Study of Δ++ Resonance Abundancein 158 A GeV Pb + Pb Collisions at CERN‑SPS

Susumu SATO

January, 2001

Study of Δ++ Resonance Abundancein 158 A GeV Pb + Pb Collisions at CERN‑SPS

Susumu SATO

A dissertation submitted to the Doctoral Programin Physics, the University of Tsukuba
in partial fulfillment of the requirements
for the degree of Doctor of Philosophy (Science)

January, 2001

Abstract
We present the results of single particle spectra and direct measurement of ∆resonance yield in pπ + decay channel in Pb + Pb collisions at the energy of 158 A
GeV, at WA98 experiment using Super Proton Synchrotron (SPS) of the European
organization for nuclear research (CERN).
For systematic study of hadron production in relativistic heavy ion collisions
near mid rapidity region, we have constructed a magnetic spectrometer, called
Arm-II. It is designed for good particle identification capability under the cond itionof high particle density and for large momentum coverage in Pb + Pb collisions at
SPS. Using the data taken by the Arm-II spectrometer, single particle spectra and∆ resonance yield are analyzed.
For the single particle, we have carried out the analysis of transverse kinetic
energy spectra for π + and proton. By using single exponential fitting, inverse slope
parameter is 142±3 MeV (fitting region mt -m>0.2 GeV), and 251±25 MeV. In thetransverse kinetic energy spectra of pion, we have observed clear low-mt
enhancement.
We have evaluated ∆ resonance yield with pπ + invariant mass distribution.
Considering the isospin asymmetry in incident 208Pb82+ nuclei, ∆/nucleon ratio is
determined as 0.62 ± 0.28(stat.) ± 0.16(sys.). This ratio is larger than thosemeasured in the lower beam energy.
Motivated by partial success of collective expanding fireball model, which can
explain both single particle spectra and HBT correlation but cannot describe low mt
region in pion spectra, different kinds of contributions are considered. Those arecollective motion, the Coulomb effect, and contribution of ∆ resonance. As thecollective motion and the Coulomb effects are qualitatively smaller than theobserved low mt enhancement, the contribution of ∆ resonance is therefore studied.
Using the value of temperature and collective velocity, evaluated from single
particle spectra and HBT measurement, about 1.5 times more contribution from ∆resonance than measured in the invariant mass is used to follow the shape of pion
spectra. The factor is consistent with the results of a cascade simulation. The
simulation tells the factor comes from such ∆ resonance that decays into proton
which is re-scattered and pion which is, ho wever, not re-scattered after decay, andthose ∆ resonances are not measured in the invariant mass.

Contents
1.

Introduction ...........................................................................................................5
1.1 Geometry of Relativistic Heavy Ion Collisions........................................6
1.2 Features of Particle Production Observed in Relativistic Heavy Ion
Collisions ........................................................................................................8
1.2.1 Single-Particle Spectra..........................................................................91.2.2 Two-Particle Correlation.....................................................................121.2.3 Interpretation with Expanding Fireball Model.............................14
1.3 Delta Resonance...........................................................................................19
1.3.1 Delta Resonance in Relativistic Heavy Ion Collisions .................20
1.3.2 Low mt Enhancement and Delta Resonance ..................................21
1.3.3 Delta Resonance Measurement at SPS Energy ............................22
1.4 Thesis Motivation ........................................................................................23

2.

Experimental Setup ...........................................................................................25
2.1 CERN-SPS Accelerator...............................................................................25
2.1.1 Ion Source (Electron Cyclotron Resonance: ECR).........................26
2.1.2 Linac, Boosters and Synchrotrons (PS and SPS) ..........................26
2.2 WA98 Experiment........................................................................................27
2.2.1 Target ......................................................................................................28
2.2.2 Magnetic Spectrometer .......................................................................28
2.2.2.1 Magnet: GOLIATH .......................................................................29
2.2.2.2 Pad Chamber: PAD.......................................................................29
2.2.2.3 Steamer Tube Detector: STD......................................................312.2.2.4 Start Counter: STR.......................................................................32
2.2.2.5 Time of Flight Detector (in Arm-II): JTOF ..............................33
2.2.3 Global Detector .....................................................................................35
2.2.3.1 Mid-Rapidity Calorimeter: MIRAC...........................................35
2.2.3.2 Zero Degree Calorimeter: ZDC...................................................35
1

3.

Data Analysis ......................................................................................................37
3.1 Clustering of Hits. .......................................................................................37
3.2 Track Reconstruction ..................................................................................39
3.3 Momentum Reconstruction and Flight Path Length Calculation ....41
3.4 Time of Flight Calibration .........................................................................45
3.5 Particle Identification .................................................................................49
3.6 Event Selection.............................................................................................52
3.7 Invariant Mass Spectra ..............................................................................53
3.8 Acceptance, Efficiency, and Decay Correction .......................................58
3.9 Isospin Consideration .................................................................................61

4.

Experimental Results ........................................................................................63
4.1 Error Evaluation..........................................................................................63
4.1.1 Statistical Fluctuation in Subtraction of Combinatorial
Background..........................................................................................63
4.1.2 Fitting Method Dependence in Subtraction of Combinatorial
Background..........................................................................................65
4.1.3 Dependence on Local Multiplicity ....................................................66
4.2 Transverse Momentum Distribution .......................................................68
4.3 ∆/Nucleon Ratio.............................................................................................70

5.

Discussions...........................................................................................................73
5.1 Ä/Nucleon Ratio............................................................................................73
5.2 Single-Particle Spectra and Two-Particle Correlation in Expanding
Fireball Picture. ..........................................................................................75
5.3 Low mt Enhancement of Pion Spectra ....................................................77
5.3.1 Proton - Proton Collision.....................................................................78
5.3.2 Source of Low mt Enhancement .......................................................79
5.3.2.1 Collective Motion...........................................................................80
5.3.2.2 Coulomb Effects .............................................................................82
5.3.2.3 Contribution from Resonances ...................................................832

6.

Conclusions..........................................................................................................87

7.

References ............................................................................................................88

Appendix A: Relativistic Heavy Ion Accelerators................................................93
Appendix B: Examples of Calculation ...................................................................94
Appendix C: Parameters Used in Relativistic Kinematics ...............................96
Appendix D: WA98 Experiment Coordinate System ..........................................97
Appendix E: Other Detectors in WA98..................................................................99
Appendix F: Selection of Radiator of Start Counter for Heavy Ion Beam...105

ACKNOWLEDGEMENTS .....................................................................................107

P U B L I S H E D P A P E R ..............................................................................................109" ∆++ production in 158 A GeV 208Pb + 208Pb interactions
at the CERN SPS" ( Physics Letters B 477 (2000) 37 - 44 )3

1. I n t r o d u c t i o n
In this chapter, current understanding of particle production in
relativistic heavy ion collisions to study of extremely hot and dense nuclear
states is described. And as an experimental probe of the state, delta
resonance is introduced
In the relativistic heavy ion collisions, hundreds of incident nucleus areinteracting for short time period of the order of fm/c in a finite volume of theorder of tens fm3. This condition initiates extremely hot and dense nuclear
states. Such hot and dense states are expected to exist at the beginning of
the universe. To study and characterize high density and high temperaturestates of nuclear matter on the earth, an effective way is to collide
relativistic heavy ions using accelerators. With this motivation, heavy ion
accelerators have been constructed or modified from existing proton
accelerators. Those are CERN-SPS or BNL-AGS. Using the accelerators,
unique features of nuclear matter in particle productions in relativistic
heavy ion collisions, like J/Ψ suppression, enhancement of low mass lepton
pairs, or collective phenomena, are observed experimentally [e.g. W98-98,
N44-96, N50-97, N45-99]. Also lots of theoretical interpretation of thesefeatures are reported, including a phase transition to a new phase of matter,called quark - gluon - plasma, where the constituent quarks and gluons
move asymptotically free [e.g. MS-86, Mu-85].
In relativistic heavy ion collisions, collision geometry determines featuresof observables. A naive geometrical picture of collision, called participant spectator model, is necessary to understand the observables. The picture is
described in section 1.1 .
In the next section 1.2 , features of relativistic heavy ion collisions havebeen studied through observables, like single particle spectra and two particle correlations. Trial for systematic description of the observables is
introduced. And a disagreement of the description in low transverse kinetic
energy regions of pion spectra is pointed out.
The difference between relativistic heavy ion collisions and nucleon nucleon collisions are discussed in the following section. For this viewpoint,
study of delta resonance is introduced in section 1.3 . And a description withthe delta resonance for an explanation of the disagreement in pion spectra is
5raised.
In the last of this chapter, the thesis motivation is described (sect. 1.4 )1.1 G e o m e t r y o f R e l a t i v i s t i c H e a v y I o n C o l l i s i o n s
In relativistic heavy ion collisions, the size of colliding system varies
depending on an impact parameter and the evolution of colliding system isknown to depending on the size of the system. Since the incoming angularmomentum (e.g. 60 GeV fm/c for 158 A GeV Pb + Pb collisions around thecenter of mass) is much larger than the typical quantum scale, ~ 0.2 GeV
fm/c, the impact parameter can be treated as a classical quantity. With theparameter, measured data in relativistic heavy ion collisions should be
sorted. When the impact parameter, b, is about a sum of radii of the nuclei,
both nuclei are touching on the surface at most closest point, and only the
nucleons in this surface will be involved in the collisions. Such collision iscalled peripheral collision. On the contrary, when the impact parameter iszero, most of the nucleons will be involved in the collisions. Such an event iscalled central collision.
In a naive picture for non-central collision, there are two domains forcolliding nuclei. One is overlapping part of the incident nuclei whichdevelops into hot and/or dense nuclear matter called fireball. Schematic
picture before, during, and after collision is shown in Fig. 1 (top, middle, andbottom drawings respectively). In the figure, impact parameter, b, is also
shown. Nucleons in the overlapping region (shown as hatched region in the
figure) are called participants. The other remaining parts, which pass awayfrom the fireball in early stage of the collision, are called spectators (shownas P and T in black letter as a projectile spectator and a target spectator,
respectively). This naive geometrical picture holds because of the following
two reasons.
(1) Elementary process of nucleus - nucleus collisions is nucleon - nucleon
collisions, because the de Broglie wavelength of incident nuclei, λdB, ismuch shorter than the size of nuclei, 2r.
(E.g. λdB < 1 fm and 2r ~ 14 fm for 158 A GeV Pb + Pb collisions in
the center of mass frame)(2) Each constituent nucleon collides dominantly with nucleons located intubular region with about nucleon radius and with length in theincident momentum direction. Because collision time, ∆tcol, is much6

shorter than the traversing time, ∆tT, for a nucleon to reach the next
(in perpendicular to incident momentum) nucleon.
(E.g. ∆tcol < 1 fm/c and ∆tT ~ 7 fm/c for 158 A GeV Pb + Pb collisions
in center of mass frame)With these three reasons, in relativistic heavy ion collisions, geometricalseparation of nucleons in participant region and nucleons in spectator
regions is considered as a good approximation.

Fig. 1: Schematic picture of relativistic heavy ion collision before (top), during (mid dle), andafter (bottom) the collision. Note that the projectile (P) and the target (T) are Lorentz
c on tracted in their center of mass frame. Hatched regions indicate hot and/or dense fir eball.
Impact parameter, b, is also shown.

In Fig. 2, dN/dy distribution of protons and anti-protons are shown for 158 A
GeV Pb + Pb central (top 5% of minimum bias) collisions. Here rapidity, y, isdefined as,y ≡ 1/2 ln { ( E +p// ) / ( E ‑p// ) },7

where E is the total energy, p// is the longitudinal component of the
momentum. Rapidity difference, ∆y, is Lorentz invariant. Rapidity of thecenter of mass is defined as zero in the figure. Note that rapidity difference
between the beam (or the target) and the center of mass at the SPS beamenergy is 2.91.

Fig. 2: Baryon rapidity distributions at SPS energy in 158 A GeV 2 0 8P b 8 2 + - 2 0 8 P b 8 2 + c en tral
(top 5%) collisions [N 4 9 -99]. As ∆ y is Lor entz invariant, rapidity of the center of mass istaken as zero. Note that rapidity difference between the beam (or the ta r get) and the centerof mass at the SPS beam energy is 2.91.

Participant nucleons are emitted around mid rapidity. About 35 protons in
dN/dy, are emitted in the mid rapidity. By subtracting small yield ofanti-particles, net protons correspond to the participant.
1.2 Features of Particle Production Observed in Relativistic Heavy Ion
C ollisions
Inclusive single particle spectra and two-particles correlations for
identified particle should give basic clue to study characteristics of the hot
and dense fireball. An interpretation of single particle spectra andtwo-particle correlation with expanding fireball model is useful to depict
collision dynamics of the relativistic heavy ion collisions.

81.2.1 S i n g l e - P a r t i c l e S p e c t r a
Transverse momentum, p t, has been measured inclusively for various
particle species not only in nucleus - nucleus collisions but also in proton nucleus and in proton - proton collisions. The spectrum is known to be welldescribed in transverse kinetic energy, mt m, rather than the transverse
momentum, where mt is a function of pt as follows.
mt =pt 2 + m2 ,where m is the rest mass of particle. In proton - proton collisions and proton- nucleus collisions, invariant cross sections show simple exponential shapes
in mt. And the mt slope is found to be very similar for various particle
species. These phenomena are often called as mt-scaling [B SM-76, A+-77,
Cr-78]. One of the example of the mt scaling is shown in Fig. 3 [B S-75]. The
horizontal axis is the transverse kinetic energy, mt-m, and the vertical axis
is the invariant cross section. This is plotted for protons, positive kaons, andpositive pions in proton - proton collisions at s1/2 = 23 GeV. Absolute values
for kaons and pions are multiplied by 1/1.5 and 1/35, respectively, to show
the similarity of the shape. The dashed line is an exponential line for an eye
guide. Clear mt scaling is seen in this collision. As an interpretation of the
mt scaling [Mi-79, Ha-83, Ta-85], a local thermal equilibrium is often
assumed where the inverse slope of spectra is considered as thetemperature.

9

E

dσ
dp

3

( m b / G eV

2

/ c

3

)

10 1

protonK+ ( x 1/1.5 )pi+ ( x 1/35 )10 0

10 ‑2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

pp̲sqrts̲23̲pikp̲mtscaling

10 ‑1

mt‑m(GeV)
Fig. 3: Invariant cross section of proton and K + , and π + in proton - proton collisions at s 1 / 2 =23 GeV [B S - 7 5 ]. Scaling in transverse kinetic energy, m t , can be seen for different particle
species. The dashed line is an eye guide in exponential function in mt.

Fig. 4 shows inclusive mt spectra in 158 A GeV Pb + Pb central of collisions
for different particle species [N44-96]. The horizontal axis is transverse
kinetic energy, and vertical axis is invariant differential yield in arbitrary
unit. Not that the normalization among different particle species is also inarbitrary. Invariant cross sections are shown to be exponential in mt as isseen in proton - proton collisions. However distinct differences are observedin nucleus - nucleus collisions.
(1)

Different inverse slope of m t exponential for different particle
species. Exponential fit is done for each particle species andacquired inverse slopes are shown in Fig. 4. The numbers in thebrackets are the fitting error only. Except low mt regions of pion
spectra, inverse slopes are in exponential. And acquired inverse
10

slopes are different from other particle species. On the other hand,particle and anti-particle, e.g. between positive pion and negative
pion, show the similar inverse slopes within the errors.
(2)

Deviation from exponential in low mt region for pion: In low mt
region (0.2 GeV) of positive and negative pion spectra,
enhancements are seen from mt exponential. These phenomena arecalled low mt enhancement. To see clearly, exponential fit done
above 0.2 GeV is extrapolated and shown in dotted lines.
As discussed in section 1.2.3 , the former distinct feature is shown to be
attribute to a radial expansion of the fireball.

Fig. 4: Invariant differential yield of proton, anti - proton, kaons, pions in central 158 A GeV
Pb + Pb collisions. Different slopes (fitted in the region above 0.2 GeV) for different part icle
species are seen. Also note that the enhancements are seen in low m t regions for pion
spec tra [N 4 4 -96].

11

1.2.2 T w o - P a r t i c l e C o r r e l a t i o n
Two particle correlations of identified particles have been measured inproton - proton, proton - nucleus, and nucleus - nucleus collisions at several
different beam energies. Identical particles are emitted from the fireball offinite size, quantum interference effect should be observed. The interferenceis used to measure the source size of particle emission, and called as HBTcorrelation, which is originally used for measurements of star size [HT -54].
Two-particle correlation function C(p 1 , p 2 ) describes the detection
probability of two particles at the momentum of p 1 and p 2 . The correlation
function is theoretically formalized based on the quantum statistics ofbosons (e.g. pions or kaons) or fermions (e.g. protons). Hereafter descriptions
for bosons are shown. Assuming the particle emitting source and two
detectors as schematically drawn in Fig. 5. For the particle source, two
identical bosons are assumed to be emitted from space-time point at x 1 andx 2 . For the detection, the two bosons are detected as energy-momentum p 1
and p 2 at space-time point at x 1 ' and x 2 ' .

Fig. 5: Schematic drawing for two particle HBT correlation. The identical particle emitted
a t s p a c e- t i m e p o i n ts x 1 a n d x 2 are detected at x 1 ' a n d x 2 '. Measured energy -m o m e n t a a r e p 1
a n d p 2 , at x 1 ' and x 2 ', respectively. Two sets of the arrows (in solid lines or in dashed lines)
show possible trajectories of the particles.

The correlation function can be described as follows,bg2
C(p1 , p2 ) = 1 + ~ρ eff q, p1 , p2 ,

b

g

b

g

where ~
ρeff q, p1 , p2 is the Fourier transform of effective density, ρeff x,p1,p2 ,q ≡ p1

p 2, and x ≡ x 1

x 2 . When the effective density of particles is12

assumed to be the Gaussian distribution,bρ eff x, p1 , p 2

N=
g assumed
2
4π Rx Ry Rzσ t
F x 2 − y 2 − z 2 − t2 I ,× expG −H 2 Rx 2 2 Ry 2 2 Rz2 2σ t 2 JK

where the normalization constant, N, and the standard deviations Rx, Ry, Rz,
and σt are valuables as functions of p 1 and p 2 . The coordinate is often taken
as follows. The incident momentum direction is z-axis, and the center ofmass of source is origin of the space coordinate. The x-axis is taken as the
direction towards the detector, and for the y-axis is the direction
perpendicular to the line joining the source and the detector. The constant,N, is chosen so that the effective density is normalized to 1, by the following
way,

b

g
≡ z dx ⋅ ρ eff b x, p1 , p 2 g

N = N p1 , p2

Therefore the Fourier transform of the effective density isFGHRx 2 q x 2 Ry 2 q y2 Rz 2 qz 2 σ t 2 qt 2~
ρ eff q, p1 , p2 = N ⋅ exp −
−
−
−
2
2
2
2

b

g

I.
JK

Finally the correlation function for the identical bosons emitted fromGaussian type of source is as follows.

afdC q = 1 + N ⋅ exp − Rx 2 q x 2 − Ry 2 q y2 − Rz 2 qz 2 − σ t 2 qt 2i

Especially for one dimensional case instead of four dimensions noted by (x, y,z, t), the correlation functions is expressed as a function of qinv as follows.

afdC q = 1 + λ ⋅ exp − Rinv 2 qinv 2

i

where
qinv = q x 2 + q y2 + q z 2 − q0 2 .
Fig. 6 shows the two-particle correlation function for Rinv = 6 fm and λ = 1.
The width of the enhanced region around qinv = 0 corresponds to the inverseof the source size, 1/Rinv.
As one of the features in nucleus - nucleus collision for HBT measurement13

is Kt -dependence of the measured radius, where Kt is average momentum of
the particles in pair. This effect is interpreted by the expanding fireball as
described in section 1.2.3 .

Fig. 6: T w o- particle correlation function of a source with R i n v = 6 fm and λ = 1 as a functionof qi n v .

1.2.3 I n t e r p r e t a t i o n w i t h E x p a n d i n g F i r e b a l l M o d e l
To depict the observables in relativistic heavy ion collisions, expanding
fireball model is used. This picture is supported by the following two
features.
(1) As mean free paths of the interactions (~ 1.5 fm) are short enoughcompared with the size of the nucleus (~ 14 fm for lead nucleus). This
leads the multiple interactions of emitted particle.
(2) Average (transverse) kinetic energy (> 100 MeV) of the emitted
particles from fireball is much larger than binding energy of nucleus (~8 MeV per nucleon). Therefore the fireball cannot keep stationary
within a certain volume, but expanding.
When expansion proceeds, the interactions among emitted particles
decreases. And when the interaction is ended, the situation is called freeze
out.
In the heavy ion collisions the slope are different for the different particle
species as already shown in Fig. 4. And the collision system dependencies of14

slope as a function of particle mass are shown in Fig. 7. Horizontal axis is
the particle mass and the vertical axis is the inverse slope parameters in mt
spectra. As low mt enhancements exist for the pion spectra, only the region
above 0.2 GeV in transverse kinetic energy is used for the fitting. For proton- proton collisions the slope is similar for all particle species, while increase
oft of the system size, the difference becomes larger.

Fig. 7: Observed exponential slope, T, in transverse kinetic energy with respect to theparticle mass.

The increase of the inverse slope can be interpreted by assumption the
expanding thermal fireball. Namely, phenomenological relation in thefollowing is applicable.

T ~ T0 + m⋅ β2,where m is the particle mass, T0 corresponds to a temperature at thermal
freeze out, and β corresponds to a collective radial expansion velocity.
In the expanding fireball model, single particle spectra and two particle
correlation is studied.
(A) Single Particle Spectra
To evaluate the temperature and the collectivity, single particle(transverse kinetic energy) spectra at mid rapidity in 158 A GeV Pb + Pb
central collisions are studied. Fig. 8 shows invariant differential yield of
15

protons, positive kaons, and positive pions. The horizontal axis is transverse
kinetic energy in GeV. The solid line is a parameterization by thermal freeze
out temperature, T, and collective (radial) velocity, <β>, [SSX-98]. The valuesof parameters are T = 139 MeV and β = 0.42c, which are common to protons,
kaons, and pions. While the low mt regions of pion cannot be described, thisparameterization tends to follow the differences of the inverse slopes among
different particle species.

Fig. 8: Single particle spectra parameterized by temperature and collectivity (Temper a ture,
T = 139MeV; Collective velocity (radial) β = 0 . 4 2 c [S S X-98]).

(B) Two-Particle Correlation
For the interpretation of the correlation function, emission function,
S(x,K), is used. The (Wigner) emission function is the quantum mechanicalanalogue of the classical phase-space distribution which gives theprobability of finding at space-time point x as a source which emits freeparticles with momentum-energy, K. The correlation function is rewrittenrrwith relative momentum, q , and mean momentum, K, as follows [W +-98].

16

za f 2,z a f

d 4 xS x , K e iq⋅ x
r r
C q, K ≈ 1 +2
d 4 xS s, K

d i

where
r 1 r rr r
rq ≡ p1 − p 2 , and K ≡ p1 + p2 .
2bg

By assuming a finite expanding source,a f

LM K ⋅ ua xf OP
a2π f3 2π a∆τ f2 N T Q
22Lτ − τ 0g
η − η0g Obbr2
× exp M −MN 2a∆τ f2 − 2 R2 − 2a∆ηf2 PPQ ,MT cosh(η − Y )S x, K =× exp −

The first term specifies the shape of the freeze-out hyper surface, the second
term is a Lorentz-covariant Boltzmann factor encoding the assumption of
local thermal equilibration superimposed by collective expansion. The third
factor represent a purely geometrical interpretation. And the values usedhere are derived as follows.
1
1+ β l1t+z
MT = m2 + KT 2 , τ = t 2 − z 2 , Y = ln
, and η = ln
.
2
1− βl
2
t−z

FG
H

IJ
K

F I
H K

For the expression of thermal equilibrium in Lorentz-covariant way, thefollowing parameterizations are used.

bg

K µ = MT cosh Y , KT , 0, MT sinh Y , and

af

a f
af

af

af
af

x
u µ x = ( cosh ηl τ , η cosh η t r , sinh ηt r ,rysinh η t r ,sinh η l τ , η cosh ηt r ) .
ra f

By assuming a linear profile of the transverse flowaf

ηt r = η f ⋅F rI ,
H RK

where η f is the transverse flow velocity strength, the scalar product in thesecond term of the emission function is rewritten as follows,K ⋅ u x = M T ⋅ cosh η − Y ⋅ cosh ηt r

af

a

f
x
− KT ⋅ ⋅ sinh ηt a r f
r
17

af

From KT (or MT) dependence, the strength of the collective flow, η f , isderived. Fig. 9 shows the MT dependence of the transverse radius, RT. For
different collective flow strength,η f , dependences are shown.

Fig. 9: M T dependence of transverse radius, R T , for different strength of the co llect flow, η f( M ⊥ a n d R ⊥ i n t h e f i g u r e a r e M T a n d R T b y n o t a t i o n s i n t h e t e x t , r e s p e ctively) [W + -98].

Average collective radial velocity,

β , is evaluated as

β ~ 5 4 ⋅ η f [P e -97]in the considering region. Fig. 10 shows the relation between the collectivity(η f ) and temperature (T ) for the measured negative charged particles. The
solid line and the dashed lines correspond to the most probable relation andone sigma deviation, respectively. For the comparison, single particle
measurement result for the negative charged hadrons is also shown. One
sigma deviation from the χ2 minimum is shown as the solid line surrounding
slant region. The common region for the two particle correlation prefers T ~140 MeV and <β > ~ 0.42. The temperature and the collectivity are wellagreed with results evaluated from different particle species in single
particle spectra.
One should note that for the extraction of the collectivity and thetemperature, low mt region of the pion spectra is not included. The reason
for the enhancements should be studied.

18

Fig. 10: [Solid line] Two- particle HBT correlation measurement for negative charged
part icles parameterized by temperature (T ) and collectivi t y (ηf : Transverse flow velocity
strength). Note that average collective radial velocity is <β > ~ 5/4

ηf . The dotted lines

correspond to one sigma deviations. [Dashed line] For the comparison, single particle
m e a s u r e m e n t result in one sigma deviation from χ 2 minimum is shown for the negative
charged part icles. The common region with two particle correlation prefers T ~ 140 MeV
a n d < β > ~ 0.42 [P e -97].

1.3 D e l t a R e s o n a n c eCollisions of relativistic heavy ions do not simply consist of nucleon nucleon collisions. To take the difference into account, an idea with excitednuclear is introduced (sect. 1.3.1 ). As mentioned in section 1.2.1 , the failureof thermal model with collective expansion in low mt region of pion spectra
should be addressed in study of heavy ion collisions, and as a possible
solution delta resonance is introduced (sect. 1.3.3 ). First experimental
measurement of the delta resonance yield in relativistic heavy ion collisions
at 158 A GeV Pb + Pb central collisions is introduced (sect. 1.3.3 ).

19

1.3.1 D e l t a R e s o n a n c e i n R e l a t i v i s t i c H e a v y I o n C o l l i s i o n s
Relativistic heavy ion collisions does not simply consist of nucleon nucleon collisions by the following viewpoint. Fig. 11 shows schematic
picture for the heavy ion collisions in center of mass frame. Colliding heavy
ions are shown by ellipses (T as target, and P as projectile) due to theLorentz contraction in incident momentum direction (shown in arrows). The
constituent nucleons (some of them as examples) are shown in circle inside
the ellipses. As explained in sect. 1.1 , the constituent nucleons are mainly
colliding with the nucleons in the direction of the incident momentum. In
the Fig. 11, the drawn constituent nucleons are mainly colliding with
nucleons surrounded by the two dashed lines. One should note that the firstpair of nucleons (shown as circles filled in black) are colliding each other,and during collisions with next constituent nucleon (shown as hatchedcircle) the nucleons are still kept to be in certain excited states for particle
formation.

Fig. 11: Schematic picture for the relativistic heav y ion collisions in center of mass frame.
The projectile nucleus (P) and target nucleus (T) are Lorentz contracted (in 1/ γ ) in incident
m omentum direction (shown in arrows) (see text for detail).

By the following comparison in time scale, importance of excited nucleus,
like nucleus including ∆(1232), can be demonstrated.
(1) Collision time for each constituent nucleon (∆tcol(constituent) ):20

The collision time for each nucleon, ∆tcol(constituent) , is comparable or shorter
than particle formation time, ∆tform.. The collision time in total, ∆tcol, is < 1
fm/c due to the Lorentz contraction, and the number of constituent nucleons,
N(constituent) , in incident momentum direction is about 4 for the lead nucleus.
Therefore by using following evaluation,∆tcol(constituent) ~ ∆tcol / N(constituent) ,a typical time for the collision per constituent nucleon, ∆tcol(constituent) , is 1/4
fm/c.
(2) Typical particle formation time (∆tprod):
Theoretical consideration in QCD give typical time for particle production,∆tprod, is of the order of 1 fm/c [e.g. GR-93].
By comparison of the above two time scale,∆tcol(constituent)∆tprodafter collision of the first pair of constituent nucleons, the collisions withnext coming constituent nucleons is not any more a simple nucleon - nucleon
collision. Projectile nucleons in subsequent collision might be in "excitedstates".
To describe such collisions in the intra nuclear cascade calculation,
resonance state of nucleon was introduced as a zero-th order approximation.
At the AGS experiments, many theoretical model calculations with suchtreatment are shown to be successful explaining the experimental data. The∆(1232) is the lowest energy level in nuclear resonance with mass of about
1232 MeV/c2, width of about 111 MeV, and corresponding lifetime of about
1.8 fm in free space. Isospin and spin of ∆ resonance is both 3/2, and there
are four charge states (∆++, ∆+, ∆0 , ∆ ). Based on these arguments,
measurements of ∆ resonance yield is awaited for the direct confirmation of
the model calculation.
1.3.2 L o w m t E n h a n c e m e n t a n d D e l t a R e s o n a n c e
As shown in Fig. 8, expanding fireball picture explains single particle
spectra for different particle species and two-particle correlation, withignoring low mt enhancement in pion spectra.
As described in the previous section, excited state of nucleon is one of the21

major features of nucleus - nucleus collisions. Thus decay product of suchresonance have to be taken into account in addition to the thermal withcollective expansion for particle production in nucleus - nucleus collisions.
The delta resonances contribute in this low mt region because of the decay
kinematics. Delta resonance has a lifetime of 1.8 fm/c (in free space) anddecays into pion and nucleon with more than 99% of decay branch as,> 99%∆  
→ π + N .
Due to the large mass difference between pion (Mπ = 0.139 MeV/c2) andproton (Mp = 0.139 MeV/c2 ), pion carries less momentum. Fig. 12 shows anexample of the decay kinematics. The random decay of ∆(1232)'s with(transverse) momentum, pt, at 0.8 GeV/c, and rapidity, y, at 2.5 are shown.
It is clearly shown that momenta of pions are much smaller than those of
proton. Thus ∆'s pion contributes dominantly to the low pt (mt) region.

Fig. 12: Example of the decay kinematics of ∆ resonance. In this example, ∆'s at p t ~ 0.8
G e V / c a n d y ~ 2.5 (note that ∆y is Lorentz invariant) are decayed randomly. Phase space inthe transverse momentum, p t , for daughter pions tends to be lower than that of ∆'s orprotons.

For the reason of the low mt enhancement, other possibilities should beconsidered, too. An example is Coulomb effects. Due to the highly
concentrated charge owing to net protons, positive and negative pions areaffected repulsively and attractively, respectively. Such kinds of othereffects on low mt enhancement are discussed in section 5.3.2 .
1.3.3 D e l t a R e s o n a n c e M e a s u r e m e n t a t S P S E n e r g y
Though in relativistic heavy ion collisions at SPS energy the excited statesof nucleons should be created and expected to play important roles,
experimental measurement of the ∆ yield has not yet been carried out before,
22which is mainly done due to experimental difficulties described below.
The WA98 collaboration measures the yield of double charged states ofdelta resonance, namely ∆++. The advantage of the double charged states isthat both of decay products, proton and π +, are suitable for precise detection
by the magnetic spectrometer. Due to the same charge polarity, thesystematic error in the detection of the identified particles is reduced (seesection 4.1 ). The yield of the ∆++ resonance is measured in the invariant
mass of pπ + pairs. The difficulty of the measurement, however, is large
fraction of combinatorial background. This is partially due to the limited
acceptance and dominantly due to the high multiplicity environments in therelativistic heavy ion collisions. The measurements of protons and pions
have been done by high resolution of magnetic spectrometer with the highcapability of particle identification by time-of-flight method (see sect. 2.2.2 ).
Those detectors are designed for the high multiplicity environments which
are unavoidable for relativistic heavy ion collisions.
1.4 T h e s i s M o t i v a t i o nThis thesis is motivated by the following points, which are introduced in
sections from 1.3.1 to 1.3.3 .
(1) Measurement of particle production of a new particle species; ∆(1232) in
158 A GeV Pb + Pb central collisions.
(2) The excited states of nucleons are one of the major characteristics ofrelativistic nucleus - nucleus collisions. As a prime approximation,
lowest states of nucleon, namely ∆(1232), is meaningful for theconsideration of excited states.
(3) The basic problem to understand both single particle spectra and HBTcorrelation, low mt pion enhancement is observed. By using the result of
explicit measurement of ∆ resonance, the contribution of ∆ to the low mtpion is acquired, and then it is aimed to get the footing of the validity ofthe expanding fireball model.
The author has contributed to the design of experimental detector(especially, time-of-flight counter (TOF) and optimal alignments ofchambers in magnetic spectrometer). He also has devoted in construction
and installation of detectors (mainly TOF and streamer tube detectors
23

(STD)). He has checked performances of TOF after the construction, andreadiness of readout electronics (STD). He has programmed operation
software (HV control code for TOF and monitoring code for STD). He has
operated detector and experiment (especially start counter, TOF, and STD).
He has calibrated the detector parameters (TOF, STD) and tuned
reconstruction routine (momentum reconstruction). He has produced mostof simulation data. And he has studied pion and proton spectrum, and yieldof ∆(1232) resonance.

242. E x p e r i m e n t a l S e t u p
To create hot and dense nuclear matter, a relativistic heavy ion collision at
the projectile energy of 158 GeV per nucleon has been provided by Super
Proton Synchrotron (SPS) at the European organization for nuclear research(CERN, "Conseil Europeean la Recherche Nucleaire" in French).
To explore the hot and dense nuclear matter, measurements of several
different signals are essential to specify the characters of the matter. As
such an experimental approach, simultaneously measurement of charged
hadrons and photons is done by WA98 experiment [W 98-91].
2.1 C E R N - S P S A c c e l e r a t o r
For relativistic heavy ion projectile, the CERN provides 158 A GeV
208Pb82+ (33TeV in total projectile energy) from 1994. As shown in Fig. 13 theacceleration and the charge stripping of heavy ion projectile are performedin several steps. For full description, see [A +-93].

Fig. 13: Accelerator complex at CERN.

25

2.1.1 I o n S o u r c e ( E l e c t r o n C y c l o t r o n R e s o n a n c e : E C R )In Electron Cyclotron Resonance (ECR) source shown in Fig. 14, which isbasically a plasma generator, the lead ions are created by evaporation of
from metal surface at a micro oven introduced and injected into plasmachamber.

Fig. 14: Electron Cyclotron Resonance (ECR) source.

Plasma is then created by microwave Radio Frequency (RF) ionization at
14.5 GHz. Longitudinal and radial confinement of the plasma is done by aset of two solenoids and by a permanent sextupole magnet. In theacceleration stage, the stripping of the electrons from lead ions is done bypassing the projectile through carbon foils.
2.1.2 L i n a c , B o o s t e r s a n d S y n c h r o t r o n s ( P S a n d S P S )Partially stripped 208Pb28+ projectiles are injected by the ECR source atthe energy of 2.5 keV/nucleon, and accelerated to 4.2 MeV/nucleon by Linear
Accelerator 3 (LINAC3). After stripping to 208Pb53+, the projectiles areaccelerated to 98.5 MeV/nucleon in Proton Synchrotron Booster (PSB), andto 4.25 GeV/nucleon in Proton Synchrotron (PS).
After the second stripping is done to fully stripped 208Pb82+, the projectiles
are accelerated to 158 GeV/nucleon in Super Proton Synchrotron (SPS). The
26

fully accelerated 158 A GeV 208Pb82+ projectiles are provided to WA98 on H3
beam line at nominal intensity of 106 Pb ions per 4.8 seconds of spill.
2.2 W A 9 8 E x p e r i m e n t
On the H3 beam line, the WA98 has following the apparatus, shown in Fig.
15, to measure and to find correlations among several different signals of
charged hadrons and of photons.

Fig. 15: Experimental setup of WA98 experiment in 1996.

For charged hadrons at mid rapidity, inclusive momentum spectrum,
Hanbury-Brown and Twiss (HBT) interferometry, and resonance yield ininvariant mass are measured by two arms (Arm-I consists of 6 MSACs and
RTOF, and Arm-II consists of 2 PADs, 2 STDs and JTOF; the name in italic
in this paragraph is explained in the following section) of magnetic
spectrometers with a dipole magnet. Each spectrometer has particle
identification performed by Time-of-Flight (ToF) method (by JTOF, TOF Arm-I,
and Start Counter).
For event characterizing, several global variables with full azimuthal27

coverage are measured. Forward and transverse energy by two calorimeters(ZDC and MIRAC, respectively), multiplicities of charged and neutral
particles at central region (by PMD and SPMD, respectively), and hadron
azimuthal distribution at target region (by Plastic Ball) are measured.
Energy (or momentum) and emission angles of photons in full azimuth atcentral region are measured by an electromagnetic calorimeter (LEDA).
2.2.1 T a r g e t
For target, 208Pb (thickness is 0.210 mm (239 mg/cm2 )) is used. Other
three kinds of targets (thicker 208Pb (0.436 mm; 495 mg/cm2), 93Nb(0.254
mm; 218 mg/cm2), 58Ni (0.250 mm; 223mg/cm2)) are also used. The summaryis in Tab. 1. For the thick and thin lead target, the interaction length isabout 1% and 0.5 %, respectively. Minimum bias cross section of each target
is shown later in section 3.6 .
TargetThickness(mm)

Thickness(mg/cm2)

208Pb

0.210
0.436
0.250
0.254

239
495
223
218

208Pb
58Ni
93Nb

Tab. 1: Target used at WA98 experiment.

2.2.2 M a g n e t i c S p e c t r o m e t e r
Charged hadrons at mid rapidity are measured by two arms of magnetic
spectrometers with a dipole magnet, including particle identification
capability performed by Time-of-Flight (ToF) method,
In this thesis the data taken in the 2nd tracking Arm (Arm-II) (For thehistorical reason, this is called the second. It is recently installed andoperated since 1996 for heavy ion beam) are presented. Arm-II is mainly for
positively charged particles, which consists of 2 planes of multi stepavalanche chambers with PAD readout system (PADs), 2 planes of Streamer
Tube Detectors (STDs) and a Time Of Flight detector (TOF) are
implemented. Geometrical acceptances for proton, π+ and ∆++ in the Arm-II
are shown in Fig. 16.

28

Fig. 16: Geometrical acceptances of proton, π + , and ∆ ++ in Arm - II of WA98 experiment intransverse kinetic energy, m t-m , and rapidity, y. Note that the rapidity o f center of mass at
the SPS energy is 2.9.

On the other side of the beam axis, the 1st tracking Arm (Arm-I), which ismainly for negatively charged particles are placed. Arm-I consists of 6planes of Multi Step Avalanche Chambers with Camera readout system(MSACs) with another Time Of Flight detector (TOF Arm-I) are installed.
2.2.2.1 M a g n e t : G O L I A T H
Magnetic field is created by a dipole magnet named GOLIATH. During
data taking for charge particles, 1.6 Tm of magnetic field was created. The
magnetic field is measured with Hall probes at 1.3ｘ106 points (in steps of
2 cm along the z-direction, and in steps of 4 cm along the x- and the ydirections).
2.2.2.2 P a d C h a m b e r : P A D
For the tracking, two planes of multi step avalanche chambers withelectronic pad-readout system (PAD-1 and PAD-2) [L TKG-98] are placed at Z B= 3,850mm and at ZB = 4,811mm, respectively. Each PAD is 1.2 m(horizontal) × 1 m (vertical) in size. Each PAD has 35,000 pads which
cover about 1 m (horizontal)×60 cm (vertical) active area.
Each MSAC has eight stainless-steel mesh planes made of 50μm diameter29

wires in 500 μm pitch, and covered by double mylar windows on both sides.
As schematically shown in Fig. 17, position detection of charged particles isperformed in following steps.

Fig. 17: Schematic drawing of the PAD chamber detector.

A charged particle traversing in the chamber ionizes the filled gas, which
is a mixture of Neon and Ethane (3%) in Ionization gap (I). The electrons
drifting in the 1st Amplification gap (A1) become an avalanche amplified up
to by a factor of 103. In a Gate gap (G), a reversed field of about 100 V/cm
prevents electrons drift through. It takes about 700 ns for electrons to reachthe gap G. During that time, a gate signal is made by trigger electronics andinvokes a pulse of about 200 V with 2 μs length on mesh 4 to change thedirection of the field. The electrons are then able to drift to the 2nd
Amplification gap (A2), which has slightly less amplification than the gap
A1. The last two gaps are for drifting, and mesh 7 and 8 are for protecting
and shielding the pad plane from sparks and pickups from the high voltage
gating of the chamber.
The electron clouds amplified in the multi step avalanche chambers by afactor about 1.5×105 are collected by 1mm (horizontal)×17mm (vertical)-size pads as shown in Fig. 18. The most probable charge for a hit is 160 fC,
which corresponds to 106 electrons. Active area is about 1 m (horizontal)×60
cm (vertical) on each PAD chamber.

30

Fig. 18: Schematic illustration of the pad plane.

Readout is done by chips directly mounted on the board. The chip reads 16
pads of induced charge. The chip consists of, from upstream of datatransmission, 16 parallel charge integrating amplifier, an analog
multiplexer [L CGKGT98], a 4 times amplifier, and a flash 6 bits
Analog-to-Digital Converter (ADC). A parity bit is added for consistency
check of data transfer to Digital Signal Processor (DSP) located on thebottom of the PADs (called detector DSP in order to distinguish from theother DSPs). Each detector DSP is for a column of 36 ADC chips andsuppresses zero data and adds 18 bits of address for non-zero data toidentify pad location. The non-zero data on each MSAC chamber aretransferred to a DSP (master DSP) located next to VME crate for the WA98
main data acquisition.
2.2.2.3 S t e a m e r T u b e D e t e c t o r : S T D
For the tracking, two planes of Iarocci-type Streamer Tube Detectors[I ar-93, B +-79] with electric pad-readout system (STD1 and STD2) are placed
at ZB = 6,311mm and at ZB = 7,811 mm, respectively. Capability of being
module and low cost performance through automatic production scheme,
and easiness of operation, STD becomes popular for larger coverage of
position detector. STD is also used as a charge particle veto detector forphoton detector on the assumption that it is negligible for high energy
photons to be converted into electron-positron pairs. Fig. 19 shows crosssection and outer dimensions of STD.

31

Fig. 19: Cross section view (top) and external dimension (bottom) of STD.

A tube consists of eight horizontally divided rooms made of poly vinyl
chloride (PVC). PVC is used for gas tight. Insides of PVC are covered bygraphite for electrical ground. Inactive area caused by walls between rooms
is 7% of total area. At the center of each room, an 100μm-diameter anodewire is placed. Positive 4.6 kV is applied on the wire during operation. The
wires are made of an alloy of cupper and beryllium plated with silver. The
STD is filled with one atmosphere of mixed gas consisting of 60% carbon
dioxide and 30% isobutane as quencher, and of 10% argon as avalanche gas.
The read out chips are modified from the original chip used for the charged
particle veto detector in the WA98 experiment. Basic architecture is thesame as one for the PAD chamber.
2.2.2.4 S t a r t C o u n t e r : S T R
Start timing for the ToF of the produced particles is measured by
Cherenkov light of a lead ion projectile in nitrogen gas (pressure: p = 1[atmosphere], refractive index: n = 1.0000297) [T su-96]. In advance ofphysics run, best radiator is investigated. After injection of 1.5×109 leadions, nitrogen gas has the least deterioration in PMT outputs (9 %), and we
32

conclude as the gas is the best radiator (see Appendix F).
The timing counter is located 3.4m up stream of the target and has two
section of radiator (from upstream, named STR1 and STR2, respectively).
Intrinsic time resolution of the timing counter is 30 ps regardless ofprojectile intensity up to around 3×105 projectile ions per second. Using
light yield information, events with double or more projectiles coming within
100 ns of window for timing measurement are able to be rejected.
STR1 has 30-mm length of radiator with readout by 1" diameter ofphoto-multiplier tube (PMT) (Hamamatsu photonics K.K., H5321-MOD).
The PMT has quartz window for transparency of Ultra Violet (UV) light, 10
dynodes. On the high voltage divider, booster capacitances at the last threedynodes with additional supplemental High Voltage (HV) power supplies
help high rate of detection of beam. The PMT has 0.7 ns of rise time, and0.16 ns of transit time spread.
STR2 has 45-mm length of radiator with readout by 2" diameter of PMT(Hamamatsu, H2431-02T). The PMT has quartz window for transparency of
UV light, 8 dynodes. The booster capacitances at the last three dynodes withadditional supplemental HV supplies are also used. The PMT has 0.7 ns ofrise time, and 0.37 ns of transit time spread.
At the windows of both PMTs, 30 % transmittance of neutral density filters
are installed in order to adjust the amount of photoelectrons.
2.2.2.5 T i m e o f F l i g h t D e t e c t o r ( i n A r m - I I ) : J T O F
Stop timing of the ToF of charged particles is measured by the JTOF
placed at ZB = 14,120 mm. The JTOF consists of 480 slats, 160 slats inhorizontal and 3 slats in vertical, of plastic scintillator (Bicron BC404,
characteristics are summarized at Tab. 2).
Physical ConstantLight output (% anthracene )Wavelength of max. emission
Decay Constant
Bulk attenuation length
Refractive index (n)

Value
68
408 nm
1.8 ns160 cm
1.58

Tab. 2: Characteristics of BC404 used for JTOF.

The light emitted in the scintillator is collected by two PMTs on the bothends. In order to avoid geometrical conflict among neighboring PMTs, twodifferent lengths of scintillator are used. In each of 160 columns, two of33

three slats are 637.7 mm long (named L) and the rest one is 433.9 mm long(named S). The order in a column is from top, the S, the L, and then the L(the SLL configuration) for the most inside column, the L, the L, and thenthe S (the LLS configuration) for the second inside, and the SLL
configuration comes for the third again. In that way, the SLL and the LLS
configuration come next to next column. After several times of lightreflection at the surface of scintillator [T C-94] and light guide on both edges
scintillation light is entered to the PMTs (HAMAMATSU R3478s). Fig. 20
shows the magnified view of the area around the light guide and cathode of
the PMT [Sa-95].

Fig. 20: Schematic drawing around light guide and cat hode of PMT.

Typical values for the characters of the PMT are, a factor of 3.9×106 for theamplification by 8 dynodes, 14 ns of transit time, 0.36 ns of transit time
spread, and 1.3 ns of anode pulse rise time by negative HV at the cathode.
Tab. 3 shows the summary of the specification.
Physical Constant
Wavelength of max. response
Current amplification
Anode pulse rise time
Electron transit time
Transit time spread (FWHM)

Value
420nm
〜10 6
1.3 ns14 ns
0.36 ns

Tab. 3: Characteristics of R3478s PMT.

34

With about 2 m of coaxial cable (Fujikura-RG58, 50 ohm impedance), anodeof the PTM is connected to custom-made Front End electronics Module(FEM). The input charge is passively split for a Time-to-Voltage Converter(TVC) with a on-board discriminator and for a charge-to-voltage converter
followed by a 64-clock-cycles pipeline analog memory unit (AMU) and a 12
bits of analog to digital converter (ADC). The AMU enables delay of AD
conversion for about 4.2 micro seconds without external huge amounts ofdelay coaxial cables. A Front End electronics Module (FEM) covers 16
channels of inputs from PMTs. In the TVC chip, which handles 4 channels,
two parallel paths per channel are implemented to subtract cross talk noise
inside the chip.
2.2.3 G l o b a l D e t e c t o r
To characterize the event, two hadronic calorimeters are implemented atzero degree (ZDC) and near the mid-rapidity (MIRAC).
2.2.3.1 M i d - R a p i d i t y C a l o r i m e t e r : M I R A C
For the transverse energy, a calorimeter named MIRAC (Mid-Rapidity
Calorimeter; while in 158 A GeV Pb + Pb colliding system, the coverage ismore forward in pseudorapidity of 3.5 <η< 5.5) are installed at 24 m
downstream from the target. Online event trigger corresponding to selection
in impact parameter is possible by hardware-weighted sum of the responsesof all towers in MIRAC.
The MIRAC consists of 30 stacks, each divided vertically into six 20 cm×20cm towers and segmented longitudinally into electromagnetic andhadronic section. The electromagnetic section is 15.6 radiation lengths deep,
and is constructed of alternating layers of lead (3-mm thickness) andscintillating plastic (3mm thickness). The hadronic section is 6.1 absorption
lengths deep, and consists of layers of iron (8-mm thickness) and scintillator.
The calorimeter has a resolution of 17.9 %/ (E/GeV) 1/2 for electromagnetic
energy and 46.1 %/ (E/GeV) 1/2 for hadronic energy. A ±5 cm vertical and ±20 cm horizontal opening around a beam pipe allow the projectile andprojectile spectators to pass through without interacting with MIRAC.
2.2.3.2 Z e r o D e g r e e C a l o r i m e t e r : Z D C
The forward energy flux is measured by Zero Degree Calorimeter (ZDC)
35

located 30 m downstream of the target. The ZDC is constructed of layers oflead and scintillating plastic, and is 105 cm×75 cm×202 cm in horizontal,
vertical, and longitudinal size, respectively. The ZDC is divided transversely
into 35 towers, 7 horizontally and 5 vertically, and each is instrumented
with a single PMT.

36

3. D a t a A n a l y s i s
To reconstruct momentum and to identify particle species, following
procedures are done.
(1) Clustering of hits on each tracking chamber(2) Track reconstruction(3) Momentum reconstruction(4) Track association to TOF(5) Particle identification
3.1 C l u s t e r i n g o f H i t s .
Each pad, sized 1×17 mm2 for PADs and sized 7×22 mm2 for STDs, isread out by 6 bits ADC. When ADC value is above a threshold value, it istreated as a fired pad. Adjacent fired pads are treated as a cluster. Fig. 21
shows number of fired pads in PAD1 and PAD2.

F i g . 2 1 : N u m b e r o f f i r e d p a d s i n c l u s t e r f o r P A D1 (top) and for PAD2 (bottom).

To reject accidental noise on adjacency pads, when three or more pads are
fired in a cluster, the cluster is used for tracking. As shown in Fig. 22, themost probable number of fired pads in a cluster which belongs to37

reconstructed track is 5 (a pad has 1mm in width), which is consistent witha 5 mm diameter acquired by simulation and bench test.

Fig. 2 2: Number of fired pads in cluster belonging to reconstructed tracks i n the trac k ing
system.

Fig. 23 shows number of fired pads in STD1 and STD2. As the pad size of
STDs is similar to region affected by ionizing particle traversing in thestreamer tube, cluster with 2 or more fired pads are used for tracking.

Fig. 23: Number of fired pads in cluster for STD1 (top) and STD2 (bottom).
38

Position (x for horizontal direction, and y for vertical direction) and theirvariance (σx and σy, respectively) of cluster are defined as follows:x=

1 N
xi ⋅ ai ( ≡ x i ),
A∑
i =1

y=

1 N
∑ yi ⋅ a i (≡ y i ),A i =1σ x = xi 2 − xi
=

2

FG
H

IJ ,
K

FG
H

IJ ,
K

1 N 2
1 N
∑ xi ⋅ ai∑ xi ⋅ ai −A i =1A i =1σ y = yi 2 − yi

2

2

1 N 2
1 N
= ∑ yi ⋅ a i −∑ yi ⋅ ai
A i =1A i= 1

2

N

where A = ∑ ai , a i is the ADC value of pad i, and N is number of pads
i =1

participating to the considered cluster.
3.2 T r a c k R e c o n s t r u c t i o nTrack reconstruction is done in 6 steps. From the 1st step to the 5th step,
track candidates are listed in the following steps from (1a) to (1e). In the 6th
step, among the track candidates, track is selected by the tracking quality
as shown in the following step (2). In this section, PAD-1, PAD-2, STD-1,
STD-2, and JTOF are called chamber 1, 2, 3, 4 and 5, respectively.
(1st step) For all combination of clusters from 2 in 4 chambers (chamber i,and chamber j) which is not positioned next to each other, make straight line,
lij. The relation between i and j is
j = i + 2 (where i = 1,2),
which yield the combination of (i, j) = (1,3), (1,4), and (2,4).
(2nd step) On different chamber (chamber k) from the 2 used chambers, findclusters around a crossing point with line lij.
(3rd step) If a cluster is found on the chamber k, deviations between the39

cluster and the crossing point (δxk and, δyk for horizontal and verticaldirection, respectively) are calculated as.

δxk = x k − xij k ,δyk = y k − yij k ,
→

→

where

x k and yk the cluster position on the chamber , and where xij k ,→yij k are the position of crossing point. If both 2 deviations, δxk and δyk→

are smaller than 7Rxk and 7Ryk, where Rxk and Ryk is expected deviationfrom position resolution of the chamber k.

δxk < 7 Rxk
δyk < 7 R yk
Tab. 4 summarizes difference of cluster position expected from the position
resolution of the tracking chambers and of JTOF.
Chamber
PAD-1
PAD-2
STD-1
STD-2
JTOF

k
1
2
3
4
5

Rxk (mm)
1.28
1.26
2.61
4.66
20.0

Ryk (mm)
2.10
2.25
6.95
7.71
50.0

Tab. 4: Deviation of cluster position expected from position resolution for the cha m bers andT O F i n A R M -II.

(4th step) Target image in y (which is not effected by magnetic field) is also
required to be less than 108 mm.
( 5 t h s t e p ) The minimum number of clusters used for tracking is 3.
For tracks satisfy the above criteria are called track candidates.
(6th step) For the track candidates, (i) χ2 values for tracking are calculated,and (ii) momentum and (iii) flight path length are reconstructed. The
candidates are sorted in ascendant order for the χ2 value. Track candidates
sharing the same cluster with other candidates with smallerχ2 are rejected.
40

3.3

M o m e n t u m Reconstruction and Flight Path Length Calculation

For the momentum reconstruction, 3 steps are performed. In the 1st andthe 2nd steps, general formula based on the relation between a momentum
kick and a charged particle in a magnetic field is applied. Then in the 3rdstep, especially for the negative px particles (namely, once going toward
ARM-I at the target, and then bending to ARM-II in the magnetic field), aMonte Carlo simulation is used to eliminate dependences of thereconstructed momentum on the polar and the azimuthal angles of theparticle trajectory. Flight path length is also reconstructed in the step 1a.

r(1st step) Momentum kick ( ∆p [GeV/c]) to a charged particle (charge q[e]) inra magnetic field ( B [T]) is generally given as follows:

z

r
r
r
∆p = 0.29979 ⋅ q A1 A2 B × ds ,

where

z

A1→ A2→

denotes an integration along the particle trajectoryr

beginning at a point A1 and ended at a point A2, ds denotes differential of
the trajectory. As in the WA98 experiment the magnetic field is generated invertical direction (parallel to the YB-axis (see WA98 coordinate system inAppendix D)) and the ARM-II spectrometer is well segmented perpendicular
to the YB-axis, momentum is reconstructed on the horizontal plane (XB-ZB
plane) as shown in Fig. 24.
Also flight path length is reconstructed as a sum of following threelengths, distance between target and A1, length of bending path (s), anddistance between A2 and JTOF.

41

Fig. 24: Schematic drawing for momentum reconstruction (on horizontal plane = on the
X B - Z B plane. Trajectory o f t h e particle: (Target →A 1 →s →A 2 →t h e n t o Second Arm ), A 1:e n trance point to magnetic field, A 2 exit point of from magnetic field, s : trajectory ofpart icle in magnetic field, C : center of extrapolated circle for trajectory,

ρ: radius ofe x t r a p olated circle for the trajectory, Δθ: bending angle of trajectory in magnetic field,
β :angle of trajectory measured by the second arm, O : center of magnetic field (i.e. origin of
W A 9 8 X B Y B Z B c o or dinate system), α: angle of A2 with respect to center O, Z 0 : distance
between target and magnet, R 0 : first order of radius of magnetic field. P (= P in = P out ):momentum of particle.

( 2 n d s t e p ) Momentum is reconstructed (p) by the following formula.

p=

42

∆p x
,
sin(∆θ )rwhere ∆p x denotes x-component of the momentum kick ∆p , and ∆θ isthe bending angle of the trajectory on the XB-ZB plane.
To calculate ∆p x , a straight line is extrapolated from the reconstructed
track with an assumption that the particle is coming from the target. In themagnetic field, the measured field values are referred at equally-divided 20
points (s(1) 〜s(20)) along the trajectory. Therefore ∆p x is calculated asfollowing:i = s( 20 )∆px = 0.29979 ⋅ ∑i = s(1) ( Byi ⋅ ∆zi − Bzi ⋅ ∆yi ),where By i , Bzi , ∆yi and ∆zi are the value at the points s(1) 〜s(20) forBy (y-component of magnetic field), Bz (z-component of magnetic field), ∆y(position kick in YB direction) and ∆z (position kick in ZB direction),
respectively. ∆θ is acquired from a geometrical calculation (see Fig. 24):

FG
H

a

R
∆θ = β − sin − 0 sin β − α
z0

fIJK

,

where α is an angle of A2 with respect to center O (O: the center ofmagnetic field, A2: an exit point of the trajectory from magnetic field), β isan angle of the trajectory measured by the second arm, R0 is the first orderof radius of magnetic field, and Z 0 is the distance between the target and themagnet.
(3rd step) To eliminate dependence of reconstructed momentum on the polar
and the azimuthal angle especially for the negative px particles, bestparameters are searched based on the following formula.

F p I F M11 M12 I F sinθ ⋅ cosφI
GG sinθ ⋅ cosφJJ = GG M 21 M 22 JJ ⋅ GJ,Hsin θ ⋅ sin φ K
H sinθ ⋅ sin φ K H M 31 M 32 K

Where Mij (i=1,2,3; j=1,2) is free parameters for lease dependence.

43

Fig. 25: Elimination of angle dependence for momentum reconstruction.

(left)

before correction, (right) after correction.

Fig. 25 shows the results of the correction, where the left and the rightfigure correspond to before and after the second step of the correction. Notethat negative px particles are plotted in the negative region of sinθcosφ for
the two top pictures (because px = p sinθcosφ).

44

F i g . 26: momentum resolution of Arm -II.

Fig. 26 shows the momentum resolution of the ARM-II. Polynomial fitting(up to second order) of the momentum resolution results in the following
equation.

σp. − 0.08 p + 0.06 p2 [%],
r ≅ 103p
where p is momentum in GeV/c. The typical values of= 2 GeV/c and ~2% at

σprr are ~1% at ppr
p = 5GeV/c. Degradation of resolution toward lower

momentum than about 1.8 GeV/c is mainly because of multiple scatteringsin the spectrometer. And degradation toward higher momentum than about
1.8 GeV/c is mainly due to position resolution of the tracking chambers.
3.4 T i m e o f F l i g h t C a l i b r a t i o nTiming chart of the timing measurement and the energy deposit
measurement at the JTOF is schematically shown in Fig. 27.

45

Fig. 2 7: timing diagram for the JTOF readout. The timing is measured as V T 3 and thee n e r g y d e p o s i t i s m e a s u r e d a s V Q 3 −V Q 1 .

Time of flight (TOF) of the charged particle is defined as a difference in two
measured timings. The one is measured by the JTOF (timing JTOF), and theother is measured by the start counter (timing Start);

TOF = timing JTOF − timing Start .
The time calibrations are done in the following 4 steps.
(1st step) To eliminate hardware channel dependence of conversion
parameter from the TVC value [channel] to time [ps], the timing at the start
counter and the JTOF are defined by the weighted timing TJTOF(J) (Jdenotes the slat of the JTOF) and TStart for the JTOF and the start counter,
respectively.

TJTOF ( J ) ≡TStart ≡bg1
k J 1 ⋅ TVCJ 1 + k J 2 ⋅ TVC J 2 ,
2

b

g

1
kS1 ⋅ TVCS1 + kS 2 ⋅ TVCS 2 ,2

These conversion parameters (ki ) are acquired at bench test using a quartz
clock generator, where i denotes the FEE channel (J1 and J2 for the JTOF,
and S1 and S2 for the start counter). Therefore the time of flight calibrated
in this step (TOF 1(J)) is following.
46

TOF1 ( J ) ≡ TJTOF ( J ) − TStart ,(2nd step) To eliminate cable length dependence for each slat, a time offset
for each JTOF slat (T01st(J) ) is derived by the following definition:

T01st ( J ) ≡ TOFπ ( J ) ,TOFπ ( J ) ≡ TOF1 ( J ) − TOFπ ( p , L) , andTOFπ ( p, L) ≡

L

F
I
c⋅G p
H mπ 2 + p2 JK,

where L and p is the evaluated flight path length and the reconstructed
momentum via track reconstruction routine. Therefore the time of flightcalibrated in this step (TOF 2(J)) is following.

TOF2 ( J ) = TOF1( J ) − T01st ( J ) .
(3rd step) To eliminate time walk effect through variation in pulse height(equivalent to QVC value here), a time offset parameters for each JTOF
FEE channel (TQ(J1),TQ(J2)) are derived by the following definition.

TQ ( J 1) ≡QVC ( J 1) ⋅ TOF2 ( J ) ,TQ ( J 2 ) ≡QVC ( J 2 ) ⋅ TOF2 ( J ) .

Therefore the time of flight calibrated in this step (TOF 3(J)) is following.

TOF3 ( J ) ≡ TOF2 ( J ) −TQ ( J1)
QVC ( J1)−

TQ ( J 2)
QVC ( J 2).

(4th step) To eliminate time dependence of the time conversion factor, thecable length and other factors, more time offsets (T02nd(run) for run
dependence, T02nd(slat) for slat dependence, and T02nd(FEE range) for
dynamic range dependence of FEE) are derived in the same way in step 2.

T02nd ( parameteri ) ≡ TOFπ ( parameteri ) ,TOFπ ( parameteri ) ≡ TOF ( parameteri ) − TOFπ ( p , L) ,47

where parameteri are run, slat, and FEE range.
This step is repeated for certain periods shown in Tab. 5 for each parameter.
And every step (step k to step (k+1), the time of flight is calibrated infollowing way.

TOFk + 1 = TOFk − T02nd ( parameteri ) .
Parameter
K
T01st
TQ
T02nd(run)T02nd(slat)
T02nd(FEE range)

Number(No.) of parameters
No. of FEE channel(960 for JTOF + 2 for Start)
No. of JTOF slat (480)
No. of JTOF FEE channel (960)1No. of JTOF slat (480)(No. of JTOF slat + 2 for start)×5 ranges(480 for JTOF + 2 for Start)×5

Cycle of calibration
Constant
Constant
Every 50 runs
Every run
Every 50 runs
Every 50 runs

Tab. 5: Time calibration parameters for JTOF and for start counter.

The y-position (height) at JTOF (YJTOF) is calculated by the time difference
between PMT located at the top and the bottom side of scintillators.

YJTOF ( J ) =v( J )⋅ ( TVC( J1) − TVC( J 2)) + YJTOF ,0 ( J ) ,2

where v(J) is the propagation velocity [mm/channel] of light in the
scintillator, , and YJTOF,0(J) is a y-position offset [mm]. The horizontal
position at JTOF (XJTOF) is a position where difference between an
extrapolated position from the tracking and a center of the scintillator isminimal. Tab. 6 shows the position calibration parameters for JTOF.
ParameterV
YJTOF,0Number(No.) of parameters
No. of JTOF slat(480)
No. of JTOF slat(480)

Cycle of calibration
Every 50 runs
Every 50 runs

Tab. 6: Position calibration parameters for JTOF.

Resolution of time of flight between the start counter and the JTOF is 85
pico seconds as shown in Fig. 28. And residuals for the hit position at JTOF
are 12.5 mm and 26.4 mm for the horizontal and vertical direction,
respectively.

48

Fig. 28: Time of flight resolution between the start counter and the JTOF.

3.5

Particle Identification

Mass of the particle (m [GeV/c2]) is reconstructed using the following
formula driven by the Lorentz transformation.

p = mβγ ,
where

β=
γ =

L
,
TOF ⋅ c11− β2.

And p [GeV/c] is momentum of the particle, TOF [sec] is the time of flight, L[m] is the flight path length, and c [m/sec] is the velocity of the light. From
those equations the TOF can be rewritten as a function of the path lengthand the momentum f1(L, p), or (square of ) particle mass can be rewritten as
a function of the path length, the momentum, and time of flight f2 (L, p,
TOF).

49

TOF = f 1( L, p)

L I m2 + p 2
F=
H c K ⋅ p2 ,or

m2 = f 2 ( L, p, TOF )2
RU|
TOF ⋅ cI
|
F
=p S
− 1V.
|TH L K |W
2

When we define expected time of flight (TOF π) for the pion (mass is mπ2) as

mπ 2 + p
LF
I
TOFπ ≡ G
H c JK ⋅ pmeasured2

reconstructed2,

reconstructed,where Lmeasured is measured flight path length and preconstructed is thereconstructed momentum. And we take difference between the measured
time of flight (TOF measured), the clear separation among particle species isseen in Fig. 29.

F i g . 2 9 : R e l a t i o n b e t w e e n T O F m e a s u r e d −T O F π a n d m o m e n t u m .

Then we derive particle mass (mreconstructed) as follows,50

mreconstructed = preconstructed2

2

R|F TOFS|GH LT

measured ⋅ cmeasured

IJ − 1U|V
K |W
2

.

Fig. 30 shows mass square distribution of positive particle with momentum
lower than 3.5 GeV/c measured in the Arm-II.

Fig. 30: Mass square (GeV 2 /c 4 ) distribution of positive particle with momentum lower than
3.5 GeV/c measured in the Arm -II.

And the resolutions of mass square are shown in Fig. 31 for π + and proton.

Fig. 31: Mass square resolution for the positive pion and proton.
51

3.6 E v e n t S e l e c t i o n
To choose central collision events, transverse energy measured by thehadronic calorimeter MIRAC, ET, is used. For hardware scheme of MIRAC,
see section 2.2.3 .1 . The top 10 % of minimum bias events in the order of the
ET are used in this analysis. The minimum bias events, MB, are defined by
the following coincidence logic made by four detectors.
MB ≡ Halo ∩ STR ∩ Veto ∩ MIRAC( low )Here, Halo, STR, Veto, and MIRAC (low) represent detection by a halo
detector, the start counter (see 2.2.2.4 ), a veto detector, and the MIRAC
calorimeter, respectively. And bars above Halo and Veto represent
anti-coincidence. The inner halo counter is a scintillation counter with ahole in its center, which is located about 5.7 m upstream of the target inorder to detect interaction in upstream. The veto detector is a scintillation
counter located about 50 cm down stream of the start counter in order todetect off-axis beam. For MIRAC (low) , threshold is set as low as possible todistinguish from noise.
The minimum bias cross section, σINT [mb], is defined as follows.
N INT ⋅ 1027
Nbeam ⋅ ρ ⋅ tHere, NINT and Nbeam are the numbers of interaction and beam, respectively,
ρ [cm-3] is the numbers of nuclei per unit volume, and t [cm] is the target
thickness. To correct target-out background, NINT should be replaced with
NINTcor calculated as follows.
Nbeam
N INT cor = N INT − N INT emp ⋅,Nbeam ( emp)
σ INT ≡

a f

where N INT(emp) and Nbeam(emp) are the numbers obtained for the empty target
runs. Tab. 7 shows the minimum bias cross section of the different target
used in WA98 experiment. The r.m.s. in the table denotes the root meansquare of run-by-run fluctuation.

52

TargetThickness(mm)

Thickness(mg/cm2)

Minimum Bias
Cross Section(mb)

Minimum Bias
Cross Section(Magnet on)
(mb)

208Pb

0.210

239

208Pb
58Ni

0.436
0.250

495
223

93Nb

0.254

218

6202±1(r.m.s.=58)−3599±5(r.m.s.=17)4332i±12(r.m.s.=24)6451±0.1(r.m.s. =53)−3704±3(r.m.s. =20)4496±2(r.m.s. =11)

T a b . 7 : M i n i m u m b i a s c r o s s s e c t i o n s o f f o r d i f f e r e n t t a r g e t s u s e d a t WA98 experiment.

3.7 I n v a r i a n t M a s s S p e c t r a
To measure ∆ resonance abundance, invariant mass spectra analysis isproceeded for proton-π + pairs. The accidental combinatorial background inspectra is evaluated by mixed event technique.
(a) Invariant Mass of Real Event
The yield of ∆ resonance is evaluated in invariant mass of real events.
For all the pairs of identified as proton and positive pion, invariant mass,
minv, is calculated by the following definition.

minv =dEπ + E p

i d
2

i

r
r 2
− pπ + p p .

Fig. 32 shows the invariant mass distribution for the real events. The pairsconsist of two components. One is the pairs decayed form the same Δ++
decay and the other is pairs essentially uncorrelated combinatorial
background.

53

F i g . 32: invariant mass distribution of identified positive pions and protons.

(b) Invariant Mass of Mixed Event
As the spectrometer covers a fraction of the kinetic phase space ofdaughter particles, not all the resonance can be reconstructed. Moreover,accidental combinatorial background contaminates resonance spectra. To
evaluate the background, mixed event technique is used. The accidental
combinatorial background is made by particles not decayed from resonance,by daughter particles (e.g. pion and proton for delta resonance) interacting
in momentum space after decay, and by daughter particles decayed fromresonance but without other corresponding daughter particles measured.
The accidental combinatorial background is evaluated by the invariant massof different event, hereafter called mixed event.
The invariant mass of mixed events is calculated as follows. Pions aretaken from an event and protons are taken form different 100 events withsame category of the centrality (central events as the top 10% of minimum
bias events). To extract the fraction of Δ ++ among pπ ＋ -pairs Npair , theassumption that the mixed event invariant mass spectrum has the same
shape as the combinatorial background in the real events. The mass
resolution of the pπ + is estimated from momentum resolution, and theabout a few MeV. A pion from an event and a proton from the other hundred
events which have similar centrality (about 10 % top of minimum bias event
measured by the hadron calorimeter MIRAC; E_MIRAC > 326.05 channel)
54and have the same local multiplicity in the spectrometer are used toevaluate combinatorial background. It is assumed that distribution of four
dimensional products of the pion's and proton's momenta not from the same
events are in similar shape with the distribution of the four dimensional
products of pianos and protons momenta not decayed from the same delta
resonance.
As described in section 4.1 , stable yield is extracted regardless of local
multiplicity in the spectrometer which follows the Poisson distribution. This
indicates dominant contribution of the background is accidental
combinations of pion and proton, and such combinations are evaluated by
the mixed events. And effects of two track separation are evaluated to besmall as the chamber resolutions (of the order of some mm) are smaller than
the nominal track distance (of the order of a few tens cm).
(c) N o rmalization of Mixed Event Spectra
The invariant mass of p p+ pairs, minv , defined as follows gives
resonances as peaks or enhancements in yields around their masses.

minv =d Eπ + E p i2 + d prπ + pr p i2

To extract delta yield, we assume that the invariant mass distribution,b g

f raw minv , is a sum of a combinatorial background and a resonance. We
evaluate the shape of combinatorial background by the mixed event
distribution,b g

f mix minv , with a normalization factor ε . Therefore theinvariant mass distribution is expressed as follows;b g

f raw minv = f ∆++bminv g + ε ⋅ f mix bminv g.

And the shape of the resonance is assumed to be expressed by a modifiedbgBreit-Wigner function, f B.W . minv ,m0 , Γ , as follows [H+-92];

55

b g

f ∆ minv = f B .W . ( minv ,m0 , Γ )
++

=α ⋅

q3
3

q +µ

⋅
3

1

F (minv. − m0 ) 2 + eΓ 2j I
H
K

,

2

where α is a normalization factor of Δ++ resonance yield, q is themomentum of the proton (or pion) in the rest frame of the pair, i.e. half ofrelative momentum, and μ = 180 (MeV). We assume m0 = 1.232 (GeV/c2),and Γ = 0.111 (GeV), which are the values in free space. The two
normalization factors, ε and α , are defined at the χ2minimum point in

the fitting.
Fig. 33 shows the extraction of Δ++ resonance yield by the subtraction.

Fig. 33: Subtraction to extract delta yield.

The extracted number of Δ++ per event by the subtraction is 0.022±0.010,
where χ2 /n.d.f. = 19.4 / 18 = 1.07. The about 45% of error corresponds to thestatistical fluctuation in normalization due to the similarity of invariant56

mass spectra between for real events and for mixed events. The details of
calculations are studied in section 4.1.1 . The extracted number of protons
per event is 1.080±0.010. The error corresponds to the statistical one. The
raw yields of proton and ∆++ per event in the Arm-II spectrometer are
summarized in the Tab. 8.

Number (raw)/spectrometer /event

Proton∆++1.080±0.010(stat.)0.022±0.010(stat.)T a b . 8 : R a w y i e l d s o f p r o t o n a n d ∆ + + p e r e v e n t i n t h e s p e c t r o m e t e r ( A r m -II)57

3.8 A c c e p t a n c e , E f f i c i e n c y , a n d D e c a y C o r r e c t i o n
For protons and positive pions identified by the time-of-flight method,transverse kinetic energy spectra are derived. Geometrical acceptance,chamber efficiencies, and particle decay correction is proceeded.
To evaluate geometrical acceptance and efficiency correction factor, aMonte Carlo simulation called GEANT [GE-93] was used. The process to
obtain the correction factors is described as follows.
(1st step) Generate a single track and make them traverse in the simulated
detector positioned according to the geometrical survey. The single tracks
are generated in random distribution in azimuthal angle, φ, momentum, p,
and cosine of the polar angle, cos(θ), are used for the kinetic value. The
random distributions are shown in Fig. 34.

Fig. 3 4: Distribution of tracks used for acceptance and efficiency correction. Randomd istribution in azimuthal angle, φ, m o m e n t u m , p, and cosine of t h e polar angle, cos(θ ), areused.

The physical reaction, like energy deposit, multiple scattering, andparticle decay, is simulated in the GEANT package. The decay effect of thepion is shown in Fig. 35 as a function of L/p, where L is the flight path
length in meter and p is the momentum in GeV/c. As mass difference
between pion and decayed particle, most of which is muon, large fraction(about 93%) of the decayed pions can be identified as pions.

58

Fig. 35: (Solid line and cross) Fraction of decayed pions which are identified as p i ons at the
TOF detector. For the comparison, fraction of decayed pion (dashed line) is shown. Notethat average flight path length from target to the TOF detector is 17.9m.

(2nd step) Store hits position for each chamber with consideration of
detector resolution. The resolutions are 0.5 mm and 1.7 mm for PADs inperpendicular and parallel directions to the Magnetic field, respectively.
And for STDs, 3.0 mm and 6.5 mm in the same manner of directions,
respectively(3rd step) Reconstruct the tracks with hardware efficiency of the chambers.
The chamber efficiencies are evaluated during the track reconstruction. The
efficiency is defined as a probability to find a hit around the track, which isreconstructed by the three chambers other than the examined one out of thefour tracking chambers. Namely,
εi ≡Number of tracks with hit on " the chamber i"
Number of tracks with hit on " all the 3 chambers other than the chamber i" or "4 chambers"

The efficiency for each chamber is shown in Fig. 36. The average chamber
hardware efficiencies are 83.2%, 79.7%, 90.7%, and 96.8% for PAD1, PAD2,
STD1, and STD2, respectively.

59

Fig. 3 6: Efficiency of the chambers in Arm -II. From top, for PAD1 (left) and PAD2 (right),
and in bottom for STD1 (left) and STD2 (right).

(4th step) Reconstruct momentum of the particles. The same reconstruction
routines as the real data are used. The procedure are already described in
section 3.3 .
(5th step) Acquire the geometrical and efficiency correction factor in eachbin, which is divided in the coordinate of rapidity, y, and transverse kinetic
energy, mt‑m. The widths of the bins for rapidity, ∆y, and transverse kinetic
energy ∆mt , are ∆y = 0.25 and ∆mt = 0.020 GeV. The correction factors areapplied to the real data in each (y, mt‑m) bin.
For the evaluation of delta abundance as a ratio to nucleon, measured
ratio is corrected acceptance and efficiency, and isospin symmetry in target
and projectile nuclei. For the Geometrical acceptance and efficiency
correction of the delta resonance, to reduce systematic error in the yield, thecorrection is applied to the ratio. The efficiency for Δ++ detection is the
product of the efficiencies for proton and pions. The tracking efficiency,
ktrack, is 0.79±0.02 both for the detection of track at least three of four60tracking chambers and for qualification of reconstruction. The particle
identification efficiency, kpid, is 0.60±0.02 both for the detection of JTOF
and for the qualification of identification. The geometrical acceptance factor,
kgeo, is 0.145±0.005 for the Δ ++/proton ratio for the limited azimuthal
coverage. About 3 % of the errors indicated here are statistical ones due tothe number of simulated tracks. Then from the raw Δ ++/proton ratio
tabulated in Tab. 8, corrected Δ++/proton ratio is calculated as 0.31±0.14.
About 45 % of the error here are dominated by the statistical fluctuation in
subtraction for ∆++ yield (for the error, see section 4.1 ). The error of thecorrections for geometrical acceptance and efficiencies are summarized in
Tab. 9.

Number (raw)/spectrometer /event

Proton∆++1.080±0.010

0.022±0.010∆++/ proton (raw)0.021±0.009

ε 1 (tacking in 3 cham. or 4 cham.)

0.79±0.02(0.79±0.02)2

ε 2 (particle identification)

0.60±0.02(0.60±0.02)2

ε 3 (geometrical)
Number (ε 1 , ε 2 , ε 3 corrected)/full-φ /event++∆ / proton (ε 1 , ε 2 , ε 3 corrected)

0.1127±0.0022

0.01634* ±0.00032

20.2±0.6

6.1 * ±2.7
0.31±0.14* indicates correction where proton is assumed to be in detector acceptance.

Tab. 9: Summary of acceptance and efficiency corrections for the ∆ ++ /proton ratio. The
errors indicated here are statistical ones.

3.9 I s o s p i n C o n s i d e r a t i o n
By using the measured ratio between ∆++ and proton (0.31±0.14, seesection 3.8 ), the abundance of the ∆ resonance is derived as a ratio withrespect to number of nucleon. In the correction the following assumptions
are taken.
The net baryons, namely proton and neutron, is taken into account. The
numbers of up-isospin, N↑,and down-isospin, N↓, are evaluated as follows.

61N = 2 ⋅ N p + Nn

A
NB = N p + 2 ⋅ Nn ,where Np and Nn denote number of net protons and net neutrons in incident
nuclei, namely lead ions, respectively. And for four states of the ∆ resonances
are taken into account as being proportional to the following factors.
3
F
NA I
N ++ ∝ G∆
H N A + NB JK
21FNA I F NB I
N + ∝G∆H N A + NB JK ⋅ GH NA + NB JK
12FN A I F NB I
N 0 ∝G⋅∆H N A + NB JK GH NA + NB JK
3F
NB I
N − ∝G∆H N A + NB JKThen, those factors are carried for all nucleons in lead ion with Np =82 and
Nn =126. Then the corresponding numbers to ∆'s are N∆++ = 41.4, N∆+ = 48.1,N∆0 = 55.1, N∆ = 63.4. At last the factor between N∆/Nnucleon and N∆++/Np
comes out to be 2.0. Therefore the isospin corrected ∆/nucleon ratio is 0.62±
0.28. The following Tab. 10 summarize the ∆++/ proton and ∆/nucleon ratios.
∆++/ proton (acceptance andefficiency corrected)∆/ nucleon (isospin corrected)

0.31±0.14
0.62±0.28

Tab. 1 0: ∆/ nucleon ratio corrected for isospin asymmetry. The measured ∆ + + / proton ratio isalso shown.

62

4. E x p e r i m e n t a l R e s u l t s
For proton and positive pion, transverse momenta are measured incentral Pb + Pb collisions. And ∆ resonance abundance with respect to the
nucleon is measured in proton-π + invariant mass in the 158 A GeV Pb + Pb
central collisions.
4.1 E r r o r E v a l u a t i o n
In the acceptance end efficiency correction, bins divided in mt and y withstatistical error within two percents are used. Especially at a few bins fromthe edge of the acceptance this requirement is applied. Therefore dominant
contribution of the statistical error in single spectra is coming fromstatistics of the real data in each mt -y bin. Also about 10% systematic error
for the efficiency due to high multiplicity is evaluated through the Monte
Carlo simulation. For the ∆++ yield, due to the similarity of invariant mass
spectra between the real events and the mixed events, the following
possibilities are studied for cause of error. One is statistical fluctuation of
the combinatorial background in the pπ + invariant mass. The other issystematic fluctuation of subtracted ∆++ yield as fitting method
dependences.
4.1.1 S t a t i s t i c a l F l u c t u a t i o n i n S u b t r a c t i o n o f C o m b i n a t o r i a l B a c kgroundThe error of Δ++ resonance yield, δ , is calculated by the following way.
The Δ++ resonance yield in the i-th bin of the invariant mass, N ∆++ (i ) , isgiven as follows.

N ∆ (i ) = N raw (i ) − ε ⋅ N mix (i ) ,
++

Eq. 1

where N raw (i ) and N mix (i ) are the number of pπ+ pairs in the i-th bin
for the raw data and for the mixed events, respectively.
We define error of the Δ++ resonance yield as a sum of errors in the i-th bins,

63

δN

∆ ++

(i ) . And the error is propagated by the partial differential of theEq. 1 as follows.

FG e (i) j2 IJ
HKF dδ N (i ) i2
I
GG
JJ
2
= ∑ i G +ε 2 ⋅ dδ N ( i ) i,J
GG +b N (i)g2 ⋅ bδ g2 JJ
ε
H mix
K

δ 2 ≡ ∑i δ N

∆ ++

raw

mix

where δ N raw (i ) , δ ε , and δ N mix (i ) are errors of N raw (i ) , ε , and N mix (i ) ,respectively. For evaluation of the δ ε , we use the following approximation.

N raw − N ∆
N mix
≡~
ε,

++

ε≅

where

N raw = ∑ i N raw (i )N ∆ = ∑ i N ∆ (i )++++N mix = ∑ i N mix (i )then δ ε is expanded by error propagation formula as follows.

F dδ N i2 I
GG
JJ
2
2
bδ ε g2 = FGH N 1mix IJK ⋅ G +eδ N j J ,
GG 2
JJ
2
GH + ~ε ⋅ dδ N i JK
raw

∆+ +

mix

where δ N raw , δ N∆+ +, and δ N mix are errors of

N raw , N ∆ , and N mix ,++respectively. Each of errors is evaluated from statistical fluctuation as64

follows.

dδ N (i) i2 = N raw (i),dδ N (i) i2 = N mix (i),dδ N i2 = N raw ,2
δe N j = N∆ ,dδ N i2 = N mix ,
raw

mix

raw

++

∆+ +

mix

We finally rewrite δ as follows.
δ 2 = N raw
+~
ε2N

mix

F b Nraw g + eN ∆+ + j + ~ε 2 ⋅ b Nmix gI
JJ ⋅ ∑ i ebN mix (i)g2 j+G2GHbN mix g
K
Eq. 2

The error of delta abundance,δN ++, is 45 %. Fraction of the three terms∆

shown Eq. 2 in the error is 50.0%, 49.9%, and less than 0.1%, respectively.
The first two terms are caused by the fact that large fraction of the
combinatorial background exists in the invariant mass of the real event.
The error is mostly dominated by the statistical fluctuation in the numberof Δ++.
4.1.2 Fitting Method
Background

Dependencein

SubtractionofCombinatorial

To evaluate systematic fluctuation in subtraction of combinatorial
background, fitting method dependences are studied. In the section 3.8 ,while whole the region in the invariant mass is used for the normalization,other method called tail method is also used.
The subtraction in the tail method is shown in Fig. 37. Horizontal axis isinvariant mass in GeV/c2. The insert shows subtracted peak of the ∆++65

resonance, and the mass, E0, and the width, Γ, of the resonance can bereasonably extracted. The fitted value of the mass and width are 1.237±
0.006 MeV and 0.086±0.014 MeV, respectively. The error shown in theinsert is only for fitting. The subtracted yield as ∆++ yield in the tail method
in an event is 0.021. The difference between the two methods innormalization (using whole region and using only tail region) is 4 % ofextracted yield.

Fig. 37: Subtraction of combinatorial back ground by tail method. Invariant mass spectra
for real events (filled circle) and for mixed events (open circle) are shown. The insert shows
subtracted yield of ∆++. The error shown is only for fitting.

4.1.3 D e p e n d e n c e o n L o c a l M u l t i p l i c i t y
The In the tail method, only the high invariant mass region is used for thenormalization of mixed event spectrum. This method may be sensitive to theshape of the tail region, the events are divided by the local multiplicity ofthe pions (Arm-II). Fig. 38 shows the local multiplicity, Nπ, distribution. The
solid line is the fitted line with Poisson distribution. From the distribution,
3% of the events are deviated. Average local multiplicity, <Nπ>, is 2.6.

66

Fig. 3 8: Local multiplicity, Nπ, distribution. Nπ is number of pion in the spectrom e ter(Arm -II). The mean value <N π> is 2.6.

For each local multiplicity, threshold dependences are studied. Fig. 39 shows
the dependence. The stable subtraction can be done for the lower threshold
below about 1.6 GeV in invariant mass, Minv. Less dependence on the local
multiplicity can also bee found. The subtracted yield in an event is 0.021
with fluctuation of 0.003. The difference among subsets of events divided by
the local multiplicity is 13 % of extracted ∆++ yield.

Fig. 3 9: Dependence on threshold valued of invariant mass in normalization for the tailmethod. Different histogram shows local multiplicity, N π, dependence.

674.2 T r a n s v e r s e M o m e n t u m D i s t r i b u t i o n
Transverse momentum distributions are usually presented in terms of theinvariant cross section. Study of the mt differential invariant yield(hereafter, simply called as the invariant differential yield) is important
singe this quality represents how much incident energy is transferred to theenergy of produced particles during collisions. Fig. 40 shows inclusivetransverse kinetic energy spectra for positive pions and protons in central
events. The centrality of the events is top 10 % of minimum bias as
described in section 3.6 . Filled circle and open circle represent positive pionand proton measured by WA98 experiment, respectively. For the comparison,
results by NA44 experiments are overlaid. Open triangle and open diamondmark represent positive pion and proton measured by NA 44 experiment,
respectively. Shapes of the spectra are similar with each other.

68

1
d2N
‑2
2π m t dy dm t (GeV )10 3

158 A GeV Pb + Pb centralπ+(WA98)
proton (WA98)π+(NA44)
proton (NA44)

10 2

10 1

10 0
0

0.2

0.4

0.6

0.8
1
m t ‑m (GeV)

Fig. 40: I n c l u s i v e m t spectra for proton and positive pion for 158 A GeV Pb + Pb central
c ollision (top 1 0% of minimum bias). (Closed circle: positive pion by WA98, Closed diamond:
proton by WA98). For the comparison, positive pion by NA44 (Open circle ), and proton by
NA44 (Open di amond) are shown.

The slope of the spectra is fitted with a single exponential as follows.

FH

1 d2 Nm −m⋅= N0 ⋅ exp − t
mt dmt dy
T

I
K

Eq. 3

Here N0 is a normalization constant and T is an inverse slope. These twovaluables are fitting parameters. Inverse slope for the positive pion above69

0.20 GeV in mt ‑ m is 142±3 MeV, and slope for the proton is 251±25 MeV.
NA44 shows 156±3 MeV for positive pion and 289±7 MeV [N44 -96]. Whenthe differential yield shown as Eq. 3 is integrated by mt, the rapidity density,
dN/dy, is evaluated as
∞
dN
d 2N
=
⋅2π mt dmt
dym 2π m t dmt dyz= 2π N 0 T (T + m).
For the rapidity density of the pion, approximation of spectrum by a sum of
two exponential is used as follows,

FG
H

d 2N
1
1 dN
m −m
=
⋅
⋅
⋅ exp − t
2π mt dmt dy 2π T1 T1 + m 1 + ω dy
T1

b

+

g

FG
H

IJ
K

IJ
K

1
ω dN
m −m
⋅
⋅
⋅ exp − t.
2π T2 T2 + m 1 + ω dy
T2

b

g

where T1, T2, w, and dN/dy are parameters. Evaluated rapidity densities
are 138±16 for positive pion, and 25±6 for proton. For the comparison,
NA44 shows the rapidity density as 155±10 for pion, and 27±5 for proton.
NA44 shows slightly higher inverse slope and rapidity density as theircentrality is slightly higher. As described in 3.6 , our centrality is top 10 %measured by hadronic calorimeter around mid rapidity. The data shown for
NA44 is top 3.7% measured by scintillation multiplicity counter (what theycall T0 counter, and the counter covers pseudo-rapidity range 0.6 ≤ η ≤3.3). Evaluation of corresponding impact parameter for NA44 is less than
4.5 fm [Ka-99], while evaluated value of the impact parameter for WA98 isless than 5 fm [Sc-98].
4.3 ∆ / N u c l e o n R a t i o
The yields of proton and ∆++, and correction factors are summarized in
Tab. 11. The errors in the table are statistical errors.

Number (raw)/spectrometer /event

Proton∆++1.080±0.010

0.022±0.010∆++/ proton (raw)0.021±0.009

ε 1 (tacking in 3 cham. or 4 cham.)

0.79±0.02
70(0.79±0.02)2

ε 2 (particle identification)

0.60±0.02(0.60±0.02)2

ε 3 (geometrical)
Number (ε 1 , ε 2 , ε 3 corrected)/full-φ /event

0.1127±0.0022

0.01634* ±0.00032

20.2±0.6

6.1 * ±2.7∆++/ proton (ε 1 , ε 2 , ε 3 corrected)

0.31±0.14∆ / nucleon (isospin corrected)

0.62±0.28* indicates correction where proton is assumed to be in detector acceptance.

T a b . 11 : B a r y o n y i e l d s a n d t h e s t a t i s t i c a l e r r o r s ( s e e t e x t )The errors including systematic errors discussed in 4.1 are summarizedin Tab. 12. The last column named Descriptions in the table shows thecorresponding section for the evaluation of the value. The ∆/Nucleon ratio is0.62 ± 0.28 (stat.) ± 0.16 (sys.), where stat. and sys. correspond to thestatistical error and systematic errors, respectively.

71

∆/Nucleon Ratio(Acceptance, efficiency
and isospin corrected)
Statistical Fluctuation in
Subtraction of Background
Uncertainty of
Tracking Efficiency
Difference inNormalization Method
Difference forDifferent Local Multiplicity

Yield and Errors

Descriptions

0.62±0.28 (stat.)±0.16 (sys.)

Section 3.9

0.28 [45 %] (stat.)

Section 4.1.1

0.06 [10 %] (sys.)

Section 4.1

0.02 [4 %] (sys.)

Section 4.1.2

0.08 [13 %] (sys.)

Section 4.1.3

Tab. 1 2: Summary of yield and errors of ∆ a b u n d a n c e a s a ∆/Nucleon ratio. For detail of thestatistical error (stat.) and the systematical error (sys.), see corresponding section shown in
the last column named Description .

72

5.

Discussions

In relativistic heavy ion collisions, excited states of nucleon are expected
to play important roles. First, in primary collisions of the constituent
nucleons, collisions may be different from nucleon - nucleon collision in freespace, which is primarily due to the short time interval of collisions (1fm/c). Participant nucleons collide at excited states. Second, the mean freepath (~1.5 fm) is shorter than the size of the nucleus (~ 7.1 fm for leadnucleus); re-scatterings of emitted particles also lead excited nucleons.
Experimental interest is how much fractions of constituent nucleons are insuch excited states. Direct measurement of lowest resonance, namely∆(1232) shed light on this information because the chance to the lowest
energy might be largest. Also by assuming two states of nucleons based on
the Ising model, a derivation of parameter corresponding to a temperature
is possible.
The effects of ∆ abundance to the inclusive spectra of pions need to bestudied. Especially for the SPS energy, as large fraction of the nucleons are
in resonance states at freeze-out, therefore the effect might be large. One
should note that the region where the enhancement of pion spectra is seen is
the low mt region where daughter pions from ∆ decay contribute. For theconsideration, other contribution like Coulomb effect should be compared.
5.1 Δ/ N u c l e o n R a t i o
As described in section 4.3 , the ratio measured in 158 A GeV Pb + Pb
central (top ca. 10 % of minimum bias) collisions is 0.62 ±0.28 (stat.) ±0.16 (sys.). The ratio shows about two thirds of the nucleons are in excitedstates at the time of freeze-out. Such fractions have been measured in lower
energy of nucleus - nucleus collisions at 95 A MeV [B +-96], and at 1 and 2 A
GeV [F OPI-97], and at 13.7 A GeV [E 814-95]. Fig. 41 shows the Δ(1232) ratios
over nucleon as a function of beam energy per nucleon. As the beam energy
goes higher, the ∆/nucleon ratio becomes higher. An increase of the error
bars in 13.7 A GeV and more in 158 A GeV reflects the difficulty of ∆resonance measurement in relativistic heavy ion collisions. This is because
larger fractions of combinatorial backgrounds due to the higher
multiplicities at higher energies.

73Fig. 41: the experimental ratio Δ(1232) / nucleons as a function of beam energy per
nucleon.

A simple description of excited nucleons using lowest nuclear resonancestates is applied to evaluate the temperature through the Ising model. Fig.
42 shows the schematic idea of the Ising model. A certain state of nucleus isexpressed by a combination of filled circles, where the circles represent
constituent nucleons. Two rows of circles correspond to the energy level of∆(1232) resonances and ground state nucleons, which are at the energy of m∆
and mN, respectively. Here m∆ and mN represent the mass of ∆(1232)
resonance and ground state nucleon, respectively. Out of N0 constituent
nucleons, N∆ of nucleons are in ∆(1232) state, and the rest of NΝ (=N0 -N∆)
nucleons are in the ground state. In the figure, an example state are shown
where 3 nucleons are in ∆(1232) state.
The temperature, TIsing, is derived from the ratio by two values. One isenergy difference, δE, and the other is entropy difference, δS, between two
kinds of nuclear matter. One is a fireball including ∆(1232) resonances andground states nucleons, and the other is a nucleus consisting of only groundstates nucleons. Namely, the relation is the following.

74

TIsing =δEδSFor the energy level, mass of the ∆(1232) resonance and ground state
nucleon, namely 1232 MeV/c2 and 938 MeV/c2, is used. When the measured
ratio is applied to the model, a parameter corresponding to temperature+95

gives 176 − 68 MeV.

Fig. 42: Schematic drawing of the Ising model for t h e resonance states. Two rows of circles
correspond to the energy level of ∆( 1 2 3 2 ) and ground state nucleon, which are in the energyof m ∆ a n d m N , respectively. The combination shown in filled circles represents a state ofn u cleus. Out of N 0 constituent nucleons, N ∆ of nucleons are in ∆(1232) state, and the rest ofN Ν (= N 0 -N ∆ ) nucleons are in the ground state. In the figure, an example state are shown
where 3 n ucleons are in ∆(1232) in state (see text).

5.2 Single-Particle Spectra and Two -Particle Correlation in Expanding
Fireball Picture.
During later stages of development of the nucleus - nucleus collision, thehadronic fireball expands. This is reasonable because the average(transverse) kinetic energy (> 100 MeV per nucleon) is much larger than the
typical binding energy (~ 8 MeV per nucleon). As the system expands,
frequency of interactions of particles in the fireball decreases. Wheninteractions cease, the situation is often called freeze out. Evaluation oftemperature at the freeze out gives information to reconstruct an equationof states of the fireball.
For experimental approaches, different kinds of observables are proposed.
75

As examples, inclusive single-particle spectra and two-particle correlations
are of prime interest. For the inclusive single spectra of transverse kinetic
energy, namely mt spectra, slopes are studied. When the fireball has
collective motion during the expansion, velocity of the collective expansion
affects the transverse spectra. Corresponding to a common expansion
velocity, the transverse kinetic energies for different particle species aredifferent due to the difference in mass. Therefore, to measure thetemperature and collectivity of the fireball, shapes of different particle
species are useful. Also two-particle correlations, like HBT effects, are used.
When collective motion exists, transverse radius measured through the
HBT correlation has mt dependences. From the study of mt dependencies, a
constrain on collective velocity and temperature can be obtained.
Though the low mt enhancement of pion spectra cannot be explained, theinterpretation with expanding fireball picture shows a consistentdescription with thermal freeze out at temperature, T, and a collective
radial expansion velocity, β, where an examples of the value are T ~ 139
MeV and β ~ 0.42c. Those values are used for mt spectra of kaons, protons,
and not-low-mt of pions and two-particle HBT correlations [SSX-98].
The fitted value to our single particle spectra of proton is 143±8 MeV for
temperature, and 0.40c±0.05c for the transverse velocity as shown in Fig.
43, which is consistent with the other experiment [SSX-98]. The
parameterization of the fit is the expression-1 in the section 5.3.2.3 , which
is used in the interpretation of for the pion spectra.

Fig. 4 3: Proton spectra with parameterization of the expanding fireball (dashed line. see
text for detail).
76

5.3 L o w m t E n h a n c e m e n t o f P i o n S p e c t r a
While the consistent interpretation can be achieved in expanding fireballpicture both for single particle spectra and for two -particle correlation, thelow mt region of pion spectra is not used to extract the temperature nor thecollectivity. The mt spectrum of inclusive positive pion is shown in the Fig.
44 for 158 A GeV Pb + Pb central (top 10 % of minimum bias) collisions. The
horizontal axis is transverse kinetic energy, mt-m, in GeV. And the verticalaxis is the invariant yield in logarithmic scale. The enhancement is easy to
see when the local slope is shown. Clear departure from a single exponential
shape is seen below 0.2 GeV. The local slopes are derived in neighboringdata points of the pion mt spectrum. The local slopes are plotted in theinsert of Fig. 44. Horizontal axis shows transverse kinetic energy at thecenter of the fitting region. A decreasing tendency of the local slope
parameters in lower mt region represents the low mt enhancement. While
rapidity and transverse momentum of our acceptance is correlated as shownin Fig. 16, difference of the pion yield in our acceptance is about 2.5%
[N49-99], which is within the marks of Fig. 44. It should be noted that
contribution of hard components is reported as enhancement in higher
region than about 2.8 GeV in mt−m0, in proton - nucleus collisions, andcalled Cronin effect [C +-75]. Therefore the effect from hard components issmall for the low mt enhancements discussed here.

77

3

10

0.2

1 d2N
2πm dydmtt‑2(GeV )

Local
Slope
(GeV)

0.15

2

10

0.1

0.05

0

0.2 0.4 0.6 0.8

1

10

π

m t ‑m
(GeV)

1

+

0

10

0

0.2

0.4

0.6

0.8

1

m t ‑m (GeV)

Fig. 44: Inclusive m t spectrum for positive pion in 158 A GeV Pb +Pb central collisions (top
10 % of minimum bias). The solid line is an exponential fit for the data above 0.2 GeV in
m t -m, and the dashed line is the extrapolation to the lower m t region. In the insert, local
slope parameters of positive pion as a functio n of center value of the fitting r e gion in m t mass (GeV) are shown.

5.3.1 P r o t o n - P r o t o n C o l l i s i o n
As a comparison, inclusive positive pion mt spectrum in mid-rapidity inproton - proton collisions at s1/2 = 23 GeV are shown in Fig. 45 [BS-75]. The
horizontal axis is transverse kinetic energy, mt-m, and the vertical axis is78the invariant cross section. The solid line is an exponential fit with χ2/ndf of
8.83/6. The inverse slope is 153±3 MeV. The mt spectrum is well describedin the exponential function. Although slight enhancement at < 0.2 GeV isseen even in proton - proton collisions, compared with nucleus - nucleus
collisions, this enhancement is much small.

Fig. 4 5: positive pion transverse kinetic energy s pectrum in proton - proton collisions at thec en ter of mass energy of 23 GeV [B S -75]. The solid line is an exponential fit with goodnessin χ2/ndf of 8.83/6.

5.3.2 S o u r c e o f L o w m t E n h a n c e m e n t
As candidates of possible source of the low mt enhancement, the following
mechanisms are considered in nucleus - nucleus collisions.
(1) Collective motion
In relativistic nucleus -nucleus collisions, hot and/or dense fireball79

regions are created. In the region, mean free paths for produced hadrons (~1.5 fm) are shorter than the size of nucleus (~ 7.1 fm for 208Pb nucleus).
And the (transverse) kinetic energy (> 100 MeV per nucleon) is muchlarger than the binding energy of nucleus (~ 8 MeV per nucleon due to thesaturation of nuclear force). Because of the kinetic energy large enough not
to be bound, and a short mean free path, it leads collective expansion of thefireball. The collectivity is expected to be commonly seen in different
particle species. From a naive relation of kinetic energy as mβ 2 where m isparticle mass and β is a velocity to characterize the collectivity, particle
species with lighter mass is affected in smaller kinetic energy. Therefore
for lighter mass particle like pions, enhancement is expected in low mt
region.
(2) Coulomb effectIn relativistic nucleus - nucleus collisions a large number of charged
particles are concentrating in an interaction region, and the net charge
must be positive. The transverse kinetic energy distributions of charged
particles are affected by the Coulomb effect. Most extreme case can beevaluated by the Gamov correction assuming all the charges of incident
nuclei are located at the collision point.
(3) Resonance contribution
In relativistic nucleus - nucleus collisions, produced particles are readily
excited. One of the reasons is short time interval of the primary collisionsof constituent nucleons. This enables the primary collisions in excitedstates rather than nucleon - nucleon collisions. And other reason ismultiple secondary interactions after primary collisions. The decay of theresonances especially resonance of the nucleons are contributing to the low
mt enhancement.
5.3.2.1

Collective Motion

In heavy ion collisions, high particle multiplicity and short mean freepaths result collective motion of participant nucleon and produced particles.
In such case, common features in transverse mass spectrum among different
particle species can be derived.
80

In order to evaluate effects of such collectivity to transverse spectra, oneof typical pictures, hydro dynamical description, is applied. Hydro
dynamical developments of the thermalized hot and/or dense system arebased on equations of state [SSX-98]. Fig. 46 shows transverse mass
distributions for protons, positive kaons and positive pions. Solid lines
represent hydro dynamical developments of collective system with a freeze
out temperature of 139 MeV and a collective (radial) velocity of 0.42c. And
the dashed line is a pure exponential line. As is expected, solid curve showsconcave shape, creating low mt enhancement relative to single exponential
shape. But still disagreement is seen in the low mt region of pions.

Fig. 46: Hydro dynamical description for three particle species (protons, K+ , and π + ).
D iscrepancy for pion is seen for lower transverse mass r egion [S S X - 98]. The dashed line forthe pion spectrum is an exponential line for eye guide.

81

5.3.2.2 C o u l o m b E f f e c t s
In the interaction region of relativistic nucleus-nucleus collisions, charges
of protons in the target and the projectile are concentrated. From thepositively charged source, negative pions get attractive forces, and positive
pions get repulsive forces [H i-99]. Fig. 47 shows invariant differential crosssection for the negative and the positive pions [Ka-99]. Both negative andpositive pions have much larger enhancements than the level of thedifference with each other. This means the main source of the low mtenhancements is different form the Coulomb effects.

10 3
1

π‑

(GeV ‑2 )π+

d2 N
2 π m dy dmttExponential

10 2

10 1

10 0
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
m t ‑m (GeV)

Fig. 4 7: Invariant cross section for the negative pion (crossing sign) comparing to positive
p i o n ( p l u s s i g n ) [ K a - 9 9 ] . F o r a n e y e g u i d e , a n e x p o n e n t i a l l i n e i s s h o w n as a dashed line.

For a closer look, the ratio between positive and negative pion is plotted in82

Fig. 48 [N44-96]. The difference from the unity in the experimental data(closed circle) is represented by considering Coulomb effects (open circle) ina cascade simulation, while without Coulomb effect (open triangle) such
representation is hardly possible. Therefore the Coulomb effect explains thedifference between positive pion and negative pion below 0.1 GeV, but thelarger enhancement seen below 0.2 GeV both for positive and negative pionshould be due to other reasons.

Fig. 48: Ratio of yield between negative pion and positive pion. E xperimental data (Closed
circle) and simulation (RQMD v.1.08) with Coulomb effects (Open circle). For thec o m p a r ison, the simulation without Coulomb effects are also shown (Tr iangle), where theslight difference from the unity is coming from acceptance effects.

5.3.2.3 C o n t r i b u t i o n f r o m R e s o n a n c e s
In the relativistic nucleus-nucleus collisions, excited states are readilycreated not only by the primary collisions, but also by the secondary
collisions. First insight of such effect is possible by taking the lowest state ofnuclear resonance, namely Δ(1232) resonances, into account. Pions decayedfrom the Δ resonances (Δ → N + π) are included in inclusive mt spectra.
Transverse kinetic energy of the daughter pion is much lower than that of
Δ resonances. This is simply caused by decay kinematics owing to large
mass difference between the nucleons (M Δ = 1.232 GeV/c2, and Mproton =0.938 GeV/c2) and the pions (Mpion± = 0.139 GeV/c2) (see Fig. 12).
To consider the contribution of Δ resonance, thermal source with83

collective velocity is assumed. The slope, T, of the resonance is assumed tobe the same as protons.
TΔ = T p.
++
The yield of Δ is evaluated by our measured ratio, NΔ++ /Np, as
dNΔ++/dy = (NΔ++/ Np ) × (dN p /dy),and the four charge states of delta are equally distributed as,
NΔ/dy = 4 × (dNΔ++/dy).
The yield of decayed pion from delta resonance are evaluated from following
procedure. Nucleon yield for 208Pb82 + 208Pb82 system is given as,
dN N/dy = (208/82) × (dN p/dy).
As four charge states of delta are decayed with following branching ratio,
Δ++ → p + π+ (100 %),Δ+→ p + π0 (50 %)→ n + π+ (50 %),Δ0→ p + π− (50 %)→ n + π0 (50 %),Δ− → n + π0 (100 %).
Ratio between π+ decayed from delta resonance and delta resonance, Nπ+Δ
/NΔ, is assumed as
Nπ+Δ/NΔ = 1.5 /4.
A factor, f1+ α, should be considered, where α is the ratio between
scat
Nπ+(∆ àp , π not-scat) and Nπ+(∆ àp not-scat, π not-scat), where the former Nπ+ isthe number of pion decayed from delta whose daughter proton of the pion
has re-scattered after the decay therefore the invariant mass hardly
evaluated as delta, and the latter Nπ+ is the number of pion decayed fromdelta whose daughter proton does not get additional re-scattering after
decay.
f 1+ α,where
αNπ+(∆ àp scat, π not-scat) Nπ+(∆ àp not-scat, π not-scat)and the value of α is about 1.5.
The shape of the enhancements is evaluated from the contribution of thedelta resonance decay. To consider the transverse kinetic energy dependenceof the factor, f, a cascade simulation JAM [N1-98, N2-98] is used, while thefactors are less dependent on the transverse kinetic energy. The contributionof the mesonic resonance is assumed to be close to the thermal spectrum.
84

The contribution of higher baryonic resonance is about a tenth of the lowest
resonance, the main ∆(1232) contributing is only considered. The results isshown in Fig. 49.
The single particle spectra, P1(mt,y), of pions from expanding fireball is
described as follows [N49-98, CSH-95]. It refers to the space-time source
function [H+-96] as was used for the correlation function described in section
1.2.3 .
P1 ( mt , y ) ∝ mt ⋅ R* 2 ⋅ ∆η *LM R a∆ηf − m a∆ηf OP
8T
N 2R
Q
L m + β bm − m g − 0.5 y OP ,× exp M−
MN T 2T bT + m β g a∆ηf + T m PQ
2

× 1+

2

*

2

*

t

t

4

t

*

G

2

2

2

2

t

2

2

t

t

t

E x pression-1
where

F
H

1
1
m
≡
1 + βt2 t
2
2
R*
RG
T

I
K

and
1
1
m
≡
+ t.
2
2
∆η *
T
∆η

a f

a f

Here T is the temperature, and β t is the transverse expansion velocity. And
RG is geometrical source radius which is assumed to be 6.5 fm and ∆η iswidth of source in the space-time rapidity, which is related to the width of
the rapidity distribution ∆y as follows.
T∆y 2 = ∆η 2 +.
mt

a f a f85

1 d 2 N (a.u.)m t dy dm t

10 3
――
●
■

10 2

Δ decay ＋ Thermal expansion(Thin:Upper and lower error)(Dash:Thermal expansion component)
π ＋ （WA98)
π ＋ （NA44)

10 1

10 0

10 ‑1

0

0.2

0.4

0.6

0.8

1

m t ‑m (GeV)
Fig. 49: Comparison of inclusive π + spectra at SPS energy. Closed circle, and closed squareshows experimental data by WA98 and NA44 [K a -99]. and thick solids line shows deltad ecay contribution plus a thermal source with expansion (2 thin lines are lower and upper
limits of error c o m i n g from uncertainty of delta measurement and uncertainty of
p a r a m eter in thermal plus expansion model). For the comparison, the dotted line shows
only con tribution from a thermal source with expa n sion.

Though the error is large due to the uncertainty of the determination ofdelta yield resulted from huge combinatorial background in the invariant
mass of the resonance, the shape of the enhancement is consistent with theexperimental measurement. A slight higher value in data than thecalculation might indicate contributions of the higher baryonic resonance866. C o n c l u s i o n s
We have presented the results of single particle spectra and direct measurementof ∆ resonance yield in pπ + decay channel in Pb + Pb collisions at the energy of 158
A GeV, at WA98 experiment using Super Proton Synchrotron (SPS) of the European
organization for nuclear research (CERN).
For systematic study of hadron production in relativistic heavy ion collisions
near mid rapidity region, we have constructed a magnetic spectrometer, called
Arm-II. It is designed for good particle identification capability under the cond itionof high particle density and for large momentum coverage in Pb + Pb collisions at
SPS. Using the data taken by the Arm-II spectrometer, single particle spectra and∆ resonance yield are analyzed.
For the single particle, we have carried out the analysis of transverse kinetic
energy spectra for π + and proton. By using single exponential fitting, inverse slope
parameter is 142±3 MeV (fitting region mt -m>0.2 GeV), and 251±25 MeV. In thetransverse kinetic energy spectra of pion, we have observed clear low-mt
enhancement.
We have evaluated ∆ resonance yield with pπ + invariant mass distribution.
Considering the isospin asymmetry in incident 208Pb82+ nuclei, ∆/nucleon ratio is
determined as 0.62 ± 0.28(stat.) ± 0.16(sys.). This ratio is larger than thosemeasured in the lower beam energies.
Motivated by partial success of collective expanding fireball model, which can
explain both single particle spectra and HBT correlation but cannot describe low mt
region in pion spectra, different kinds of contributions are considered. Those arecollective motion, the Coulomb effect, and contribution of ∆ resonance. As thecollective motion and the Coulomb effects are qualitatively smaller than theobserved low mt enhancement, the contribution of ∆ resonance is therefore studied.

Using the value of temperature and collective velocity, evaluated from single
particle spectra and HBT measurement, about 1.5 times more contribution
from ∆ resonance than measured in the invariant mass is used to follow the
shape of pion spectra. The factor is consistent with the results of a cascade
simulation. The simulation tells the factor comes from such ∆ resonancethat decays into proton which is re-scattered and pion which is, however, notre-scattered after decay, and those ∆ resonances are not measured in theinvariant mass.
87

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91

Appendix A: Relativistic Heavy Ion A ccelerators
To create and study states of matter at extremely high temperature andhigh density, relativistic heavy ion accelerator is operated at a few or more
GeV per nucleon in their center of mass energy. Tab. A-1 shows the current
status of the relativistic heavy ion accelerators.
Accelerator Laboratory
AGS

BNL

SPS

CERN

RHIC

BNL

Accelerated Nuclear
First
Nuclear s1/2(A GeV) Operation
16O, 28Si
197Au

16O, 32S
208Pb

197Au

5.4
4.8
19.4
17.4
130

1986
1992
1986
1994
2000

Tab A -1: Current status of relativistic heavy ion accelerators.

93

Appendix B: Examples of Calculation(1) Angular Momentum
To see applicability of the impact parameter, an example of angularmomentum calculation is shown for 158 A GeV Pb + Pb collisions in thecenter of mass frame.
Assuming impact parameter, b, is the radius of the lead nuclei, rPb,
assumed

b

=

rPb

~
~

1.2 ⋅ A1 3 ( fm ) ,7.1 ( fm )and incident beam momentum, p in, is 8.6 GeV/c (which is equivalent to Ein =8.7 GeV = s SPS 1/2 / 2 ),=F s I 2 − bm g 2
GH 2 JK N~

8.6 GeV / cassumedp

SPS,

angular momentum around the center of mass, |lc.m.| defined as (twice of) a
product of b/2 and p is calculated as follows.
assumedl c. m.

F b ⋅ pI
H2 K

≡

2⋅

~

60 GeV ⋅ fm / c .

The angular momentum, |lc.m.|, is much larger than the typical scale ofquantum effects, h ~ 0.2 GeV fm / c.
l c. m.

( ~ 60 GeV ⋅ fm / c )>>h ( ~ 0.2 GeV ⋅ fm / c )Consequently, the classical parameter such as impact parameter, b, isapplicable.
(2) Nucleon - Nucleon Coll isions as Primary Processes
To see the applicability of picture where primary process of relativistic
heavy ion collision (nucleus - nucleus collision) is nucleus - nucleus collisions,an example of calculations is shown for length comparison between de
Broglie wavelength of incident beam and nuclear size. The example is for94158 A GeV Pb + Pb collisions in center of mass frame.
The de Broglie wavelength, λdB, of incident nuclei ishc
λ dB ≡
p~ 0.9 fm .
And the size of lead nuclei, 2rPb, where is the radius, isot

2 ⋅ rPb ~ 2 ⋅ 1.2 ⋅ A1 3 ( fm )~14 ( fm ) .

The de Broglie wavelength is short enough than the size of the nucleus.
λ dB << 2 ⋅ rPb .
Consequently, collision unit is constituent nuclei, but not nucleus as awhole.
(3) Distinction between Participant Region and Spectator Region
To see the reasonability of distinction between participant region andspectator region, an example of calculation is shown for time comparison
between transverse direction and parallel direction with respect to theincident beam.
The collision time, ∆tcol, is in the order of 1 fm/c due to the Lorentz
contract. Note also that corresponding number of nucleons in the diameter
direction is about 4, and the collision time is for those plural nucleons.
The traversing time, ∆tT, for the nucleon with average transverse
momentum (~ 250 MeV/c, β ~ 0.25) to reach nucleon located in the next (~1.7 fm) perpendicular to incident momentum is about 7 fm/c.
The average transverse momentum after a nucleon - nucleon collision issmaller enough than longitudinal momentum to have following collisions
dominantly in tubular region in the same direction of incident momentum.
∆tcol, << ∆tTConsequently, geometrical distinction of participant region and spectator
region is applicable.

95Appendix C: Parameters Used in Relati vistic Kinematics
At high energy physics, kinetic parameters are chosen as, from theLorentz transformation,
E = γmp = mβγm 2 = E 2-p 2( γ = energy / mass, β = momentum / energy ).
where m is the mass of the particle, E is the total energy, p is themomentum.
Transverse momentum, pt , is the transverse component of p, and it isLorentz invariant.
The rapidity, y, is defined as,y ≡ 1/2 ln { ( E +p// ) / ( E ‑p// ) }In the case of non-relativistic limits (E >> p > p// ),y= 1/2 ln { ( E +p// ) / ( E ‑p// ) }= 1/2 ln { ( 1 +β ) / ( 1‑β ) }~ β.

In the case of relativistic limits (E ~p),y

= 1/2 ln { ( E +p// ) / ( E ‑p// ) }~ 1/2 ln { ( p +p// ) / ( p ‑p// ) }= 1/2 ln { ( p +p cosθ) / ( p ‑p cosθ ) }= ‑ ln { tan(θ/2) }Generally, ‑ ln { tan(θ/2) } is called pseudo rapidity, η.

96Appendix D: WA98 Experiment Coordinate System
In the coordinate where origin is center of magnet, and horizontal(positive in left side), vertical (positive in upward), and beam (positive indown stream) directions are XB, YB, and ZB, respectively, as shown in Fig.
D-1, the Arm-II is located in positive XB and the Arm-I is in negative XB.

F i g u r e D -1: WA98 coordinate system.

The position and the tilted angle with respect to the beam axis (ZB) of thestart counter, the target, the magnet and the tracking detectors are
summarized in Tab. D-1.
Arm

Detector

Start counter
TargetCenter of Magnet
PAD-1
PAD-2
ARM-II
STD-1
STD-2
JTOF
MSAC-1
MSAC-2MSAC-3MSAC-4

Position(the center for ARM-II, andthe inner edge for ARM-I)
XB (mm)
ZB (mm)0-6,6800-3,28000+1,233+3,850+1,396+4,811+1,637+6,311+1,995+7,811+3,595+14,120-1,156+3,175-1,504+4,130-1,938+5,322-2,372+6,51397

Tilted angle
from XB axis
(degree)
0
0
0
+14.6
+14.6
+8.6
+8.6
+14.6
-19
-19
-19
-19

ARM-IMSAC-5MSAC-6
RTOF-2,805-3,239-3,892+7,705+8,896+13,039

-19
-19
-19

Tab. D -1: Position of each detectors in WA98 magne tic spectrometers in (X B , Z B ) coord inate(refer Fig. D -1).

98

Appendix E: Other Detectors in WA98
We have other detectors in WA98 to measure simultaneous signals for thecharacterization of heavy ion collisions.
(1) Multi Step Avalanche Chamber: MSAC
In the Arm-I, there are 6 planes of multi step avalanche chambers haveactive area. First plane is a size of 1.2 ×0.8 m2 and the other five is sizes of
1.6 × 1.2 m2 (called "small chamber" and "big chamber", hereafter),respectively.
The chambers are filled with Ne and Ar based mixture with Triethylamine(TEA). As schematically shown in Fig. E-1, (the gap size and the applied HVvalue are shown in Fig. E-2) position detection of charged particles is donein following steps [R u-98].

Fig. E- 1: Schematic cross section of MSAC. W: double window with a flow of pure Argon, I:
ionization gap, A: amplification gaps, D: drift gaps, G: gate gaps, L: light gap, WLS:
wavelength shifter.

99

F i g . E -2: (Left) Gap size in the MSACs. (Right) Voltage setting for the MSAC.

The primary ionization is performed in the 11 mm long ionization gap (I).
The emitted electrons are directed with a low electric field to the first 4 mmlong amplification gap (A1). At the gap (A1), a strong electric generates anavalanche. The avalanche enters a 29 mm long drift gap (D1), which provide
time for the trigger decision. Next the electron cloud enters the first gate
gap (G1) where reversed electric field is applied except when a trigger comes.
A 450 V pulse with 1μs width is used for electrons to pass through and toreach the second 4 mm (for big chamber; for small chamber, 5 mm) longamplification gap (A2). The second gate gap is opened 1400 ns after the firstgate (G1) has been opened. Then the electrons traverse the last high electricfield of amplification gap (A3). Finally the electrons enter the 7mm longlight production gap (L) where a lower electric field favors the excitation of
the light emitting TEA molecules. In order to match the spectral sensitivityof the cameras, a Wave Length Shifter (WLS) plate is mounted after thelight production gap (L).

100

Fig. E - 3: Emission spectra for the TEA and the Wave Length Shifter (WLS), and a b sorptions p e c t r a f o r t h e C C D c a m e r a . T h e s p e c t r a a r e n o t n o r m a l i z e d with respect to the ot h ers.

The wavelength shifter absorbs 280 nm light emitted by TEA and emit 400
nm light as shown in Fig. E-3. The total number of produced photons aremeasured to be around 5×107 to 5×108.
(2) Time of Flight Detector ( i n A r m -I): TOF A r m -I
Time Of Flight detector in Arm-I (TOF Arm-I) is made of 480 (120 in width,and 4 in height) plastic scintillators (similar to NE110 plastic), which
results in an active area of 398 mm in width and 1920 mm in height. The
sizes of each scintillator are 32 mm in width, 480 mm in height, and 24 mm
in depth. On the both edge of scintillator, a photomultiplier (PMT) XP2972
is directly coupled via optical grease. Each analog signal from the lastdynode of PMT is, in time wise, discriminated by a leading edge
discriminators and is carried in 108 m to the counting house. The logicalsignal starts a overlap coincidence unit, and the trigger timing is used forthe stop of the overlap unit. The integrated charge as an output of theoverlap unit is digitized by ADC (LeCroy, LRS2280) with the conversion
parameter of 20 ps/channel, and typical time of flight resolution is about
100ps as shown in Fig. E-4.

101

F i g . E - 4 : R T O F r e s o l u t i o n ( σ T O F = 1 0 3 ±1 p s ) .

(3) Lead Glass Calorimeter: LEDA
For the photon measurements in region of 2＜η＜3, an electromagnetic
calorimeter LEad glass Detector Array (LEDA) is installed 21.5m down
stream of from target. The LEDA consists of 10,000 lead-glass modules, andeach module is made from a lead-glass block sized 40 mm (width)×40 mm(height) × 400 mm (depth) with PMT readout. The measured energy
resolution by 10 GeV electron beam is [P e -97]

b g = (5.5 ± 0.6)% + (0.8 ± 0.2)% .

σ E
E

E GeV

(4) Plastic Ball
For the charged particles around target fragmentation region (-1.7＜η＜
0.5, or 160°＜θ＜30°) in full azimuthal are measured by the plastic balldetector [G+-89]. The plastic ball consists of 665 Δ E-E modules, as
schematically shown in Fig. E-5.

102

F i g . E -5: Schematic view of the Plastic Ball detector.

Each module has a 4mm-depth CaF2(Eu) crystal as ΔE counter, and a
356 mm-depth plastic scintillator as E counter. ΔE-E measurement allows
identification of charged pions, protons, and heavier fragments (deuterons,
tritons, 3,4He). Protons up to 240 MeV are stopped in the plastic E counter.
Positively charged pion are measured and identified in the energy window of
11＜Eπ＋＜110 MeV via a coincidence tag from their delayed decay π＋ →μ＋＋ ν → e ＋ ＋ ν ＋ ν in the plastic E counter in addition to Δ E-E
measurement. In condition of high particle densities the plastic ball canresolve single particles nominally in the region of -0.7＜η＜0.1. The plasticball is useful for reaction plane determination [Ku-98, W 98-99].
(5) Silicon Pad Multiplicity Detector: SPMD
For the charged particle passing in 2.35＜η＜3.75, a circular pad detector
named SPMD (Silicon Pad Multiplicity Detector) is used [S t-98]. The
detector is a 300 μm n-type wafer implanted with p+ pads to create p-njunction. To fully deplete the silicon, 50V is applied across the junction.
When a charged particle traverse the silicon wafer, the energy loss invoke
electron-hole pairs (most probable value for energy loss is about 84 keV
which corresponds 24,000 electron-hole pairs). The liberated charge induces
a signal on aluminum pads, which is separated from p+ pads by dielectric.
The readout is done using the IDE VA-1 chip, which has a 128-channel
103charge sensitive amplifier and storage capacities.
(6) Photon Multiplicity Detector: PMD
At mid rapidity (2.4＜η＜4.4), photon multiplicity is measured by a large
photon multiplicity detector called PMD (Photon Multiplicity Detector). The
PMD consists of 3X0-depth lead converter sheets and 53200 pads of 3
mm-depth scintillator. The scintillator pads are sized in four manners from15(width)×15(height) mm2 to 25(width)×15(height) mm2, and arranged in
28 modules. Each module contains 1900 scintillator pads and coupled with a
CCD camera through wavelength shifting fibers and clear fibers (each pad iscovered by one wavelength shifting fiber followed by one clear fiber). Eachcamera consists of a 3 stage electrostatic image intensifier, a multi channel
plate and a Charge Coupled Device (CCD) with 31600 pixels. The total light
amplification is 4×104. Photon detection efficiency is about 80% for photons
with energy greater than 0.4 GeV, and the hadron contamination isestimated to be about 20%.

104

Appendix F: Selection of Radiator of Start Counter for Heavy Ion BeamIn advance of physics run, best radiator is investigated among following
tree materials. (1) Nitrogen gas in p = 1 atm. (n = 1.000297) and in 75 mm ofthickness (0.5 % interaction length) is for Cherenkov light radiator (named
RAD-1). (2) Quartz in 0.2 mm of thickness (0.5 % interaction length) is also
for Cherenkov light radiator (RAD-2). And (3) plastic scintillator in 0.5 mmof thickness (0.6 % interaction length) is for scintillation light radiator(RAD-3).
Name
Type
Description(n: refractive index)
Thickness
Interaction rate
PMT
Timing resolution
Charge resolution(ΔZ/Z)
Deterioration of
PMT output (*)

RAD-1 (used forheavy ion beam)gas Cherenkov
counterN2 gas, 1 atm.,(n= 1.000297)
up: 3.0 cm,
down: 4.5cm
0.5%
Up: H5321 -MOD
down: H2431-02T
30 ps
2.0%

RAD-2

RAD-3

Plastic scintillation
counter
scintillator: BICRON
BC404
0.5 mmquartz Cherenkov
countern = 1.45

0.6%
H2431
(glass window)
48-135 ps
> 5%

0.5 %
H2431-02T

17%

18%

9%

0.2 mm55 ps
2.6%(*) (Decrease of the PMT output during the exposure to 1.5×109 lead ions)Tab. F -1: Selection of radiator for heavy ion beam.

Tab. F-1 shows the summary of the results. After injection of 1.5×109 leadions, RAD-1 has the least deterioration in PMT outputs (9 %, 18% and 17%,
for RAD-1, 2, and 3, respectively; most of deterioration for RAD-1 is caused
by degradation of PMT itself because of its operation at the maximum
dynode currents; for RAD-2 and 3, additional radiation damages arecontributing). We conclude, therefore, RAD-1 is the best radiator.

105

Acknowledgements
I appreciate Prof. Dr. Y. Miake for providing me chances to makeresearches in this field of physics and showing me importance of steady
attitude for research. I thank Prof. Dr. K. Yagi for showing importance tohave both experimental and theoretical skill and understanding. I owe myexperiences in WA98 experiment to Prof. Dr. H. Gutbrod. By his strong
attitude for taking experimental data to get profound understanding, I
realize interests of experimental physics.
To Dr. T. Awes I thank very much for his direction as a devoted
spokesperson of WA98 collaboration. I should show my regards to Dr. S.
Nishimura for his hundreds of daily advices depending on my achievements.
I owe lots to Dr. K. Kurita for the basic attitudes for the young scientist.
From Dr. H. Gustafson, I learned how experiments need patience and steadyefforts, and I would like to appreciate him very much for the strong
direction for the new Arm-II spectrometer. Owing to Prof. Dr. R. Santo andProf. Dr. H. Lohner, I could experience a new experimental apparatus,
namely STD tracking detector, with responsible attitude. With very
experienced guide by Dr. B. Kolb, I experienced stable and robust software
structure both in DAQ and control of experiment. Also I cannot forget his
fair attitudes to defend for un-attending persons. I appreciate Dr. M.
Purschke for spending lots of time to persuade me things and encouragealmost every day. To Dr. T. Peitzmann I thank for showing faithful attitudes
in discussion. I need to show my deep regards to Prof. Dr. S. Nagamiya toassist and guide our collaboration from far institute. I feel lots from Dr. C.
Chi for careful attitudes in any kinds of situations.
I should show many thanks to Dr. M. Kurata, Dr. K. Chenawi, Dr. S.
Garpman, Dr. K. Enosawa, Mr. Y. Yokota, Ms. Y. Miyamoto, Dr. T. Chujo, Dr.
H. Sako, Mr. S. Kato, Ms. M. Aizawa, Mr. D. Hakozaki, Dr. Y. Nara, Mr. T.
Hirano, Mr. H. Hayashi and Ms. M. Hirose for encouragements and forspending time with me at Tsukuba and at CERN.
I cannot proceed with this thesis without experienced support by Mr. H.
Cunitz, Mr. Y. Au, Mr. N. Heine, Mr. H. Wolfgang, and technicians at NEVIS
laboratory and CERN laboratory. Especially to Mr. A. Przybyla I deeply say
thank-you for continuous encouragements. I like here to show myappreciations to collaborators of WA98 experiment.
107

I'm always happy with memories with my grand parents, Take Yamakawa,
Kaneko Sato, and cap. Yasuhiko Sato, who keep me doing things by myself
from very early childhood. I thank my elder brother, Kazuhiko Sato, whokeeps me away from stubborn attitude to things, and my younger sister,
Natsuko Sato-Fukunishi, who shows me an importance of smiling
continuously. I cannot complete this work without steady trusts from myfather, Tadashi Sato, and dedicated encouragements from my mother,
Satoko Sato.

108

PUBLISHED PAPER" ∆++ production in 158 A GeV 208Pb + 208Pb interactions at the CERN SPS "( Physics Letters B 477 (2000) 37 - 44 )109

23 March 2000

Physics Letters B 477 Ž2000. 37–44

Dqq production in 158 A GeV 208 Pb q208 Pb interactions
at the CERN SPS
WA98 Collaboration
M.M. Aggarwal a , A. Agnihotri b, Z. Ahammed c , A.L.S. Angelis d , V. Antonenko e,
V. Arefiev f , V. Astakhov f , V. Avdeitchikov f , T.C. Awes g , P.V.K.S. Baba h ,S.K. Badyal h , A. Baldine f , L. Barabach f , C. Barlag i , S. Bathe i , B. Batiounia f ,T. Bernier j, K.B. Bhalla b, V.S. Bhatia a , C. Blume i , R. Bock k , E.-M. Bohne i ,i
Z. Borocz, L. Carlen m , V. Chalyshev f ,¨ ¨ i, D. Bucher i, A. Buijs l, H. Busching¨
cenS. Chattopadhyay , R. Cherbatchev , T. Chujo , A. Claussen i , A.C. Das c ,M.P. Decowski r, H. Delagrange j, V. Djordjadze f , P. Donni d , I. Doubovik e,
S. Dutt h , M.R. Dutta Majumdar c , K. El Chenawi m , S. Eliseev o , K. Enosawa n ,P. Foka d , S. Fokin e, V. Frolov f , M.S. Ganti c , S. Garpman m , O. Gavrishchuk f ,F.J.M. Geurts l , T.K. Ghosh p, R. Glasow i , S.K. Gupta b, B. Guskov f ,˚ Gustafsson m , H.H. Gutbrod j, R. Higuchi n, I. Hrivnacova o, M. Ippolitov e,
H.A.
H. Kalechofsky d , R. Kamermans l , K.-H. Kampert i , K. Karadjev e, K. Karpio q ,i
S. Kato n , S. Kees i , B.W. Kolb k , I. Kosarev f , I. Koutcheryaev e, T. Krumpel
,
¨
o
r
n
n
f
k
A. Kugler , P. Kulinich , M. Kurata , K. Kurita , N. Kuzmin , I. Langbein ,p
A. Lebedev e, Y.Y. Lee k , H. Lohner, L. Luquin j, D.P. Mahapatra s , V. Manko e,¨jM. Martin d , G. Martınez, A. Maximov f , R. Mehdiyev f , G. Mgebrichvili e,´Y. Miake n , D. Mikhalev f , Md.F. Mir h , G.C. Mishra s , Y. Miyamoto n ,B. Mohanty s , D. Morrison t , D.S. Mukhopadhyay c , V. Myalkovski f , H. Naef d ,B.K. Nandi s , S.K. Nayak j, T.K. Nayak c , S. Neumaier k , A. Nianine e,V. Nikitine f , S. Nikolaev e, P. Nilsson m , S. Nishimura n , P. Nomokonov f ,J. Nystrand m , F.E. Obenshain t , A. Oskarsson m , I. Otterlund m , M. Pachr o ,A. Parfenov f , S. Pavliouk f , T. Peitzmann i , V. Petracek o , F. Plasil g ,W. Pinganaud j, M.L. Purschke k , J. Rak o , R. Raniwala b,
S. Raniwala b, V.S. Ramamurthy s , N.K. Rao h , F. Retiere j, K. Reygers i ,G. Roland r, L. Rosselet d , I. Roufanov f , C. Roy j, J.M. Rubio d ,H. Sako n , S.S. Sambyal h , R. Santo i , S. Sato n , H. Schlagheck i ,H.-R. Schmidt k , Y. Schutz j, G. Shabratova f , T.H. Shah h ,0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 2 2 4 - 0

M.M. Aggarwal et al.r Physics Letters B 477 (2000) 37–44

38

I. Sibiriak e, T. Siemiarczuk q , D. Silvermyr m,1, B.C. Sinha c ,N. Slavine f , K. Soderstrom¨¨ m , N. Solomey d, S.P. Sørensen g,t ,i
P. Stankus g , G. Stefanek q , P. Steinberg r, E. Stenlund m , D. Stuken
,
¨
o
m
c
e
M. Sumbera , T. Svensson , M.D. Trivedi , A. Tsvetkov ,L. Tykarski q , J. Urbahn k , E.C. van der Pijll l , N. van Eijndhoven l ,G.J. van Nieuwenhuizen r, A. Vinogradov e, Y.P. Viyogi c ,A. Vodopianov f , S. Voros¨ ¨ d, B. Wysłouch r, K. Yagi n,
Y. Yokota n , G.R. Young gaUniÕersity of Panjab, Chandigarh 160014, IndiaUniÕersity of Rajasthan, Jaipur 302004, Rajasthan, IndiacVariable Energy Cyclotron Centre, Calcutta 700 064, IndiadUniÕersity of GeneÕa, CH-1211 GeneÕa 4, Switzerlande
RRC ‘‘KurchatoÕ Institute’’, RU-123182 Moscow, RussiafJoint Institute for Nuclear Research, RU-141980 Dubna, Russiag
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6372, USAhUniÕersity of Jammu, Jammu 180001, IndiaiUniÕersity of Munster,D-48149 Munster,Germany¨¨jSUBATECH, Ecole des Mines, Nantes, FrancekGesellschaft fur¨ Schwerionenforschung (GSI), D-64220 Darmstadt, GermanylUniÕersiteit Utrechtr NIKHEF, NL-3508 TA Utrecht, The NetherlandsmLund UniÕersity, SE-221 00 Lund, SwedennUniÕersity of Tsukuba, Ibaraki 305, Japano
Nuclear Physics Institute, CZ-250 68 Rez, Czech Republicp
KVI, UniÕersity of Groningen, NL-9747 AA Groningen, The NetherlandsqInstitute for Nuclear Studies, 00-681 Warsaw, Polandr
MIT Cambridge, MA 02139, USAs
Institute of Physics, 751-005 Bhubaneswar, IndiatUniÕersity of Tennessee, KnoxÕille, TN 37966, USAb

Received 18 January 2000; received in revised form 11 February 2000; accepted 11 February 2000
Editor: L. Montanet

Abstract
The Dqq-resonance production in central 158 A GeV 208 Pb q208 Pb collisions at the CERN SPS has been studied. The
Dqq production was estimated from the invariant mass spectrum of ppq-pairs by subtracting a mixed event background.
The measured Dqq abundance is compared with the results from other experiments at lower energies, and with a model
calculation assuming thermal and chemical equilibrium. q 2000 Elsevier Science B.V. All rights reserved.
PACS: 25.75.Dw
Keywords: Ultra-relativistic heavy ion collisions; Dqq resonance production; Mixed event technique; Freeze-out temperature

Energetic heavy ion collisions provide the means
for studies of nuclear matter under extreme condi-

1E-mail: david.silvermyr@kosufy.lu.se

tions in the laboratory. The copious interactions between pions and nucleons in the final state of ultrarelativistic heavy ion collisions make the determination of the DŽ1232. abundance an interesting probeof the thermal conditions during the collision.

M.M. Aggarwal et al.r Physics Letters B 477 (2000) 37–44

The D-resonance, apart from playing a role inparticle production and interaction dynamics, mayprobe the conditions in heavy-ion collisions at earlyfreeze-out times and high freeze-out densities w1x. It
has been suggested that a chemical freeze-out temperature can be extracted from the DŽ1232.rnucleon
ratio w2x. The D-resonance is known to be readily
produced in photon w3x- lepton w4x- and hadron w5x-induced nuclear interactions and the cross sections for
production of D-resonances in elementary nucleonnucleon collisions are large w6x.
Recently, results on DŽ1232. production in nucleus-nucleus collisions at 95 A MeV w7x, at 1 and 2
A GeV w8x and at 13.7 A GeV w9x have been reported. In this paper we present measurements on the
production of Dqq by means of an invariant mass
analysis of ppq-pairs in 158 A GeV central 208 Pb
q208 Pb central collisions at the CERN SPS. The
measurement utilizes the new high resolution tracking arm of WA98 w10x, which consists of multi-stepavalanche chambers, streamer tube detectors and ahigh resolution Time-Of-Flight system.
The fixed target experiment WA98 is a largeacceptance photon and hadron spectrometer designed
to study ultra-relativistic heavy-ion collisions.
Charged particles, produced in the interactions, traverse a large magnet and are deflected into two
tracking arms, horizontally placed on both sides ofthe beam which allow for momentum determinationand particle identification. For the Dqq measurements, reported in this paper, we use the full data
sample from the tracking arm for the positively
charged particles w11x. This second tracking arm wasinstalled and operated for only a portion of the final
WA98 run period.
The tracking arm consists of two planes of MultiStep Avalanche Chambers ŽMSACs. w12,13x and twoplanes of streamer tube detectors, all equipped withelectronic pad readout and a highly segmented TimeOf-Flight ŽTOF. wall. Fig. 1a shows a schematic
drawing of the second tracking arm as seen fromabove, with two tracks entering the acceptance. Herethe z-axis is pointing along the beam and the x-axis
is parallel to the bending plane of the magnet. The
position resolution of the MSACs was sx s 0.5 mm
in the horizontal direction, and sy s 1.7 mm in thevertical direction whereas the streamer tube detectors
had an intrinsic resolution of sx s 3.0 mm and sy s

39

6.5 mm. The time resolution of the TOF wall was
better than 90 ps and its spatial resolution wassx s 12.5 mm and sy s 26.4 mm. Fig. 1b and 1cshow p versus t tof y texp assuming pion and protonmass, respectively. Here p is the momentum, t tof themeasured flight time of the particle and texp the
expected flight time calculated from the track lengthand momentum of the particle. Separation between
different particle species, especially for pions andprotons, is good over a wide range of momenta.
Kaons and pions are no longer separable at momenta
above 4 GeVrc and thus a small contamination ofkaons is present among the pions at larger momenta.
The momenta of the particles are first approximatedassuming a uniform magnetic field and straight line
fits through the tracking arm and then corrected by
GEANT w14x calculations using the measured field.
The momentum resolution, D prp, is limited by themultiple scattering, mainly in the air between thetarget and the detectors, the intrinsic detector resolution and by methodical uncertainties. Based on
GEANT simulations we estimate D prp to be about
1% at 2 GeVrc and 2% at 5 GeVrc.
The most interesting events are those where thebulk of the nuclear matter interacts, i.e. the mostcentral events. A trigger based on the transverse
energy as measured by the Mid-Rapidity CalorimeterŽMIRAC. is used to enhance central collisions. The
present analysis has been performed using the 8.5%
most central events of the WA98 minimum bias
cross section Ž6450 mb for the used data set. basedon an offline cut on the measured transverse energy.
To reject beam particles other than Pb and possible
event pile-up, lower and upper cuts in the ADC and
TDC values from the start-counters, placed in thebeam, were performed.
During and shortly after electrical discharges, theMSACs exhibited reduced efficiencies. This has been
discussed in a previous paper w12x. Thus events
recorded within a short time after such a discharge,
are removed from the analysis.
The tracking procedure connects hits in at least
three out of the four tracking planes, by means ofstraight line fits, and combines a track with a valid
time measurement in the TOF wall at the correct
position. Due to the excellent two-track resolution
and two-dimensional position resolution of the tracking planes, this procedure works almost without

40

M.M. Aggarwal et al.r Physics Letters B 477 (2000) 37–44

Fig. 1. Ža. Overview of the tracking arm with two tracks within the acceptance. Žb. Particle identification bands calculated assuming that all
particles have the pion mass. Žc. as in Žb. assuming proton mass. Žd. The distribution of accepted particles in terms of pt and rapidity for
protons and pq.

ambiguities, in spite of the large track multiplicity
within the acceptance. Cuts have been applied on the
hit association in the TOF wall and on the verticaldistance between the track extrapolation and theinteraction point. Finally, the particle identity is obtained by cuts in t tof y texp . This works up to aparticle momentum of 8 GeVrc, where the separation no longer can be done unambiguously. In order
not to lose any observed Dqq resonances, we havechosen to use particles up to 16 GeVrc, thereby
introducing a small systematic error. The small
amount of contaminating kaons among pions above

4 GeVrc only gives marginal effects on the extracted Dqq yield. This sort of contamination will
also be present in the mixed events and its effects areto a large extent removed.
Fig. 1d shows the distributions of accepted particles for the second tracking arm in terms of transverse momentum pt and rapidity for protons andpions. Notice the signŽ p x . factor, which unfolds the
spectrum for particles with negative p x and momentum low enough to bend across the beam line. Furthermore, a momentum cut of 8 GeVrc has been
applied.

M.M. Aggarwal et al.r Physics Letters B 477 (2000) 37–44

For all pairs of identified p and pq, the invariant
mass, Minv , was calculated from
Minv s(Ž E q E . y Ž p q p . .
2

p

p

2

p

p

The mass resolution of the ppq-pair, estimated fromthe momentum resolution, is a few MeV. An invariant mass spectrum of such pairs Žreal spectrum. willconsist of one part where the pion and the proton are
coming from the same Dqq-decay and an essentially
uncorrelated combinatorial background. Due to thehigh multiplicity of protons and pions, the combinatorial background will be by far the dominant contribution to the invariant mass spectrum. To accountfor this combinatorial background, the invariant mass
spectrum was calculated also with protons and pions
taken from different events Žmixed event.. To extract
the fraction j , of Dqq, among the ppq-pairs, Npair ,we assume that the mixed event invariant mass
spectrum has the same shape as the combinatorial
background in the real spectrum. This assumption
has been verified by studies of ratios between real
spectra and mixed event spectra. To essentially eliminate the statistical errors in the mixed event spectrum, it contains about ten times the statistics in thatof the real spectrum. The real spectrum, F Ž Minv . canthen be written as

41

Fig. 2a shows the distribution of accepted Dqq
obtained from FRITIOF7.02 w16x events filteredthrough GEANT, i.e. for Dqq where both decay
particles fall inside the acceptance of the arm. The
spectrum is unfolded in the same way as in Fig. 1d.
Fig. 2b shows the invariant mass spectrum ofF Ž Minv . y Nev P Npair P Ž 1 y j . g Ž Minv . ,i.e. the real spectrum with the background subtracted. Also shown by the solid curve is
Nev P Npair P j P BW Ž Minv , M0 , G . ,i.e. the acceptance-filtered modified Breit-Wigner
function obtained from the best fit.
The extracted number of Dqq has to be corrected
for acceptance and inefficiencies. Table 1 gives thevalues of the different correction factors with theirestimated errors.
The efficiency for Dqq detection is the productof the efficiencies for protons and pions. The efficiency factors given in the table are the ratio between those Dqq efficiencies and the corresponding
efficiencies for protons. k trk , which is about 80%, isthe probability for a particle entering the arm, resulting in a track seen in at least three out of the fourF Ž Minv . s Nev P Npair Ž j P BW Ž Minv , M0 , G .
q Ž 1 y j . g Ž Minv . . .
Ž 1.
BWŽ Minv , M0 , G . is a modified Breit-Wigner function, filtered through our geometrical acceptance,
normalized to unity. M0 and G are the peak position
and width respectively of the modified Breit-Wigner
function. Note that neither the real spectrum nor themixed event spectrum are corrected for acceptance.
Nev is the number of events and g Ž Minv . is the unit
normalized mixed event spectrum. The modified
Breit-Wigner function, before filtering, is given byBW Ž Minv , M0 , G .
q3
A

3

1
3

Ž q q m . Ž Ž Minv y M0 . 2 q Ž Gr2. 2 .

,where q is the momentum of the proton Žor pion. in
the rest-frame of the pair, i.e half of the relative
momentum, and m s 180 MeVrc w15x. The real
spectrum can now be fitted using Eq. Ž1., treating j ,M0 and G as free parameters.

Fig. 2. Ža. The distribution of accepted Dqq obtained from Fritiof
events. Žb. The extracted Dqq resonance together with the corresponding acceptance-filtered modified Breit-Wigner.

42

M.M. Aggarwal et al.r Physics Letters B 477 (2000) 37–44

Table 1
Summary of the different correction factors and their estimatedsystematic errors.
Correction factors

Valuetracking efficiency, k trk
identification efficiency, k pid
geometrical acceptance, k geo

0.79"0.02
0.60"0.02
0.145"0.005

tracking planes and with a quality sufficient to pass
the applied cuts, i.e. vertex association, x 2 of thestraight-line fit, et cetera. The k pid factor corrects forthe particle identification efficiency, including hardware efficiencies, effects of applied cuts on the flighttimes and particles decaying before reaching the
TOF wall. The k geo factor corrects the Dqqrproton
ratio for the limited azimuthal coverage of the arm
estimated by GEANT simulations. The values of all
the correction factors depend on the cuts we applyon the data and the systematic errors were estimatedby varying these cuts within reasonable limits.
Table 2 gives the reconstructed and correctedratio between the number of Dqq and protons within
the arm. Within our acceptance RQMD2.3 w17x
predicts about 2.4 protonsrcentral event and
FRITIOF7.02 predicts about 5.5 protonsrcentral
event. Thus our proton multiplicity, which is about
1.83 proton per central event after efficiency corrections, seem to be in fair agreement with RQMD,
whereas FRITIOF seems to overestimate.
The extraction of the Dqq signal is by no means
trivial as the peak is broad and the combinatorial
background is large. Three different extraction methods were applied to simulated data to investigate theinfluence of the methods on the reconstructed number of Dqq w18x. The method described above proved
to be the most robust for different projectiles p, Si
and Pb upon Pb target at the relevant beam energy.
Regarding the error of the extracted ratio we notethat this is dominated by the statistical fluctuations in
the number of combinatorial pairs under the resonance peak. Thus it is impossible to obtain the ratiowith higher precision with the given statistics, independent of the extraction method. A study based on
simulation results with different event generators,
and variation of cuts applied to the data, indicatesthat the systematic error contributions resulting fromthe various cuts and correction factors applied to thedata are considerably smaller Žof the order of 10% of
the obtained value. and therefore negligible in comparison to the statistical error.
However, it was observed that the chosen extraction method tended to systematically overestimate
the number of Dqq in simulations. A special simplified Monte Carlo event generator was constructed inorder to study this effect. With this generator, several
hundreds of samples of the same size as the real data
sample was studied w19x. The reason for the overestimation is that although the background estimatedwith mixed events is almost identical to the background in the data, small differences are present. For
instance, correlations between the decay products
from different Dqq resonances are believed to add
to the systematic error of the extraction method.
Pairs with the pion and proton from two different
Dqq decays, are almost identical to a pair originating from the same Dqq due to the restricted acceptance of the tracking arm. The magnitude of theoverestimation and associated error has been determined from the simulations and a correction has
been applied for the ratio and error as shown in
Table 2. The correction leads to an increased relative
error in the ratio.
The ratio of DŽ1232.rnucleons has been studied
and an increase as a function of incoming beamenergy has been established w8x. In a thermal model
this can be interpreted as an increase of the freeze-out
temperature which determines the relative populationof the nucleonic resonances. The same ratio can be
estimated from our data. In an isospin symmetricsystem, one could obtain the total number of DŽ1232.
resonances, i.e. Dy, D 0 , Dq and Dqq, by multiplying the number of Dqq by an isospin factor four. In
the same way, the number of nucleons, including
those from resonance decays, could be estimated bymultiplying the measured number of protons with afactor two. In our case, where we have an isospin

Table 2
Summary of the results.
119677 central events

Dqqrproton ratio

reconstructed Žuncorrected.
corrected for systematic fitting error
full f and eff. corrected

0.031"0.015
0.021"0.013
0.309"0.190

M.M. Aggarwal et al.r Physics Letters B 477 (2000) 37–44

43

freeze-out. For this and other reasons, e.g. the saturation of the ratio as a function of temperature, it ispremature to use the experimentally extracted ratio
for a precise temperature estimation and any temperature above 100 MeV seems to be in qualitative
agreement with the obtained ratio.
Besides the yield, the fitting procedure also provides the width and mass of the delta peak. However
the systematic errors in these values, estimated bychanging cuts and extraction methods and by applying the methods to Monte Carlo samples with known
parameters, are sufficiently large to preclude a meaningful discussion of a possible mass shift or changesof the width of the delta peak.

Acknowledgements
Fig. 3. The ratio DŽ1232.rnucleons as a function of beam energyrnucleon.

asymmetry, in a first approximation the nucleons andthe D-resonances are affected in the same way, andthus no correction for the isospin asymmetry isapplied. Only a small contribution of baryon number
is present in deuterons and weakly decaying hyperons, where the decay proton might be lost in the
tracking due to the secondary vertex being far fromthe interaction point.
Our obtained ratio for nucleons originating fromDŽ1232. resonances, is found to be quite large at
central rapidities, 0.62 " 0.38. Fig. 3 shows our results in comparison with similar results from experiments at lower beam energies. Note that the target
and projectile rapidities are separated by 5.8 units at
158 A GeV. In this experiment the influence ofspectator matter is thus much less than at lower
beam energies.
Our obtained value of the DŽ1232.rnucleon ratio
can be compared to the ratio obtained from thermal
model calculations, assuming chemical and thermal
equilibrium. In such a calculation the maximum ratio
obtained is around 0.33 w2x. Furthermore this ratio is
obtained over a large range of temperatures andbaryon densities, used as input to the calculations.
However, it should be pointed out that the experimental ratio also contain contributions from prior toThis work was supported jointly by the German
BMBF and DFG, the US DOE, the Swedish NFR
and FRN, the Dutch Stichting FOM, the Stiftung fur¨
Deutsch-Polnische Zusammenarbeit, the Grant
Agency of the Czech Republic under contract No.
202r95r0217, the Department of Atomic Energy,
the Department of Science and Technology, theCouncil of Scientific and Industrial Research and the
University Grants Commission of the Government ofIndia, the Indo-FRG Exchange Program, the PPE
division of CERN, the Swiss National Fund, the
INTAS under Contract INTAS-97-0158, ORISE,
Grant-in-Aid for Scientific Research ŽSpecially Promoted Research & International Scientific Research.
of the Ministry of Education, Science and Culture,
the University of Tsukuba Special Research Projects,
and the JSPS Research Fellowships for Young Scientists. ORNL is managed by Lockheed Martin Energy
Research Corporation under contract DE-AC0596OR22464 with the US Department of Energy. The
MIT group has been supported by the US Dept. ofEnergy under the cooperative agreement DE-FC0294ER40818.

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Curriculum Vitae
General:Name:
Susumu Sato
Date of birth: 26, September, 1969 in Amagasaki, Hyogo, Japan
Domicile:
Maizuru, Kyoto
Marital Status: Unmarried
Education:
1976-1978
1978-1981
1981-1982
1982-1985
1985-1988
1989-1993
1993-1998
1995.3

Naruo-Higashi Elementary School, Nishinomiya, Hyogo
Japanese International School in Duesseldorf, Germany
Naruo-Higashi Elementary School, Nishinomiya, Hyogo
Hama-Koushien Junior High School, Nishinomiya, Hyogo
Ikeda Senior High School attached to National Osaka
Kyouiku University, Ikeda, Osaka
University of Tsukuba, College of Natural Science
University of Tsukuba, Graduate School of Physics
Master of Science, University of Tsukuba

Employment:
1998-present Research Associate, Institute of Physics,
University of Tsukuba