Исследование корреляционных и коллективных характеристик процессов взаимодействия пи+ и К+ мезонов с протонами при 250 ГэВ/с тема автореферата и диссертации по физике, 01.04.16 ВАК РФ

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ЕРЕВАНСКИЙ ФИЗИЧЕСКИЙ ИНСТИТУТ

Меграбян Сурик Сергеевич

ИССЛЕДОВАНИЕ КОРРЕЛЯЦИОННЫХ И КОЛЛЕКТИВНЫХ ХАРАКТЕРИСТИК ПРОЦЕССОВ ВЗАИМОДЕЙСТВИЯ п* И К+ МЕЗОНОВ С ПРОТОНАМИ ПРИ 250 ГэВ/с

А.04.16 Физика ядра, элементарных частиц и космических лучей

АФТОРЕФЕРАТ дисертации на соискание ученой степени кандидата физико-математических наук

ЕРЕВАН 1996

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Работа выполнена в Ереванском физическом институте

кандидат физико-математических наук Г.Р. Гулканян

доктор физико-математических наук академик НА РА Р.О- Авакян (ЕрФИ) доктор физико-математических наук Ю.П. Малакян (ИФИ)

Ереванский государственный университет (кафедра ядерной физики) июля 1996 г- в _ часов на заседание

Научный руководитель: Официальные оппоненты:

Ведущая организация:

Защита состоится _

Специализированного совета 024 при Ереванском физическом институте (375036, Ереван» ул- Братьев Алиханян) С диссертацией можно ознакомиться в библиотеке ЕрФИ. Афтореферат разослан _ июня 1996 г-

УченнЫй секретарь Специализированного совета

и, а

_А. Т. Маргарян

GENERAL CHARACTERISTICS

Actuality: The multiparticle production is the most characteristic feature of high energy pi?sics. The creation of soft hadrons, a major fraction of the total cross section, relates to the strong-coupling long-distance regime of Quantum Chromodynamics (QCD), at present one of the least explored sections on the whole of high-energy physics. With increasing collision energy y/s, the role of hard like-efTects (characterized by short-distance or large transfer momentum) increases. Thuse effects give rise to scaling violation in spectra of produced hadrons, particularly, in correlation between their transverse and longitudinal momentum. The present models (LUND, FRITIOF etc.) of hadron'c interactions do not treat properly all principal underlying mechanisms of hadronic interactions and are not able to reproduce satisfactorily the whole complexity of the multiparticle production. A more and detailed experimental data, especially on the correlation and collective characteristics of produced hadrons, are needed to obtain new information about the dynamics of the hadronization process. .

A powerful tool for the investigation of the space-time structure of the multiparticle production process is provided by the boson interferometry. The interferometric correlations of two (or more) identical bosons (Dose-Einstein correlations) at small relative momenta reflect both geometrical and dynamical properties of the particle-radiating source. The experimental study of these correlations provides a measurement of the size, shape and radiation time of the source, contains an information on its non-static properties, on the underlying mechanisms of multiparticle dynamics.

Purpose: The main goals of the thesis are:

• Investigation of collective and correlation characteristics of hadron system produced in fragmentation regions of ir+p interactions at 250 GeV/c in NA22 experiment, performed at the CERN SPS with the help of European Hybrid Spectrometer (EIIS).

• Investigation of Bose-Einstein correlations between two or more (up to four) identical pions in (7r+//\+)p interactions at 250 GeV/c in NA22 experiment.

Scientific novelity:

1. First time collective characteristics of the hadron system produced in fragmentation region of non-diifractive hadron-hadron interactions are studied.

• First estimation of the inelasticity coefficient in leading hadron cluster production is extracted. An experimental evidence is obtained that non-single-diffractive proceses are less peripheral than diifractive dissociation.

• First time the collective "sea-gull" effect is observed. It is demonstrated that hard-like processes, both in the collision phase and in the fragmentation phase, are not properly treated in the currently used models of multiparticle production.

2. First time a detailed study of nose-Einstein correlation in meson-proton interactions is performed.

• It is shown that the pion sourcc is elongated along the collision axis. First time indication is found for an increase of the elongation with increasing event multiplicity, pion pair momentum and particle transverse momentum. The source size is found to be larger for pions from central rapidity region than for larger rapidity pions.

• First time higher-order Bose-Einstein correlations arc studied in meson-proton interactions. It is shown that genuine third-order correlations essentialy have an interference origin.

Practical usefulness: The results of this thesis can be used for improvment of models of mulliparticlc production process the underlying mechanisms of which are not well established yet,, particularly those concerning space-time evolution of the hadronic matter, hard-like effects of gluon scattering and emitting which can take place in higher-energy hadronic and nuclear interactions. The results could be useful also for planning of future experiments devoted to the study of multiparticle prodution processes at higher energies.

Structure of thesis: The thesis consist of an Introduction, six Chapters and Conclusions. The thesis is presented in 119 pages which includes 44 figures, 31 tables and 138 references.

Contents of thesis

In Introduction it is shown the actuality of investigation carried out, the purpose is formulated and the structure and brief contents of thesis are presented.

In Chapter one the experimental setup is presented. It consists of an active vertex detector IfCDC (Rapid Cylcing Bubble Chamber) and down-stream spectrometer. The RCliC filled with //2, operates in a 2T magnetic field and is exposed to a 250 GeV/c tagged (7r+//v + /p) enriched positive beam. Beam particles are reconstructed from hits in the two upstream wire chambers, and identified with two helium filled differential Cherenkov counters. The downstream spectrometer consists of one multiwire proportional chamber and six large drift chambers. It is subdivided in two lever arms by a second magnet with a 1.5T magnetic field to improve the momentum resolution for tracks above 50 GeV/c.

Tracks of secondary charged particles are reconstructed from hits in the wire and drift chambers, and from measurments in the bubble chamber. The momentum resolution < Ap/p > varies from (1-2)% for tracks reconstructed in the bubble chamber only (up to ~ 2 GeV/c in laboratory frame), to (1-2.5)% for tracks reconstructed in the first lever arm. Tracks reconstructed in the full spectrometer have an average momentum resolution of 1.5%.

Gamma quanta from meson decays are detected by two electromagnetic calorimeters covering almost full forward hemisphere in the c.m.s. of mcso-proton interaction.

Measured and reconstructed events are accepted for further analysis if the following conditions are fulfilled.:

1. the measured beam track is successfully connected with hits in the upstream wire chambers.

2. all charged tracks are reconstructed and the charge balance is correct.

8. the number of rejected tracks is at most equal to 0, 1, 1, 2 and 3 for events with charged multiplicity 2, 4, 6, 8 and > 8, respectively.

4. none of the secondary tracks is an electron or positron, identified in the bubble chamber.

Additional two physical cuts are applied:

The event is called elastic and excluded from further analysis if for a two prong event the missing transverse momentum is less than 0.1 GeV/c and the absolute missing longitudinal momentum in the laboratry frame docs not exceed 9 GeV/c.

The event is called single-difTractive and excluded from further analysis if the total number of charged particles is less than 8 and it contains a beam type particle with xp > 0.88 or a proton with if < —0.88.

In Chapter two collective characteristics of hadron systems produced in beam fomentation of 7r+p collisions are studied. For the data selection we require tracks to have a momentum resolution Ap/p < 0.1 in the forward hemisphere, but no restriction js imposed on A p/p in the backward hemisphere. Furthermore, to avoid loss of fast neutral particles in the beam fragmentation region, we select events with acceptable total momentum balance. To achieve this, we firstly accept events for which the total longitudinal momentum pBCBC of all charged and neutral particles detected in RCDC is within the interval 245 < pBCBC < 255 GeV/c and the total transverse momentum pjCBC is less than 0.5 GeV/c. Secondly, if pfrlCBC is less than 245 GeV/c, we add to it the total longitudinal momentum of 7's or 7r°'s and r/'s reconstructed in the electromagnetic calorimeters, and accept events with total longitudinal momentum within the interval 225 < p^CBC + ?>fAf < 255 GeV/c and total transverse momentum \pBCBC + pfA'l 'pss than 0.5 GeV/c. This allows a loss of no more than 10% of the total momentum and does not significantly affect the characteristics of hadrons in the beam fragmentation region.

Since no clear boundary exists between particles produced in beam fragmentation and central production, three different methods are applied in order to select particles arising from beam fragmentation.

According to the first method (the cut method), a selection y > ycut is applied to the rapidity of each particle. From the range of forward-backward correlations in our data and the size of the scaling region, we deduce that at our energy the "optimal" value of ycui is in the interval 1 < ycut < 2 (in the c.m.s.).

According to the second method (the maximum rapidity gap method), a "boundary" y0 > 0 is determined separately for each event by the maximum rapidity gap (Ay)max between neighbouring particles. If (At/)maI is reached between the fc-th and (k + 1 )-til particles (t/jt > yk+i), we set ya = \j\t and assume all particles with y > 1/0 to belong to the beam fragmentation region. (Note, if the largest gap includes y = 0, all particles in the forward hemisphere are accepted). Two variants of this method arc used: a) 110 restriction on the {Ay),nnT, b) a restriction (Ay)mar > lis used and events with (Aj/)mnl < 1 arc rejected.

According to the third method (the cluster rapidity method), we assume that the differ-" ence between the leading cluster rapidity Yc and the nearest particle not belonging to the cluster exceeds some minimum value AV^, where AVC f« 1.5 — 2. If the rapidity difference between the fastest particle and the nearest one exceeds Al^, only one (the fastest) particle is assumed to be in the beam fragmentation region. If not, the fastest particle is combined,

one after the other, with the neighbouring particles, until the composed system (cluster) rapidity Yc exceeds the nearest particle rapidity by the value of AV'C. We, furthermore, require the last particle included into a cluster to have y > 0.5. If this requirement is not satisfied the event is rejected.

To see the effect of the cuts described above and to be able to compare our experimental results to model predictions, the same cuts are applied to Monte Carlo events generated according to the Lund and Fritiof models.

For all three used methods, the average fraction of incident longitudinal momentum (see Fig.l) carried by fragmentation products, i.e. the average "elasticity" coefficient, lies in the range (A')=0.8±0.1 (both in c.m. and lab. frames) and the mean inelasticity (part of the incident hadron momentum used for particle production in the central region) is (k) « (1 — (X)) ~ (0.2 ± 0.1). This value is significatly smaller than that extracted from our data on the leading hadron (instead of the leading hadron cluster) spectrum: < kh > = (1— < Xh >) = 0.56 ± 0.02. Thus, we conclude, that the momentum loss, accompaining the multiple scattering process in the hadro-nucleus interaction, should be much smaller than it was usually supposed.

The distribution on the four-momentum transfer t from the incident 7r+ to the leading hadron system has an approximately exponential form with a slope b varying between 0.8 and 2.0 (GeV/c)-2. This value is much smaller than generally observed for single-dilfractive processes (ba¡¡ «6—10 (GeV/c)~2). Thus, experimental evidence is obtained that the non-singlc-diffractive process hp —► II'X is less peripheral than single-diffraction dissociation.

The thrust distribution for the leading cluster fragmentation is peaked at lower T values than in diffraction dissociation (see Fig.2). Nevertheless, the mean value of (T) ps 0.76 — 0.83 indicates non-isotropy also for leading cluster fragmentation. The distributions expected for isotropic clustcr decay (obtained by Monte-Carlo calculations using the experimentally observed cluster multiplicity distribution) do not agree with our data. The average charge of the forward jet, i.e. the charge in the forward hemisphere with respect to the total momentum of the fragmentation products, calculated in the rest frame of this system of particles, is (Q/)=0.45±0.04 for methods II and III, i.e. close to the average charge of the 7r+-mcsoii valence quarks. The average charge of the backward jet is smaller due to a loss of slow particles not accepted as fragmentation products.

In Chapter three the correlation between the longitudinal and transverse momenta of hadron system in fragmentation regions is studied. As observed recently, scaling violation in the dependence of the average transverse momentum (py) on Feynman if (lifting of the so-called "sea-gull" wings with increasing energy \/s) docs not only occur in hard collisions such as e+e~ annihilation or lepton-nucleon scattering, but also in "soft" hadron-hadron collisions. In hard collisions, the non-scaling effects are attributed to hard gluon emission by one or two leading quarks, but the underlying mechanism is not yet established in soft hadron-hadron collisions. In meson-proton collisions, strong non-scaling effects are observed for hadrons produced in the meson fragmentation (x¡.- > 0.2) and proton fragmentation (;ff < —0.4) regions, i.e. for the fast products of valence quark (or diquark) hadronization. In the fragmentation regions, the s-depcndencc of (pj) is not reproduced by currently used models of soft hadronic interactions (LUND,FRITIOF). This and the comparison to c+c~ and lit collisions indicates the presence of hard-like effects causing larger values of (pr) than predicted so far. It is important to establish in what phase of the interaction these hard like effects (not properly treated in models) might occur: in the collision phase or in the fragmentation (hadronization) phase.

Hard-like processes can be devided as follows, the type (a) processes: gluon bremsstrahlung by the interacting constituent of the projectile or quark-gluon scattering, both leading to gluon emission with relatively large pr and small |if|i followed by gluon hadronization into the central rapidity region, the type (b) processes: quark-quark (diquark) scattering leading to large-pr hadron production in the two fragmentation regions. Finally, the type (c) processes: a gluon with a comparatively large pr and large |x;.-| being radiated by the spectator quark of the incident hadron or by the excited state of the collided hadron behaving as a colour antenna.

The hard-like processes of type (a) and (b) take place in the collision phase, processes of type (c) in the fragmentation phase of the hadronic interaction.

In case (c), hard-like effects observed in the single particle spcctra should, at least partially, be cancelled in the dependence of the collective transverse variable Pr = I^ptI on the collective longitudinal variable Xp — YiXp, where the sums include the charged particles in the beam fragmentation or the target- fragmentation region, respectively. On the other hand, for cases (a) and (b) no cancellation takes place within the fragmentation region and a hard-like effect will be observed in the .Xf-dependence of Pr- The experimental study of the correlation between collective variables Xp and Pr is, therefore, expected to give new information on the relative importance of these processes.

We compare the data with two versions of the FRITIOF model: FRITIOF2.0 and the recently proposed FRITIOF7.0 which include hard-like processes both in the collision phase and in the fragmentation phase.

The /.'-dependence of (i'r) has a characteristic sea-gull shape (see Fig.3). Two main observations can be inferred:

• For a system of hadrons produced at small cms angle 0* < 9° or 0* > 171° (or at rapidity |_y| > yc„i = 2.5), the collective sea-gull can be described by the FKITIOF model. This suggest, therefore, that hard-like processes yielding particle with small c.m. emission angle are properly treated in model. For this sample, hard-like elTects (not properly treated in the model) mainly originate from the fragmentation phase. This phase is treated as colour-antenna radiation in the FRITIOF model, which, however, fails (especially in the FRITIOF7.0 version) in reproducing the single particle spectra.

• However, when including larger emission angles 0' < 21° or 6' > 159° (or at |y| > Vcut = 1-5), the collective sea-gull effect is underestimated by these models. For this sample, hard-like processes not properly included in the model take place at least in the collision phase.

Thus, hard-like processes (not properly included in model) take place in both principalc pases of the mult,¡particle production in hadron-hadron interaction.

In Chapter four influence of multiplicity and kinematica! cuts on Bose-Einstein (BE) correlation is studied.

The experimental investigation of interference effects allows, in principle, to measure the space-time size of the emitting region in an arbitrary direction and for specific classes of interactions, differing by the multiplicity of secondaries, their transverse momentum, their rapidity and other characteristics.

The coincidence rate for the observation of two identical pions normalized to an uncor-

related "background" is

Л = 1 + A/,(q)/2(?0) (1)

whore q=pi — P2 is the three momentum difference and q0 = — E2\ is the energy difference of the two pions. The functions /i(q) and f?(qo) are squared Fourier transforms of the space and life time distributions of the emitters, respectively. These distributions are assumed to be independent.

For example, if emitters are distributed uniformly on a disk or a spherical surface of radius r, then (iri units h = с = 1):

/.(7г) = 4Л2(7тО/(<?гг)2 (2)

J\(x) being the first-order Bessel function and qr the modulus of the component of the vector q transverse to pi -f p2.

If emitters have a spherically-symmetric Gaussian distribution then:

/,(q) = ^P(-|q|V) (3)

where v is related to the r.m.s. radius of the distribution by r(r.m.s.) = уДг.

If emitters are excited simultaneously and decay exponentially with lifetime r, then:

bMHl+^T1 (4)

The parameter A in (1) characterizes the strength of the interference effect, with a maximum possible value of A = 1. The experimentally observed values are practically always A < 1. Different reasons can lead to a value A < 1, for example a contamination from coherently radiating emitters for which interference effects are absent, from point-like emitters radiating two or more like pions; the presence of two pion sources of different size, or simply detector induced bia-ses (as misidentification of particles, wrong charge assignment or track losses).

lixprossions (l)-(4) are not Lorcntz-invariant. In general, the variables arc, therefore, calculated in the centre of mass of the initial collision.

Л possible Lorentz-invariant parametrization (known as Goldhaber parametrization) is

Л = 1 + Асхр(-г2<?2) (5)

with Q2 = —(pi — ;>г)2 = A/2 — 4m», where M is the invariant mass of the pion pair and rn„ is the pion mass. It corresponds to a Gaussian shape of the source in the centre of mass of the pair, where <70 = ДE = 0.

The experimental data are analyzed in terms of the following parametrizations:

1. The one-dimensional Kopylov-Podgoretzkil parametrization

R(qr) = 7*11 + Ал-(4.7|2(гл-?г)/(гл<7т)2)](1 + 6КЧТ). (6)

2. The two-dimensional Kopylov-I'odgoretskil parametrization

Щчт,Я,) = 7A-I1 + Afv(4J12(rA-9r)/(r„?T)2)(l + r4V]- (7)

3. The Lorcntz-invariant parametrization of Goldhaber

R(Qr) = 7g[1 + Адсхр(—7-^Q2)](l + bcQ2). (8)

4. the Lorentz-invariant parametrization with two Gaussians

R(QorQ2) = 7[1 + A]exp(—rjQ2) + A2exp(-r2Q2)];

In the present analysis two additional track cuts are applied:

• the track momentum error is required to be below 4%;

• each accepted track is required to lie in the region of the Fcynman variable \xp\ < 0.5.

The resolution in Q7 and qT is estimated to be <jq? = 8 • 10"4 (GeV/c)2 at Q2 < 0.04 (GeV/c)2 and <7,r = 5 ■ 10"3 GeV/c at qT < 0.05 GeV/c.

Two methods are applied to form the "background" (reference) sample in the ratio R. In the mixed-event method, the reference sample is formed by combining a pion from one event with pions randomly chosen from different events of the same topology. In the unlike-pair method, the reference sample is formed from pairs of unlike charged pions in the same event.

Using the Kopylov-Podgoretskil parametrization (6), the ratio iiiisa function of qr (see Fig. 4), for pairs with energy difference limited to q0 < (</o)cu! = 0.2 GeV/c in the overall cms, we obtained, with free 5k and with 8k fixed to 0. In all eases, the radius rk is of order 1.3-1.6 fm.

More complete information on the emitting region can be obtained from the two-dimensional distribution B(qr,qo) using the Kopylov-Podgoretskil parametrization (7). Within errors, the values obtained for r;4- and A a- are equal to those obtained from the one-dimensional distribution R{qr) <»t the corresponding values of (70)™«-

Our values of r= 1.59 ± 0.14 fm and r = 0.83 ± 0.25 fm are close to those obtained in the high-statistics experiments, where data are analyzed with the same parametrization (7). It is important to note that the fit by (7) cannot reproduce the sharp peak for qr —> 0 at small <7o-values.

The results of an analysis under the assumption that pions are generated by two sources of different size using parametrization (9) gives for extracted radii rj = 1.79 it 0.20 fm, 7*2 = 0.5G ± 0.04 fm and correlation strengths A! = 0.44 ± 0.06, A2 = 0.18 ± 0.03 are similar to those obtained for \/J=G3 GeV pp interactions (rj = 2.1 ± 0.5 fm, r2 = 0.66 ± 0.09 fm and A, = 0.48io.i9> = 0.28 ± 0.05).

The charge multiplicity dependence of the BE correlation shows, that the radius ra is noticeably smaller for reactions in which only one negative pair is produced (n=6) than for higher multiplicities. For n >8, no definite «-dependence of ra is found at our energy. Also the radius is larger (by a factor ~1.5-1.9) for the highest multiplicities (n>14) than for the lowest.

An angular dependence of the space-time size of the source is observed in the overall cms, when using the Kopylov-Podgoretskil pa.rametrizations (6) and (7). The longitudinal size of the source is larger than the transverse one. This is more significant for the two dimensional parametrization (7) than for the one-dimensional (6).

Using the mixed-event technique and parametrization (6) at qa < 0.2 GeV, we observe a dependence of r/,- on the pion pair momentum |p| = |pi + p2| in the overall c.m.s.. Our result establishes (see Fig. 5), that the radius decreases with increasing pion momentum, and the strength is noticeably smaller for the lowest momentum pions (|p| < 0.4 GeV/c) than for higher momentum ones. The decreasing effective radius r(;7) with increasing |/7| is

exported for pions emitted from the surface of a thermally excited (with a temperature T) and spherically expanding (with a radial velocity v) source:

r(p) = r0[(ztanhz)_1 - (sinhz)"2],/2 (10)

where z — l/2|p|7i>/7' and 7 = (1 — u2)1'2 is the Lorentz factor. The curves in Fig. 5 arc the fits by (10) leading to the parameter values

r0 T/tv x2!ndf

mixed-event: 2.07 ± 0.16 fm 0.30 ± 0.11 GeV 0.9/2 unlike-pair: 2.09 ± 0.20 fm 0.20 ±0.10 GeV 2.3/2

The physical explanation of the monotonically decreasing behavior of r(p) is that faster pions are more likely to be emitted near a point on the shell expanding with a velocity in the direction of p, whereas pairs with smaller momenta can come from more widely separated points.

As mentioned above, expressions (l)-(4) are not Lorentz-invariant. They are derived for the reference frame in which the pion source is motionless. The observed values of r and r must be minimal in this so-called "symmetric" reference frame. In order to establish whether there is an unique reference frame in which the pion source motionless for each 7r+p-collision, we analyzed HE correlations (with parametrizations (6) and (7)) in different reference frames with different values of the incident momentum ratio a = V*vlv*w

Our data on tk do not indicate the minimum at «=1.5 ("quark reference frame") seen earlier in x~p interaction at 40 GeV/c. In our experiment, relatively low values (r/<- ~ 1.3 — 1.5 fm) are achieved over a wide interval 1 < a < 10, including the overall c.m.s. (o=l), the "quark reference frame" (a=1.5) and the reference frame of equal rapidities of the incident hadrons (a = mp/m„ ss 6.7).

In other words, there is no unique "symmetric" reference frame in which the pion source is motionless for each 7r+;>-collision. This is probably due to the fact that the colliding constituents (quarks or gluons) can carry very different fractions of the initial hadron momentum and not the constant fraction of 1/2 for pion and 1/3 for nucleoli.

In Chapter five angular dependence of Bose-Einstein correlations are studied. Pion iiilerferoiuetry not only allows to measure the average radius of a pion source, but also to determine its shape. The latter can be obtained from the dependence of the size on a direction given by the angle 0 of the c.m.s. momentum difference q = i>\ — tfj with rcspect to the collision axis. In general, the angular distribution of if for pion pairs with | q\< qcut and very small c.m.s. energy difference <70 =| — ¿2 I is given by

V(cos0)cc /'"' |/[?24 + <72(r£-r2)cos20] I2 q2dq (11)

Jo

= H + (rl - r2r) cos2 0]-1-5 p' I /(x2) I2 x2dx , Jo

where ,r2 = <72['j- + (r[ — r2r) cos2 0] and the function f{x2) is the Fourier transform of the spatial distribution of the source, normalized to unity as 7 —> 0. One can show from (11) that, independently of the particular form of f(x2), the function ip(cosO) becomes constant at sufficiently small qcvi, qcui <C l/' j,. At sufficiently large qcui (i.e. above the correlation

region) the integral in (11) is practically independent of qcut, and the angular distribution <p(cosO) (normalized to unity in the interval —1 < cosd < 1) turns out to be

a2

f{cos6) --J-J7T5 (12)

2[a2 + (1 - a2) cos2 0J

The ratio a = ry/rt can be determined by fitting distribution (12) to the experimental angular distribution obtained after subtraction of a background (reference) distribution for which like-pion interference effects are absent. More simply, it can be determined from the asymmetry parameter A = (Ni — 7Vj)/(JVi + N2), where and are the numbers of correlated pion pairs (i.e. pairs after subtraction of the reference distribution) with | cos 0\ < 1/2 and | cos0| > 1/2, respectively, as

»'^(TTaF-1*- (13)

The (large) advantages of the method described above are that it does not require a fit to any particular form of the spatial distribution of the source, it is insensitive to the strength of the correlation, and it can be based on a smaller statistics than that required for separate measurement of rr and r/,.

The angular distribution of the correlated pion pair, is presented in the corresponding sub-figures of Fig. 6. The ratio a is obtained from fits by (12). The results are given as solid lines, the obtained parameter values a/ti are indicated in the figure. We have verified that, within errors, the values of a extracted from the asymmetry parameter according to (13) are the same,as those obtained from the fit.

The ratio a extrapolated to (<Jo)cui =0 at qcut =0.5 GeV/c has a value of 0.55±0.06 for jK+)p, i.e. the pion source is elongated along the collision axis. While no dependence of the elongation is found on the rapidity of the pair, indication for an increase of elongation is found with increasing event multiplicity, pair momentum and particle transverse momentum.

In Chapter six higher order Bose-Einstein correlations are studied. In the most general case, the inclusive g-particle densities pq( 1, ...,<?) (where the kinematical variables of the particles are abbreviated to their number 1,...,<7) are expressed in terms of the cluster expansion familiar from statistical physics:

P2( 1,2) = C2(l,2) + M1V»(2), (14)

/>3(1,2,3) = C3(l,2,3) + (l)/)2(2,3) — 2/)i(l)/>1(2)p1(3), (15)

№

^(1,2,3,4) = 64(1,2,3,4) -f pi(\)p3(2,3,4) -f 2)/i2(3,4)

H) (3)

- 2X>,(1)M2)M3,4) +6M1)/., (2)M3)M4), (16)

(<5)

etc, where the summations indicate that all possible permutations have to be taken. The number under the summation sign indicates the number of terms. The correlation functions or (factorial) cumulant functions Cq(l, ...,q) vanish whenever any one of their arguments becomes statistically independent of the others. They represent the genuine q-particle correlations, while the other terms in the expansions (14)-(lf>) reflect the "trivial" contributions from lower-order densities.

It is often convenient to use the normalized inclusive densities and correlations:

Rq(l,...,q) = p,(l,...,q)/pt{l)...pi(q), (1?)

A',(l,...,i) = C,(l,..., ,)//.,(!)■• •/».(?)• (13)

The normalization of the inclusive densities pt,p2,p3 and p4 for identical particles is defined from the condition that their integration over phase space results, respectively, in («), (n(n— I)), (n(n — l)(n — 2)) and (n(n — l)(n — 2)(n — 3)), where n is the particle multiplicity.

Pion radiation by a partially coherent source (with the chaoticity parameter p =< ncj > /<)!>, where < nci, > denotes the chaotic fraction in the pion average multiplicity) can be described in the framework of quantum statistics, applying an approach analogous to that used in quantum optics.

The normalized two-, three- and four-pion inclusive densities arc:

R2{Ql) = 1 +2p(l — p)cxp(—r2Q\) + p2 exp(—2r2Q\), ('/<»)

R3(Q2) = l+6Hl-p)exp(-ir2Q2) + 3p2(3-2rtexp(-pQl)

+ 2j? exp(—r2Qz), (20)

R,(Q]) = 1 + 12j)(l — p) cxp(—^r2Q2) + 6p2(7 — 8p -f 2p2)exp(—^r2Q2)

+ 4p3(ll-9p)exp(-ir2Q2) + Vcxp(-^r2Q2). (2J)

where Q] = (£*=, l\f ~ (<?A/,)2-

The genuine three-particle correlation function C3(Q3) and its normalized form A'3(Ql) nre extracted by means of (15). The. product P\P\P\ in (15) is determined by combining three particles with a given Q3 randomly chosen from different events with n„- > 3. The product P2P1 is determined by combining three particles with a given Q2, two of which are chosen from the same event and the other from another event with n,- > 3. The density p3 is determined by combining three particles with a given Ql chosen from the same event.

Two methods of normalization are applied for the density function p3 and the combinations p2p\ and P\P\Pi ■ In method I, we use the total number of three-pion combinations in the interval 0 < Q2 < (Q2)max as described above. In method II, we use (n(n — l)(?i — 2)) f°r P3< (")("(" — 1)) p'ipi am' (n)3 f°r PiPtP\- These two methods lead to very similar results.

In Figs. 7a,c,c the measured ratios H,(Q2) = Nq(Q2)/N^a(Q2) are shown for q=2,3,4, respectively. Figures 7b,d,f present the same distributions corrected for Coulomb repulsion of the like-charge pions in the final state: each two-pion combination in N2(Q22) is weighted by a factor (known as Gamov factor)

= G-\Q2) = exp(2;")~1, (22)

with if = otm*/q2 and a = For a triplet and a quadruplet of pions containing, respectively, three and six pair combinations with variable Q,} a factor

H^nG"'«?,,), (? = 3,4) (23)

is used.

The q-dependence of the radius r and chaocity parameter p are shown in Fig. 7 and the fit results are presented in Table 1. An increase of r with increasing q is observed, while p does not vary significantly.

In the quantum-statistical model, the parameters r and p are supposed to be the same for all orders, in clear contradiction with the trend of the combined data on r.

Our data allow to extract the normalized genuine three-particle correlation function K3{Ql). The function I(3(Ql) + 1 is shown in Fig. 8 after Coulomb correction. A nonzero K3 is observed for < 0.2(GeV/c)2. We have checked that the elTect is also present before Coulomb correction. If the genuine three-particle correlations have an interference origin, the function K3(Q^) + 1 can be described by the parameters r2 = 0.85 ±0.01 fm and A2 = 0.38 ± 0.02 deduced from the fit of the normalized two-particle density 7?2(Q2) by (8)

KÁQI) + 1 = 7[1 + 2Af exp(-ir22Q2)](l + SQl). (2*)

We, therefore, fit the data of Fig. 8 by (24) and compare the resulting r2 and A2 to the values given above. The fit results, practically the same for normalization methods I and II described above, are presented in Table 2. Considering the large errors, the resulting parameters r2 and A2 do not contradict those of the two-particle correlations.

In Conclusion the main results of the thesis are summarized.

1. Collective characteristics are studied in beam fragmentation of non-single-dilfractive 7r+p-interactions at 250 GeV/c.

• It is shown that the pion fragmentation products carry on average a fraction of 0.8±0.1 of the incident momentum, so that only 0.2±0.1 of the incident momentum is spent for particle production in the central region. This value is considerably smaller than that deduced from leading hadron spectra.

• The momentum transfer distribution shows that the non-single-dilfractive processes are less peripheral than the dilfractive ones.

• The analysis of thrust and sphericity shows jet-like structure of pion fragmentation, but less prominent than in diffraction dissociation. The forward charge (Q¡) = 0.45 ± 0.04 agrees with the average charge of the beam valence quarks.

2. The correlation between longitudinal and transverse momentum is studied for a system of fast hadrons produced in the fragmentation region of non-dilfractive 7r+p-intéractions at 250 GeV/c. The "collective sea-gull effect" is observed. The effect is not reproduced by the FRITIOF fragmentation model in its details. It is demonstrated that hard-like processes, both in the collision phase and in the fragmentation phase, are not properly treated in the models.

3. A detailed study of Bose-Einstein correlation of negative pious is performed in 7r+p -interactions at 250 GeV/c.

• From the observed correlations of negative pions we obtain, using the Lorentz invariant parametrization (8) of Goldhaber, an average radius of the pion source (as observed in the dipion rest frame) of r<j=0.85±0.04 fm. Using the Kopylov-Podgoretskn parametrizations (6) and (7) (in the overall cms) we find for the average radius r/< = 1.59 ± 0.14 fm and for the life-time r = 0.83 dt 0.25 fm.

• A more detailed study shows that the pion source can be characterized by two different radii. Obtained with parametrization (9), these radii are ri = 1.75±0.25 fm and r2=0.60±0.08 fm in the dipion rest frame, very close to those observed in higher energy pp-interactions.

• Our data allow to find a multiplicity dependence of the correlation effects, but smaller than observed for higher energy pp and pp-interactions, nucleus-nucleus collisions and highest energy e+e~ annihilation. For the cases of parametrizations (6) and (7), the radius r/i increases with increasing multiplicity, being a factor 1.6-1.9 larger at n > 14 than at n = 6 — 8. For the case of parametrization (8), the radius ryj is significantly smaller at multiplicity n=6 than at higher ones, but at n > 8 no significant n-dependence is observed.

• From the rapidity dependence, an indication is obtained that the source of pions produced in the central region has on average a larger size than that produced in the fragmentation region.

• The source size "seen" by pions with different momenta in the overall cms decreases with increasing momentum, as is expected for a thermally excited and spherically expanding source with T/fV = 0.3 i 0.1 GeV.

• In our study of Dose-Einstein correlation in different reference frames of tt+p interaction, no evidence is found for a unique frame in which the pion source is motionless for each w+p collision, i.e. where the spatial size and the life-time of the pion source arc definitely smaller than in other reference frames moving along the beam direction. The emitting region has a prolate shape in any frame.

4. From the angular dependence of Dose-Einstein correlation in (7r+//f+)/p interaction at 250 GeV/c, the pion source is found to be elongated along the interaction axis in the c.m.s., with the ratio 0.55±0.06 between transverse and longitudinal dimension. While 110 dependence of the elongation is found on the rapidity of the pair, indication for an increase of the elongation is found with increasing event multiplicity, pair momentum and particle transverse momentum.

5. A study of higher Bose-Einstein correlations is performed in (n+/K+) interactions at 250 GeV/c. Genuine third-order correlations are observed which, except for small effects, can be described in terms of second-order correlations.

The main contents of the thesis has been presented in the following publications:

1. l.V. Ajinenko,...,S.S. Megrabyan et al.:Z.Phys.C49, 1991, p.367

2. N.M. Agababyan,...,S.S. Mehrabyan et al.:Z.Phys.C59, 1993, p.195

■ 3. N.M. Agababyan,...,S.S. Mehrabyan et al.:Phys.Lett.B320, 1994, p.411

4. N.M. Aga.babyan,...,S.S. Mehrabyan et al.:Z.Phys.C66, 1995, p.409

5. N.M. Agababyan,...,S.S. Mehrabyan et al.:Z.Phys.C68, 1995, p.229

Table 1. The results of fitting the data sample by the functions (19) to (21) multiplied by 7,(1+ «,<??)

Order q r v 7 Ä x2/ndf

(fm) (GeV~2)

Without Coulomb corrections

2 0.80 ± 0.03 0.19 ±0.01 0.953 ± 0.004 0.035 ± 0.006 113/96

3 0.86 ± 0.03 0.15 ±0.01 0.969 ± 0.010 -0.004 ± 0.007 140/96

4 1.17 ±0.07 0.19 ±0.03 1.081 ±0.020 -0.070 ±0.011 106/95

With Coulomb corrections

2 0.83 ± 0.03 0.22 ± 0.01 0.954 ± 0.004 0.030 ± 0.005 123/96

3 0.87 ±0.03 0.17 ±0.01 0.974 ± 0.009 -0.013 ±0.007 145/96

4 1.07 ±0.07 0.18 ±0.02 1.060 ±0.024 -0.070 ±0.013 98/95

Table 2. The results of fitting the normalized three particle correlation function by (24)

normalization method r2(fm) A2 7 8 x2/ndf

Without Coulomb corrections

/ ■ 99+0.25 33 0.33 ± 0.15 1.000 ±0.008 -0.002 ± 0.007 77/96

II 1 24+0-28 '-0.37 0.32 ±0.15 1.007 ±0.008 -0.001 ±0.007 77/96

With Coulomb corrections

/ 1 ?4+0'21 • —0.27 0.40 ±0.15 0.999 ± 0.008 -0.001 ±0.007 76/96

II i or+0.23 1 ■ ¿■)_n2h 0.39 ±0.15 1.001 ±0.008 -0.001 ±0.007 76/96

FIGURE CAPTIONS

Fig. 1 The X distribution of the leading hadron cluster, for the three different methods of cluster separation: a the cut method (yCUj = 1.5), b the maximum rapidity gap method ((Ay)max > 1), c the cluster rapidity method (AYc = 2). d The x distribution of the leading hadron in tt+p interactions, normalized in two different ways. Also the Fritiof 2.0 model predictions are presented.

Fig. 2 The thrust T-distribution for the leading cluster fragmentation for events with n = nch + r)„eui > 4 particles in the pion fragmentation region. The data on n+//C+ -diffraction at 250 GeV/c and isotropic decay predictions are also presented.

Fig. 3 The AV-dependcnce of < Pj > for a system of hadrons with |y| > ycui. Dash-dotted curves are the FRITIOF2.0, solid curves FRITIOF7.0 predictions.

Fig. 4 The ratio R as a function of qr, as obtained with the a mixed-event and b unlike-pair reference sample. The curves correspond to the best fit according to parametrization (6). The point qr < 0.025GeV/c in Fig. 4b is excluded from the fit.

Fig. 5 The radius r/<- and correlation strength A«, based on parametrization (6), for pion pairs in four momentum intervals |p| = |pi -j- P2I in the overall cms. The lines correspond to parametrization (10).

Fig. 6 The angular distribution of the vector q at different '/cui and (?o)cui values in (w+/K+)p -interactions.

Fig. 7 The normalized two-, three- and four-particle inclusive densities not corrected (a,c,e) and corrected (b,d,f) for Coulomb interaction in the final state, as a function of Q Curves show the fits results.

Fig. 8 The normalized three particle correlation function added to 1. The curve

is the result of the fit.

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С.С. Меграбян

ИССЛЕДОВАНИЕ КОРРЕЛЯЦИОННЫХ И КОЛЛЕКТИВНЫХ ХАРАКТЕРИСТИК ПРОЦЕССОВ ВЗАИМОДЕЙСТВИЯ гс+ И МЕЗОНОВ С ПРОТОНАМИ ПРИ 2?0 ГэВ/с

Диссертация состоит из введения, шести глав и заключения. Работ; изложена на 119 страницах, включая 44 рисунков, 31 таблиц и 131 наименований цитируемой литературы.

Диссертация посвящена изучению коллективных характеристик адронног( кластера в области фрагментации и корреляций Бозе-Эйнштейн) тождественных пионов в (н*/К*) р взаимодействиях при импульсе 250 ГэВ/с Экспериментальные данные были получены на установке ЕНЭ/СЕГчМ в эксперименте под кодовым названием N022.

Впервые в недиффракционных пион-протонных взаимодействиях были изучены коллективные характеристики адронного кластера в области фрагментации пучка. Получено значение коэффициента неупругости из коллективных характеристик адронного кластера. Показано, что недиффрак-ционные процессы менее периферичны, чем диффракционные. Наблюде! коллективный эффект "чайки" для адронного кластера в области фрагментации. Показано, что жесткие процессы не полностью включены I модели, используемые для адрон-адронных взаимодействий, как в фаз« столкновения, так и в фазе адронизации.

Подробно изучены корреляции Бозе-Эйнштейна в мезон- протонныз взаимодействиях. Получены пространственно-временные харак- теристик! области излучении пионов. Показано, что область излучения вытянута ш оси взаимодействия и что вытянутость увеличивается с увели- чение! множественности, суммарного импульса парыи поперечного импульса пионов, Изучены многочастичные ( до четырех частиц) корреляции Бозе-Эйнштейна. Показано, что трехчастичные "истинные" корреляции имеют интерференционный характер.