N U C L E A R PHYSICS A

~LSEV[~ Nuclear Physics A655 (1999) 218e-223e www.elsevier.nl/locate/npe

Pion Correlations and Resonance Effects in ~p Annihilation at Rest

Peter Weber a

~ETH Zurich, Switzerland

for the C P L E A R collaboration:

A. Angelopoulos 1, A. Apostolakis 1, E. Aslanides u, G. Backenstoss 2, P. Bargassa 13, O. Behnke it, A. BeneUi 2, V. Bertin u , F. Blanc r'13, P. Bloch 4 , P. Carlson 15, M. Carroll 9, F,. Cawley ~, M.B. Chertok 3, M. Danielsson 15, M. Dejardin 14, J. Derre 14, A. Ealet u , C.A. Eleftheriadis le, L. Faravel r, W. Fetscher lr , M. Fidecaro 4, A. Filil~ie m, D. Francis 3, J. Fry 9, E. Gabathuler 9, R. Garnet ~, H.- J. Gerber 1~, A. GolS, A. Haselden 9, P.J. Hayman °, F. Henry-Couannier H, R.W. Hollander s, K. Jon-And 15, P.-R. Kettle 13, P. Kokkas 2, IL Kreuger s, R. Le Gac 11, F. Leimgruber 2, I. Mandi~ TM, N. Manthos s, G. Mare114, M. Miku~ l°, J. Miller s, F. Montanet ll, A. Muller 14, T. Nakada 13, B. Pagels 17, I. Papadopoulos 16, P. Pavlopoulos 2, G. Polivka 2, tL Rickenbach 2, B.L. Roberts 3, T. Ruf !, M. Sch~.fer 17, L.A. Schaller r, T. Schietinger 2, A. Schopper 4, L. Tauscher 2, C. Thibanlt 12, F. Touchard u, C. Touramanis 4, C.W.E. Vail Eijk6, S. Vlaehos 2, P. Weber 17, O. Wigger 13, M. Wolter 17, D. Zavrtanik m, D. Zimmerman s

and

M.P. Locher is, V.E. Markushin TM

IUniversity of Athens, Greece; 2University of Basle, Switzerland; 3Boston University, USA; 4CERN, Geneva, Switzerland; 5LIP and University of Coimbra, Portugal; eDelft University of Technology, Nether- lauds; 7University of Fribourg, Switzerland; SUniversity of Ioannina, Greece; 9University of Liverpool, UK; 10j. Stefan Inst. and Phys. Dep., University of Ljubljana, Slovenia; 11CPPM, IN2P3-CNRS et Uni- versit~ d'Aix-Marseille II, France; 12CSNSM, IN2P3-CNRS, Orsay, France; 13Panl-Scherrer-Institut(PSI), Switzerland; 14CEA, DSM/DAPNIA, CE-Saclay, France; 15Royal Institute of Technology, Stockholm, Sweden; 16University of Thessaloniki, Greece; lrETH-IPP Ziirich, Switzerland; lSpaul Scherrer Institut (PSI), Theory Group F1, Villigen, Switzerland

We study 7rTr correlations in the exclusive reactions pp --~ 27r+27r - and ~p -4 2r+27r-Tr ° at rest with complete reconstruction of the kinematics for each event. A new analysis technique has been developed which is model independent. With this new technique, which relies on double-differential distributions, no reference sample is needed to extract the correlation signal. The correlations are studied as a. function of the four-pion invariant mass.

1. I n t r o d u c t i o n

Any emission amplitude for identical bosons must be symmetrized. In particular, ob- servable effects can be expected for a pair of pions if their momenta become equal, i.e. for vanishing relative momentum. Bose-Einstein (BE) correlations is the name often assigned

0375-9474/99/$ see front matter © 1999 Elsevier Seienee B.V. All rights reserved. PII S0375-9474(99)00204-3

A. .4ngelopoulos et al. /Nuclear Physics A655 (1999) 218c-223c 219c

to a very specific dynamic picture - the Hanbury-Brown-Twiss (HBT) mechanism [1] - linking the two-pion correlation function at small relative momentum to the space-time propertie,,; of the pion emitting source [2-4].

In the past, inclusive correlation functions were presented for many reactions and various prescriptions of reference samples. However, the use of reference samples has some problems, in particular, the reference sample related to the unlike-sign pion pairs is strongly distorted by the p meson and other resonances [5,4,6,7] and the reference sample based on the single particle inclusive distributions (event mixing) suffers at low energy from kinematical distortions due to constraints from the energy-momentum conservation [5]. To avoid the complications with reference samples, we are concentrating on differential distributions. The correlation signal can be isolated by considering a double-differential density provided the full event kinematics is reconstructed, event by event.

2. Different ia l two-pion corre la t ions

For simplicity we present the formalism for the 2~r+2r - system, which however can easily be generalized to a 2~r+21r-n~r ° system (n > 1), as long as the final state is a specific channel. We introduce the two-pion subsystems a and b with four-momenta Pa -~ (Pl ~ p2) and Pb = (P3 -Jr P4) and invariant masses Ma and Mb. Integrating over the angles specifying the relative orientation of the momenta in the final state the double- differential cross section is:

da N W(s, Ma, Mb) / [ T ( k , {pi})[~_~od~tabd~12d~34 (1)

dM~ dM~ ~

where T(k, {pi}) is the matrix element of the annihilation process, s is the CM energy, and the factor W(s, M~, Mb) is given by

W ( s, M, , Mb ) = - ~ 1 - --~ ] 1-- --~bb ] ' (2)

P~b = ~/(s -- (Ma + Mb)2))(s -- (M, - Mb) 2) , (3)

(# is the pion mass). Removing the phase-space factor W(s, Ma, Mb) we define the double- differential density:

1 f o(M,, M~) = W(s, .]Via, Mb) dM~dMg ~ [T( {Pi} )12dfl~bdfl12df134 (4)

The den,fity e(M~, Mb) is fiat for a constant matrix element T. Therefore, the measure- ment of Q(M~, Mb) gives information about the matrix element. In Fig. 1, the double- differenti.al density of ~p --~ 2r+2r - is shown for like-sign pion pairs M++, M__ (left plot) and for lmlike-sign pion pairs M+_, M+_ (right plot). The density plot of like-sign pion pairs exhibits a strong enhancement in the lower left corner with M~+, M 2 --~ 4# 2. The density plot of unlike-sign pion pairs shows no enhancement in this region but a strong peak around the p mass is visible. By excluding the events from the pp region it has been verified that the enhancement does not result from the events in the pp region.

220c A. Angelopoulos et al. /Nuclear Physics A655 (1999) 218c-223c

1,5

o.s

o 0

, m I , , , . o . , .

: : : : : :

: : ° : : : : : , . l l l a m . . .

- : : : : : : : ; ; : . i m i m m l w l . .

m • i m m i l w . . . - w l • I I m m m m . o . . : . . . . : : : . : : , : : : , , , • a J . .

! : i ! ! ! ! i i l i i : : ; ; . : : : : | : | , | | : : , , ,

i "~i; . . ! I i U U i U l I I i i : , zU l I I I I I ! !U I ! I I I I " " | : ; ; ; . • I I I m i I I I I I I e I m m I I i , - . : N U I D I I N , n N I I , I , I . . . . . . . I i i i i I i m i i l m l l i m u i i l i , i , -

O i i I ~ l l l I I I i i l l l l l l e . , . . . . • I U i I i i I l I I I m I l I O l l l l l O W ' ' " ~ m N ~ I I ~ I l m I i I I i I I . . . . • . . . . . . . . . .

~ I i I i I m I I I i I i i m w I I l i i - , , - , , I ~ l l m m m m I e l m I l m l I I m ' l l l m l , IlmmImommImmmmwnm..,II~.i,

: : : : : : : : : : : : : : : : : : : : : : : : • I m I I I i

0.5 1 1,5 2

I ~ . ( G e V ~)

1.S

~>

0.5

2 . i i = , . i i , .

i i = i i i , i i i , I i .:: :;.

: | l : | | l l I l g : ; . " I l l I I l I I m ' • l I l i I I m i l e . , i i l I I I i l l , • i i l i I I I I l i , . , • l l l i l I I i l i i - i l i I l I I I I I I m I i O , , • l l l l e l l I I i I I l I , - • l l l I I I m I I I I I l I i , i l I I I l I I I I I l i l W - , ...... i i J J ....... • 1 1 1 1 1 I I I l l a i - i l I I I I W - , • . - ! -~i . . . . I I I I i l i i i I I I N I I i l l , . i i | m I i i i i i m . , . I i i l i I I I i i l . - I l l l l l l I I l I l l i I l I l I I I I l I ' I " . . . . . . . . . i I I l l m I I I I I I I I I l i I I I l i i I I l i I e m i l 1 . . . . . . . . . i , . . . . . . . . . . . . . . : = " J I ~ M . . . . . i I I O I I l I n m l I l p l l l l l l l l I i i I I l I I i I I l I l l l m

O0 . . . . I . . . . . I . . . . . O . . . . . I . . . . . I . . . . ~ . . . . . i . . . . . 0.5 1 1.5 2

M~_(GeV 2)

Figure 1. (a) The differential density o(M++, M__) vs. the invariant-masses squared of the like-pion pairs in the 2~r+21r - channel. The solid line shows the boundary P~ -- 0.7 GeV. (b) The differential density o(M+_c~), M+-(b)) vs. the invariant-masses squared of the unlike-pion pairs in the 2r+2r - channel. The circle shows the region of pp events.

For the five pion reaction ~p --~ 2~r+2~r-lr °, the four-pion invariant mass M++__ of the 2~r+2~r - sub-system is related to the energy carried away by the Ir °. Hence the double- differential density ~(M=, Mb) can be measured as a function of M++__, shown in Fig. 2 for like-sign pion pairs. The enhancement is found to depend on the value for M++__ and is anticorrelated with the relative strength of w production in the three-pion invariant mass (M+-0) spectrum (not shown). The role of the resonances has been investigated by separately analyzing the double-differential densities of Fig.2 for the events without pw and for the complement with only pw events. The ~w events were selected in the (M+-0, M+_) physical plane. The plots with the pw events removed show a clear enhancement in the lower left corner while the corresponding plots for only pw events are almost fiat. The details of this analysis are described in Ref. [8].

To visualize the correlations in a more quantitative manner, the two-dimensional space (M+2+, M 2 ) is divided into slices M~ < M_2_I++ < M~+] and the projections of ~(M++, M__) are defined by

= [M2+, R(M++, M__)dM_2_l++ (5) oi(M++l--) JM2 #PS(M=, Mb)

The projections gi(M++) are shown in Fig.3 for the 27r+27r-~r ° channel. For small values of M__, the projections Q/(M++) are much more strongly enhanced at M~+ --+ 4# 2 in comparison with the inclusive correlation function (not shown). For values of M2__ > 0.5, the projections oi(M++) become gradually flatter and correlations are absent. When the projections o/(M++) are summed the correlation signal gets washed out. The much

A. Angelopoulos et al./Nuclear Physics A655 (1999) 218c-223c 221c

> (D (D

Od > (.9

1 . 5

0 . 5

1 . 5

0 .5

1.20<Mab<l .30 GeV I1 1.30<Mab<l .40 GeV 73 kEvents 134 kEvents

n o = l i n e

m i D

I N D i a n a

• l i l i i i i l i

• ;=iiiiii i: " . . . . . . . .

n l i n m m m m i ~ . =

: , , | | | | = = = I ; I : ; ; , ' , , , . . . . i . . . . i . . . . i . . . . . . i . . . . = . . . . i ,

1.40<Mab<l .52 GeV 1.52<Mab<1.70 GeV 223 kEvents : 341 kEvents

• II i n n n i t

m i @ w o u = | R a m ~ n m m u i i

m e l i i e i l

. . . . . I I " " " ~ I , i w m l l m a i m m u m = m R i m m i l m g m m

|i ii i: . . . . . . . . . . | i i i n u m m a l U i

• i l l U n m i l i l l l i | l ~ I Z l t t t t . . . . . . . . . . . . . . = = i a O m a m g g n u g m m e n

n N l l O l U n U U l l i l i l i l u m e n w i i l O l n l l U U i l D i l l l i m i i i i l l u l l m n l m l l m m m l l i l

miiiiiiii ii!!:::.., iiiii[iii i! i iii ::=... . . . . 0 : 5 . . . . i . . . . 1 : 5 . . . . . 0 : 5 . . . . i . . . . 1 : 5 ' '

M~+ [GeV 2 ] M~+[GeV 2 ]

Figure 2 The differential density Q(M++, M--)rM,,.,, M,,,,,= 1 as a function of the invari- t + + - - ~ + + - - J

ant m a s ~ s squared of the like-pion pairs in the 27r+27r-lr ° channel for various ranges of the 27r+27r - invariant mass as indicated. The numbers inserted in each subfigure indicate the number of events used for the calculation of #.

222c A. Angelopoulos et al./Nuclear Physics A655 (1999) 218e-223c

Data, acceptance corrected

i 2.25 1.20<Mab<l .30 11 i 1.30<Mab<l .40

2 ............ all M.. ] ] i i ............ allM.

1.75 i M.2.<0.5 ] ~ i - - M.2.<0.5 1.5 1 ~ . . . . . . M~<0.4 , "i 2 t l h l . . . . . . . . . < o 4

Q: 1.25 1!-~ . . . . . . M ~<o.3 t i i -~ . . . . . . M_~<o3

0.25 i , ~ I

2 1~ i ............ a l I M /1 ~! ........... a, M 1.75]L~ - - M~<os [] i, - - M~<O.S

0.5

0.25 0

0.5 1 1.5 2 0.5 1 1.5 2 M+2+ [GeV 2] M+2+ [GeV 2]

Figure 3. The experimental project ions yi(M++) of y(M++, M__)[M%__,M%__],-, . . . . for the

2r+27r-lr ° channel corrected for the detector acceptance. The 27r+21r - mass ranges are indicated in each subfigure. Different lines correspond to (M_~2=) 2 as indicated.

A. Angelopoulos et al./Nuclear Physics A655 (1999) 218c-223c 223c

smaller correlation effects observed for inclusive correlation functions are therefore due to this integration.

3. Summary and Conclusions

The complete kinematical information available from the CPLEAR experiment for the pionic final states in ~p -+ 2r+2~r - and ~p --+ 2r+2~r-r ° at rest has allowed us to study pion correlation signals for inclusive and differential distributions. The inclusive distributions were found to be in agreement with previous results [9,10]. A novel technique was developed which relies on double-differential distributions. This technique is based on removing the phase space factor event by event requiring exclusive data selection and full event information. It is model independent (measurement of matrix elements), i.e. it does not require the use of reference samples which are unavoidable when the correlation information is extracted from inclusive distributions.

Correlations of like-sign pion pairs have been observed in kinematical regions where the effects are expected. The new technique allows for kinematically controlled studies of pion correlations. Thus the observed behaviour of the differential distributions explains why the correlation signal for ~p --+ 2~r+2r - is small for the inclusive distributions [5]. Furthermore, pion correlations have been analyzed for ~p --+ 2r+2~r-lr ° as a function of the four..pion invariant mass M++__ of the 2 r+2r - sub-system. The strong variation in the correlation signal found for different ranges of M++__ is surprising. The absence of correlations in part of the data is related to pw production.

Theoretical simulations of the p3r and p a r channel show an enhancement in the M++,M__ correlation corner which is qualitatively similar to the observed effect (see Ref. [8] for details). By studying partial projections of the differential correlation signals, this enhancement has been traced to the P-wave nature of the p meson resonance in combination with the trivial quantum mechanical Bose symmetrization of the resonance production amplitude. At least part of the observed correlation strength is therefore likely to be connected to resonance production while the interpretation by a conventional stochastic HBT mechanism is questionable. Fhrther work on ~p --+ 3~r+3r - is in progress and will also allow the study of three-pion correlations.

R E F E R E N C E S

1. R. Hanbury-Brown and R.Q. Twiss, Phil. Mag. 45 (1954) 633. 2. G. Goldhaber et al., Phys. Rev. Lett. 3 (1959) 181; G. Goldhaber et ai., Phys. Rev.

120 (1960) 300. 3. G. Cocconi, Phys. Lett. B49 (1974) 459. 4. G.I. Kopylov and M.Y. Podgoretskii, Soy. J. Nucl. Phys. 19 (1974) 215. 5. A. Angelopoulos et ai., CPLEAR Collaboration, Europ. Phys. J. CI (1998) 139. 6. M. Gaspero, Nucl. Phys. A588 (1995) 861. 7. H.Q. Song, B.S. Zou, M.P. Locher, J. Riedlberger, P. TruSl, Z. Phys. A342 (1992)

439. 8. A. Imgelopoulos et al., CPLEAR Collaboration, Europ. Phys. J. (1998), in print. 9. K..qarigiannis et al., CPLEAR Collaboration, Nucl. Phys. A558 (1993) 43c. I0. R. Adler et al., CPLEAR Collaboration, Z. Phys. C63 (1994) 541.