Nuclear Instruments and Methods in Physics Research A295 (1990) 443-449North-Holland

A method of q' rejection in charged-pion interferometryKarin Kulka and Bengt Lörstad

Department of Particle Physics, University of Lund Sö1vegatan 14, S-223 62 Lund, Sweden

Received 9 May 1990

The two-particle correlation function used to study Bose-Einstein interferometry is sensitive to the dynamically correlatedsame-charge pion pairs from the decay chain q1 -" ,tnr +,R -, -q -" ir °ir+ % - . This is verified for a sample of Monte Carlo generatedevents, obtained using the Lund model of fragmentation . A method to reject these pairs b sed on a kinematical analysis of the MCdata is presented, thereby opening the possibility to separate the interferometry signal .

1 . Introduction

The analysis of Bose-Einstein (BE) interferometryrelies on the ability of isolating the symmetrizationcontribution and of comparing it with an uncorrelatedbackground. It is well known that if, in rm correlations,the reference distribution is constructed from opposite .charged pions, it is influenced by the decay of severalresonances, e.g. p, w, q, and proper corrections must bemade. For the correlated, same-charge distribution (S),a corresponding effect should be obtained through thesequential decay of q',

il~-* 'rlIr+,f ,

The problem is addressed e.g. in ref. [1] . As the q'production rate is not well known at present, it isdifficult to estimate the size of this additional effectwhich, however, irrespective of its ~ize, will appear inthe same region of small relative momenta as the BEcorrelations, thus constituting a potential problem .

3 . The Lund 1VIC data

il --> IT 0rT+,

TT

In this report we use the Lund Monte Carlo (Jetsetversion 6.3) 121 . based on the Lund model, to generatee + e- events, which do contain resonances but have noBE symmetrization . Specially, the multiplicity of q' wasfound to be 0.58/event . In the proposed e:,,perimentaltreatment, the MC events were passed through the fastsimulation program FASTSIM of the DELPHI detectorat LEP. These simulated events, at V~s =100 GeV, werethen subject to the same analysis as for BE studies .Pairs of same-charge mesons were compared to a back-ground constructed by mixing particles from differentEvents (D) and studied as a function of Q, the four-

3 . Method of analysis

0168-9002/90/$03 .50 n 1990 - Elsevier Science Publishers B.V . (North-Holland)

443

momentum transfer . The simulated events were re-quired to have a clean twojet signature, as defined interms of the thrust variable : T > 0.97. It is of interest inBE analysis to study such single-string systems and it isalso of importance for our method of background con-struction : Eveats of different characters, i .e . T values,should not be mixed. For these analyzed events, themultiplicity of charged pions was 7.9 .

In the Lund model, particles produced nearby uponstring fragmentation, are predomhiantly of oppositecharge . This leads to a suppression of close same-chargeparticles, as compared to oppositely charged ones . Inthe absence of interferometry effects, one therefore ex-pects a slight negative correlation for pairs of identicalparticles when forming the correlation ratio R, and acorresponding positive one for pairs of oppositelycharged particles. This feature is illustrated in fig . 1 forKK pairs, where, apart from the clear 4 signal in theKK( + - ) ratio, no strong resonance effects are present .Turning to -mr correlations, the picture looks quite dif-ferent - see fig. 2 -, with a strong peak in theirn(+ + , -- - ) ratio at low Q values . This agrees withthe expected contribution from reaction (1). To settlethe influence of 9' on the correlation ratio R, a MCsample with -q' decay inhibited but other conditionsunchanged, was generated . The result in fig. 3 for

r:~ .. .ut ..

,a:,~;,*,c T1,arPfnrP ifTTIT(+ +, - - ) 4onfi 1I1J

ec prcu.~~ .,., . ., .

. ... ., . . ... . ,

,9' production is nonnegligible, it will present a problem

in studying the BE effect, which it not only qualitativelyresembles but also kinematically overlaps.

The method of identifying same-charge pion pairs

from the T1' decay in reaction (1) starts off with a

R

0.4

l', . . - i . � ,1, .

, . . .1e .1

0.4

lii .,i . . . . i .-li-1,_J. . 1l-1 �� 1 � ~0

0.4 0.8

1 .2

1 .6

2

2.4 2.8

0

0.4 0.8

1.2

1 .6

2

2.4

2.8Q(GeV)

Q(GeV)

Fig . 1 . The correlation ratio R (pairs from the same event)/(pairs from mixed events) vs Q, for kaon pairs, based on 200000 LundMC events, passed through DELPHI simulation, with 4 =100 GeV and T > 0.97 . (a) KK(+ +, - - ), (b) KK(+ - ) . The (~ meson

occurs at Q = 0.25 GeV in (b), with R = 6.85 ± 0.20 .

R

0 .8

0 .6

K Kulka, B. L6rstad / q' rejection in chargedpion interjerometry

.nrv( ++,__)

0.40 0.4 0 .8 1 .2 1 .6 2 2 .4 2.8

0(GeV)

R

0.8

0.6

1

fE1

E

1 ;

+i V

I I II

I

0.4

' �� 1 �� . �� I ,v � :,1 �� 1 �0 0 .4 0.8 1 .2 1 .6 2 2 .4 2.8

Q(GeV)Fig. 2 . As fig . 1, but for pion pairs, based on 5000 MC events . The peak in (b) at Q = 0.72 GeV is due to the p meson .

m21, _

R

0.8

0.6

71

--0, 71 'IT+

IT

0 0.4 0 .8 1 .2 1 .6 2 2.4 2.8Q(GeV)

Fig. 3 . As fig . 2a, but with +1 decay explicitly inhibited in theMc.

kinematical analysis, based on conserved squared four-momentum,

IT7T(++p_-)

No 77' decays

--m2 + [ E, rt ..+ ET-12 - [ P,~ + +P.~ - ]2

+ 2[ En( E,++ ER-) - I P,, I I P,+ +P� -

x cos 0(11 ; IT+,n- )] ,

A( M2) = M2 (1r+,n - ) + 4E, r [E�++ E� _-]

x sin220(q ; -n +~- ),

(2)

where A(m2 ) --- (m7, - m2 ), and the approximation Ep I

has been made. The last term in eq. (2) ispositive, hence by insertion of numerical values :M2(1r+.r-) , ®(m2 ) =0.616 (GeV/c')', i . e . pion pairswith

M 2(1r+,T- ) > 0.616 (GeV/c2)2

can be excluded as decay products of reaction (1) . Asimilar treatment of iq decays q --,1r°1r+i,- and of thecombined reaction q' -> ( ,qff +,rr - -~ ),iro,n-+,rr-,IT ',IT - en-ables us to exclude also the following regions of squaredinvariant masses :

Eqs. (3)-(5) define, however, only upper limits of theallowed M2 and the results can be further refined bystudying the actual M2(21T) and M2(41x) distributionsas given by the MC generated particles. To this end, wefind the reactions (1) in the MC sample and form thesquared invariant masses of iT+ir-(,1'),'IT+,iT-(,q'),T+,T-(q),

��here

arguments

indicate

theancestors . The results are shown in fig. 4 for 20000 MCgenerated events. In order not to lose too much statis-tics in the following "experimental" application, thetails of the distributions are cut off, and although eqs .(3) and (4) are different, for all practical purposes wefind it justified to use the same interval for both 2-ndistributions . The following regions are defined for sub-sequent rejection :

M 2 (1r +,n- ) : (0.080 - 0.175)(GeV/c2 ) 2 ,

M 2 (21r + 21r- ) : (0 .44 - 0.68)(GeV/c2)2

.

4. Application to interferometry

The general procedure for studying BE interferome-try is extensively described e.g . in ref . [3], from which itis clear that the analysis deals with combinations ofpions, rather than with single particles . It will turn outthat although excluding a substantial fraction of the -1'descendants, >_ 75% of the pairs picked up by ourrejection algorithm will have a non-,q' origin . With thisrelation in mind, we take advantage of the pair char-acter of the correlations and exclude pion pairs insteadof single pions. Thereby combinations of otherwise;falsely rejected pions with nonrejected ones are kept,hence minimizing the loss of statistics . We refer to asubsequent section for a discussion of the proper han-dling of the fake, rejected pairs .

As a first step of analysis, all combinations of,n+,n -,T+,T- were formed, out of which only those be-longing to the interval in eq . (7) were kept . There arenow two combinatorial ways of forming (+ - )(+ - ) ;both were investigated with respect to M2(1r+,T-), andit was required that for at least one of these two4n-configurations, both 1r+ ir - pairs should lie in theM2 interval given by eq . (6) . In this case, a rejection

flag was set for the two corresponding same-sign pion

pairs, and which subsequently was checked for before

incrementation of the correlation variable.

Ideally, the background distribution used when for-

ming the ratio R, should in all respects apart from the

interferometry contribution, resemble the signal distri-

bution. Particularly, any kinematical restrictions im-

posed on the signal should appear in y e reference as

K Kulka, B. Lörstad / n1 rejection in charged-pion interferometry 445

M 2(,,r +, n - ) > 0.283 (GeV/c2 )`, (4)

M 2(2,ir+2,ir - ) > 0.900 (GeV/c2)2. (5)

N40

35

30

25

20

15

10

N100

80

60

40

20

0

K. Kulka, B. Lörstad / vj rejection in chargedpion interjerometry

0.4 0 .5 0.6 0.7

M2: 41T

M2 ; 2-n(?7')

0.8 0.9M2(GeV/c 2 )2

I . . . I I . . . .II . . . . I . . . . I .1 . . . I . . . . I . . . . I . .I0 0.04 0.08 0.12 0.16 0.2 0 .24 0.28

M"(GeV/c 2 )2

Fig. 4. Distributions of (a) M2(2,rr+ 2,r - ) from -9' -+ (-qiT+,T--+ )ir°,Tr+,T-,r+-rr

, (b) ,%f 2(Ir+ , T

) from q' -+',IT+ir -, (c) M2(Ir+IT-

from (,1' --+ ),q --> rr °ir+m

-, based on 20000 MC events . N = number of combinations per bin.

N

90

80

70

60

50

40

30

20

10

K. Kulka, B. Lörstad / 71' rejection in chargedpion interferometry

0.04 0.08 0.12

well . Therefore, the constraints to eliminate 9' descen-dants described above, were applied, in general form,also to the background . For construction of this distri-bution, we used the method of mixing particles fromdifferent events. This procedure is relevant in the pre-sent case of highly collimated twojet events, after properalignment of the jet (= thrust) axes, and exclusion ofregions with reduced detector efficiency near the beamdirection.

Combinations of four pions, 2,r+ 2-r- , were pickedup with one particle from the current event and theremaining ones irom each of the three preceding events .Conditions (6) and (7) were imposed exactly as de-scribed above for the signal, and a rejection flag was setin such a way as to match the overall method ofbackground construction, namely combining particlesfrom every particular event with particles from each ofthe three preceeding events.

From the S and D distributions obtained after ap-plication of the rejection algorithm, the normalized cor-relation ratio R(+ +, - - ) was calculated in bins of Qand is shown in fig . 5 . The result is consistent with theexpectations of the Lund model with resonance contri-butions excluded, cf. figs . l a and 3 .

M2 : 27r(71)

Fig. 4 (continued) .

R

0.16 0.2 0.24 0.28M 2(GeV/c 2 ) 2

0 .4

r . . .-' 1 -' . .

't . . . . . . . . L

.''1 .0 0.4 0.8 1 .2 1 .6 2 2 .4 2.8

Q(Gev)

447

Fig. 5 .

R(ir± IT ±

) vs Q for 10000 Lund MC events afterapplication of the 9' rejection algorithm .

448

5. Rejection efficiency

To estimate the rejection efficiency, the number ofsame-charge pion pairs originating from the reactionchain in reaction (1) was calculated, using the MCinformation of particle history, before and after thequoted rejection algorithm was applied. The rejectedfraction of such pairs is displayed versus Q in fig . 6,upper set of data points and indicates a constant levelof rejection of - (0.7-0.8) over the entire Q rangewhere rejection takes place, Q :5 0.5 GeV. The corre-sponding ratio for pions required not to originate from,q' or -q is shown by the lower set of data points in fig . 6.This fraction is _< 0.15 and decreaces with increasing Q,as expected from the fact that the overall spectrum ofsuch pairs continues also beyond Q >_ 0.5 GeV.

It is obvious that the rejection also affects pairswhich are not the decay products of q' . We consider theimplications of this in two steps, namely application toMC data and to physics data, respectively . It is apowerful principle that the same kinematical constraintsare applied to both signal and background, and anydeviations as compared to the initial, unrestricted distri-butions should cancel upon taking the ratio SID. Thisis true as long as the signal contains no additionalcorrelations as compared to the background: Obviously

f

0.6

0.4

Fig. 6. Filled circles : Fraction j ofCrosses: Correspondingly, but for

dC Kulka, B. Lörstad / n' rejection in charged-pion interjerometry

the q' descendants represent a noncompensated correla-tion which, in agreement with the intensions of therejection, should not be cancelled. For the non-,q' de-scendants, an explicit test of the cancellation by thebackground was made by applying the 9' rejectionalgorithm to a MC sample in which q' decay wasinhibited, other conditions being left unchanged . Withthis new sample, the rejection acts on only the false q'descendants in the signal, and we are able to separatelystudy the compensation of this component . The result-ing R(,q' -,4 , + -q' rejection) versus Q, is compatiblewith the corresponding function in fig . 5, where q'reject ;on was applied to the full MC sample. This isillustrated in fig. 7 by taking the ratio R(MC, q' -, , +,q'injection)/R(MC, +,q' rejection) versus Q, whichis consistent with one, showing that adequate com-pensation takes place, and we conclude that theelimination of the q' peak at low Q values in the fullMC sample by means of the rejection procedure is adirect result of the elimination of the -q' descendants .

Turning to physics data, things are slightly morecomplicated . In the signal, the rejected non-,q' compo-nent is now subject to Bose symmetrization, whereasthis is not the case for the corresponding rejected partin the background. Hence no cancellation occurs, givinga systematic reduction of the net correlation function .

Rejected fraction f of 7T7T from :

+ non-r7, non-r7 '

1

1

1

~~

1

1

~

~

~

1

10.6

0.8

10(CeV)

± from reaction (I) and in bins of Q that are rejected upon application of the q' algorithm.,T ± that do not originate from 9' or -1 . The data sample is 20000 Lund MC evet .!s with

T > 0.97.

r

0.8

0.6

K Kolka, B. L6rstad /

R(rejection)r R(rejection, no 77' decays)

0.4 ~. . . .I . . . .11 . . . . . .0 0.4 0.8 1 .2 1,6 2 2 .4 2 .8

p(GeV)Fig.

7.

r= R(TI' -, TI'

rejection)/R(T1' -'->,,1'

rejection),

theratio of correlation functions, vs Q, for 10000 Lund MC

events.

On the basis of fig. 6, we estimate thi :- ^ffect to be-(10-201% . By means of an iterative procedure itshould, however, be possible to compensate to someextent, for this effect : By not rejecting just a certainnumber of background combinations, in bins of Q, butby weighing each rejected such pair with a BE enhance-ment factor with suitably chosen parameters, the re-jected part of the background should more closely cor-respond to the rejected part in the signal . The kinemati-cal 1 :1 correspondence between S and D found abovejustifies this. The ratio SID, where the rejection in Dhas been accordingly BE corrected, should then befitted to yield the appropriate BE parameters, which inturn could be used in an iterative procedure as input inthe D correction, and the iteration continued untilachievement of satisfactory convergence . The fact thatnot all rejected pion pairs in S are subject to inter-

Ti' rejection in chargedpion interjerometrt- 449

ference, namely those due to 9' decay, represents aremaining source of uncertainty. An independent mea-surement of the q' p:oûu-tion rate would settle thispoint . Alternatively, for a very Nrge statistics data sam-ple, it could be possible to determine the fraction of therejected background pairs that should be BE weighed,so as to give the best convergence of the iterations .Apart from a more correct correlation ratio, this wouldalso give an indication of the amount of produced -q' .

6 . Summary and conclusions

Same-charge pion pairs from the decay chain q' -,introduce a noninterference

contribution into the correlation ratio used for studyingBE symmetrization. A method based on a purely kine-matic analysis, has been developed to eliminate thesecontaminating pairs, with a resultant rejection efficiencyof = (70-80)9 . The unavoidable simultaneous rejectionof pairs of non--q' descendants can be handled by properconstruction of the reference distribution. For MCevents, without inherent BE symmétrization, it is suffi-cient to just impose the same kinematic cuts on signaland background . For symmetrized physics data . this istranslated into a (10-20)% systematic underestimationof R . An iterative procedure for construction of back-ground corrections would reduce this suppression, aswell as provide an estimate of the I' production rate.We also point out the value of a comparative, largestatistics KK correlation study : Assuming similar un-derlying mechanisms for im and KK interference, use-ful clues could be obtained to whether or not one wouldexpect a fully developed interference: effect in a reso-nance-free i ',n i svstem .

References

[1] M. Arneodo et al . (EMC Collaboration), Z . Phys. C32(1986) 1 ;M .G . Bowler, Phys . Lett . B1ß0 (1986) 29) .

[21 T. Sj6strand, Comp . Phys. Conimun . 27 11982) 243, and 28(1983) 229 ;T. Sj6strand and M . Gengtsson, Comp . Phys . Commun 43(1987) 367.

[31 T. kkesson et al . (AFS Collaboration) . Phys . Lett . 8129(1983) 269 ;B . L6rstad, Int . J . Mod . Phys . A4 (1989) 2861 .