were used to determine the number of accidental events Na m the signal region, and the interval At2 = 2.56 ns to obtain the sum Nta of true and accidental events. In the interval A t 2 the ratio of true to accidental events is 0.36. The true coincidences Aft are caused mainly by + n - pairs produced in the target. The fraction of zc+ zt- pairs generated in the accelerator vacuum pipe and in the beryllium target holder was measured to be less than 3% of the total number of Art. The measurements and simulation have shown that ~+~zpairs from K +, K - and K ° decays are strongly re-

N ,10 4

4O z

50

J t

20

10 ¢ t

--,20

-- 10

¢¢

6

1'0

2%

¢o~= [ m r - ~ d ]

Fig. 2. DxstribuUon of tr- mesons from time-correlated n + n pairs over the vertical plane deviation from the target &rectlon. The peak Is formed by n - mesons produced in the target The smooth background is caused by n - mesons from K decays near the spectrometer magnet

202

00-15

,

,

,

,

-10

J

,

,

,

I

-5

,

,

o

''~

....

lo ....

15

tH [ns] Fig. 3. Distribution of the u m e difference between hits in the hodoscopes The peak is formed by time-correlated x + x - pairs, and the umform background is due to accidental comodences.

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duced by cutting on ~0yand that n u m b e r is about 10- 2 ×Art. The admixtures of K + K - and p,0 pairs are equal to 10 -4 Nt and 5 × 10 -3 Art, respectively. The e + e - pair admixture due to some inefficiency of the Ch erenkov counters is 6 × 10- 3Art. The ~ + K - , zr - K +, ~r+p and ~r-p pairs are absent in the true coincidence peak because the ~r, K and p hmes o f flight from the target to the hodoscopes are essentmlly different. From the above it follows that the number of 7r+~rpairs is more than 97% o f the total n u m b e r of true events detected. In order to get a better seperatlon o f the " a t o m i c " from the "free" pairs we analyzed the distribution o f the events in the variable F instead o f Q: 2 L\O'QL /

2

\O'Ox]

2 1/2

\GQr] J

The true event distribution in F (and in other variables) was found from the obvmus relation dart dF -

aNt, dF

(

At2

-\At~-At3]

~dN,

(4)

dF"

The distributmn (4) was fitted for F > 3 (where " a t o m i c " pairs are absent) by an approximating distribution. The number o f " a t o m i c " pairs is then determined by the difference between the number of ~ + ~ - pairs in the interval F < 2 and the corresponding number of "free" pairs, obtained for F < 2 by an extrapolation of the curve fitted to the data in the region F > 3.

4. Approximation procedure for the zt+n - pair distribution

tribution was found with the Lund model. The fraction of protons in the m o m e n t u m interval 0.8-2.4 G e V / c is calculated to be N ~ / N ~ = 0 . 6 5 . This relative number o f protons was measured in the interval 0.8 ~
To obtain the approximation o f the "free" pair distributmn we have taken as a base the acodental n + n pair distribution d N ~ ' / d F = - ~ ( F ) because the latter and the true n + n - pair distribution d N ° / d F , without taking into account the final state interaction, should have the same shape. This follows from the fact that both d~stnbutlons are proportional to the product o f the single inclusive production cross sections o f n+ and n - mesons [6]. So d N ° / d F equals to q~(F). The d i s t n b u t m n q~(F) was obtained from the accidental event dlstrlbutmn d N , / d F by subtracting the n - p and nK accidental pairs, their con-

24 June 1993

~=-~/~, a = ~ .

1],

(5)

The relativistic corrections to Ac(fl) under the present experimental conditions do not exceed 0.5% [ 9 ]. An observation of the Coulomb interaction effect m the ~ + ~ - system was realized m the experiment [ 8 ] carried out with the present setup, and this effect was confirmed later [ 10]. Henceforth we call the pmrs from short lived sources " C o u l o m b " pairs and those from long lived sources "decay" pmrs. From the above we can write the approximating distribution in the form 203

Volume 308, number 1,2

PHYSICS LETTERS B

24 June 1993

02

dNt

dF =qqb(F){Ws(F)Ac(fl)+~l-Ws(F)]}'

(6) 2

where q is a normalization factor, f i s a free parameter which accounts for the uncertainty of Ws(F). With such a description of the data the particle production dynamics as well as the setup efficiency are taken into account. In the analysis interval 0 ~
dN,

- - =qqb(F) [Ac(fl) +f~ ] , dF

[" 1

1

0 ÷1 0

0

5

10

i '5

~'0

2'5

3'0

.3'5 ~ ©

(6a)

where f~ accounts for the "decay" pair fraction.

2 2 1

5. Determination of the A:,~ number

1 6

The distributions dNt/dF for "thick" and "thin" targets are shown as points with errors in figs. 4a and 5a and contain 5.9 X 104 and 4.4 X 104 events, respectively, m the interval 0 ~
~=1.28, ~=0.75.

(7)

The excessive pair number for the "thin" target, normalized to the proton interaction number for the "thick" target, ~s n~ =47 + 55. We carried out a comparison of the excessive pair number (7) w~th the expected number of "atomic" pmrs. In this analysis the "Coulomb" pair numbers, experimentally obtained for Q < 2 MeV/c, N~=983_+ 54, 204

N~=757+42,

(8)

1

F

2

...... ~__t_-++÷-~-~-d-r t--+---t-t++-L~-~Lt++t-+ ~-f-+-I] 0 ~0

g - - '~'0

1'5

2'0

2'5

3'0

5'5-~0

F-

Fig 4. (a) Experimental distribution of n + n - pairs produced m the "thxck" target as a function of F (points with errors) and approximating distribution of "free" pairs on the same varmble (dashed hxstogram) (b) The ratio of the experimental to the approximating d~stnbutlon. The deviation of the ratio from unity m the two first bins xs due to extra pa~rs originating from xonxzatmn ofA2. m the target matter.

were used as follows. The ratto of the produced atom number to the "Coulomb" pair number in the interval Q < 2 MeV/ c was found by a numerical integration of ( 1 ) and of the Coulomb pair distribution tn this interval, taking into account the multiple scattering in the target and the setup resoluhon X~=0.97N~,

X~=0.95N~.

(9)

The break-up probability of A2~ in the target was calculated using ionization and excitation cross sections [ 11 ], the A2~ lifetime z~ = 3.7 X 10- ~5s and the quantum number distribution of the produced A2~: wtk=0.384,

wtn=0.105.

(10)

Note that in the present experimental conditmns W 'k depends only weakly on r~, w~k(zI=2X 10 - ' 5

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24 June 1993

~1 0 3

R~xp= 1.56+0.47,

1 6

R~ xp = 5 . 0 9 + 0 . 3 0 .

z

R~,alc=2.2, (13)

1 4 1 2

;f)~'ffff~f~'f'{'~'f~,ff)tfft,ffkf,({t f+'÷-F f+

i+'

1 0

8

I

1 o° ~ i " O

O

5

10

15

20

25

30

55

4"0

R~ xp was o b t a i n e d by averaging this ratio for both targets. The presence o f excessive n+n - pairs for the " t h i c k " target, their absence for the " t h i n " target (7) and the agreement of the observed excess o f pairs with the expected value in the full interval F~< 2 ( 11 ) as well as in the two separate intervals ( 13 ) allow us to conclude that the observed excessive n + n - pairs in the " t h i c k " target arose from the n + n - a t o m s produced and b r o k e n up in the same target.

1 5 1 4. I

6. Test of the stability of the result

5

1 2

ftft#@

q

(3

tttt fttlti: tt t

O

10

O

1'5

2'0

2'5

3'0

5'5

40 F

Fig. 5. The same distributions as in figs. 4a and 4b but for the "thin" target. The absence of extra pairs in the first two bins is caused by the low A2nIonization probabdlty in the "thin" target. s) = 0 . 3 5 , wtk(~" 1 = 6 × 10 -~s s) = 0 . 4 0 , and Wtn does practically not d e p e n d on Zl. It was calculated that 71% and 74% o f the " a t o m i c " pairs p r o d u c e d m the " t h i c k " and " t h i n " target, respectively, lie in the interval F~< 2. Then we obtain the following expected " a t o m i c " pair numbers: n~=260+

14,

nk"=56+3.

(ll)

The errors in (11 ) reflect only the precision m the " C o u l o m b " pair number. The excessive pair n u m b e r in the interval 0-4
nt~"A=23+16,

tk = 1 6 6 +--4 3 , n2A

n2Atn= 12+36_ .

(12)

The ratio RXxp o f n[ k to nlAtkis In agreement with the corresponding calculated ratio RXal~ for the 1S state, but differs from the corresponding one for the "free" pairs, R~P:

We tested the mfluence o f uncertainties in the setup resolution and the e + e - pair admixture, o f the F interval width in the analysis, of the n - p admixture and o f the a p p r o x i m a t i n g d l s m b u t i o n type on the " a t o m i c " pair n u m b e r selected. The setup resolution influences the shape o f the " a t o m i c " and "free" p m r distributions. The uncertainty o f the resolution m p and OL,2 cited above is 10%. It was shown that a 10% simultaneous resoluUon variation leads to a 4.3% change in n ~ . The influence o f the e + e - pair a d m i x t u r e in the d i s t n b u U o n d N t / d F (that is 0.6% in this experim e n t ) on the n u m b e r o f " a t o m i c " pairs was checked by adding to this distribution a 2% and 4% a d m i x t u r e o f e + e - pairs relative to the total n u m b e r o f analyzed events. The corresponding changes in n ~ are 0.5% and 2.5%, respectively. Therefore one can conclude that a small a d m i x t u r e o f e + e - pairs does not affect the final results. The n u m b e r o f " a t o m i c " pairs remains constant within 5% if the fit interval is enlarged from F~< 20 to F~< 100. A change o f n ~ was also o b t a i n e d when replacing m ( 6 ) the distribution ~ ( F ) by dNa/dF, i.e. the n - p and n K admixtures were not subtracted from the accidental events: t k = 2 6 7 --+49, X-~= 1.21, hA

n~=29+41,

~=0.81

.

(14)

To evaluate the influence o f the m o d e l d e p e n d e n t 205

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function W s ( F ) on the " a t o m i c " p a i r n u m b e r the analysis was p e r f o r m e d with the formula ( 6 a ) where one neglects the difference in the p r o d u c t i o n d y n a m ics o f " C o u l o m b " a n d " d e c a y " pa~rs: n~=268+49, nt'=31 +41,

Z-~= 1.28, ~=0.76.

24 June 1993

Later [ 12 ] the necessity was p o i n t e d out to take into account the different sources o f n ÷ n - pairs (short lived a n d long lived) when C o u l o m b corrections are i n t r o d u c e d into experimental distributions o f identical pions.

(15)

Acknowledgement By c o m p a r i n g ( 7 ) with ( 1 4 ) and ( 1 5 ) we conclude that the n u m b e r o f " a t o m i c " pairs does not dep e n d on corrections calculated with the L u n d model.

The authors wish to t h a n k J. Schacher for the interest in this work and helpful remarks.

7. Conclusions

References

In the present e x p e r i m e n t we o b s e r v e d 272 + 4 9 n +zr - a t o m s p r o d u c e d in an inclusive process. The m e t h o d to observe new h a d r o n i c a t o m s p r o p o s e d in ref. [ 1 ] was successfully applied. It is worthwhile to note that fitting the d i s t r i b u t i o n d N t / d F by the function ( 6 a ) a n d d e t e r m i n i n g the termf~ allows to o b t a i n a relation between the n u m ber o f zr +it - pairs generated from short lived and long lived sources. The relative n u m b e r o f n + n - pairs from long lived sources, d e t e r m i n e d in the present experiment, is (26 + 5 )% o f the total n u m b e r o f n + n pairs p r o d u c e d in the target. The same value determ i n e d by means o f the L u n d m o d e l a m o u n t s to 17%. The applicability o f this m e t h o d to separate n +zc pairs generated from short lived and long lived sources was indicated in our previous publication [ 8 ].

[ 1] L.L Nemenov, Yad Flz 41 (1985) 980 [Sov. J. Nucl. Phys. 41 (1985) 629]. [2 ] J Uretsky and J. Palfrey, Phys. Rev 121 ( 1961 ) 1798 [3]S. Welnberg, Phys. Rev Lett. 17 (1966) 616; 18 (1967) 188, Phys. Rev 166 (1968) 1568; Phys~caA 96 (1979) 327 [4] J. Gasser and H. Leutwyler, Ann. Phys. 158 (1984) 142. [5] J. Gasser and H Leutwyler, Nucl. Phys. B 250 (1985) 465, 517, 539. [ 6 ] V.G. Grlshm, Inclusive processes in hadron interactions at high energy (Energolzdat, Moscow, 1982) p. 131 [m Russian ] [7l A.D. Sakharov, Zh Eksp Teor. Flz. 18 (1948) 631. [8] L G. Afanasyev et al., Yad Fiz. 52 (1990) 1046 [Soy. J. Nucl. Phys. 52 (1990) 666], Phys. Lett. B 255 (1991) 146. [9] V.N. Bayer and V.S. Fadm, Zh. Eksp. Teor. Flz. 57 (1969) 225 [ 10] L.K. Wlencke et al, Phys. Rev. D 46 (1992) 3708. [ 11 ] A V. Tarasov and I.U. Chnstova, Commun. JINR P2-91l0 (Dubna, 1991 ) [ 12] M.G. Bowler, Phys. Lett. B 270 ( 1991 ) 69.

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