The BRAHMS result on the proton-to-pion ratio pT-dependence in nucleus-nucleus collisions at √sNN = 62.4 GeV and 200 GeV

w zale»no± i od pedu

ι

poprze znego w zderzenia h jadro-j

ι

adro

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przy energii

√

_s

NN

= 62.4 GeV oraz 200 GeV w eksperymen ie BRAHMS Natalia Katry«ska Pra a doktorska pod kierunkiem

Prof. dr. hab. Zbigniewa Majki

oraz

Dr. Pawªa Staszla

Wydziaª Fizyki, Astronomii i Informatyki Stosowanej

Uniwersytetu Jagiello«skiego

the proton-to-pion ratio

p

T

-dependen e in nu leus-nu leus ollisions at

√

_s

NN

= 62.4 GeV and 200 GeV Dissertation by Natalia Katry«ska Supervisors:

Prof. Zbigniew Majka

and

Ph. D. Paweª Staszel

Fa ulty of Physi s, Astronomy and Applied Computer S ien e

Jagiellonian University

Highperforman e ofmeasurementsatRHICby fourexperiments:

BRAHMS, PHENIX, PHOBOS and STAR allows to provide omprehensive

re-sear h,thedeepestinsightonmesonsandbaryonsprodu tioninheavyionsrea tions

atultra-relativisti energies amongothers. Thisthesis presentsproton-to-pionratio

measurementsin Au+Au and p+p intera tions at

√

_s

N N

=62.4 GeV and 200 GeV as a fun tion of transverse momentum and ollision entrality within the

pseudo-rapidity range 0

≤ η ≤

3.65. The data were measured over a broad rapidity and

p

T

overage by BRAHMS Collaboration using two unique spe trometers. For the indi atedheavy ion ollisionsthebaryo- hemi alpotential,

µ

B

,spans from

µ

B

≈

25 MeV(

√

_s

N N

=200 GeV,

η

=0)to

µ

B

≈

260MeV(

√

_s

N N

=62.4 GeV,

η ≈

3). The top value of

p/π

+

(

p

T

) ratio for Au+Au ollisionsat

√

_s

N N

= 200 GeV doesnot go beyond 3at intermediatetransverse momentum at

η ≈

3. The

p/π

+

ratio in reases

with entrality inthe overed

p

T

range. The ratio of

p/π

¯

−

rea hes the maximumof

0.5 at

η ≈

2.3 for Au+Au system at the top RHIC energy and de reases for more forward pseudorapidities. For Au+Au rea tions at

√

_s

N N

= 62.4 GeV

p/π

+

ratio

rea hes large value of8-10 at

p

T

=1.5GeV/

c

. Weak entralitydependen e of

p/π

+

ratioinheavy ionsrea tions for

η

>2.5atlower ollidingenergyisobserved. More-over, a striking agreement between

p/π

+

(

p

T

) ratio measured for Au+Au ollisions at

√

_s

N N

=200 GeV(

η ≈

2.2)andat

√

_s

N N

=62.4 GeV(

η ≈

0)isnoted,wherethe properties ofthe bulkmedium an bedes ribed withthe ommonvalue of

µ

B

=62 MeV. Thedes ription of hadronizationof the strongly intera ting matterformed in

heavy ion ollision at ultra-relativisti energies by parton oales en e and

expand-ingreball with olle tiveowis presented and omparedwith measured

p/π

+

and

¯

p/π

−

ratiosatdierentbeamenergiesandrapidities. The oales en emodelutilizes

the dynami softransforming partonsintohadroni bound statesinthe presen e of

partoni medium. The non-boost-invariant single-freezeout approa h aptures the

I would like to express my gratitude to all those who gave me the possibility to

omplete this thesis.

IexpressmydeepsenseofgratitudetoProf. ZbigniewMajkaandDr. Paweª

Staszel,for their invaluablehelp and guidan e duringthe ourseof the proje t.

I am grateful to Prof. Zbigniew Majka for having given me the support and

onden e. Heisaperson, whogaveand onrmed thispermissionand en ouraged

metogo aheadwith my thesis.

I amhighly indebted to Paweª Staszel for onstantly en ouraging meby giving

his riti sonmywork. Hishelp,stimulatingsuggestionsanden ouragementhelped

me in all the time of resear h for and writing of this thesis. I am deeply thankful

forhis heartiness and understanding.

This thesis would not be possible without the essential and gra ious support

of BRAHMS Collaborators and BRAHMS Collaboration spokesperson Flemming

Videbæk. My sin ere thanks for their generous and varied ontributions to this

work.

I would like to express my thanks to all parti ipants of Division of Hot Matter

Physi sat JagiellonianUniversity. I appre iate theirwillingness and warmth.

I would like to thank Aleksandra Gu«kiewi z for a patien e and apa ity to

orre tmy mistakes duringall my studies.

W sz zególno± i h iaªabym podzi

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ekowa¢...

...Agniesz e - zaJej iepªo, oddanie oraz zrozumienie.

...Bartkowi-zapokazanie minowej drogiiwiar

ι

ewzmienianie najtrudniejszego. Dzi

ι

ekuj

ι

e Wam, »e zawsze jeste± ie blisko.

1 Introdu tion 1

1.1 New era

of relativisti heavy ion ollisionphysi s . . . 1

1.2 Basi issues studied using the BRAHMS Experiment'ssetup . . . 4

1.2.1 Net-baryon density distribution . . . 4

1.2.2 Nu lear Modi ation Fa tor . . . 5

1.2.3 Color Glass Condensate . . . 6

1.2.4 Elementary ollisions . . . 7

1.3 Organization ofthe thesis . . . 9

2 Motivations 10 2.1 Nu leus-nu leus ollisions atRHIC energies . . . 10

2.2 QCD phase diagram . . . 11

2.3 Theoreti al Developments . . . 14

2.3.1 Thermodynami al des ription . . . 14

2.3.2 Quark re ombinationmodel . . . 16

2.3.3 Hydrodynami almodels . . . 19

2.3.3.1 The non-boost-invariantsingle-freezeout model . . . 21

3 Broad RAnge Hadron Magneti Spe trometers at RHIC 24 3.1 Relativisti Heavy Ion Collider. . . 24

3.2 BRAHMS dete tor setup . . . 26

3.2.1 Time Proje tion Chambers . . . 28

3.2.2 Drift Chambers . . . 30

3.2.3 Time of Flightdete tors . . . 34

3.2.4 Cherenkov dete tor . . . 35

4.1 Data re onstru tion . . . 40

4.2 Parti leidenti ation . . . 47

4.3 Corre tions . . . 50

4.3.1 RICH e ien y . . . 50

4.3.2 Absorption and in-ight de ays orre tions . . . 53

5 Results 55 5.1

P/π

ratio in Au+Au ollisions at

√

_s

N N

= 200 GeV . . . 55

5.2

P/π

+

ratio inAu+Au ollisions at

√

_s

N N

= 62.4 GeV . . . 64

5.3 Comparison of

p/π

+

ratio inAu+Au ollisions at

√

_s

N N

= 62.4 and 200 GeV . . . 67 6 Con lusions 68 7 Appendix 1 72 8 Appendix 2 75 Referen es 88

1.1 The rapidity lossas a fun tion of beam rapidity for heavy ions

olli-sions atAGS, SPS and RHIC.The solid linerepresents the ttothe

SPS and RHIC data. The grey band is the statisti al un ertainty.

The dashed line is linear t to the AGS and SPS results [21℄. The

plot is published in [19℄. . . 5

1.2 Thenet-protondistributioninp+p ollisionsasafun tionofrapidity

shifted by

y

beam

,

y − y

beam

, ompared with datafromNA49 at

√

_s

N N

= 17.2 GeV. The pi turehas been published in [35℄. . . 8

2.1 S hemati spa e-timepi ture of nu leus-nu leus ollision. . . 11

2.2 The s heme of QCD phase diagram: the dashed-dotted red line

em-blematizes the rossover between Quark Gluon Plasmaand hadroni

phase. The red solid line symbolises the 1st order phase transition.

The dottedblue urve represents the hemi alfreezeout. The arrows

denotethevalueofbaryo hemi alpotentialfordenite olliding

sys-tems. . . 12

2.3 Transverse momentum distribution of pions

π

0

(left-hand side) and

protons(right-handside)forAu+Au ollisionsat

√

_s

N N

=200GeVat the midrapidityregion. Dierent ontributions to the re ombination

of partons are depi ted. The plots are taken from [53℄. . . 17

2.4 Theevolutionofthereballalonglongitudinalaxis(redarrows) with

depi ted tra ksofprodu edhadrons forparti ularvalueof

pseudora-pidity

η

(dashed lines). The pi ture istaken from [50℄. . . 22 3.1 Overview of Relativisti Heavy Ion Collider in Brookhaven National

Laboratory. . . 25

3.2 BRAHMS dete tors layout. . . 27

3.3 The photo of the ba k part of the Forward Spe trometer with the

drift hamberT3 at the front right side of the pi ture. The D3 and

the dete tion planes. The thirddete tion plane ("Vview") allows to

reje t spurious tra ks (dashed lines). . . 30

3.5 Single module of the T3 dete tor. . . 31

3.6 The photoof the drift hamberT3 with omplete setup of front-end

ele troni s read-out boards. . . 32

3.7 The e ien y of the tra king dete tors: T1, T3, T5 as afun tion of

x

position (upper row), tra k

x

-slope (middle row) and momentum (bottom row). Theresultsare shown forp+p ollisionsat

√

s

=62.4 GeV, settings: 3A1723 (greenstars) and 3B1723(grey rhombuses). . 33

3.8 The numberof ounts of the hits registered in the parti ular slats in

H2 Time of Flight dete tor is displayed (on the left side). On the

right, the

y

resolution of the tra k positionbetween

y

position of H2 hit and extrapolated FS tra k up to H2 dete tor plane is presented.

The results are for p+p ollisions at

√

s

= 62.4 GeV. . . 35 3.9 Parti les distributions of RICH ring radius (blue solid line). The

plotted lines represent the Gaussian t to muons (magenta dashed

line) andpions(green dashedline)distributions. The bla k solidline

marks the sum of Gaussian fun tions used in the PIDanalysis. The

dataaredisplayed forAu+Au ollisionsat

√

_s

N N

=200GeV,setting: 10B430. . . 36

4.1 TheZDCsandBB 's layout(left olumn). Onthe right-topthe

x −y

map re eived fromthe Beam-Beam ounters is displayed. The

right-bottom plot shows the dieren e between the vertex determination

from the BB 's and extrapolation of the re onstru ted tra k in FS.

TheanalysisreferstoAu+Au ollisionsat

√

_s

N N

=62.4GeV,setting: 8A1219. . . 41

4.2 The PID pro edureisbased onttingofmulti-Gaussiandistribution

toseparatetheparti ularspe ieofparti les(

e

−/+

,

µ

−/+

,

π

−/+

,

K

−/+

,

p/

¯

p

). Here, the series of histograms in luding lines representing ts with multi-Gaussian fun tion (bla k solid line) are displayed for

Au+Au rea tions at

√

_s

N N

=200 GeV, setting: 4B2442. The Gaus-sian fun tion for pions is marked with dashed green line, for kaons

- dashed orange line, for protons - dashed pink line. The blue line

representsexperimentaldata. Themeanofsquaredinvariantmasses,

<

m

2

X

> (

X

= e,

µ, π

, K, p), are displayed for indi ated momentum

4.3 The same as Fig. 4.2, but obtained for the p+p ollisions at

√

s

= 62.4 GeV, setting: 4A608. The Gaussian fun tion for ele trons is

depi ted with dashed red line, for muons - dashed yellow line, for

pions - dashed green line. The overlapping of muons and pions for

p

> 4GeV/

c

is learly visible. . . 46 4.4 The results of PID analysis in ase of using H2 and RICH dete tor

forlow(608[A℄)andhigh(2442[A℄)magneti eldinthe D1magnet

of Forward Spe trometer. Ele trons are highlighted with the violet

points,muons-yellowpoints,pions-greenpoints,kaons-pinkpoints

andprotons-orangepoints. Intheleft olumntheresultsforAu+Au

ollisions at

√

_s

N N

= 200 GeV are depi ted (setting: 4B2442). The left-topgureshowsthe identiedspe iesmomentumdependent uts

applied onring radiusvs. parti lemomentum map. The left-bottom

pi ture displays the identied pions, kaons and protonsapplying the

squared invariant mass,

m

2

, vs. parti le momentum map. In the

right olumn the gures present the out ome of PID pro edure (H2

PID - top panel, RICH PID - bottom panel) for low magneti eld

(setting: 4A608) for elementary ollisions at

√

s

= 62.4 GeV. In the bottom row the veto antiprotons are marked with the orange points

at

m

2

= -0.1

GeV

2

/

c

4

. . . 48

4.5 The RICH ine ien y orre tion as a fun tion of momentum and

ring radius for Au+Au ollisions at

√

_s

N N

= 200 GeV. The fun tion and obtained ttingparameters displayed inthe right-handinset are

re eived ina ordan e with the equation 4.3. . . 50

4.6 The RICH ine ien y orre tion as a fun tion of

p/p

th

for Au+Au ollisions at

√

_s

N N

= 200 GeV for low (bla k line) and high (red line) magneti eld settings. The pi ture presents the onsisten y of

applied pro edure of RICH ine ien y orre tion - the points for

p

<3GeV/

c

standsforpionsfromlowmagneti elddata andprotons from high magneti eld data, the points for

p

> 7 GeV/

c

- pions from high magneti eld data. . . 51

4.7 The

p/π

¯

−

ratio vs. transverse momentum for the most entral (0

-10%) Au+Au ollisionsat

√

_s

N N

=200 GeV without(left-hand)and with (right-hand)applied RICH ine ien y orre tion. . . 53

4.8 Absorptionandweak-de ays orre tionsfor pions,kaonsand protons

5.1

η − p

T

maps for pions (left-hand pi ture) and protons (right-hand pi ture) for p+p ollisions at

√

s

= 62.4 GeV. The plots show the overageofpseudorapidityandtransversemomentumofexperimental

data. The transverse momentum an be expressed as a fun tion of

η

:

p

T

= p sin [2 arctgh [exp (−η)]]

. In the pi ture the lines represent this fun tion with onstant value of momentum:

p

= 2.3, 9 and 15 GeV/

c

whi h orrespond withthe initialvalue ofmomentumforToF (red line),RICH(bla kline)andveto-RICH PID(blueline) pro edure. 56

5.2 Proton-to-pionratioasafun tionof

p

T

forAu+Aurea tionsat

√

_s

N N

=200 GeV for midrapidityregime. The gureis taken from[9℄. The

PHENIX experiment results are shown in [77℄. The re ombination

model predi tions are presented in [53℄. The hydrodynami al

al u-lations are in luded in [78℄. . . 56

5.3 The

p/π

+

(

p

T

) for Au+Au ollisions

√

_s

N N

= 200 GeV for dierent values of pseudorapidity for two intervals of entrality: 0-10% (blue

triangles)and 10-20% (dark grey open rosses). The proton-to-pion

ratios for p+p rea tions

√

s

= 200 GeV are shown (orangeopen ir- les). Thedataforthemost entralheavyionrea tionsare ompared

with single-freezeout model al ulations [66℄ (red rosses).. . . 57

5.4 The same as Fig. 5.3, but for entralityintervals: 0-10%(blue

trian-gles) and 20-40% (dark blue rhombuses). . . 58

5.5 The same as Fig. 5.3, but for entralityintervals: 0-10%(blue

trian-gles) and 40-80% (open green squares). . . 59

5.6 The

p/π

¯

−

(

p

T

) for Au+Au ollisions

√

_s

N N

= 200 GeV for dierent values of pseudorapidity for two intervals of entrality: 0-10% (blue

triangles)and 10-20% (dark grey open rosses). The proton-to-pion

ratios for p+p rea tions

√

s

= 200 GeV are presented (orange open ir les). Thesingle-freezeoutmodelpredi tionsareshownforAu+Au

system for0-10 % entrality interval (red rosses). . . 60

5.7 The same as Fig. 5.6, but for entralityintervals: 0-10% (blue

trian-gles) and 20-40% (dark blue rhombuses). . . 61

5.8 The same as Fig. 5.6, but for entralityintervals: 0-10%(blue

trian-gles) and 40-80% (open green squares). . . 62

5.9 The proton-to-pionratio for set of

η

bins in the range 2.6

≤ η ≤

3.8 for p+p rea tions at

√

5.10 The

p/π

¯

−

ratio vs. transverse momentum for 2.6

≤ η ≤

3.8for p+p ollisions at

√

s

= 200 GeV (left). On the right the results of ratio for p+p rea tions are ompared with the one for 0-10% and 40-80%

entral Au+Au ollisions at

√

_s

N N

= 200 GeV at the same value of pseudorapidity,

η

=3.3. . . 63 5.11 The p/

π

+

ratio vs. transverse momentum for Au+Au and p+p

ol-lisions at

√

_s

N N

= 62.4 GeV for

η ≈

2.67,

η ≈

3.2and

η ≈

3.5. . . 64 5.12 The results of re ombination (upper plot) and single-freezeout

(bot-tomplot)model al ulations omparedwithBRAHMSresultsforthe

most entralAu+Au ollisionsat

√

_s

N N

=62.4GeV for

η ≈

3.2. The upperpi ture has been taken from [49℄. . . 65

5.13 The

p/π

+

ratio vs. transverse momentum for p+p and entral

(0-10%)Au+Au ollisionsat

√

_s

N N

=62.4GeVand200 GeVfor midra-pidity and

η ≈

2.2, respe tively. The al ulations of single-freezeout model forAu+Au rea tionsat

√

_s

N N

=200GeVand

η ≈

2.2arealso shown. . . 66

Introdu tion

1.1 New era

of relativisti heavy ion ollision physi s

In 2000, the Relativisti Heavy Ion Collider (RHIC), lo ated in

Brookhaven National Laboratory, started delivering beams of protons and ions to

the four experiments: BRAHMS, PHENIX, PHOBOS and STAR. The main goal

of the resear h was to deliver eviden es for reation of new state of matter, alled

Quark Gluon Plasma (QGP) [1, 2℄ inheavy ion ollisions at ultra-relativisti

ener-gies. During re ent nine years at RHIC, p+p,

p

↑

+p, d+Au, Cu+Cu and Au+Au

intera tions were investigate at

√

_s

N N

= 22, 62.4, 130 and 200 GeV and a lot of new issues have been brought up [3, 4, 5, 6℄. The unique BRAHMS experimental

setupallows tomeasure produ ed hadrons in the widerange of rapiditywhat gives

the possibility to investigate properties of reated matter versus the longitudinal

dire tion.

Although dis overy of QGP at RHIC might be questioned, new

equili-bratedpartoni stateofmatterwithtypi alperfe tuidpropertieshasundoubtedly

been found [7℄. The data of ellipti ow [8℄and

p/π

+

(

p

T

)ratio around midrapidity [9℄have shown that the nal hadroni state remembers the partoni uid features.

This is ree ted in onstituent quark s aling of ellipti ow oe ient,

v

2

, and an enhan ementof baryon-to-meson ratiosthat s ales with the size of the reated

ν

n

≡ hexp (in (φ − Φ

R

))i = hcos (n (φ − Φ

R

))i

(1.1) where:

φ

- azimuthal angle of anemitted parti le,

Φ

R

-azimuth of the rea tion plane [10℄. The results of the ellipti ow

ν

2

measurements[8℄ strongly suggestthat at RHIC in nu leus-nu leus ollisions at top energy the new state of strongly

in-tera ting matter is observed. These observations orrespond with the perfe t uid

hydrodynami almodel al ulations[11,12℄. ThePHENIX [8℄,PHOBOS[14℄,STAR

[13℄datashowthatthe ellipti ow oe ient

ν

2

s ales almostperfe tlywith e en-trity (see the denition in [11℄),system size and transverse energy.

The eviden es of new state of matterare:

1. Theellipti ow oe ients aleswiththenumberofvalen equarksformesons

and baryons (

π, K, p, d, φ, Λ, Ξ, Ω

).

2. The s alingof the ow of parti leswhi h ontain heavy quarks - espe iallyD

mesonwith harm quark as the omponent.

3. Studies of the pre-hadroni phase on the basis of the ellipti ow

measure-ments.

4. The observed jet quen hing as the eviden e of parton energy loss (inter alia

hadron formation time, momentum dependen e of hadron suppression,

en-trality dependen e of hadron suppression, jet-likehadron orrelation, high

p

T

azimuthal anisotropy,data at lower olliding energy) [15℄.

The observations of ellipti ow behaviour are also supported by the

BRAHMS results [16℄ whi h data span to the value of pseudorapidity

η

= 3.4. The theoreti al hydrodynami al des ription [12℄ together with forward ellipti ow

resultssuggestthattheexpansionoftheprodu edmediumalonglongitudinal

dire -tion is even greater than previously has been thought [17℄. The onstituent quark

s alingis observed.

At RHIC the signi ant jet quen hing is exposed for entral

nu leus-nu leus ollisions. Theresultsofsuppressionhigh-

p

T

singlein lusivehadronspe tra and suppression of ba k-side jet-like orrelations tellabout the nale state

intera -tionswiththe medium. As highlightedin[15℄these measurementsstronglyindi ate

that itis an ee t of partons loosing their energy in the dense, olour mediumand

inthewiderangeofpseudorapidityforheavyionsystem onstituteatestingground

of apturingthepropertiesofbulkmedium. Unquestionably,thefeaturesofparti le

produ tionaredriven withthevalueofbaryo hemi alpotential,

µ

B

. The studiesof

η

dependen eof

p/π

(

p

T

)deliverinformationhowhadronizationpro essgoesthrough inthewiderangeof

µ

B

. Withtheseresultswewanttondoutwhi hre ombination orhydrodynami s enarioisfollowedinthenalstateofstronglyintera tingmatter.

using the BRAHMS Experiment's setup

1.2.1 Net-baryon density distribution

Wide rapidity a eptan e of the BRAHMS spe trometers provides

uniqueopportunitytostudynu learstoppingintheultra-relativisti nu leus-nu leus

rea tions. Theaveragerapidityloss,<

δy

>=

y

b

-<

y

>,quantiesstoppinginheavy ions ollisions:

< δy >= y

b

−

2

N

part

Z

y

b

0

y

dN

B− ¯

B

dy

dy

(1.2) where:

y

b

-rapidity ofin omingbeam (

y

beam

=4.2for Au+Au at

√

_s

N N

=62.4GeV,

y

beam

=5.4for Au+Auat

√

_s

N N

=200 GeV),

N

part

-numberof nu leonsparti ipatingin the ollisions,

dN

B− ¯

B

dy

-net-baryonrapiditydensity. Ifinitialbaryonparti ipantslose allthekineti energy(<

δy

>=

y

b

)weobservefullstopping,for<

δy

>=0thesystem is ompletely transparent. Before RHIC era, at S hwerionen Syn hrotron (SIS18)

in Darmstadt, Alternating Gradient Syn hrotron (AGS) in Brookhaven National

Laboratory and Super Proton Syn hrotron (SPS) in CERN, it was noti ed that

<

δy

> is linearly proportional to the beam rapidity. The BRAHMS results [19℄ showthat thislinears alingisbroken abovetop SPSenergies -Fig. 1.1. Assuming

thatunderlyingphysi sisthesame athighestattainableenergies, theextrapolation

of <

δy

> to the beam rapidity for Large Hadron Collider (

y

b

≈

8.7) is depi ted as the solid bla k lineinFig. 1.1.

Whilethenu leiare olliding,the nu leonslose theirkineti energy. The

energy lossper parti ipant baryon an be expressed:

< δE >= E

b

−

2

N

part

Z

y

b

0

hm

T

i coshy

dN

B− ¯

B

dy

dy

(1.3) where:

E

b

-initialenergy of beam.

It is estimated that <

δE

> = 21

±

2 GeV for Au+Au at

√

_s

N N

= 62.4 GeV [19℄ and <

δE

> = 73

±

6 GeV for Au+Au at

√

_s

N N

=200 GeV for the most (0-10 %) entral ollisions [20℄. For two olliding nu leons the al ulated energy loss is

2<

δE

>,whi his70%of the initialenergyofbeam. This energylossistransformed mainlyintoparti le produ tionand random (thermal) motionof produ ed partons

atAGS,SPSandRHIC.ThesolidlinerepresentsthettotheSPSandRHICdata.

Thegreybandisthe statisti alun ertainty. The dashedlineislinearttotheAGS

and SPS results [21℄. The plot is published in[19℄.

FromBRAHMSmeasurementsattopRHICenergyone an on ludethat

the midrapidity region of the ollision is almost net-baryon-free. It orresponds to

pi ture of intera ting matter proposed by Bjorken [22℄ with near free net-baryon

ontent at midrapidity. At lower energy,

√

_s

N N

= 62.4 GeV, for Au+Au rea tions at

y ≈

0 the net-proton

dN

dy

indi ates that the medium is also quite transparent ompared withdata at SPS and AGSenergy [21℄.

1.2.2 Nu lear Modi ation Fa tor

At extremely high energy density, whi h is supposed to be obtained

duringheavy ions ollisionsatultra-relativisti energies, one an expe t that inthe

olour harged medium the suppression of the produ ed parti les might be

signi- ant. Due toenergy lossof high-

p

T

partons aused by the gluon radiation,parti le produ tioninAu+Au ollisionsatRHIC energiesisregarded tobesuppressedwith

referen e to the p+p rea tions yield. The measure used to explore the medium

ef-fe tsis alled nu lear modi ation fa tor,

R

AA

. The

R

AA

is dened as the ratio of the parti leyieldprodu edin the nu leus-nu leus ollision,s aledwith the number

R

AA

=

1

hN

coll

i

d

2

_N

A+A

_/dp

T

dy

d

2

_N

p+p

_/dp

T

dy

(1.4) where:

N

coll

-the number of binary ollisionsatgiven entrality ut.

Atlow

p

T

, where the produ tions ales with the number of parti ipants,

N

part

,

R

AA

should onverge to

N

part

/

N

coll

whi h is1/3 forheavy ions systems. Par-ti leswith high

p

T

are primarilyprodu ed inhard s attering, earlyin the ollision. Innu leus-nu leusrea tionshards atteredpartonsmighttravelinthemedium.

As-sumingthat the partons traverse through QGP,they loose a large fra tion of their

energyby indu ed gluonradiation,suppressingthe jet produ tion. Experimentally,

knowing as the jet quen hing [15℄, it an be observed as adepletion of the high

p

T

regionin hadronspe tra. ForAu+Au rea tions at

√

_s

N N

=200 GeV itis observed [24℄ that, in fa t,mesons and baryons are suppressed for nu leus-nu leus ollisions

inreferen e tothe elementary(p+p) rea tions inthe whole rapidity range at

p

T

< 1.5 GeV/

c

. At larger transverse momentumthe nu learmodi ation fa tor at mid-and forward rapidity for pions is

R

AA

< 0.6and

R

AA

< 0.4, respe tively. Though, for protonsthe value of

R

AA

su essively in reases with rising

p

T

. These out omes might indi ate that the dense state of quarks and gluons produ ed at midrapidity

remains right up to the forward region. The in rease of

R

AA

for protons may be related to radial ow of medium reated in Au+Au rea tions that boost produ ed

protonstolarger

p

T

. This phenomenon an be alsoexplainedby quark oales en e models [51, 25℄. Considering the above presented s rutiny it is also additional

mo-tivationtostudy the pion and protonprodu tionratioin onjun tion with rapidity

dependen e.

1.2.3 Color Glass Condensate

The observations for d+Au ollisions at

√

_s

N N

= 200 GeV, whi h might indi atethe existen e of ColorGlass Condensate state, were one of the most

ex iting results obtained by BRAHMS experiment at RHIC. It is dis ussed widely

in[18, 27℄.

From equation 1.4 one an on lude, in the absen e of nu lear ee ts,

thenu leus-nu leus ollisions an beinterpretedasasuperpositionofhard

nu leon-nu leon intera tions at high

p

T

(

R

AA

≈

1). At RHIC energies, for d+Au ollisions we do not expe t to produ e an extended hot and dense medium. The nu lear

typ-as the Cronin ee t and is asso iated with partoni multiple s attering - an initial

statebroadeningofthedistributionofquarkmomenta. Whenwegotomoreforward

rapiditiesBRAHMS has observed [18℄ a signi ant suppression at high

p

T

starting alreadyat

η

=1andin reasingwithin reasingpseudorapidity. Theexisten eofthe ColorGlassCondensatemightbeanexplanationofthisee tinforwardregime[28℄.

Thegroundstatenu lei hasalargenumberof low-

x

gluons-where

x

isthefra tion ofthe longitudinalnu leon momentum arried by parton. Asa resultof intera ting

gluons with ea h other an augmenting of gluons takes pla e with de reasing

x

. It happens untilthe hara teristi momentums ale,knownasthe saturations ale

Q

s

, isrea hed. Pre isely,not the wholeamountof gluonsstop in reasing,but onlythat

onewith gluonsizelargerthan 1/

Q

s

. This stateisseen ind+Au intera tions where the low-

x

omponents (mostly gluons) of the wave fun tion of the gold nu lei are probed by deuteron parton res attered atforward region.

Comparing the nu lear modi ation fa tor for pions, kaons and protons

for entral and peripheral entrality at the same rapidity for d+Au rea tions at

√

_s

N N

= 200 GeV there is noti eable dieren e [18℄. In the ase of

y

= 0 we an observe a signi ant enhan ement, espe ially for protons near

p

T

≈

2 GeV/

c

. For entral ollisionsatforward rapidity the suppression of

R

AA

isevident forall kinds of hadrons. Forperipheral rea tions the ee t is not so appre iable.

On the other hand, in Dual Parton Model the addition of dynami al

shadowing orre tion has been in orporated todes ribe the

R

dAu

behaviour [29℄.

1.2.4 Elementary ollisions

Thep+p ollisionsat

√

s

=200GeVand62.4GeVareoftentreatedas the referen e tothe heavy ions intera tions to extra tthe nu learee ts. AtRHIC

it has been shown that parti le produ tion in p+p rea tions at ultra-relativisti

energies onveys new tasks to a omplish, espe ially in the ontext of rapidity

de-penden e. The single-transverse-spin asymmetries

A

N

or net-baryon distribution issues are worth pointing out [31, 35℄.

TheBRAHMS measurementsatforward rapidityare ex eptionally

inter-esting. At forward rapiditiesin p+p rea tions the produ ed parti les are from the

kinemati region where large-

x

valen e quarks (0.3 <

x

< 0.7) from the beam side res atter on small-

x

gluons (0.001 <

x

< 0.1). In 2007, BRAHMS Collaboration published data for

π

−

_{, K}

+

_{, p, ¯}

_p

for p+p ollisions at

√

s

= 200 GeV for

y ≈

3 and omparedthemwiththe Next-to-Leading-OrderperturbativeQuantum

Chromody-Figure 1.2: The net-proton distribution in p+p ollisions as a fun tion of rapidity

shifted by

y

beam

,

y − y

beam

, ompared with data from NA49 at

√

_s

N N

= 17.2 GeV. The pi turehas been published in[35℄.

mentation fun tions (FFs), namely the modied 'Kniehl-Kramer-Potter' (mKKP)

fragmentation fun tions (FFs), a 'Kretzer' (K) and 'Albino-Kniehl-Krame'(AKK)

fun tions. For pions and kaons the agreement is remarkable for mKKP FFs and it

isinterpretedasaneviden eofthe dominationofgluon-gluonandgluon-quark

pro- essesat

y ≈

0. Thisobservationatforward regimeissupported by the omparison with neutral pion and dire t photon spe tra obtained by STAR experiment [30℄.

At high rapidity a good des ription of baryon yield is provided by AKK fun tions

revealing that the ontribution of gluons fragmenting into protons (antiprotons) is

dominant (80% for

p

T

< 5 GeV/

c

). One an say that NLO pQCD al ulations des ribes the BRAHMS results very well and it is a milestone in understanding

elementaryintera tions.

In elementary ollisions,atmidrapidityregimeBjorken s enario[22℄

net-protondistributioninproton-proton ollisionsatboth energies:

√

s

=62.4GeV (

y

beam

= 4.2

) and

√

s

= 200 GeV (

y

beam

= 5.3

) as a fun tion of rapidity shifted by

y

beam

ispresented inFig. 1.2. Theresults ofNA49 experiment [36℄are alsoshown. As it has been observed the in reasing dieren e between antiproton and proton

yield with in reasing rapidity, viewing from the rest frame of one of the protons,

does not depend on the in ident beam energy. The remarkable overlap of

experi-mental data strongly suggests that we should not expe t any new me hanisms in

proton-proton rea tions inthe overed ollidingenergy interval.

1.3 Organization of the thesis

1. Chapter 2 in ludes the theoreti al interpretation of

p/π

ratio

p

T

-dependen e inthe RHIC range of baryo hemi alpotential.

2. Chapter 3 presents the BRAHMS experimental setup used to measure data

presented in this thesis.

3. Chapter 4des ribesthe details of the data analysis.

4. Chapter5displaystheobtained resultson

p/π

ratiosand omparesthemwith dierent hadronizations enarios.

5. Chapter 6presents the summaryof analysis.

6. Appendix 1 introdu es the main kinemati alvariables.

7. Appendix 2lists the numbers of runs forparti ular settings for ea h olliding

systemandenergy. Thespe i ationofworking triggersduringmeasurements

Motivations

2.1 Nu leus-nu leus ollisions at RHIC energies

At RHIC, where the gold and opper nu lei are ollided, the heavy

ions rea tions give the great opportunity not only to sear h for eviden es of QGP

reation, but alsoto explore properties of hot and dense medium.

Heavy ions ollisionat relativisti energies is oftendisplayed as two

at-ten "pan akes" passing through one another [43℄. That attening appears due to

Lorentz ontra tion. In the wake of nu lei is left melting oloured glass, whi h

nallymaterializesaspartons(quarks andgluons) [27℄. Thesepartonswould

natu-rallyemergeintheirrestframe, hara teristi forsaturated olourglass,mi ros opi

time s ale whi h at RHIC is

1

Q

s

≈

0.2

fm

c

(where

Q

s

- saturation momentum [44℄). Withrapidity along beam axis and be ause of the Lorentz time s ale dilation

par-ti les with small rapidity (low momentum) are produ ed in the enter of ollisions

andwith large

y

- away from entre, lose tothe beam fragmentationregime. That viewis lose to the Bjorken s enario [22℄ whi h is a des ription of hydrodynami al

expansionon whi h, nowadays, a lot of hydrodynami s al ulations are based [12℄.

The hydrodynami s approa hes delineate the spa e time evolution of perfe t uid

systemwithvis osity loseto0. Theverygoodagreementofthe omputationswith

experimentaldata[8℄-themomentumdistributionand olle tiveow-indi atethat

atthe very beginningof the intera tion the strongly oupled Quark Gluon Plasma

isformed [7℄.

The expansion of the intera ting matter during ollisionis s hemati ally

sket hed in Fig. 2.1. Just after the moment of ollision the hot and dense system

starts to expand and ool down. It is supposed that in the moment of intera tion

the energy density of matter is

ǫ ∼

5 GeV/

fm

3

[6℄. At the pre-equilibrium state

equilibrium with well-dened spa e-time expansion. The partons may thermalize

after 0.2

fm

c

. If the lo al equilibrium is rea hed in the system before 1

fm

c

, the olle tive ow of QGP an be hara terized by the hydrodynami evolution. With

in reasingtime,de reasingenergydensityandtemperaturetheQuarkGluonPlasma

state turns into the mixed phase of quarks, gluons and hadrons - QGP starts to

hadronize. Theprodu edhadronsmightde ayintostableparti lesandintera twith

ea hother. Eventually,theprodu edparti lesarebeingdete tedintheexperimental

ounters.

2.2 QCD phase diagram

Phase transitions are ommon phenomena related not only to water

orwidespreadsubstan es, but alsotonu learmatter. Almost everybodyknows the

transitionsbetweeni e

→

water

→

steamwhileaddingheattothesystem. Asimilar pro essesareexpe tedtoo urwhenweaddheattothesystemofnu learmatter(or

blematizes the rossover between Quark Gluon Plasma and hadroni phase. The

red solid line symbolises the 1st order phase transition. The dotted blue urve

represents the hemi al freezeout. The arrows denote the value of baryo hemi al

Ingeneral,inthermodynami alframeworkone omponentsystem anbe

des ribed using three variableswhi honly two of themare independent. The QCD

phase diagramis a plot of two independent thermodynami variables,temperature

τ

and baryo hemi al potential

µ

B

. The points (

τ

,

µ

), where a phase transition o urs, tra e a line in the phase diagram thus a phase transition plot be omes a

spe i map of the dierent phases of intera ting matter.

Inthelastde ades,theintensetheoreti alandexperimentalinvestigations

ofthe QCDphasediagraminthe regimeofpartoni andhadroni gas phasesledus

tothepi turedepi tedinFig. 2.2[46,47,48℄. Thedashed-dottedredlinerepresents

the rossover from Quark Gluon Plasma to the hadroni state pro ured from the

latti e QCD al ulations [37℄. The omputations show that the smooth rossover

between the quark-gluon state and hadroni state should o ur below

µ

B

≈

400 MeV(although, forinnitelylargestrangequarkmassthe modelspredi t

µ

B

≤

700 MeV [38℄) and above that value the rst order transition of partoni and hadroni

matter is predi ted. Moreover, the theory predi ts the riti al point at the end

of rst order phase transition line. The riti al point o urs for the se ond order

phase transition and the value of riti al temperature

τ

c

varies from 160-170 MeV [12, 37, 48℄. The experimentalmeasurements of hadroni spe ies abundan es allow

ustooutlinethe dottedblue lineasthe hemi alfreezeoutofthe hadroni gas. Itis

remarkablethatatlowbaryo hemi alpotentialthe rossoverand hemi alfreezeout

urves overlap, albeitat large

µ

B

a signi ant gap between the temperature of the transition from the partoni to the hadroni phase,

τ

c

, and the temperature of hemi alfreezeout is predi ted. At very high baryon density and lowtemperatures

the olour super ondu tivity domain is predi ted. It is also expe ted that the ore

of neutron stars an be hara terized by high value of

µ

B

and low

τ

.

In this thesis I study the

p/π

(

p

T

) ratio in nu leon-nu leon and nu leus-nu leus ollisions at dierent olliding energy in the wide range of pseudorapidity.

Thisresear hgivesthe possibilitytoanswerthequestionhowthe propertiesof bulk

medium arry out in the system with the in reasing value of baryo hemi al

po-tential. As it has been show at low value of

µ

B

the re ombination of partons is maintained [9℄. To determine the essen e of nal state intera tions the new

explo-rationisdesired. Forstudied experimentaldata thebaryo hemi alpotentialvaries

Theintentionofthenext twose tionsistopresentsele tedtheoreti al

models that an be onfronted with experimental approa h of baryon and meson

produ tion.

2.3.1 Thermodynami al des ription

In order to apply thermodynami al approa h to the nu lear matter

produ edinrelativisti heavyion ollisionsthefollowing onditionsmustbefullled:

1. the system must be omposed of many parti les and its dimensions must be

largerthan the typi alstrong intera tion s ale (

∼

1fm)

2. theintera tingmatterisinthethermodynami al(thermaland hemi al)

equi-librium

3. the lifetime of system,

t

, is longer than the typi al relaxation time (

t ≫

1 fm/ ).

Instatisti alphysi sthereare threepossiblegraspsofthe hara terizationof

thesystem: mi ro anoni al, anoni alandgrand anoni alensemble[39℄. Assuming

the requirement of the variable number of parti lesduring the ollision, the grand

anoni al ensemble is the most appropriate. It in ludes opportunity to ex hange

the parti les and energy for the lo al subsystem with the reservoir i.e. the whole

system. In this ase, we x the temperature

τ

, volume

V

and hemi al potential

µ

as a lo al ondition. Consequently, if the system is des ribed by a Hamiltonian

H

withaset of onserved numberoperators

N

ˆ

i

,the statisti aldensityof matrixmight bepresented as:

ˆ

ρ = exp[−

1

_τ

(H − µ

i

N

ˆ

i

)]

(2.1) whi h results inthe grand anoni al partitionfun tion as follows:

Z = Tr ˆ

_{ρ → Z =}

X

n

< n|e

−(H−µ ˆ

N )/τ

|n > .

(2.2) Other thermodynami properties an be derived from

Z = Z(V, τ, µ

1

, µ

2

, ....)

:

P = τ

∂lnZ

∂V

→ P =

τ

N

i

= τ

∂lnZ

∂µ

i

s =

∂(τ lnZ)

∂τ

ǫ = −P V + τs + µ

i

N

i

where:

P

- pressure,

N

i

- number of parti les,

s

- entropy,

ǫ

- energy. A ording to that, we an get statisti al multipli ity distribution, assuming that neither bosons nor

fermions intera t with ea h other when they are put in a box with sides of

L

[39℄. On the other hand we should not forget that the thermal equilibrium is required

whi h implies that the intera tions of parti les must exist. In this ase the grand

partitionfun tiontakesform:

lnZ = V

Z

d

3

p

(2π)

3

ln(1 ± e

−(ǫ−µ)/τ

₎

±1

(2.3)

referingthe(+)tofermionsand(-)tobosons. Eventually,thenumberofparti les

an be des ribed as:

N = V

Z

d

3

p

(2π)

3

1

exp[−(ǫ − µ)/τ] ± 1

(2.4) fromwhi h the dierential multipli ity iseasy to obtain:

d

3

_N

dp

3

=

V

(2π)

3

1

exp[−(ǫ − µ)/τ] ± 1

.

(2.5) At RHIC the hemi al potential (

µ ∼

MeV) is in omparably smaller than the energies (

ǫ ∼

GeV),so

→ exp[(ǫ − µ)/τ] ≫

1. Thus inBoltzmann limitit leads to:

d

3

_N

dp

3

=

V

(2π)

3

exp[(µ − ǫ)/τ] → exp[−ǫ/τ].

(2.6) The last expression isused with the assumption of the xed value of the

hem-i alpotential. This equation is just the Boltzmann distribution of the many body

system, being inprin iple the rootfor the hadroni spe tra deliberations.

Through the exploration of the proton-to-pion produ tion it might be

studiedthe main dieren ebetween produ tionof baryon- asa parti le ontaining

three valen e quarks - and meson building up from quark and antiquark. From

that point of view it is important tointrodu e variables su h as strange and baryo

µ

i

= −τ

∂S

∂N

i

!

U,V,N

j6=i

(2.7)

with the denition of entropy

S = S(U, V, N

1

, ..., N

k

) → U

- internal energy,

N

1

, ..., N

k

- the numberof

i

parti les. In high energy physi s the hemi alpotential isassignedwiththesymmetriesand hargesandfulllsthe onditionofthequantity

onservation. For every onserved quantum number we have a hemi al potential

i.e. baryon quantum number - baryo hemi al potential,

µ

B

, strangness - strange hemi alpotential,

µ

S

, harge onservation- hemi alpotential onne tedwiththird omponent of isospin,

µ

I

3

. In the simplest way the baryo hemi al potential,

µ

B

, an be interpreted asthe energy indispensable to reate the parti lein the system.

In strong intera tions the net-baryon density is onserved and in ase of

nu leus-nu leus ollisions

6=

0. Thetotalnet-strangness isalso onserved andequals 0.

With the assumption that hemi al and thermal equilibrium has been

obtained, the thermodynami al models des ribe the AGS and SPS experimental

dataquite well[41, 46℄. The baryo hemi al potentialvaries forthat data from200

to 600 MeV, for AGS and SPS, respe tively. Studying parti les yields and their

ratios we an only on lude about the pro ess of hadronization and the value of

temperature and baryo hemi al potential. With the thermodynami al approa hes

itis not possible to say if the Quark Gluon Plasma state has been reated.

2.3.2 Quark re ombination model

BelowI givethe briefintrodu tionof the quark re ombinationmodel

( ompletedes ription an befound in[49℄, [51℄,[52℄, [53℄, [54℄,[55℄,[56℄, [57℄).

InRudolphC.Hwa'sgrasp,theongoingpro essofhadronizationis

dividedintotwopartsdependingonhowthepartonsre ombine. Onetou hesonthe

midrapidityregime(hereprimarily onsideredatintermediate

p

T

be auseBRAHMS setup does not identify parti les beyond

p

T

> 8 GeV/

c

) where the partonsat high

p

T

are the sour e of thermal and shower partons whi h undergo oales en e. The whole al ulations are done in the 1D-momentum spa e where the momentum

p

of measured hadron is dened in appointed dire tion. The R. Hwa's deliberations

start with the distribution of quarks and antiquarks just before the pro ess of

re- ombination that indi ates that initial pro esses whi h ome out from dynami al

originsare nottaken intoa ount. Thespe i re ombination anonlyyieldquarks

andantiquarks, however gluonshadronize by onversion to

q ¯

q

pairs. The quark(q)-antiquark(q')(quark-quark-quark),in ase ofmeson(baryon), anre ombineinthe

Figure2.3: Transverse momentum distributionofpions

π

0

(left-handside) and

pro-tons(right-handside)forAu+Au ollisionsat

√

_s

N N

=200 GeVatthe midrapidity region. Dierent ontributions to the re ombination of partons are depi ted. The

plots are taken from[53℄.

medium only if these partons are ollinear (e.g. for mesons - quarks momentum:

p

q

= p

q

′

= p

; azimuthal angle of emitted quarks from the ollision:

φ

q

= φ

q

′

= φ

). Moreover, the hard s attering proves the in rease of the number of partons with

high

p

T

,butinpresen e ofmatter reated afterthe ollision,that numberde reases due to the intera tions with the olour harged medium indu ing the energy loss.

This ee t is implemented phenomenologi allyby use of ee tive parameter

ξ

. For

y

=0the in lusivedistribution foraprodu ed pionwith momentum

p

an bewritten:

p

dN

π

dp

=

Z

dp

1

p

1

d(p − p

1

)

p − p

1

F

_{q ¯}

_q

′

(p

₁

, p − p

₁

)R

_π

(p

₁

, p − p

₁

, p)

(2.8) where:

F

_{q ¯}

_q

′

is the joint distribution of a quark

q

at

p

1

and antiquark

q

¯

′

at

p − p

1

whi h re ombine and

R

π

(p

1

, p − p

1

, p)

designates the re ombination fun tion for

q ¯

q

′

→ π

dened as follows:

R

π

(p

1

, p − p

1

, p) =

p

1

(p − p

1

)

p

2

δ

p

1

p

+

(p − p

1

)

p

− 1

!

.

(2.9)

In there ombinationfun tionitis introdu edalmost'by-hand' the Krone ker

δ

fun tiontoguarantee the onservation ofmomentumin the re ombinationpro ess.

That is the major weakness of all of the re ombination (other name: oales en e)

models wherethe onservation of momentum and energy doesnot ensuein natural

For mesons the joint distribution fun tion might be expressed

s hemati- ally:

F

_{q ¯}

_q

′

= T T + T S + (SS)

₁

+ (SS)

₂

(2.10) where:

T T

- represents ontribution where two thermal (soft) partons eventually produ e the thermalhadron

T S

- stands for the thermal-shower pairs of quarks ( onsidered in the 3 <

p

T

< 8 GeV range)

(SS)

1

- represents the ontribution of two shower partons having originated from one hard parton

(SS)

2

- ontributionof two shower partonsbut omingfromseparate hard partons (atRHIC energies this ontributionis negligible).

Ea h of these fra tions ontribute to the invariant in lusive pion

distri-bution shown in Fig. 2.3 (left hand). Even at the highest RHIC's energy the

shower-shower(2-jet)-

(SS)

2

omponent ontributesatleast one orderofmagnitude less than the other omponents. Ea h ontributionwhi h in ludes the shower part

is suppressed by the

ξ

fa tor hara terizing fra tion of existing partons whi h an hadronizegoing outsidethe rea tion. In otherwords,it isdened as the fra tionof

theenergy loss. Atlow

p

T

the mostsigni ant ontributioninthejointdistribution seemstobethethermal-thermal

T T

fra tionusually onne tedwiththesoft ompo-nent of pion spe tra. For larger

p

T

the thermal-shower

T S

partplays animportant role.

Forbaryons the invariant in lusive distribution goesas follows:

p

dN

p

dp

=

Z

dp

1

p

1

dp

2

p

2

dp

3

p

3

F

_qq

′

q

′′

(p

1

, p

2

, p

3

)R

p

(p

1

, p

2

, p

3

, p)

(2.11) where:

R

p

(p

1

, p

2

, p

3

, p)

-the re ombinationfun tion of proton,

F

_qq

′

q

′′

isthe joint distributionof three relevantquarks whi hform aproton.

For baryon the joint distribution fun tion may be depi ted in the s hemati way:

F

_qq

′

q

′′

= T T T +T T S +T (SS)

1

+T (SS)

2

+(S(SS)

1

)

2

+(SSS)

3

whereatRHICrange of energy onlythe rst four ontributions there are meaningfulwhere, atmost, the

showeroriginateone hard parton.

therightpanelofFig. 2.3. When

p

T

<2GeV/

c

the massee t be omesimportant. The dominan e of thermal-shower-shower (1-jet)-

T (SS)

1

is observed espe ially at high

p

T

, but at lower value of transverse momentum the thermal-thermal-thermal

T T T

omponentisalsovalid. There ombinationofthethermalandshowerpartons dominates atthe intermediate

p

T

. The pion and proton spe tra,obtained fromthe model al ulations, have been used in attempt to get the proton-to-pion ratio vs.

transverse momentum. This results are onsistent with the

p/π

+

ratio obtained

experimentally and they are presented in se tion5.1.

The revision of the forward hadron produ tion in the framework of the

quark re ombination model has been done re ently [49℄. It was inspired by the

presented experimental data of

p/π

+

ratio for Au+Au ollisions at

√

_s

N N

= 62.4 GeV [58℄.

In forward produ tion of hadrons one an distinguish two me hanisms

whi h ontributetothe re ombination. Oneof themis relatedtothe valen equark

distribution,taking into a ount the three (forbaryons, two - formesons) ollinear

nu leons, oming from the proje tileintrodu edas the tube with the same impa t

parameter

|~s−~b|

inthe target(

~s

- ongurationofnu leonsinthe target,

~b

-impa t parameter;notations the sameasused inthe Glaubermodel[59℄). Of ourse,those

three (two) nu leons, from whi h the ontributing onstituent quarks ome, pass

throughthe rea tingzone andundergo ollisionswiththetargetwhi hisimpliedin

thesenseofthedegradationparameter

κ

. Moreover,theee tofsu essive ollisions is inan indissoluble manner onne ted with the se ond ontribution to meson and

baryonprodu tion- regeneration. After

ν

ollisions (notationslike in[56℄), the net momentum fra tion lost dened as

1 − κ

ν

is gone in for onversion to soft partons

(quarks+gluons)assisting the regeneration ofthe sea quark distribution. Similarly,

as in the midrapidity regime, gluons an not re ombine dire tly into hadrons, but

rstly they are onverted to

q¯q

pairs.

Thewayhowbothpro esses ontributetothehadronprodu tiondepends

on the spe ies of parti le. For protons, the valen e quark fra tion dominates over

seaquarksatFeynman'svariable

x

. Duetothat impa tthe enhan ementof proton overpion yield inthe fragmentationregion an be generated.

2.3.3 Hydrodynami al models

The hydrodynami al approa hes [12, 65℄ are based on the following

2. the intera ting matter is treated as the ontinuous system where the

dimen-sions are mu h larger thanthe distan e between parti les(in the sense of the

s aleof strong intera tions

≫

1 fm)

3. as the dynami s of the medium we understand the dynami s of units of the

ontinuous system-uid

4. ma ros opi variables are usedto des ribethe thermodynami sof the system

(i.e. entropy,initialenergy);the olle tivemotionsof theunitsofthe uidare

hara terizedby typi alkinemati alvariables(i.e.

~p

)

5. the evolution of the uid is des ribed by the following equations:

(a) energy and momentumtensor of ideal uid

T

µν

= (ǫ + P )u

µ

u

ν

_{− P g}

µν

(2.12) where:

u

µ

- four-velo ityof the unit of the medium,

g

µν

-metri tensor

(b) energy and momentum onservation

∂

µ

T

µν

= 0

(2.13)

( ) the thermodynami al variable an be expressed as the fun tion of the

proper time:

ǫ = ǫ(t)

,

p = p(t)

,

τ = τ (t)

with the thermodynami al relations

ǫ + P = τ s;

dP = sdτ ;

dǫ = τ ds

(2.14) where:

ǫ

- energy density,

P

- pressure,

τ

- temperature,

s

-entropy

(d) for boost-invariant expansion in the longitudinal dire tion the equation

of motion takes form:

∂ǫ

∂t

+

ǫ + P

t

= 0

→

ǫt

4/3

_{= constant.}

(2.15)

6. initial onditions of evolvingsystem

•

entropyand baryondensityare proportionaltothe parti ipatingnu leon distribution

s(x, y, τ

0

) =

C

s

τ

0

dN

p

τ

0

dxdy

;

n

B

(x, y, τ

0

) =

C

n

B

τ

0

dN

p

dxdy

(2.16)

•

equation of state -[12, 61, 62℄

The equation of state is asso iated with the state variables su h as

tem-perature, pressure,baryondensity,energy density. Ingeneralthestateof

nu lear matter might be deliberated with dierent assumptions: 1) the

matteristreatedasidealrelativisti gaswith masslessparti lesor2)the

phase transition between partoni and hadroni state o urs and nally

parti les with mass are produ ed or 3) going from high energy density

statedes ribedbybag modeltolowenergy densitymatterwherethe gas

of hadroni resonan es is on erned.

•

whilethereballofuidisevolving,thetemperatureanddensityde rease unlessthesystema omplishesfreezeoutstage;theinvariantsingle-parti le

distributionfromfreezeoutsurfa eis al ulateda ordingtothe

Cooper-Fry's formula[63,64℄:

E

dN

d

3

_p

=

Z

f (x, p)p

ν

_{· dσ}

ν

=

d

(2π)

3

Z

p

ν

· dσ

ν

exp[(p

ν

· u

ν

− µ(x))/T (x)] ± 1

(2.17) where:

E

-energyoftheparti le,

p

-momentumoftheparti le,

f (x, p)

- Lorentz-invariantdistributionfun tion,

u

-four-velo ity,d

σ

ν

=

(d

3

_x,~0)

-freezeout

(hyper)surfa e,

µ

- hemi al potential,

d

- degeneration omponent (e.g.

d

=3for pions),

T

- freezeout temperature.

2.3.3.1 The non-boost-invariant single-freezeout model

The des ription of the non-boost-invariant single-freezeout approa h

ispresented in[50, 65℄. The modelutilizesonly the spa e-time hadron distribution

after the simultaneously kinemati al and thermal freezeout, hen e it is so- alled

single-freezeout model. The produ ed hadrons evaporate from hypersurfa e,

Σ

, at the su essive stage of the expansion of the reball. It does not in lude the

depi tedtra ksofprodu edhadronsforparti ularvalueofpseudorapidity

η

(dashed lines). The pi ture istaken from [50℄.

parti les in relativisti heavy ion ollisions. The non-boost-invariant dynami s of

thesystem are parti ularlyinteresting with takingintoa ount itssimpli ity. With

alltypi alhydrodynami alinitial onditions,the evolutionoftheintera tingmatter

is shown as the evolving reball (as presented in Fig. 2.4) with the well-dened

3+1-dimensionalhypersurfa e

Σ

fromwhi hthe olle tiveemissionofhadronstakes pla e. In every step of iteration of parti les "evaporation", the produ ed hadrons

o upystatesdes ribedbyFermi-Dira orBose-Einsteindistribution(withregardto

parti lespe ie). Thedeterminedthermodynami parametersare temperature

τ

and hemi alpotentials:

µ

B

(baryon),

µ

S

(strange),

µ

I

3

( onne tedwiththird omponent

ofisospin)dependingonthepositionoffreezeouthypersurfa e

Σ

. The Hubble-type owof produ ed parti leshas two- longitudinal and transverse - omponents:

longitudinal flow:

v

z

= tanhα

k

=

z

t

(2.18)

transverse flow:

v

ρ

= tanhα

⊥

.

(2.19) Hen e, the spatial rapidity an bedened asfollows:

α

k

= arc tanh

z

transverse radiusexpressed as follows:

ρ =

q

x

2

_{+ y}

2

_{= τ}

1

sinhα

⊥

.

(2.21)

Moreover, three parameters:

τ

1

,

ρ

(0)

max

,

∆

are introdu edtodeliberatethe spatial evolution of the reball where the rst one hara terizes the proper time, se ond

one - the transverse size at midrapidity and the third parameter is used to ontrol

the spatialrapidity

α

⊥

.

If the reball expands in the longitudinal dire tion(

z

-axis on the Fig. 2.4)

α

k

in reases. The maximum spatialrapidity an be expressed as:

0 ≤ α

⊥

≤ α

max

⊥

(α

k

) ≡ α

max

⊥

(0)exp

−

α

2

k

2∆

2

!

.

(2.22)

In this equationthe

∆

parameter des ribesde rease of hypersurfa e

Σ

in trans-verse dimension with

α

k

. It isalsointrodu ed thedependen e of hemi alpotential onspatial rapidity

α

k

:

µ(α

k

) = Bµ

B

(α

k

) + Sµ

S

(α

k

) + I

3

µ

I

3

(α

k

).

(2.23) It entails some onsequen es. The standard performan e in the thermal model

adoptsthe hemi alandthermalvaluesoftemperature(

τ

chem

≥ τ

kin

) onsistentwith hemi al and kinemati al freezeout [41, 67, 68℄. In the single-freezeout model the

onstantvalueofthetemperatureissetforboth hemi alandkinemati alfreezeout

-τ

=165MeV(for0<

µ

B

<250MeV).Moreover,thehadronsresonan esareapplied inthe al ulations. It is estimated that at relativisti energies 75% of pions origins

from the de ays of resonan es. Additionally,it is an ee tive way to ontribute to

de rease the temperature of spe tra

∼

35-40 MeV and inuen es the slope of the parti lesspe tra.

Themodelin ludesten parameterswhi hshouldbettothe

experimen-taldata (the details of tting pro edure is presented in [66℄). The simulations are

done using the THERMal heavy IoN generATOR (THERMINATOR) to get the

MonteCarloevents. As theresultofthe al ulationsone an getthe net-strangness

of the system equals 0 for gold-gold ollisionsthat is asu ess of the model.

The main attainment of the single-freezeout model is good agreement

with the BRAHMS spe tra of mesons and baryons for Au+Au ollisions at

√

_s

N N

=200 GeV in the wide range of rapidity [50℄. The results of single-freezeoutmodel

obtainedforAu+Au ollisionsat

√

_s

Broad RAnge Hadron Magneti

Spe trometers at RHIC

3.1 Relativisti Heavy Ion Collider

TheRelativisti HeavyIonColliderislo atedinBrookhavenNational

Laboratory on Long Island in the USA [43℄. It is dedi ated to ondu t resear h of

heavy ion rea tions at the ultra-relativisti highest available energies. At the main

a elerationrings there are situatedfour experiments whi h engagevarious aspe ts

of the strong intera ting matter. STAR and PHENIX experiments have the ability

to dete t the wide spe trum of the parti les at midrapidity with high momentum

overage. The PHOBOS experiment is designed to explore the low

p

T

regime of the intera tions with the overall look of the ollisions. The BRAHMS experiment,

in turn, an identify parti le over the widest range of rapidity,

y

, and transverse momentum,

p

T

.

TheRHIC fa ility-depi ted inFig. 3.1-is omposedof the apparatures

whi h are used in the su essive steps of nu lei a elaration. The rst step is to

prepare the bun hes ofthe ions in the TandemVander Graa. The Tandem peels

o the ele trons fromthe atoms (gold or opper) and boostpositive harged ions

tothe of 385 MeV. Afterwards, bun hes are transferred by the Tandem-to-Booster

linetothe Boostersyn hrotron. The Boostersyn hrotronand thenthe Alternating

GradientSyn hrotronare apabletopropeltheionstotheenergyof 1GeV/nu leon

and 10GeV/nu leon, respe tively. The spe ial design of the magneti eld

gradi-ent of the a elerator's magnets allows to be fo used in the verti al and horizontal

dire tion. It auses that the transfer of energy might be larger and the eld makes

possible to on entrate the beam in the little tight spa e. It is worth mentioning

elerator radiofrequen y avities. From the AGS the bun hes of the nu lei migrate

to the AGS-to-RHIC rossroads where some of the ions are dire ted to lo kwise

RHIC ring and the other part goes to the ounter- lo kwise RHIC ring (it is often

des ribed as blue and yellowbeam). The beams are ir ulated and are rumped up

todesired energy inthe RHIC ring where the ions are ollided inthe four so- alled

beam interse tion regions: BRAHMS, PHENIX, PHOBOS and STAR fa ilities.

I fo us onthe data for Au+Au ollisions and p+p rea tions at

√

_s

N N

= 62.4GeVand200GeVwhi hwere olle tedin2004(Au+Au)and2005/2006(p+p).

The number of runs taken during three BRAHMS experiment ampaigns together

with information of olliding system, beam energy and spe trometer settings are

listedin Appendix 2.

3.2 BRAHMS dete tor setup

The BRAHMS dete tor setup - Fig. 3.2 - onsists of two movable

spe trometer arms: the Midrapidity Spe trometer (MRS) whi h operates in the

polarangle intervalfrom

30

◦

_{≤ Θ ≤ 90}

◦

(that orresponds with the pseudorapidity

interval

1.3 ≥ η ≥ 0

) and the Forward Spe trometer (FS) that operates in the polarangle range from

2.3

◦

_{≤ Θ ≤ 15}

◦

(

4 ≥ η ≥ 2

). Moreover, the overall parti le multipli ity, ollisionvertexand entralityaredeterminedusingtheglobaldete tors.

Although both of the spe trometers are very narrow, by the rotation of arms the

spe trometer an over a lotof phase spa e (see Fig. 5.1in se tion5.1).

The Midrapidity Spe trometer is lo ated perpendi ular to beam axis,

loseto the nominalrea tionvertex. In the MRSthe parti les are registered inthe

transverse dire tionto thebeam axis. The singledipolemagnet,D5 (notations like

inthe Fig. 3.2),pla edbetween twoTimeProje tionChambers,TPM1 andTPM2,

whi h omposethemidrapidityarm,areusedfortra king. Cherenkovdete tor(C4)

andTimeofFlightWall(TOFW) measurementsallowtoidentifyparti leswiththe

separation of

π

/K and p/K up to2 GeV/

c

and 3.5GeV/

c

,respe tively.

The front forward arm is omposed of two Time Proje tion Chamber

(TPCs), T1and T2 ( onstitutingtra kre ognitioninthe highmultipli ity

environ-ment),theba kpart-ofthreeDriftChambers(T3,T4, T5). Allthe hambers-T1,

T2, T3, T4, T5 - operate in a high momentum mode. The forward going parti les

are swept by the two dipoles (D3, D4) toward the ba k end of the spe trometer

where they are tra ked in Drift Chambers - Fig. 3.3. The parti le momenta are