1. FEB1S33

a tt «aj= ii

IC/82/216

INTERNATIONAL CENTRE FORTHEORETICAL PHYSICS

THE LONGITUDINAL PHASE SPACE (LPS) ANALYSIS

OF THE INTERACTION np •* ppir" AT P Q= 3-5 GeV/c

INTERNATIONALATOMIC ENERGY

AGENCY

UNITED NATIONSEDUCATIONAL,

SCIENTIFICAND CULTURALORGANIZATION

Burhan Fatah

Calin Beshliu

and

Gruia Silviu Gruia

1982MIRAMARE-TRIESTE

IC/82/216 Analysis of the experimental data for the reaction

np ppn (1)

International Atomic Energy Agency

and

United Nations Educational Scientific and Cultural Organisation

INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

THE LONGITUDINAL PHASE SPACE (LP8) ANALYSIS

OF THE INTERACTION np •* ppiT AT P =3-5 GeV/c *n

Burhan Fatah

International Centre for Theoretical Physics, Trieste, Italy,

Calln Beshliu and Gruia Silviu Gruia

Department of Nuclear Physics, University of Bucharest, Romania.

ABSTRACT

The react ion np •+ ppiT i s analyzed at P = 5.10 and 3.83 GeV/c using

longitudinal phase space (LPS) ana lys i s . The d i s t r ibu t ions of u {Van Hove's

angle) along with the hexagonal p lo t s are investigated in d e t a i l . From the

w-distr ibut ions i t i s possible to conclude t h a t , whenever, allowed, the

di f f rac t ive mechanism (Pomeron exchange) dominates the three Trody f ina l s t a t e .

For the f i r s t time the approximate percentage, on the basis of hexagonal

d i s t r i b u t i o n s , of the different processes involved (d i f f rac t ive , per iphera l ,

e t c . ) i s calculated which may very well agree with the expectations at these

energies .

The Invest igat ion has been performed at the Laboratory of High Energies,

Laboratory of Computing Techniques and Automation, JINR., Dubna and Laboratory

of Nuclear Physics, University of Bucharest.

MIRAMARE - TRIESTENovember 1932

To be submitted for publ icat ion.

i s d i f f i cu l t due to the large number of kinematical variables needed for

every event. For example, in the case of n -pa r t i e l e s in the f ina l s t a t e

3n~h independent variables are needed (or 3n-5 var iables when the incident energy

i s f ixed) . Therefore one always looks for different p o s s i b i l i t i e s in order

to minimize t h i s large number of parameters.

One of the most successful methods, in t h i s d i rec t ion , i s Van Hove's

Longitudinal Phase Space {LPS) analysis [ l ] . We r eca l l here b r i e f ly the

or ienta t ion of the three f ina l p a r t i c l e s , In react ion ( i ) , in the hexagonal

d i s t r i bu t ions : de t a i l s of the hexagonal p lots can be found elsewhere [ 2 , 3 ] .

The general scheme of the longitudinal phase space p l o t , along with the

different exchange diagrams, i s presented in F i g . l , where the axis marked

P. refers t o the longitudinal cm . momentum of the f ina l s t a t e p a r t i c l e s .

I f the masses and the t ransverse momenta of the f ina l p a r t i c l e s are small

compared with the t o t a l c m . energy, the experimental events tend t o l i e along

the kinematical border of t h i s plot which at large energies becomes a regular

hexagon. The angle in between the three p a r t i c l e s i s 120 . The signs

marked "+" and " -" refer t o the "forward" and "backward" motions of the final

par t ic les , respectively.

Three exchange diagrams (Feynman graphs) wil l be discussed in detail

throughout th is a r t ic le . The f i rs t diagram refers to the displacement of

particles when P f (Fast Proton) [k] along with Ps (Slow Proton) [h] goes in

the backward direction. The most protable part ic le exchanged trajectory,

between the two vert ices, i s a pomeron.

Similarly in the second diagram we consider the movement of f . in the

forward direction while the combination p ir~ goes backward, in cm. Clearlys

a Tr-meson exchange takes place. Lastly an exotic exchange Is expected when

both nucleona appear at the same vertex.

In this paper we are presenting an anlysis of experimental data

obtained by Dubna-Bucharest University Collaboration. The 1-w hydrogen

bubble chamber was irradiated at J.I.S.R, Dubna using, a monochromatical

neutron beam ( — ^ - 3 %, A6<li0.3 m rad) [5] , The reaction channel

np •* PP"" wa identified at four different incident momenta P = 1.73,

2.23, 3.83 and 5.1 GeV/c having a s t a t i s t i c s of 1*623, 2933, 2093 and 892

events, respectively [6].

- 2 -

A3 it w b e «••-. from U-.r- o-ptrii .-.^tal distributions cf th.-: transverse

momenta for Lhe t,.,ree final state p a r t i e s of the reaction under discussion

(see Figs.2,3,4), their valves are sufficiently low anfl constant (the figures

are self-explanatory, the solid line refers ...• ... • : • . . . observation which

allows us to be within the demands of the longitudinal phase space (LPS)

analysis. In such a situation a transverse momentum cut could fce made in

the total incident momenta.

An eventual inclusion of the transverse phase space in the calculations

(along with LPS) may not lead to significant physical informations, moreover,

this has the disadvantage of introducing another parameter, something which

evidently makes the calculations difficult without obtaining an efficiency in

the physical analysis of the experimental data.

Hext we consider the experimental distributions of the longitudinal

momenta, in cm., for reaction ( i ) . If Fig.5 the corresponding distribution

for the TT -meson are given whereas Figs.6,T represent the longitudinal momenta

distributions for the p f and p s , respectively. All the three distributions

are considered at four different incident momenta P = 5.10, 3.83, 2.23 and

1.73 GeV/c. The solid line represents phase space.

As i t was expected before, the longitudinal momenta distributions for

the » -meson are isotropic around zero whereas the "p " and "p " are more

dominant in the "forward" and "backward" directions, in cm. , respectively.

This kind of movement of the particles grows with an increase in the incident

neutron momenta. These experimental distributions indicate, strongly, the

existence of particle exchange Feynman diagrams, for the process under

consideration, which favours the selection of the LPS analysis.

The previous differential applications of the existing data showed

the importance of LPS analysis [ 7 , . . . AT]. A characteristic parameter,

of LPS analysis, is the radial vector p (see Fig.8) which is

presented, for all three possible combinations, at two different incident

momenta FQ = 5.10 and 3.83 GeV/c. According to these distributions the length

of the radial vector is almost constant for all the combinations in the

framework of the same energy considered. The small lengths of the p-distributions

as well as their constant positions, at both of the energies, together with the

transverse momenta representations (also having values practically constant

and Independent of the incident energy) show the grouping of majority of the

events to the boundaries of the hexagon.

In Figs.9,10 two Van Hove plots for the incident momenta P = 5.10,

3.83 GeV/c, respectively, are presented. On the three axes, having an angle

of 120 between them, the longitudinal momenta (P ), in cm., for the three

- 3 -

final particles are shown. These diagrams, based on the phenomenologieal

characteristics, show the grouping of events, in the plots, under the form

of regular hexagon, with the observation that this geometrical form is more

pronounced with the increasing incident energy. Under the circumstances

when p is approximately constant the polar angle u becomes the only decisive

parameter and shall be used in the following discussion very frequently. The

tendency of the events to group around the boundaries of the hexagon corresponds

to the kinematical fact that the transverse momenta, of al l the outgoing

particles, is relatively small.

In Figs.11,12 we present the distributions of the polar angle ID for

the combinations p ir~ and p it", respectively, at P = 5.10 and 3.83 GeV/c

(892 and 2093 events, respectively). The grouping of the events can be

observed very clearly at ID i< 60° and i< 120° for the combinations p• IT" and

p IT , respectively. These distributions are allowed by the phase space,

graphically represented with the solid line. The values which exceed the

phase space curves, in the central regions, refer to the resonance process which

appear in the irN combination. In order to understand more explicitly the

presence of resonances, in the u distributions, we use the double plots

ID vs. M (where co is the Van Hove's polar angle, M stands for an effective

mass distribution).

In Figs.13,11* we present M _ vs. m _ and M ^- vs. « _ ,M_ « _

respectively, at tile two incident momenta ?n » 5.10, 3.83 GeV/c (statistics

is 892 and 2093 events, respectively). Grouping of the events is quite clear

at m i> 60 and ^ 120 , respectively for Pffl~ and V if . Resonance masses

seem tobelong to the regions from 1-2 GeV/c2. A detailed study is needed in

order to understand the physical structure of these resonances.

These experimental observations allow us to believe the presence of

some dynamics of the type peripherical and diffractive In the reaction channel

( i ) . For a better understanding of the dynamical process involved, in the

reaction under discussion, we think i t useful to have a. phenomenological

discussion of the experimental data from the point of Van Hove's hexagonal plots.

We again go back to Figs.9)10 where the two hexagonal diagrams, for

the three final particles In reaction U ) , are plotted at ?n = 5.10 and 3.83

GeV/c having number of events 892, 2093, respectively. In the region u 1 60

(conform notions from Fig.l) one can observe a preferred movement of Pf and

- l t -

::. s ZWt S

the IT -meson in the forward hemisphere whereas the P continues i t s motion ins

the backward direction. The dominance of these dynamics corresponds to the

region 0° < cu < l£0° having a maxinum of i> 60°. This kind of movement

of the particles, generally speaking, refers to the diffraction dissociation

process (the exchanged particle trajectory between the two vertices being

a pomeron). In the second region 60° < <J) < l8o° one sees a dominance of

the displacement of p^, along with v~, in the 'backward direction while the

p f moves in the opposite hemisphere. This region is dominated by a grouping

of events in about the value of a i> 120 corresponding to a process with the

exchange of a meson.

A special remark must be made for an agglomeration of the events, in

Figs.9,10, in the intermediate region between 60° and 120° which corresponds

to the direction of flight of one of the final protons in the backward direction.

Aa a matter of fact these are the non-resonant events (see Figs.11,12). By

looking at the distribution in the longitudinal momenta (Figs.5,6,T) one can

drav the evident conclusion that p , most probably, appears at the second

vertex. Therefore i t may be said that the majority of the events from the

overlapping, observed in the mentioned area (a bit before), corresponds to

the situation in which Pg and ir~ move together in the backward direction.

Events which are spread around u ^ O°/36o° show the absence of some

anomalies in the direction of flight of the two protons ( i .e . small probability

for both the protons to appear at the some vertex), this fact being only

possible in the allowed limits of phase space. Therefore i t may be concluded

that the data, from the experiment ttnder discussion, shows the absence of some

dibaryonic (PP) resonant states.

In the spirit of the classical ideology of Van Hove, therefore in the

limits of the analysis of experimental material froffl the point of view of

longitudinal phase space, one can, approximately, calculate the contributions

of the dominant process from reaction ( t ) . Calculations were done for the

highest neutron incident energy, at disposal, in the present experiment

Pn = 5.10 GeV/c, stat ist ics being 892 events.

The procedure consists of an analysis of the two intervals, in the

hexagonal representation, of flu = 36°, each having values in between:

and

102" for peripherical process

- 5 -

for diffractive process

By looking at the distributions of the experimental events in these

subdivided regions (see Tables Tl, T2) i t may be remarked, with a good

approximation, that the bias of other types of diagrams is sufficiently

reduced. Weighing these numbers of events to the to ta l number of events

one can get the rough approximate results:

Diffractive processes ^ 50 %

Peripheral processes "» kO %

Other types of processes i< 10 %

In the end some final concluding remarks can be made about the analysis

performed!

The first conclusion, which one can draw, is the satisfactory interpretation

of the experimental data using the longitudinal phase space (LPS) analysis,.

Though energies considered were rather low for an application of this analysis

but s t i l l the results were good. It was further observed that the overall

efficiency of the analysis was Improved with an increase in the incident

neutron energy.

The most important result from this analysis, applied to np •* ppif at

P = 5.10 GeV/c, was the estimation of the different processes dominating

the reaction channel under discussion. Using the hexagonal representation

an approximate percentage of the diffractive aa well as peripheral processes

was calculated which came out to be 50 % and !»0 %, respectively.

The last conclusion is a very general one. The LPS analysis seems to be

an effective tool to explain some of the final state particle properties,

e.g. diffractive behaviour etc. in a fairly nice way. On the other hand,

i t was felt that the LPS analysis is unable to explain some very Important

factors in the experimental hadron physics, e.g. resonance production mechanism,

etc. It was further noticed that at moderate energies *v> 5 GeV the analysis

may not be very effective as the contribution of the transverse momenta, to the

total outgoing momenta, is higher and one may not be in a position to neglect

i t totally. c

ACOOWLEDGMKiraS

We are grateful to A.P. lerusaliwov and Yu,A. Troyan for stimulating

discussions. One of the authors (B.F.) would like to thank Professor Abdus Salam,

the International Atomic Energy Agency and UNESCO for hospitality at the

International Centre for Theoretical Physics, Trieste.

REFERENCES AND FOOTNOTE

[1] L. Van Hove, Nuel. Phys. B9, 331 (1969); Phys. Lett. 28B, 1*29 (1969).

[2] V. Kittel, L. Van Hove and W. Wojlck, CERH (D. Ph.Il) Phys. 70-8.

[3] A. Bialas, A. Eskreys, W. Kittel, S. Pokorskl, J.K. Tuominiemi and

L. Van Hove, Nucl. Pays. Bll, 1*79 (1969)-

[It] In order to make a distinction between the tvo final protons ve assign

each of them a label which is based on their energies. The proton vhich

has more energy Is called fast proton while the other one is called slow-

proton .

[5] Abdlvaliev A. et al., Hucl. Phys. Bg£, ^ ^ 5 ) PAU5.

[6] Abaivaliev A. et al., D1-81-T56 preprint, Dubna (19-81).

[7] L. Van Hove, Proc. of the Colloquium on Multiparticle Dynamics, Helsinki

(19T1).

[8] J. Bartsch et al., Nucl. Phys. B19, 38l (19T0).

[9] G. Bossompierre et al., Hucl Phys. BlU, 1U3 (1969).

[10] W. Kittel, Proc. of the Colloquium on Multiparticle Dynamics, Helsinki

(1971).

[ll] M. Deutschmann, Rapporteur's talk given at the Amsterdam International

Conference on Elementary Particles, Amsterdam (1971).

[12] w. Kittel, S. Ratti and L. Van Hove, Nucl. Phys. B30, 333 (1971).

[13] J.E. Brau, F.T. Dao, M.F. Hodous, I.A. Pless and R.A. Singer, Phys. Rev-

Lett. 27-2, 1U81 (1971).

[Ik] E. De Wolf et al., Nucl. Phys. BU6, 333 (1972).

[15] J. Beaupre et al., Nucl Fhys. B35, 6l (1971).

[16] J. Beaupre et al., "How does am LPS analysis separate production mechanism*

in IT p interaction at 8 and 16 GeV/c" CERN preprint, CERN (D. Ph.II)

Phys. 72-1.

[17] J. Benecke et al., Phys. Rev. 188, 2159 (1969).

-7-

TOTAL EVENTS

CAPTIOUS

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Table Tl

TOTAL EVENTS

102* Xtf lit 120 126 132*

12

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11

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3

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Fig.2

FiR.3

Fig.lt

Fifi.5

F1J;.6

Fig.7

Fig.8

Fig.9

The most probable exchange diagrams from the point of view of Van

Hove's hexagonal representation.

Transverse momenta of the ir~-meson at P = 5.10, 3.83, 2.23 and 1.73

GeV/c. Solid curve represents corresponding phase space.

Transverse momenta of the "fast" protons (p ) at P = 5.10, 3.83, 2.23and 1.73 GeV/c. Solid curve represents corresponding phase space.

Transverse momenta of the "slow11 protons fp ) at P = 5.10, 3.83, 2.23s n

and 1.73 GeV/c. Solid curve represents corresponding phase space.

Longitudinal momenta of the Tr"-meson, in cm. , at P = 5.10, 3.83, 2.23

and 1/73 GeV/c. Solid curve represents corresponding phase space.

Longitudinal momenta of the "fast" protons ( p J , in cm. , at P = 5.10,

3.83, 2.23 and 1.73 GeV/c, Solid curve represents corresponding

phase space.

Longitudinal momenta of the "slow" protons (u ) , in cm. , at P = 5.10,

3.83, 2.23 and 1.73 GeV/c. Solid curve represents corresponding

phase space.

Experimental distributions of Van Hove's radial vector "p" calculated

for al l the possible final state particles combinations, in cm. , at

PQ = 5.10 and 3.83 GeV/c.

Distribution of the experimental events in Van Hove's hexagonal plotat P = 5.10 GeV/c.

Distribution of the experimental events in Van Hove's hexagonal plot

at P = 3.83 GeV/cnVan Hove's polar angle "«" distributions, calculated for the

combination pfw~ at Pn = 5.10 and 3.83 OeV/c. Solid line represents

the corresponding phase space.

Van Hove's polar angle "u>" distributions, calculated for the

combination p fl~ at P =5.10 and 3.83 GeV/c Solid line represents

the corresponding phase space.

102*<uj<138*

Table T2

-9 -

-10-

Fig. 13 Double p lo t s H v s . to at ? * -,-iu tin a 3.83 GeV/c.P f - '

Fia. lU Double p lo t s M VB' ID - tit P = 5.10 and 3.S3 GeV/c.

Data Tables: Tl , T2.

Pf

P .

n

P .

Pf

Flg. 1- 1 2 -

B . 2

- 1 3 -

nP —ppnT

Q75

Fig. 3

- l i t -

np

50

5.10 GeV/c

892 ev.

15

tf>

100

50

0

180

90

0400

£ 300

z 200

100

0

750

500

250

np

Pn=5.10 GeV

892 ev.

Pn-3.83GeVc

Pn=2.23G*/c

Pn=1.73GeVc

4623 ev.

- 1 5 -

-15 -10 -0.5 0.0 0.5 10 1.5

Flg.5

-16-

150

100

50

270

«180ztuiuu. 90O

I0

300

200

100

0

500

250

np •—— ppji

P n -510GeV / c

892 ev.

Pn=3.83GeV/c

2093 ev.

Pn= 2.23 GeV

2933 ev.

Pn=173GeV/c

4623 ev.

-15 -10 -05 0.0 O5 10 t5

Fig. 6-17-

150

HI

u.O

np ppjr

Pn = 510GeV/c

892 ev

Pn=3.83GeV/c

2093 ev

2.23 Gev>c

2933 ev

1.73 GeV/c

4623 ev

-15 -1.0 -05 0.0 05 1.0 1.5

Flfl. 7-18-

150

100

LU

50

300 F

200

100

np

15.10

3.83 GeV/c

np —-pprc"

5.10

np

383GeV/c

510GeV/c

5 10 15 2 0 5 1 0 15 205 10 15 20e P f * - e p ^ - epf Ps

Fig. 8-19-

Fig. 9-20-

MA*

\ /*

np

V\ .\ v

0.

• '

/

/

f

\

\

>

.5 1.

/ »

• f t

• • A

\\

\

2093 «v.

\

f

Fig. 10

-21-

200

Ato

Io6

300

np

Pn-5.10GeW/c

892 ev.

Pn-5.10G<*//c

892 «v.

90° 180° 270° 360°

Fig. 11

-22-

300

200

100

en

IIu.O

i 450

300

24

16

1.2

24

Mp./r'

1.6

1,2

np

- I •—I

Pn=51O(3eV/c

892 ev.

,/-25»v.

/ / / • /

H ^ 1 h

2093ew./-25ev.

0° 36° 72° 108° 144° 180°270° 360u

Fig. 12

-23-

Fig. 13

-21.-

72° 108'

Fig.14

-25-

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IC/82/113 P. RACZKA, JR. - On the class of simple solutions of SU(2) Yang-MillsINT.REP.* equations.

IC/82/lllt

IC/82/115

IC/82/116

IC/82/117

IC/82/118

lc/82/119INT.REP.*

IC/82/122

IC/82/121*INT.REP.*

IC/82/127INT.REP.*

IC/B2/128INT.REP.*

IC/82/129INT.REP.*

IC/82/130

IC/82/131INT.REP.*

IC/62/132IHT.REP.*

IC/82/133

IC/82/131*INT.REP.*

IC/82/137INT.REP.*

IC/82/138INT.REP.*

IC/S2/l!*0

IC/82/llt2INT.REP.*

IC/82/HI3

IC/82/1M4INTLREF.*

IC/82/llt5

IC/82/1U6

IC/82/1147INT.REP.*

IC/82/lWIMT.REP.*

IC/82/lk9IHT.REP.*

G. LAZARIDES and Q.-SHAFI - Supersymmetric GUTs and cosmology.

B.K. 3HARMA and M. TOMAK - Compton profiles of some 'id transition metals.

M.D. MAIA - Mass splitting induced by gravitation.

PARTHA GHOSE - An approach to gauge hierarchy in the minimal SU(5) modelof grand unification.

PARTHA GHOSE - Scalar loops and the Higgs mass in the Salam-Weinberg-Glashow model.

A. QADIR - The question of an upper bound on entropy.

C.W. LUNG and L.Y. XIONG - The dislocation distribution function in theplastic zone at a crack tip.

EAYANI I. RAMIREZ - A view of bond formation in terms of electron momentumdistributions.

N.N. COHAN and M. WEISMANN - Phasons and amplitudons in one dimensionalincommensurate systems.

M. TOMAK - The electron Ionized donor recombination in semiconductors.

S.P. TEWARI - High temperature superconducting of a Chevrel phase ternarycompound.

LI XINZ HOU, MAUG KELIN and ZHANG JIAMZU - Light spinor monopole.

C.A. MAJID - Thermal analysis of chalcogenides glasses of the system

( A 32 Se3>l-X

K.M. KHANNA and S, CHAUBA SINGH - Radial distribution function and secondvirial coefficient for interacting bosons.

A. QADIR - Massive neutrinos in astrophysics.

H.B. GHASSIB and S. CHATTERJEE - On back flow in tvo and three dimensions.

M.Y.M, HASSAN, A. RABIE and E.H. ISMAIL - Binding energy calculations usingthe molecular orbital wave function.

A. EREZINI - Eigenfunctions in disordered systems near the mobility edge.

Y. FUJIMOTO, K. SHIGEMOTO and ZHAO ZHIYONG - No domain wall problem inSU(ti) grand unified theory.

G.A. CHHISTOS - Trivial solution to the domain wall problem.

S. CHAKRABARTI and A.H. NAYYAR - On stability of soliton solution in HLS-type general field model.

S. CHAKRABARTI - The stability analysis of non-topological solitons ingauge theory and in electrodynamics,

S.N. RAM and C.P. SINGH - Hadronic couplings of open beauty states.

BAYAIJI I. RAMIREZ - Elctron momentum distributions of the first-rowhomonuclear diatomic molecules, A .

A.K. MAJUMDAR - Correlation between magnetoresistance and magnetization inAg Mn and Au Mn spin glasses.

E.A, SAAD, S.A. El WAKIL, M.H. HAGGAG and H.M. MACHALI - Pade approximantfor Chan.drasekhar H function.

G.A. El WAKIL, M.T. ATIA, E.A. SAAD and A. HEBDI - Particle transfer inmultiregion.

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