Study of D ++ Resonance Abundance in 158 AGeV Pb + Pb Collisions at CERN-SPS

CERN-SPS-WA98 Susumu 　 SATO

Study of ++ Resonance Abundance in 158 AGeV Pb + Pb Collisions at CERN-SPS

Susumu SATO

Contents1) Introduction ~ Relativistic heavy ion collision ~2) Thesis motivation ~ measurement ~ 3) Experimental setup ~ WA98 at CERN-SPS ~4) Data analysis ~ corrections and errors ~5) Experimental Results ~ ,p spectra & yield ~6) Discussion ~ low mt enhancement of inclusive spectrum

~• Summary

Study of ++ Resonance Abundance in 158 AGeV Pb + Pb

Collisions at CERN-SPS



Picture of Relativistic Heavy Ion collisions

To understand fireball, need picture during “cooling with expansion”

[1: Before collision (~17 at SPS)]

- Lorentz contracted [2: During collision (~1fm/c)]

→stopping/heating

→hot/dense fireball [3: After collision]

→(thermal/chemical equilibrium) →”cooling with expansion” →thermal/chemical freeze out →hadrons(,K,p,…), e, …detection

Fireball



10-2

10-1

100

101

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

protonK+ ( x 1/1.5 )p+ ( x 1/35 )

mt-m(GeV)

Ed

dpmb GeV c

3

2 3/e je j

Ed

dp

mb

GeV c

3

3

2 3

FHG

IKJ

mt – m (GeV)

mt-scaling in proton – proton collisions

Single Particle Spectra (pp collisions)

s GeV23Nucl.Phys.B100(75)237

(1)Similar shape, and(2)Similar slope

for different particle species

(called mt-scaling)



mt – m (GeV)

Single Particle Spectra (nucleus - nucleus collisions)

158 AGeV Pb PbNucl.Phys.A610(96)175c

(1)Different shape, and(2)Different slope

for different particle species

1

m

dN

dm

a u

t t

( . . )

Different shape and slope are observed.



Two particle HBT correlation

Source size as a function of relative momentum

C p p R q

q q q q q

q p p

p p p p p i

inv

inv x y z

i x y z

2 1 22 2

2 2 20

2

1 2

0

1

1 2

( , ) exp

,

( , , , ) ,

e j

quantum interference to measure source size (R)

R

C2: detection probability of two particles at the momentum of p1 and p2

(R=6fm,=1)



Two particle HBT correlationin nucleus nucleus collisions

Source size as a function also of average momentum

C p p

R q f R q q

q q q q p p

K p p p p

z z

x y

x x y y

2 1 2

2 20 0

2 21 2

1 22

1 22

1

1

2

( , )

exp ; ,

,

b gd i

b g d i

Beam Direction (z)

TransverseD

irection (x,y)

p1p2

KT

q

q

Eur.Phys.J. C2(98)661



Expanding Fireball Model (1)

mass dependence of mt spectra slope

p

－

p －

+

K+ K －　

Naively, Expansion Fireball is applicable !

NPA610(96)175

→linear mass dependence　　　　　↓ 　　 parameterized 　　 naively　 T = Tf +mass ・〈 f 〉 2

Mass(GeV/c2)

Slo

pe(G

eV)



Expanding Fireball Model (2)~ example of good parameterization ~

Good explanation both for singles and two particle correlation,

but not using lower mt-region

(1) Single spectra: transverse kinetic energy (mt) spectra

PRL80(98)3467→parameterization for

different particle species Tf ~139MeV, 〈 f 〉 ~0.42c (2) Two particle HBT correlation

Habilitation(’97/T.Peitzmann)

→Boost invariance for expansion 〈 f 〉 =R/f ~ 0.430.16c



Thesis Motivations

(1) Measurement of particle production of a new particle species;

→(1232) in 158 A GeV Pb + Pb central collisions.

(2) As a basic problem to understand both single particle spectra and HBT correlation, low mt pion enhancement is observed.

→By using the result of explicit measurement of resonance, 　 the contribution of to low mt enhancement is acquired, then aiming to get footing of the validity of the expanding fireball model.



Authors Contributions

Design of experimental detector ● 　 Time-of-Flight (TOF) detector ● 　 Optimal alignment of chambers in magnetic spectrometer

Construction, test, installation, and operation of detectors ● 　 TOF detector ● 　 Streamer tube tracking (STD) detector ● 　 Start counter

Programming of control and reconstruction software ● 　 HV control for TOF ● 　 Online monitoring for TOF, STD

● 　 Momentum reconstruction

Physics Analysis ● 　 Pion and proton single spectrum ● 　 Yield of (1232) resonance



Δ++ 　 resonance● 　 Lowest resonance of nucleon

● M ~ 1232MeV (in Breit-Wigner function ）● c ~ 1.8 fm; (~111MeV)

● Isospin3/2, Spin 3/2

● Decay into pion and proton with >99% branching ratio 99% p

cf

n

p

n

p

n

.

~

~

~

~

R

S

||||

T

||||

50%

50% 0

99%

0 50%

50% 0

e j

e j● Decayed pion gives lower transverse kinetic energy

y

Pt(mt)(GeV/c)

0-1 10

0.4

0.8 ++

p

+



PAD Cham.

Beam( 208Pb:158AGeV)

Magnet

Start

TOF (Stop counter)

Streamer Tube Det.

LEDA(EM.Cal.)

+P.ball, SPMD

PMD

ZDC(Had.Cal.)

MIRAC(Had.Cal.)

21.5m

Target (208Pb: 0.239mg/cm2)

Characterize Fireball from various aspects• [Hadron] momentum + PID; w/Mag. Spectr.• [Photon] E w/EM.Cal. • [Hadron] global ET, E0; w/Had.Cal.• [Photon] mult. distr.; w/PMD • [Charged particle] mult. distr.; w/SPMD, P.ball

WA98 experimental setup



Magnetic spectrometer is in good operation

～ 1% at 2GeV/c

0 1 2 3 4 5 0

1%

σ p /

p

2%

0.5%

1.5%

-0.4 0 0.4

10k

5k

N start~30ps

Detector resolutions (p, Tstart, Ttof)

p(GeV/c)

Tdif (ns)

Ttof (ns)

N800

400

0 0.8-0.8

~85ps tof

~1.3mm, //~2.1mm (PAD1)~2.6mm,// ~7.0mm(STD1)



0

• Clear Particle Identification by ToF method

FH IK

RSTUVWp

TOF c

L2

21

~0.02 (GeV/c2)2 at 2GeV/c for π

0.00

0.10

0 2

0.05

41 3

m2(GeV2/c4)

p(GeV/c)

2

4

6

8

0 0.5 1 1.5

p(G

eV/c

)

pK ＋

Particle Identification

σm

2

(GeV

/c2 )

2



Ed N

dpE

d

dp

Ed N

dpE

d N

m dm dy d

d N

m dm dy

trig

t t

t t

3

3

3

3

3

3

3

2

1

2

Parameterization [1]for , p single particle spectra

Kinematical parameters

yp m p

p m p

z

z

1

2

2 2

2 2ln

m m p p m mt x y 2 2 2

Transverse kinetic energy

(longitudinal) rapidity

y : Lorentz invariant

Lorentz invariant differential yield

if symmetry



　 Measure around mid-rapidity, where hot fireball is expected the most.

(←ytarget =0) ycm=2.9 ( ybeam=5.8 →) 　y

Geometrical Acceptance

Fireball

mt-

m(G

eV)



Data selection

• Event selection Single beam (3 in ADCstart) FEE linear region (5.7% in Tdynamic) not after-chamber-spark (0.8sec) event

ADCstart 1 [ch]

AD

Cst

art 2

[ch]

•Track selection image on target (3 in B// direction) image on TOF2 (2.5on 2-D plane)

•PID selection m2 (2.5 in the p)



Geometrical acceptance and Efficiency correction

Averaged eff. PAD1 83% PAD2 80% STD1 91%STD2 97%

geo t cham cham cham decaycham

m y X Y L p, ( , ) ( / ). . ..

a f

p

PAD1

STD2STD1

PAD2

By the Monte Carlo Simulation (GEANT3.15)

cXmt

gyY



100

101

102

103

0 0.2 0.4 0.6 0.8 1

d2N

mt-m (GeV)

mt

dmt

dy1

158 A GeV Pb + Pb central(GeV-2)

● + (WA98)

○ + (NA44)

◆ proton(WA98)

◇ proton(NA44)

Single spectra

Slope(MeV)

WA

98

NA

44(*)

π+142

±3

156

±3

p251

±25289±7

mark in plot

filled open

(*) Nucl.Phys.610(96)175

mt-m(GeV)

Consistent shapes with other experiments



Parameterization [2] for yield by invariant mass method

m E E p pinv p p e j e j2 2

Yield m

Yield m

Yield m

raw inv

inv

comb B G inv

a fa fa f

. . .

Invariant mass

Invariant mass distribution

should be evaluatedYield mcomb B G inv. . .a fInvariant mass (GeV)



Mixed Event technique

Combinatorial background is assumed to be proportional to mixed events

Yield m Yield mcomb B G inv

assume

mixed inv. . .a f a f

Mixed events: p and + from different events paired in 100 every events

EVENT 1p

p

p

EVENT 2p

p

p

example

Invariant mass (GeV)



Two normalization methods

Two methods should be consistent

q:relative momentum of the pair in its C.M. frame,:180MeV/c

Yiled mq

q m minv

assume

inv

LNM OQP

a fe j

3

3 3 21

4 1 /

(1) Tail method

normalize only in higher minv region

(2) Breit-Wigner + Background method

normalize in any minv region,assuming Yield++ follows Relativistic Breit-Wigner

(PRL79(’97)4354) Invariant Mass (GeV)



Clear yield can be extracted by tail method

Tail method

=0.0860.014

(GeV)

E0=1.2370.006




Breit-Wigner + Background method

Again, clear yield can be extracted by B.W.+BG. method




(3)Local multiplicity (N) on TOF

Systematic error of N/ ev. on extraction method

Less dependence on extraction parameters

(2) Tail method: 0.021

(1) Breit-Wigner + B.G. method: 0.022

N

/ ev.

Mth. (GeV)

1.4 1.5 1.6 1.7 1.4 1.5 1.6 1.7 1.4 1.50

0.05

0.10

0.022 0.022 0.018N=2 N=3 N=4

Nev . Poisson

<N>=2.6

0

1k

2k

N2 4 60



N N Nraw mix For ,

F

HGG

I

KJJ

FH IK

e ja fa f e j a f

a f e i

2

2

2

2

2

N

N

N N N

NN

whereN N

N

raw

mix

raw mix

mixmix ii

raw

mix

~

~

,

~

,

Statistical Error

Major contribution of error is large Combinatorial Back Ground

Error propagation gives

( 50.0% )

( 49.9% )

( < 0.1% )

~ 45% N



Isospin consideration

Factor from Np/N++ to Nnucleon/N is 2.0.



Yield summary table

At SPS, delta yield is, for the first time, directly measured

Value and Statistical Error

++ / spectrometer /ev. (raw) 0.022 0.010

proton / spectrometer/ev. (raw) 1.080 0.010

++/proton (raw) 0.021 0.009

trk (3or4cham.) 0.79 0.02

PID 0.60 0.02

geo 0.145 0.005

++/proton ( trk , PID, geo corrected) 0.31 0.14

/nucleon (isospin corrected)

0.62 0.28 (stat.) (45%)

Systematic Error

Uncertainty of Tracking efficiency 0.06 (sys.) (10%)

Difference in normalization method 0.02 (sys.) ( 4%)

Difference for different local multiplicity 0.08 (sys.) (13%)



Higher population is seen at SPS

PLB477 (2000) 37-44 Δ

(123

2)

nuc

leon

(%) 100

80

60

40

20

0 1 10 100Ebeam(AGeV)

Population ratio: Δ/ nucleon

Acquired from / p,Isospin correction done for

82208Pb



100

101

102

103

0 0.2 0.4 0.6 0.8 1

Low mt enhancement is seen in local mt slope (Next)

mt – m (GeV)

0 0.4 0.60.2

102

10

1

2

2

2

m

d N

d y d m

GeV

t t

( )

+

Neighboringseveral points for

local mt slope

1

Low mt enhancement in Pb + Pb (1)

103

0.8 1



0.05

0.1

0.15

0.2

0 0.2 0.4 0.6 0.8 1

The mt enhancement is seen in + spectrum in Pb + Pb collisions

Center of fitting region in mt – m (GeV)

Loc

al s

lope

(G

eV)

Low mt enhancement in Pb + Pb (2)



pp collision is described well in mt exponential

1

10

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7mt-m

0(GeV)

Ed

dpmb GeV c

3

32 3

/e je jFitting Liney=a*exp(-x/b)

a=82.48 (er. 3.71)b=0.1532 (er. 0.0026)

chi square / n.d.f = 8.83 / 6

mt – m (GeV)

pp collisions

100

10

1

Ed

dp

3

3

mb GeV c/ /2 3e j

0 0.4 0.60.2

Fitting Liney=aexp(-x/b)a=82.5±3.7b=0.153±0.0032/n.d.f=8.8/6

s GeV23

Nucl.Phys.B100(’75)237

+ at mid-rapidity



Candidates of low mt enhancement

There are more than one candidates

(1) Collective motion

(2) Coulomb effect

(3) Resonance decay

+

++

e.g. Collective radial expansion

Repulsion/Attraction from Charges

+ decay gives lower mt by kinematics

y

Pt(mt)(GeV/c)

0-1 10

0.4

0.8 ++

p

+

p



Collective motion (Thermal+expansion)

spectra shape is little affected by Collective motion

MeV〈〉 =0.42c

Describing well for different particle species

except low mt , and shape of is little

affected by collective motion

PRL80(’98)3467

consistent also with two particle HBT correlationDashed line:

exponential for eye guide

1

m

dN

d m

a ut t

( . . )

mt – m (GeV)



101

102

103

0 0.1 0.2 0.3 0.4 0.5 0.6mt-m (GeV)

d2N m

tdm

tdy

1(GeV-2)

◆ + ◆ －

---exponential

RatioN

N

0 0.40.20

1.0

2.0w/Coulomb

No Coulomb

Low mt Enhance

1

2

22

m

d N

d y d mGeV

t t ( )

Low mt enhancement is seen in both charge, and Coulomb effect appears as difference between + and –.

Coulomb effect

Coulomb

mt – m (GeV)



10-1

100

101

102

103

0 0.2 0.4 0.6 0.8 1

d2Nmt

dmt

dy1 (a.u.)

mt-m (GeV)

Δdecay +Thermal Expansion

●

■

(---- Thermal expansion component)

――

π ＋ WA98)（

π ＋ NA44)（

――

( Upper and lower error )

N

Np Sc Not Sc

NotSc p NotSc

( .) ( . .)

( .) ( .)

Contribution of Δ Resonance

“thermal source” + “Δ resonance decay” isconsistent with the low-mt enhancement of π ＋ .

Δ( invariant mass) with a factor (1+α)

→consistent with simulation

thermal modelT=139 MeV,〈〉 =0.42c

+

included evaluation

mt – m (GeV)

1 2

m

d N

d y d mt t

(a.u.)



Conclusion(1) For the systematic study of hadron production in 158 A GeV

Pb + Pb collision, magnetic spectrometer with good PID capability is constructed.

(2) At 158 A GeV Pb + Pb collisions, + and p inclusive single mt spectra are measured. Inverse slopes are 142 3 MeV (fitting region: mt – m > 0.2 GeV) for + and 251 25 MeV for proton. In the pion spectrum, clear low mt enhancement is observed.

(3) 158 AGeV Pb + Pb collisions, resonance yield is, for the first time, measured directly. The /nucleon ratio is

0.62 0.28 (stat.) 0.16 (sys.).　　　

(4) Spectrum shape with consideration of decay on thermal expanding fireball follows low-mt enhancement of π ＋ . The additional factor is consistent with a cascade simulation that gives contribution of decay with re-scattered proton.



At SPS, is not measured, while AGS tells its importance

At AGS, good description with decay

in RQMD

PLB351(95)93

at AGS (not directly measured) andMeasured PID at SPS

Documents

Study of D ++ Resonance Abundance in 158 AGeV Pb + Pb Collisions at CERN-SPS