ilanarity of High Energy Collisions Aachen - Berlin - Bonn - CiiHN - Cracow - Heidelberg - Warsaw - Collabdration"Cprosented by H. Schiller) I.) Introduction In the last years there was an increasing interea • in the study of new kinematical variables. These new'-'y^labies'-eh^^^'help to understand the dynamics of multiparticle production in strong interaction. They were constructed in a way to be more sensitive to at least some aspects of the expected underlying dynamical mechanisms. In this ряпег we report about the results of a search for plana- rity of interactions at medium energies* By planarity we mean the alignment of f inial state particles - an alignment in such a way that the events appear flat* To study the effect of planarity-one obviously needs a variable which is "global" in the sense of taking into account all par ticles of a Given interaction, conseauently a multiparticle vari able. To separate the effect of planarity from the mechanism which reflects themselves mainly in the longitudinal momenta we look for an alignment in the planes perpendicular to the beam or to the principal axis of the jet, reeoectively* It is reasonable to assume that this alignment is caused by the high angular momentum in the intial state* Indeed in 16 GeV/c interactions and for an impact parameter of 1 fermi we find an angular momentum of <"" 14 n. We used the method suggested inflj. Additionally we applied this method in the principal axis frame. 4C events In the energy range from 4 to 25 GeV/c from ftp interactions were studied* In section II we give a short description of the methods used for analyzing the planarity. Section III contains the discussion of the experimental results, the dependences of multiplicity, energy and resonance production. In Section IV are summarized the conclusions.
II. Method and Definitions Starting from the system (x,y,z) where x is parallel to the beam* we obtain for each event a new coordinate system (x'.y'.z') by the requirement that the rotation around the (x'= x)-axis gives 2 £ (pjy.) = MIN. all particles (1)
In fig* 1 are illuetred the old and the new coordinate systems.
In the rotated system (x'^r, y*f z') one defines the relative thickness of one event от
T- ' ty1
ElpizJ
A complete alignment gives T=0. Similar quantities were defined by Glasser 0*3 and by Foster, Friedman and Nussinov £з1. We have calculate the relative thickness in two different systems 1. in CMS ( marked by ж ) 2. in the Principal Axis system QQ (marked by PA) In this system is the x - axis defined as the direction of that group of particles which has the biggest momentum in the CHS i.e. 1г^Ц PIA.
(R~A.J2? max (I Vj)2 o) all сотЫ- ' nations
«#PA |Д*Л with, i = number of the given combination; y™ and г are perpendicular to and to each other. The analysis in terms of T consists in a systematic comparison between the experimental values of
165 <ТИС>-<ТЕХР> ;: <ТМС * ' '-х-;^П®У^:+ ,„
In the Monte Carlo calculations we used for weigHting eyente a matrix elorarit which is obtained from Cylindrical -ftaw Space including leading particle effects:
2 |ll| *exp C-A-DJ (proton)-B.p£(all рЮпв)-»^-!)^^ Jr»)
The coefficents Л, В, С and D were adjusted to reproduce the 4, D,Cproton)> , ^Px^all^ and *t>t>dis *riQU*ions» ^be values of the coefficents are listed in table 1. The foia of the natrix element was chosen to assure the observed deviations between experimental and KonteCarlo values of ^T^i beinc caused neither by the strong dumping of transverse momenta nor by the existence of leading particles. However it was chocked that a change of the coefficents Л, В, С, Ь within reasonable limits effects
Ill» BCTerimental Results The values T°*<^q>»2<^ calculated for the reactions sumarized in table 2. ^ei8 and 16 GeV/c experiments were done by the:..^BBCt^^-^vColiaDbratiph. The data of 25 GeV/c come-from ah experipe^ ^
x of Wisconsin 't the data of 4 GeV/c from the АВШШ- Collaboration. xy '': . . r,:~'»...::~:'.. y We are very ihdepted to A.R. Erwin and \7.D. Walker for the ' permission to use some of their data -fsom the "*p experiment "at 25 GeV/c.
tee To look for a possible systematical error we checked the iaotropy of the 0 = A(y, y*) angle distribution, Tfce worst case has a %2-probaoility of 16 %. The result for the CMS and the P. A. system aark<-1 by *> and I'. A. resoeatively, are listed in table 3* It could be seen that for four particle final states {#*> is always smaller in the experiment than in the corresponding Monte Carlo sample, that means that the experimental events are more planar in average. In the six particle final states planarity becomes developed for pj^B 3» 16 GeV/c and the effect is not observed in eight particle final state In energy range studied* We havelooked for^planarl^ in the P.A. system, trying to check If thiseffeot Is due to the existence of flattened aets. The results show that the majority ofthe experimental points lie close toi the points obtained from the Monte Curio sample.As is shown In the lower part of fig. 3 the deviations are consistent with zero. The energy variation of the effect in the G»M. system can be seen at the left side of the upper part of fig. 3 tor reactions £ p -•> p3Jtv The effect is increasing with energy* On the other hand if we have fixed the energy and looked for the multiplicity dependence we found a rapidly decreasing of the planarity with Increasing multiplicity* In the right part of fig* 2 the typical behaviour Is shown for some 16 GeV/oflti reactions* It was interesting to check if the observed effect is caused by resonanoe' production* It is known that the production of reso nances covers the few particle final states and that's way it can contribute to the planarity* For this analysis we have chosen the reaction 3t*p —» рЖ+*+Ж~ at 8 and 16 GeY/c* The 4 GeV/o data were excluded due to -the smallness of the effect at this low energy* Since it is Impossible to find a reasonable large sample o;Z events without resonanoe production in the available reaction channels, the only possibility is to check whether the effect shows a struc ture at the reasonanoes region*
167 Fur several particle: combinations we '"calculated \^^0^!Ш&^(^^ as а Г unction of their invariant 13ass.es)* The generali ohseryatlpn is that the :>laaarity effect is in no case greater in the reaso- nance and difi'ractive bump region than in the other* is exanoles are shown in fig. 4a - 4d the results for the two particle soabinatiuhs CpJr+) and (JST'*'3fc'"')« ..e have chosen them because of finding there the largest effest in the corresponding resonance renion* The shaoe of the К^хсУ values (denoted bv a cross) as a function of the invariant laass is quite similar to the shape of {Ч&гт,} (denoted by a point). It could be seen that there is no structure in the relative deviations of the \^(а)Х values itfiich can be correlated with the resonance production»
Additional we have found that К^хрУ is "in tixc resonance region larger than the, overall value of К^шрУ * that means that events outside the resonance region are more planar and they are respon sible for the ^"jxp^ being less than
References
£0 ?• Kostka, H. Schiller, Preprint Berlin-Zeuthen,
PHE 72-7;
(gj R.G. Glssser* private communication;
£3(J M.C. Poster et al, Phys. Hev. D6 3135, 1972; £4] If. Danysz, W. Wojoik, Acta Physioa Polonica Vol. XXXIII 81, 1968.
169 Table 1 Coeffioente lieed in the a&fcrlx eleieifte for Monte Carlo calculntiona5
a c D iMi ~txP с -A-if - *-*i>L- t *«. IP iJ* PP лг
PlAB REACTION (GtV/cl IP- A В С О
-» p 3w 2.2 4.0 1.5 4 a 19 04 a
-» p 3tf 2-5 4.4 23 Q 8 — p 5r 0. 2.0 1.2 a — p Щ 1.0 1.4 0.4 o.
— p ЗУ 4.0 4.2 0.7 ae 16 -» P 5r 2.0 3.2 085 d -* p 7»r 1.2 12 04 0
-r:p;5r:{ 225 ЗЛ5 2.3 a 135 3J0 OB a
170 Table 2 Summary of investigated 4C reactions in the p^g region from 4 to 25 GeV/oj
ny —-- pr'ir*ir" ( 2067 events ) IT* p—-•> p г* яг* ir* w" it" ( 163 events ) РЦ^ 4C*V/c v*p — • pir*w*ira ( 5721 events)) W*P"-> PJT*W 7T*F" F* ( SOS events)) •W e fcw* F*p—-* P/ГJT*r*F*F"F"F • ( 299 events )
F*p—* ptr*r*T~ i 10209 events ) wy -— pwtir'rr'ir-r' ( 3112 events ) 16GtV/C try—» PF*F*F"*F*F>"F" ( 534 events ) LAB r"p— • pr*ir"r" ( 3998 events ) F"p—'* pir*r*W"rr"ir" ( 1224 events ) PUB8 16 GeV/c Г>—f pF^F* F*F"F>"r* ( 283 events)
F*p—•• р*Г*Т*>"г"*Г* ( 471 events ) - ^ 25 0еУ/с Г"р—» pF*r*r*F r"r"r" ( 133 events ) двЯ Table -У Average Tvaluou obtained from experiment and Konte Cwlo calculations and relative deviations in the Centre of Mass си) and Prlncljwl Axle (PA) systems for different energies and multiplicities. t'Al p REACTION
— p»*r* u3»«a«3 0420 5.3*07 0296*0003 O3G0 1.0 * 1.0
6 A ж' - pir*ir 0536 '• Q009 0532 -07* 1.6 05061 0.009 &4S9 -ЗЛ* 19 — p*F'2F* QS96 * ООП O560 -11 « 2.0 0566 - 0.011 0.574 tO * 1.9
• —• plr'ir" 0426 6.4 t Q5 0300 г 0002 0.301 03 * 0.7 Ы Ж* — p3r*2»* 053610.004 0542 1.1 s 07 0469 г 0004 04891 -02 «06 0.596 : aooi 0596 -1.7 iU 05662 0006 0569 02 * 1.4
0393» Q003 0426 7.7 «06 0295*0003 0301 \M * W 16 # T" — р1ж 3т- 0539*0036 0542 24-1.9 0495-0006 0466 Ql - 1,2 QSMsaon 0566 -03 * IJ 0556*0011 0569 2,4 * 1.9
25 — p2T*3r" 052120009 0547 1Б-М.6 0465 г 0009 0Ц4 W~ — pt'r* 0566 * 0015 0.572 -2.3 г 25 0572 * 0.016 0555 -11* 26 Pig* 1 Illustration of the new coordinate system (j\ z') deteiv mined by "the requirefflent (1);
173 тр^р*птг
п = 5
•^ п=4 0.5-
^ Л «— п=3 V
0.4 - - ^
п=2 0.3 -~ ^ а.
"- >«• 10 400
PLAB •/ m,t
Fig. 2 Dependence of the <Ф> values obtained;from Monte -.'aplo
calculations on РгдВ;
174 w*p-*pv*w*T л*р-*р*ттг AT 16 GeV/c
6 8 PiAB GeV/c MULTIPLICITY Fig. 3 Dependence of the Mlatlve'deviation
, (<%> - <Тетр> >/
a.) on PUB for the reactions *-p-pjrtat>~ шеазигчй In the С.K. and the.P.A. systems ; ЬТ on the multiplicity-t inrthe reactions »*р-р*«» at 16 ReV/o; measured In the 'C.E. and the Р.Л.systems. 175 1г*р—р»г*»г*г AT 8 GeV/c Qо J*
•-—H- 1 я 1 *—• x MC Ml . EXP МЛ-Ч Г AO- T-+
* .3« +
и 10- л* V 1± ?5- f-4—*^-4
и z
2. 3. 4. EFFECTIVE MASS iprr*j , OfN Fig.Да Effective mass spectra,- average.T. values obtained from experimentv(denoted byjBolnt).and fconte Carlo calcula tions (denoted by"cross) and the relative deviation ( TMC^ - -'ТЕХРЛ)/<ТМС^ measured in the СП.:, system versus a) effective mass (pV^yifor the reaction P *P* at 8 (leT/o. W * p-*p IT* 1Г*!Г AT 8 GeV/c g |800f- m z uо
E Ui m z Э »-*-»*4
.42- ++ л »MC v • EXP .38- 3L 1С 44+"+- + u Z i 1 2. 3. EFFECTIVE MASS (IT* ir"\ . GeV Flg.4h Effective mass spectra;.-average T balnea obtained from experiment,(denoted;by'poiiit) and Konte Carlo calcula tions (denoted Ъу cross), and the relative deviation Ci<94HC> ~
* 9- V4 v + > * "' »— V + {
* + ъ з 11 к 5* EFFECTIVE MASS(pFf) GeV Fig.4с Effective mass spectra,average T values obtained from experiment (denoted by point) andMonte Carlo calcula tions (denoted Ъг cross) and the .relative deviation ( <"ВцС>_ -ЛаХР* V
<л 1500-
А2- ПН
* .40- + х МС .38- ^—ь • ЕХР
EFFECTIVE MASS(ir*jr-) . GW Flg.4d Sffeetlve mass spectra, aveiage T values obtained from experiment (denoted Ъу point) and Jionte Carlo calcula tions (denoted by cross) and the relative deviation ( -'TKCN ~