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Introdudiorl Our work is devoted to ,study of so called li'ide correia/ions of

protons with pions produced in electron - nucleus interactions. It' continues the work f1l. where two proton correlations were analyzed.

The term wldl;~ correlations is used to distinguish this type of correlatIOns from small relative momentum. correlations, called narrow correlations. which appear due to identical particles interference and final state interaction [2]. The "'ide correlations are mamly caused by the momentum conservation law, Contrary to the narrow correlations. they are observed in full region of relative momenta.

\,\i'e can observe ~ide correlations. for example, as two partICleS divergence' angle correlations. Indeed. as far ac; the total momentum of all particles must be fixed, two secondary particles will more probably be emitted in the opposite directions, than in the same one, So, the correlation function wiJI grow with the divergence angle between two particles. and the less the total number of the se.condary particles, the stronger the growth. Generally. we can estimate the number of freedom degrees of the system. involved into interaction, bystudying wide correlations.

Protons and pions may be considered as representatives of two secondary particle classes: nuclear fragments, and particles. produced in the reaction. Nevertheless slapes of inclusive spectra are the same for cumulative protons and cumulative pions [3). Ifa source of ditferent secondary particles have the common nature, we can expect the similar behavior not only for their inclusive ·spectra. but a:Iso for correlations. Such similarity has been already observed in hadron-nucleus interaction ([4], and references there) mainly for nuclear fragments, such as protons, neutrons, deuterons.

In our work we study wide correlations between protons and pIOns. and compare ttk.'"1TI with two proton correlations.

2

The data-on 5" GeV electrons (and positrons) interactions with the residual gas (water steam) in vacuum beam pipe have been .obtained by-product from the large acceptance detector ARGUS (DESY) [5). It has been kindly placed at oat disposal for physics analysis by ARGUS collaboration. We study me reaction: e± 160 ~ p7[± X. The scattered electrons were not detected by ARGUS. Having' in mind the strong dependence .of eA·... interactions on· transferred momentum, one·should attribute our

events to small if « I (GeV I C)2 region. ARGUS triggers biased the events sample. There were 4 types

oftriggers: ­

t The total energy trigger .. an energy deposited· in shower counters in each z-hemispberes exceeds.700 MeV.

·2 The high energy shower trigger - a local energy deposition in the barrel shower counters ({cosSl < 0.75) exceeds I GeV"

. 3 The charged particle. trigger - there· should be at. least two charged tracks in the barrel region and· they must. present jf] each z-hemisphere.

4 The coincidence matrix trigger - presence a pair of charged tracks in the barrel region wilhthe azimuthal difference >120°.

The procedure of selection' of the eA--events from e+e- is described in [6J. Hear we shelf give only a brief list of selection criteria: I

t Eh <3. GeV ~ Eh ::: LE - Np'fllp , where 'LE is the

total energy of secondary particles. Npis the number of

detected protons and mp .is . its m~s. This criterion· selects ;

events with small total deposited energy. which is smaller in

• eA·interaction than in e+e-.

3

1 At least 1 proton 'must·bedetected. Demanding this one can -'1Cject 1he great part of.eIectrort;1ositron ~OII$, where ,protoRs appeatsvery rarely. 'Meanwhile -1heyare -·atmost always -presents among..products ,bfnudearTeaction.

.3 (~E.t. -~pzr)12Eo<O.07y where E. is the energy deposited mshower calorimeter, Eois.thebeam energy, Pz is the' z--component ofpartitle momentum ( ·z-axis .is directed

'. along positron'beam). Summation is made over all detected teCOfJdaryparticles. The criterion is-based on the fact, that the products of eA-interaetion, contrary to ·e+e--, moves mainly to one side relativdyto 2-axis.

\ ...' • The total longitudinal momentiJm of particles CQlitted in one haJt:.sphere for one of them must not'cxc:etd Q.6 GeV:

Ipz<MGeV •.;.. 1IP.j< 0.6 GeV. p::>O - ~%<O

The criterion rejects symmetrical ,events with_high total deposited energy. .

5 The distance between event v~x and beam ~is must not be greaterthan.2cm. This rejects interootiQllSwitb the walts of vacuum chamber.

In, the events sample we ~ed there were only events with at least three charged .particles. So, this is an additional criterion. In events sample, ~lQcted U$ing the described criteria, the background ofe+e- -interactions is about 7%. The same criteria were used in the work [1,6].

Because of the residual gas is· water, there could take place interactions not only with oxygen, but also with hydrogen. Trigger condition and selection criteria make preference to nuclear events in comparison with bydrotcn one. Multiplicity. d1stribution in events sample-and proton inclusivcspeetra proved to be similar·to that from hadron-nuclear collisions {6J. Thus cne can hope" that hydrogen have a tittle contribution in nur CV,t~~lts sample.

We -bad to place allevcnls.. produced hblh by electrons and positrons, in one coordinate system. where initial particle moves

(­. aIdilg~is. So we had .ctistinpislt-this.~ofev.ents.Ttrc fig. 1 shOws the distribUtioDover thetotaJ longitudiMI ti1omeidumof deteetedpivtides; The. sign of thtsvaJue was ..m-, to. identify the initial particle. The tirisideatifteatm ofprimaty particle is -4%.

We selected "Particb with polar' angk: jcos9J< 0.75.. and"

momentum: for protons: 0*3< Pp <l2. Oev, and for pions:

0.08 < PK <: o~ 9 GeV. bt" this. kmematicalregioa pqnides "e registered with high', etTteieney, which slightly depend ,on ~ momenta~ On fig. 2 tItca alCmomentum and angu:ar distributions for selected, pions and' protons. One Call see singularity in protOB

spectrum at p - 0.45 GeV I c which is due· to triggercollditions The mean momentum ofpions (0.31 (icY) is much smaBer, than that for protons (0.58 OeV); tltatwill be essential bellow.

The corieJation function is .the ratio of the probability of particle pair prodtlction~ to· such probability as if ,they were prQduced independently. We calculated it as the following ratio:

N (, -- )R(- -)== plt Pp~PTC (I).L~ Pp~P'fC N. (;; p-)

nulC Yp' It

,where Np1t(p ,P l is the distribution for pairs, taken from p r

real events, while Nmix (pP"P/E) is the distribution for "mixed"

pairs. To create mixed pairs. we do the follo\vtng: we take two different even~, and make an" possibk pairs of proton from one event, and pion from aoother~ So we make pairs' (if independently produced particles. Certainly we can create much more mixed pairs, ~all real. So statistical error of Rp1t is defined by Nplt error.

We didn't made absolute normalization of correlation function. Although the geometry acceptance eftici~"1lCY iscanceJcd in

equation ( 1)7' trigger conditions and our c-\enl selectionproc.~ure

may themselves create correlation~. So we have to take th..-:m mto account

We calculated the detector efficiency· lr'.dng the following procedure. We generated events sample according to some phenomenological- model {7.RI. It reproduces mure Of Jess correctly inclusive (8land correlation [II charactenstics of our

5

data. Wecalem.d two correlali<m. fUnctions: ~ for generated .events, and~;EiF.for,them 'passed '.:tbmugb effICiency simulation program. We used their ratio. as.the ,4etector eftieiP.ncy correctien ooefllcient. 'Wenadtipliedottr ;experimental f1.mctionRuXOJTClC:tedOft~ir 'ratio: '

.... ~ ·~Otftleted ~ Ruacorteaed • '/4.tOdd .Eft'. ( 2)

We used such a simple met~,*ause ~. Eft', well coincides with '~Jft(;orrected.and',efticiencydependence on event parameters is ROt very strong.

Both ,two ,proton ~ and ·proton-pioD ~corrtlatiOn

functions. "'were calcnIatedin·the same way.

~:Restltts..

Fig. 3 shows tile· dependenc~ of tbeCorrclation .funeti~nover ' the 'oivergc,mce angle 'R(cosw).Onecma see that correlation function for p.~~. anC;f P't:_.navc similar dependencies o~.c.~Stv'! whileR.pp deCtte4~e:s \W,~;"<t~s,,,, c.os~ h\OU 'Npide~i~~ f2~p. We $t.<ppo,eth~t 'is due tOfhe dillerence ofse.condary pattlcles momt:nta. .

We studied the dependence of c!Jrrelution function '00 two ~ariablcs: ,cosine of dlvcrgcncc angle. f/I. and the product of .two '

.' particks momenta p,' P2: .General, picture of the '. tunction ~lfK.'onected(PI ·1'2' cosw) is s}wwn on fig: 4 ,-as. a tw,,""

dimensional, plot. We can see that corn:latitlu fun(.."tion dccre..\Ses heth by cos\V and by PI . fJ1. .,

Fig. 5 shows shc.esof t~')·dimcnsional lunction Runcor,eaed (Pi'; pz ' .. cOs 9') ovt:r PI . 1'2 tor uncc.ltrected exp...'Ti~(;ntal data r..,dark pointS - ..LiglttpoilltsO stand for mockl gc~rat~d C\'cnts pa.~s£d throug.h ctlicicncy sUllulation program ~ Rt\t.."'<ki. FIT)' "ic ean SCt; th~lt they' coincide nlthcr good.

On fig. 6 then.: arc correlation functions Rc(lllt:dCd' Oncacb plot

.,

6 .

thCf:tuiterv. o,f Pi' P2 is showiL· We can· see that efticicncy corieCtion· do not ·Change' qualitative. correlation .. pattern; mall caSes, it's dependence on the divergence angle cos~ is close f1)'

exponential, and .its slope is similar forrJifferent pairs at similar nwmentumproduc.t. E~tial fits:

'R__ e-/koati (3)

are also shown on each plot, as straight line. . Unfortunately \W,coulda'tmade the efficiency corfection'for

the total' range of Pi' Pz. It; ~ that the motnentum distribution in generated events decreases with Pt . P1. faster, than in detected ones. So the number of generated. pairs .~. to be ; insufficient for effiCiency cOrrection at high PI .P2.

There is another, more important reason to show uncorrected and corrected data. ARGUS selects <;>tUy events of some special type, whiCh is a little part of all events. Uncorrected and corrected distributions differs from' eaCh other .not only because of experimental errors,. but also because the)!. have different event characteristics. Specifically, they have Jdifferent multiplicity distributions (fig. 1). As it was described in .' introduction, multiplicity is a very important parameter for wide correlations.

We can see, thatqualitatively b .olb pictures (fig. 5 and fig. 6) look similar. We can~ a conclusiort, that qualitatively, effICiency do: not change the general pictUre of coaelation function. Still, we bope,that our model can help us to cpinpare our results with other experiments.

Ontig. 8 we show the dependence of the slope p' on the product PI' P2 of two particle. momenta It is shown· both .fur uncorrected experimental data and conceted fOr efficiency. Each. point on these pictures conesponds to one plot on fig. 5 and 6. We can s~ that the slope p is equal for different pairs of particles. being measured at the same.PI •P2. It cJ~ be consi<kred as an evidence for the conunon nature of the? source for different secondary particles.

7

Data of fig. 8 were fitted in form:

p= a'(PI' P2)b (4)

Both data and fitted lines are shown on fig. 9. The fitting parameters are stored in the table:

P1t+ p1t~ pp .­

Uncorrected Data. a 1.45 ± 0.08 2.10 ±0.07 1.88 ± 0.04 b 0.78 ± 0.04 Looio.03

-0.94 ± 0.02

. X2 / ndf 18.1 I 14 47.9/15 59.5/15 Corrected Data.

a 0.81 ± 0.15 1.5 ±0.2 1.24 ±0.10b 0.55 ± 0.10- ­

"­~88±O.08 1 O.14±O.~

•~~.OO! 8 I24.3/9x2 / mlf 7.40/7

It should be taken into account in tllJ da.ta amllysis. that mean value of llo1aranglc decrease with increasing PI' Pz. 011 Jig. J0 and Hg. 11 \\i'e show mean momentum and mean cosine of polar angle a~ a function of PI . p~.

Conclusion.

\Ve observe that wide corrclatJOn~; f(\f all ltl\'estigateu pair:-> of particles: P1t+ . p1t-. and (JP arc similar. It C~lll he l.·on~jdcred 1.1:' an cv,denc~ thal aU sccondaJ.~· paf1ick~. 0\\1h nudct\l1s and mesons have common u;lturc of th~ s,,,urcc.

Acknowledgments.

Wit \H1Utd h!.l' ({, thank ail m~mhl:rs (~r AR( it tS cnlla~)rillil!ll

"h,) maJc m'liJahh: ri'f us the data Sl:t t~'r lx';ull-g,as. c\.:ms an.\l:,-sl~

1111.." Wl'lk. \\.1" !'OIlPP()rt~J h) }(ussial1 h'lld of Fundal11C'l1tal Invc~tigath'lb (94-0.:!-JQO-l).

8

"-­

.............--------------_.__ .--L.. _ ~ __

0.2 0.. O. 0 .•

Ccv,k

Fig. 1 Distribution ov·er th~ .sum of longitudinal m'omentum of all detected pmicJes for events which were s-;lected as electron - nucleus interactions.

=p.~~ _m ;--1 ::r'-;---- ---/~/fl l.:,.

a 1OO4t .' ~ ! 2000 ....../' !

r , I I I I ---rJ 01.. ~.~ I-,---,--,-~.~J •• J 0.4 0.. 0.' , 1.2 -1 -0.5 0 0.5 1

Momentum,CcV/C cos 9

::fj\~ --. ---;;F-j 500f! '\..~ I oL,. I ..........~ I J

0.2 0.. 0.' OJ

Momentum.C.V/c .--_._. __.....

~-- '-~-l t ~ /'~ ,2000 f.'. 1te J1.t I

1000

u-..~-,-,,-,,--"-I.........~_~.O...;; _ I'-:Lc::~' .J_

0." 0.& 0 .• -1 -0.5 0 0.5 1

Momentum. C~V/c COS 8

Fi,~ 2 Momentum and~g,~I&rdistributions for protons and pion'S.

9

Unconected.

R r I

ro-~ : . I , -o-~:::::::=-0--0-0-:-0--0­

0.1 -0--0-<>--0- -0-0­ I 0:1 ~-0--o-,-o-~ -0­

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I

-0.. I

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cos...

cos.

Fig;J Correlationfun<:tion ofdive..~ence angle cosign. cos. .

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~ • a.... r • J r,... •• ". • J .•• ' • , I 1 ': 10 .~I •Jr I~J= " ~I '.C". I, .' l.t.. " :~, • '" , , • , ·t I•

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fig. ~a. 0

pn W

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~r' -. · 1'., l'r'" ·-, - 'r..."""'..............- ..........;...;. I .J--"-~.-..-....-L'"""---,_ (~_! , ! I .....4_......-.4J 'Of , ! I ! ,~ ..t., \ II • I

, • , t • • ., • , ·f • •

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·r~~~..., .l·~~~..lt~ I~ f - ..t,....-.; ~ 't-i'~J ~' .

..L_...._............_.Lo....-l---~ ..,..J ..l! , ,~~..f.!', I I • t • • • t •

"I ':.f:.::~ .,,-a-;;o-l·~ r:;;'~::~"" ····l ..ff~ :1~C:I:~ ~;.'2 a.v' 1~4. -.!...~~'!. I 'tlf-t ~4t_1 · 1+1~.j;-+.1t:r .. ....~. . E' ~ t"; , ,.......! ...+1 ''''h-'tt 'I ' ­:; I -~' f Til ,i.~+1 J 1\ t I

•. L'L I' l~ I' I'.~""_oL-~_,, __,'_.~""_-' '" ......._-'-~ __ -'-.1~_>._J..L.-' ..u" I I !~

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Fi,. Sb;

..~( ,.4 ".

i « ...

pp I r·--O-'Q.~P,;.~~~t7o.v' ,r--';:;:"~;'\;:'<;~40~~' ; U4<P,P."U'O.V~ ; """'IP.CISlO.V'

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~PfP'-C-~~7;O~'i ~ o.7ICP,fI,<U1G~ [0.•, <PtP.~O .•;·;.v·-·-' r-;M-;;'~P.< •."Q.V'

H I • -t "'!t-+ W~~. I'" -~ I f ~. ,l~·,·, I'~! I ·L~4.. l"r~~ • ;~ I ! I ~;.+

• ~"f,. ,~~. , ,~·t, , ~3t...!.. • , , • It... , .1 • I

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I I I. --......_ unc~rrect~d cJ'a~a '. _Model )( E.fficiency co~\ 'Y

Fig. $c Correlation function over cosign of the two particles divergence angle tor different values of momentum product. Filled points, • are e~perimental data without any corrections. Empty points. 0 are

model distributions calculated taking into account ARGUS efficiency. Exponential!its of experimental data with its parameters are also shown on each picture.

---- --------, ---l'" r-- ----- '- vI· l t + iI ~ .. I. ::I C)

I. ~ ..

: v..

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~.,~~~ ~ + j'

......; ......._._... _._.~.-"_.--'-. ~ L ..... -+_~,..L-, I !! I ' ! Itil • 1

.\ 0 , ·t O. t ,rl • 1"lo4o.

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•

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;:""~ • ...; i- ..~: 'i't-:t I!. ' ""-Ie I '7" f I .... ,I I ,-+ .J:-,

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G , ., 0 I .·1 0 ,I c"s'V

Fig.6c Correlation function of uvoparticles divergence angle corrected fot erticiency. fot d~rretebi momenturnprndutts. Exponenli.1 fit js also show,'!;

. ,~

,.; .,.~.

M41~jp1isi~y .

::::: f .- ~:. Da~~' ! :::: ~--~-----~X.~-:~;;'--l :::h----:·~;;:;-----l f 1-'" i:l + ­

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• I. 0 t. •• 4

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'lOt tt,' I P ·1 2000, t. n, " , ."

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~

Pig. 7 Protons and pions multiplicity distributionsfof uncorrected experimental data. rnndet generated eveots; passed thronah effjciency simulation p1o~natn. aud pure model events.

IS UftCOf~l8IlData.

Jl Z f-+ p1t+ I "I I ,

,.

·f ~-T tl I -r =-:~~++t- t I

:~~E-- L' .LYt-0- f I~. ___ •I

0;2' U 0.. ... ,a.,2

I I . tr-

Fig. 8 Dependcnc:e of tbe correlation fun~,ioD slope ~ over tht­

ptoductof two partidesmomenlum PI' PZ' On the firs:tpicturc the

data ar" not cor.·ectcd fOJ efficiency and OIl the s~cuHd ·lhey arc corrected.

Unc'orre.cted' Corrected

o,Sk( UJ',' o.s~ ~f1~ Ii [I

., I, .. o ,~II!!I. '0 !

0~25 . as. 0.75 1 0..25 0.5 0.75

a f p1t- . lfl 2 t· ~~-"~l----" l.sl . . ',/.,;,t1 1 I 1.sl .' I

~ .~t' I I,j

1

1! /+. t It' ~l+ I 0.5'. ".,,'" 0.5 I':tJ-ft' It I I

*- ~. I of~~l~~...J_~ o,"'! ,1 , ...Ll.~ I, I,; ,1I

a.as 0.5 0.75 1 0.25; 0.5 0.75 1

2 f--------------, /",1' 2 F--~-~-----i---1 t pp ,/ "I ~,PP': -+- I j

1,5 f- }'/"'_~+, 0, . ~+j, II i1.5 [t­t "...... I, i I II

1 l _...'~ , I 1 : /,' i 1 11 t;/ ~.. ;~~/ ttl III

0.5 ,-.' 0.5 t ""," .,++. l 'I,',:- .~.. r ...... ! I; ~~ . r 11

o '~_~~..L""'___ ! , 0 i~ .... L_..... 4_,_L_,....._"___...... " ,II 1.~ 0.25 0.5 0.75 O.2S 0,.5 0.75 1

Fig. 9 Fits of the dependence ~{Pl' P2) (see' ~so fig~ 7) as

~ = a(Pl . pz t. See table in the text for.fit parameters.

20

Mean Momentum a."

1 I

0" ,

pin pp

1't in on'

..-...._ ...... ..... , •.•.~. ..• ,p-+ ~__ ....~_ ... _,_'" ."A.._ .... __ .....~ ~ .~

#.t OA a. O' 1 l.

PI P2,(CeV/C)

Fig. 10 The dependence between mean mo"'.'entum of one panicle from the pair and the momentum product of the particles pair.

<cos 9>

01· ..

pan pp

p In pro >. •... -"

1't In p1tea. ..".. , .10

pin pl'l:j .")..1; :S

•.1 • ~_ ~.. ..L

•.• J ..... _-..o

o. ." ...~.•. _ .. ..J. __

0.. ~_ ....,J.__ ....

, ~ _......

1't 10 pC

1.% ,. PI P2, (CeV/c)'"

Fig. JJ The dependence between mean cos-ign (If the ant:1e of one partkle from a pair and the momentum product of the pair.

:....

. ..- ..\~ .'",

'}' ...:'

>:'::'~'::.:" r~:::~f~\'7 ':.A\ '-.'

. '\.'"

-,,'

", 'j~ .

-'"'..~ "

~- ..

"\ ..;'~

. .... ,"

...".

:... -".

....-'.::;: .. "