Studia porównawcze oddziaływania w niskoenergetycznych układach ppη i ppη'

WYDZIAŠ FIZYKI, ASTRONOMII

I INFORMATYKI STOSOWANEJ

INSTYTUT FIZYKI im. MARIANA SMOLUCHOWSKIEGO

Studia porównaw ze oddziaªywania

w niskoenergety zny h ukªada h

ppη

i

ppη

′

Paweª Klaja

pra aprzygotowanawZakªadzieFizykiJ¡drowej

InstytutuFizyki im. MarianaSmolu howskiego,

WydziaªuFizyki,AstronomiiiInformatykiStosowanejUniwersytetuJagiello«skiego,oraz

wInstytu ieFizyki J¡drowejwCentrumBadaw zymJüli h,

pod kierunkiemProf. PawªaMoskala.

FACULTY OF PHYSICS, ASTRONOMY

AND APPLIED COMPUTER SCIENCE

MARIAN SMOLUCHOWSKI INSTITUTE OF PHYSICS

Comparative studies of the

intera tion in the low energy

ppη

and

ppη

′

systems

Paweª Klaja

dissertationpreparedat theNu lear Physi sDepartment

oftheMarianSmolu howskiInstitute ofPhysi s,atFa ultyofPhysi s,AstronomyandApplied

ComputerS ien eoftheJagiellonianUniversity

andin InstituteofNu learPhysi satResear hCentreJüli h,

guidedbyProf. PaweªMoskal.

The COSY-11 ollaboration measured the

pp → ppη

and

pp → ppη

′

rea tions in

order to perform omparative studiesof the intera tions within theproton-proton-meson

system.

Thisthesis presents indetail the analysis of the

pp → ppη

′

rea tion whi h wasmeasured

attheproton beam momentumof 3.260GeV/ .

Theelaborationresultsindierentialdistributionsofsquaredinvariantproton-proton(

s

pp

) andproton-

η

′

(

s

pη

′

) masses,aswell asinangular distributions and thetotal ross se tion atan ex ess energy of16.4MeV.

The dierential distributions

s

pp

and

s

pη

′

are ompared to theoreti al predi tions and to theanalogous spe tradetermined for the

pp → ppη

rea tion.

The omparison of theresults for the

η

and

η

′

meson produ tion rather ex ludes the

hy-pothesis that the enhan ement observed inthe invariant mass distributions is due to the

meson-proton intera tion.

Further, the shapes of the distributions do not favour any of the postulated theoreti al

models.

Stresz zenie

W rama h grupy badaw zej COSY-11 wykonano pomiary reak ji

pp → ppη

oraz

pp → ppη

′

w elu przeprowadzenia studiów porównaw zy h oddziaªywania w ukªadzie

proton-proton-mezon.

W rozprawie doktorskiej zaprezentowano analiz dany h z pomiaru reak ji

pp → ppη

′

wykonanegoz wykorzystaniem wi¡zki protonowej o pdzie 3.260GeV/ .

Wynikiem analizy przedstawionej w niniejszej pra y s¡ ró»ni zkowe przekroje zynne w

funk ji mas niezmienni zy h proton-proton (

s

pp

) i proton-

η

′

(

s

pη

′

), rozkªady k¡towe oraz aªkowityprzekrój zynnydla energiiwzbudzenia Q=16.4MeV.

Rozkªady ró»ni zkowe

s

pp

oraz

s

pη

′

zostaªy porównane z przewidywaniami teorety znymi orazanalogi znymi widmamiotrzymanymidlareak ji

pp → ppη

.

Porównanierezultatówotrzymany hdlaproduk jimezonów

η

i

η

′

pozwalanawyklu zenie

hipotezy,»ewzmo nienieobserwowane wwidma h masniezmienni zy h jestpowodowane

oddziaªywaniem mezonu zprotonem.

1 Introdu tion 11

2 Low energy intera tion within a proton-proton-meson system 15

2.1 Ex itation fun tionsfor

pp → ppη

and

pp → ppη

′

rea tions . . . 15 2.2 Comparison of

η

,

η

′

and

π

0

mesonintera tion withprotons . . . 16

2.3 Denitions ofobservables . . . 18

2.4

pp

and

p − meson

invariant massdistributions . . . 19

3 Experimental fa ility 23

3.1 CoolerSyn hrotron COSY . . . 23

3.2 COSY-11 dete torsetup . . . 25

3.3 Triggerlogi . . . 27

4 Calibration of the dete tor setup 29

4.1 Spa e-time relationfor drift hambers . . . 29

4.2 Time-of-ight alibration ofs intillatordete tors . . . 30

4.3 Monitoring ofrelative beam-targetsettings . . . 31

5 Identi ation of the

pp → ppη

′

rea tion 35 5.1 Identi ation ofprotons . . . 35 5.2 Identi ation ofthe

η

′

meson . . . 36 6 Luminositydetermination 39

7 Determinationofthe spread andtheabsolutevalueof thebeam

momen-tum 43

8 Fine tunning of the relative dipole- hamber settings 47

9 Evaluation of the dierential distributions 49

9.1 Kinemati al t . . . 49

9.2 Ba kground subtra tion . . . 52

10.2 Totaland dierential rossse tions . . . 64

10.3 Comparison withresults for the

η

mesonprodu tion . . . 70 10.4

s

pp

and

s

pη

′

distributions inviewof theoreti alpredi tions . . . 72

11Summary 77

A Pseudos alar mesons 79

B Parameterization of the proton-proton FinalState Intera tion 81

C Formalism ofa ombinedanalysis ofphoto- andhadro-produ tionof the

η

′

meson 83

The knowledge of the meson-nu leon intera tion at the hadroni level is one of the

ma-jor goals in nu lear physi s, nowadays. Also, studies of meson stru ture and produ tion

me hanisms onstitute a huge interest of nu lear and parti le physi ists. During the last

de adesmanymeasurementsprodu edinterestingresults[1℄,butvariousquestionsarestill

open.

In the SU(3)-avour s heme the

η

and

η

′

mesons belong to the nonet meson family of

pseudos alar mesons. The

η

and

η

′

mesons onstitute a mixture of states: singlet-

η

1

and o tet-

η

8

.

It is important to stress that the strength of the

pη

and

pη

′

intera tion depends on the

stru tureofthe

η

and

η

′

mesonsand isdire tlyrelatedto thesinglet-

η

1

ando tet-

η

8

on-tributions inthe wave fun tionsofthese mesons[2 4℄.

Taking into a ount the mixing angle the resulting ontribution of the various quark

avours inthe

η

and

η

′

wave fun tionisalmost the same. However, inspite of the

postu-latedsimilar quarkstru turethe

η

and

η

′

mesonsoweunexpe tedlydierent features.

Themost drasti onesare:

ˆ

η

and

η

′

mesonspossessdierentmasses,the

η

(547)mesonisalmosttwotimeslighter than the

η

′

(958) meson [5℄.

ˆ Thebran hingratiosofBandD

s

mesonsfor thede aysintothe

η

′

meson arehigher

than for the de ays into the

η

meson, and deviate strongly from model predi tions [6,7℄.

ˆ There isno experimental eviden efor baryoni resonan ewhi h de aysby the

emis-sion of an

η

′

meson [5,8℄ while e.g. the resonan es N(1535) and N(1650) de ay via

the emissionofthe

η

mesonwitha signi ant probability [5℄.

These dierent features ould imply a possible dieren e in the intera tion of

η

and

η

′

mesons with elementary parti les, and indi ate that also the produ tion me hanism of

both mesonsinelementary parti le ollisions might vary.

Due to the short life-time of the avour neutral pseudos alar mesons, experiments with

meson beams or targets are di ult or hardly feasible. Therefore, the nu leon-meson

in-tera tion anbestudied onlyviaits inuen eon the rossse tionsoftherea tionsduring

whi h they areprodu ed (e.g.

N N → NN Meson

) [1℄.

Quantitative information about theintera tion an be gained fromthe shapeof the

ex i-tation fun tions for the

pp → ppη

and

pp → ppη

′

rea tions as well as from a omparison

ofthose to the

ppπ

0

Up to now, only the proton intera tion with pions and the

η

-meson [1℄ was studied moreexhaustivelydue tomu hmorehighertotal rossse tionsin omparisontothe ross

se tionfor the

pp → ppη

′

rea tion.

Besides the ex itation fun tion also dierential distributions of invariant proton-proton

and proton-meson masses onstitute a sensitive toolfor studies of the intera tion within

the meson-nu leon system. The distribution of the proton-

η

invariant mass showed a lear enhan ement in the region of small proton-

η

relative momenta [9℄. The observed ee t ould be explainedbythenonnegligiblerole oftheproton-

η

intera tion inthenal state [10,11℄, the admixture of higher partial waves during the

η

produ tion [12℄, or the energydependen eoftheprodu tion amplitude[13℄. Usingonly the

pp → ppη

data, itis howevernot possible to justifyor falsify anyof the above mentioned hypothesis.

Theendeavour toexplaintheobservedenhan ementmotivatedtheexperimentandthe

analysisof the

pp → ppη

′

rea tion whi h ispresented inthis thesis. This experiment was

performed using theCOSY-11 dete tor setup[14 16℄, installedat the ooler syn hrotron

COSY[17℄attheResear hCentreJüli hinGermany. Itwas ondu tedinanenergyrange

losetothekinemati althresholdforthe

η

′

mesonprodu tion,wheretherelativevelo ities

oftheprodu ed parti lesaresmall.

The analysis and results of the

pp → ppη

′

rea tion measurement, ondu ted in order to

determinethe distributionof eventsoverthephasespa efor anex essenergy rangeequal

to the one measured before for the

pp → ppη

rea tion are presented in this thesis. The measurementwasperformedat thenominalbeammomentumof3.257GeV/

orrespond-ingto thenominalex ess energy for the

ppη

′

rea tion equal to 15.5MeV.The analysisof

the

ppη

′

data wasperformed ina similarway asithasbeen done for the

ppη

system. The omparison of the dierential distributions for theproton-proton and for the

proton-meson invariant masses inthe

η

and

η

′

produ tion ouldhelpto judge about thevalidity

ofpostulatedtheories on erningtheobserved enhan ement and allows for aquantitative

estimationofthe relativestrengthoftheproton-

η

andtheproton-

η

′

intera tions,provided

thattheee t is aused bythe proton-meson intera tion.

Inthe following hapter the urrent statusof the

pp → ppη

and

pp → ppη

′

total ross

se tionmeasurements ispresented. Furthermore,thepossibilityofproton-

η

andproton-

η

′

intera tionstudies isdis ussed andthedes ription oftheobservables usedintheanalysis

des ribed in this thesis is given. The results a hieved for the

pp → ppη

measurement as well astheavailable theoreti aldes riptions ofthe results arepresented.

Chapter3 is devoted to thepresentation of the experimental fa ilityused to perform the

pp → ppη

′

measurement. In the next hapter, themethods used for the alibrationof the

COSY-11 dete tors and their relative geometri al settings are presented. The time-spa e

relation of the drift hambers and the pro edure for the time-of-ight alibration is

In hapter5 the method ofthe

pp → ppη

′

rea tionidenti ation willbe depi ted and the

method ofidentifyingmeasured andalso unobserved parti leswill be given.

Furtheron,the pro edureoftheluminosity(

L

)determinationwillbepresentedin hapter 6,andinthe onse utive haptersitwillbeshownhowtheabsolutevalueandthespreadof

thebeammomentumwasextra ted,andthemethodfor thedeterminationoftheposition

ofthedrift hambers relative to theCOSY-11 dipole willbeexplained.

Chapter9 omprises the evaluation pro edure of thedierential distributions. First, the

kinemati altpro edureand thentheba kground subtra tion dueto themulti-pion

pro-du tionwill bedis ussed.

The nal results on erning the total ross se tion and dierential distributions are

pre-sented in hapter 10. The a eptan e orre tions are dis ussed and the a hieved

experi-mentalresults are ompared to theoreti al predi tions.

The on lusionsarepresentedin hapter 11.

In the appendi es at the end of the dissertation some issues dis ussed in the thesis are

explained inmore detail. In therst one thestru ture of thepseudos alar meson nonet,

mesonmassesandquarkstru turearepresented. These ondoneisdevotedtothe

des rip-tion of the parameterization of the on-shell proton-proton intera tion. General remarks

about the ombined analysis of the

η

′

meson formalism in photo- and hadro-produ tion

arepresentedinthe third addendum,and the linearenergy dependen e oftheprodu tion

system

The intera tion of hadrons is the ree tion of the strong for e between the quarks, and

provides information about the hadron stru ture and the strong intera tion itself [1℄. In

theframework of theopti al model, the intera tion between hadrons an be expressedin

termsofphase-shifts, whi hinthezeroenergylimit aredes ribedbythes atteringlength

andee tive rangeparameters [1℄. Thesevariablesarequitewell establishedfor the

(low-energy) nu leon-nu leon intera tion [18,19℄, but they are poorlyknown for the

nu leon-meson or meson-meson intera tions. The estimated real part of the s attering length of

the

η

-proton potential, depending on themethod of the analysis and studied region, is 3 to10 times[1℄ largerthan for the

π

0

-proton s attering (

a

pπ

0

=0.13fm)[20,21℄, whilefor the

η

′

meson only anupperlimit isknownof 0.8fm[22℄.

Theintera tion of mesons(e.g. pseudos alar mesons 1

:

π, K, η, η

′

) withnu leons ould be

dedu edfromtheexperimentsrealizedbymeansofmesonbeams,butsu hexperimentsare

notfeasiblein aseoftheavourneutralmesonsduetotheirshortlifetime[1,5℄. However,

the study of their intera tion with hadrons is ertainly a essible via their inuen e on

the rossse tion of rea tions like

N N → NN Meson

in whi h they areprodu ed [1℄. In su h a ase, the intera tion within the nalmesonnu leon system will modify theshape

of the ex itation fun tion and of the dierential distributions of invariant masses of the

nu leon-nu leon-meson systems.

2.1 Ex itation fun tions for

pp

→ ppη

and

pp

→ ppη

′

rea tions

Nearthekinemati althresholdmeasurements ofnu leon-nu leon ollisions allowto study

theparti le produ tion witha dominant ontribution from one partial wave only. Inthis

energy range, the dependen e of the total ross se tion as a fun tion of the

entre-of-mass ex ess energy is predominantly determined by the available phase spa e and the

intera tion between theexitparti les. The ex itation fun tionsfor the

pp → ppη

′

[23 28℄

and

pp → ppη

[28 33℄ rea tions are presented in gure 2.1. Comparing the data to the arbitrarily normalized phase-spa e integral reveals that proton-proton FSI enhan es the

total ross se tion by more than one order of magnitude for low energies. In ase of the

η

′

meson produ tion one re ognizes that the data are des ribed well assuming that the on-shellproton-proton amplitude ex lusively determinesthephase-spa e population.

1

1

10

10

2

10

3

10

4

10

5

1

10

10

2

pp

→

pp

η

pp

→

pp

η

´

Q

[

MeV

]

σ

[

nb

]

Figure2.1:The

pp → ppη

and

pp → ppη

′

ex itationfun tions[2333℄. Thedashedlinesindi ate

arbitrarilynormalizedfun tions obtainedunder theassumption ofthehomogeneousphasespa e

o upation. Solidlines orrespondto al ulationsofthephasespa eweightedbytheproton-proton

on-shells atteringamplitude[22℄.

Thisindi atesthattheproton-

η

′

intera tionistoosmalltomanifestitselfintheex itation

fun tion within the presently a hieved statisti al un ertainty. However, for the

η

meson produ tionthe enhan ementisbyaboutafa toroftwolargerthanin aseofthe

η

′

meson

and annot be des ribed bythe

pp

-FSIonly.

2.2 Comparison of

η

,

η

′

and

π

0

meson intera tion with protons

Thestrength ofthe intera tion dedu ed fromthe omparison ofthedata andthe linesin

gure2.1 depends on the model of theproton-proton intera tion usedin the al ulations

for the

ppη

and

ppη

′

systems [22℄. Therefore, inorder to estimatea relative strength

be-tweenthe

pη

and

pη

′

intera tions inamodelindependent wayone an ompare theshape

oftheex itationfun tionofthe

pp → ppη

and

pp → ppη

′

rea tions. Moreover,one angain

somequantitativeinformation abouttheseintera tionsbya omparison oftheseshapesto

the

ppπ

0

system [1℄,sin e the

π

0

0

0.5

1

1.5

2

2.5

3

10

-1

1

10

10

2

10

3

V

_phs

[

MeV

2

]

|M

0

η

| / |M

0

π

| a.u.

0

0.5

1

1.5

2

2.5

3

10

-1

1

10

10

2

10

3

V

_phs

[

MeV

2

]

|M

0

η

´

| / |M

0

π

| a.u.

Figure2.2: The ratios

|M

η

0

|/|M

0

π

|

(left) and

|M

η

′

0

|/|M

0

π

|

(right) extra ted from data al ulat-ing the

pp

-FSI a ording to the formulas from referen e [22℄, and negle ting the proton-meson intera tion[1℄. Theratioisshownasafun tionofthephasespa evolume[22℄.

For thatpurpose, one an ompareonly the dependen eof theprodu tion amplitudes

|M

0

|

derived fromthe datatakinginto a ount the

pp

-FSI only. The dependen e of

|M

η

0

|

and

|M

η

′

0

|

as a fun tion of the phase spa e volumes normalized to

|M

π

0

|

arepresentedingure 2.2. The

|M

0

|

for the

η

,

η

′

and

π

0

mesonswere extra ted

from data, disregarding any proton-meson intera tion. When the negle ted

η

(

η

′

)-proton

intera tion would have been the same as the one for proton-

π

0

, the points in the plots

should have been onsitent with unity as an be seen for the

pp → ppη

′

rea tion, when

really the intera tion shows its weakness, independently of the pres ription used for the

proton-proton nalstateintera tion [22℄. In the aseof the

η

′

meson produ tionits weak

intera tionwithnu leons at the low-energyrangeisexpe teddueto thela kofany

bary-oni resonan es whi h ould de ayinto a

N η

′

system[1,8℄ 2

.

Statisti alun ertaintiesallowedto getonly avery onservativeupperlimitfor thereal

partofthes attering lengthof the proton-

η

′

potential resulting in:

|Re a

pη

′

| < 0.8 f m

[1,26℄.

Thus,independentofthemodelusedforthepres riptionofthe

pp

-FSI,froma omparison ofthe energy dependen e of the produ tion amplitudes for the

pp → ppη

,

pp → ppη

′

and

pp → ppπ

0

rea tions,itwas on luded thattheintera tion within theproton-

η

′

system is

mu h weakerthan theintera tion between theproton and the

η

meson.

Another possibility of learning about intera tions within nu leon-nu leon-meson systems

2

ontribu-is given by the dierential distributions of the invariant masses. This is why thepresent

analysisofthe

ppη

′

systemhasbeenperformedinasimilarwayasithasbeendoneearlier[9℄

for the

ppη

system. The determined

pp

and

p

-meson invariant mass distributions will be usedfor a omparative study of the intera tion withintheproton-meson system.

In the next se tion the denitions of the studied observables whi h will be used in the

furtheranalysis arepresented.

2.3 Denitions of observables

To des ribe thestudied three parti le (

ppη

′

)systemone needs onlyve independent

vari-ablesinthe entre-of-mass system. Inthisframe,dueto energy andmomentum

onserva-tion, momentum ve torsof protons and

η

′

lie inone plane, alled rea tionplane. In that

plane (shown s hemati ally ingure 2.3) the relative momenta of parti les are des ribed

byonly two variables. Thesequantities may be hosenassquare oftheproton-proton

in-variantmass

s

pp

and squareof theproton-

η

′

invariant mass

s

pη

′

. Invariant massesdepend on the relative velo ity of the parti les and are therefore well suited for a des ription of

theintera tions betweenthese parti les. Besidesthe relativemovement ofparti lesonthe

rea tion plane three other variables have to be dened for xing the orientation of the

rea tionplaneinthe oordinatesystem.

Figure2.3:S hemati denitionsofthe entre-of-masskinemati alvariablesusedforthe

des rip-tionofthe

ppη

′

system. Inthe entre-of-massframethemomentumve torsofthethreeoutgoing

parti lesarelo atedwithin therea tionplane. Inthisplanetherelativemotionof theeje tilesis

xed by the square of theinvariant masses

s

pp

and

s

pη

′

. Three remainingvariables the

φ

∗

η

′

,

θ

∗

η

′

and

ψ

anglesareusedtodenetheorientationoftheemissionplaneinspa e.

Inthisthesis, byanalogyto the evaluationofthe

ppη

system[9℄,theazimuthaland polar angles of the

η

′

meson momentum ve tor relative to the beam dire tion, denoted as

φ

∗

η

′

and

θ

∗

aroundthedire tion ofthe momentum ve torof the

η

′

meson.

Theintera tion between nalstate parti lesdoesnot alter theorientation oftherea tion

plane[9℄. Therefore,it willmanifest itself onlyinthe distributionof theinvariant masses

s

pp

or

s

pη

′

,or generallyinthe population ofthe Dalitz plot(

s

pp

vs.

s

pη

′

).

In the ase of non-intera ting parti les in the nal state these distributions should

or-respond to a homogeneously populated phase spa e. Therefore, their intera tion should

showupasa deviation fromthese expe tation.

2.4

pp

and

p

− meson

invariant mass distributions

Only two invariant masses of three subsystemsare independent and therefore the whole

a essible information about the nal state intera tion an be shown in the Dalitz plot.

One an also usethe proje tion of thephase-spa e distribution onto theinvariant masses

ofproton-proton or proton-meson subsystems[9℄.

Thequalitativephenomenologi alanalysisofthedetermineddierentialinvariant

proton-protonandproton-

η

massdistributionsrevealedanenhan ementofthepopulationdensity atthekinemati alregion orrespondingtoasmallproton-

η

momentum. Theproton-proton andproton-

η

invariant massdistributions determined for the

pp → ppη

rea tion at an ex- ess energy of 15.5 MeV are presented in gure 2.4

3

. The dashed lines in both panels

of the gure depi t the results of al ulations where only the on-shell amplitude of the

proton-proton intera tion hasbeen taken into a ount.

In those al ulations the enhan ement fa tor has been estimated as the square of

the on-shell proton-proton s attering amplitude derived using the modied

Cini-Fubini-Stanghelliniformula in ludingthe Wong-Noyes Coulomb orre tions[22℄.

One an easily see that the mentioned ee t is too large to be des ribed by the on-shell

in lusionof the proton-proton FSI.

In fa t a better des ription is a hieved when ontributions from higher partial waves

or o-shell ee ts of the proton-proton potential are taken into a ount. These

al ula-tions ompared totheexperimentallydetermineddierential proton-protoninvariantmass

distribution arepresentedingure 2.5. Inthe leftpanel of this gurethe experimentally

determined dierential rossse tion as a fun tion of the squaredinvariant proton-proton

massis ompared tothe al ulations ofV.Baruand ollaborators[39℄ underthe

assump-tionof a

3

_P

0

→

1

S

0

s

transitiona ording to the models des ribed in[39℄, depi ted as the solidline.

Dashed and dotted lines on the left panel of gure 2.5 represent the al ulations of

K. Nakayamaand his group[12℄. The authors laim that the ontribution of the S-wave

aloneisunabletoexplaintheobservedenhan ementinthesquaredproton-protoninvariant

3

0

20

40

60

80

100

120

3.52

3.54

3.56

3.58

s

_pp

[

GeV

2

/c

4

]

d

σ

/ds

pp

[

µ

b/(GeV

2

/c

4

)

]

COSY-11

phase space

FSI

_pp

on-shell

0

20

40

60

80

100

2.2

2.22

2.24

2.26

s

_p

_η

[

GeV

2

/c

4

]

d

σ

/ds

p

η

[

µ

b/(GeV

2

/c

4

)

]

_COSY-11

phase space

FSI

_pp

on-shell

Figure2.4:Distributionsofthesquareoftheproton-proton(

s

pp

)(left)andproton-

η

(

s

pη

)(right) invariantmasses determinedexperimentallyforthe

pp → ppη

rea tion( losedsquares). The inte-gralsofthephasespa eweightedbythesquareoftheproton-protonon-shells atteringamplitude

(dotted lines)-FSI

pp

have been normalized arbitrarily at small values of

s

pp

. The expe tations undertheassumptionofahomogeneouslypopulatedphasespa eareshownassolidlines.

0

20

40

60

80

100

120

3.52

3.54

3.56

3.58

s

_pp

[

GeV

2

/c

4

]

d

σ

/ds

pp

[

µ

b/(GeV

2

/c

4

)

]

COSY-11

1

_S

0

s

1

_S

0

s

1

_S

0

s +

3

_P

0

s

0

20

40

60

80

100

120

3.52

3.54

3.56

3.58

s

_pp

[

GeV

2

/c

4

]

d

σ

/ds

pp

[

µ

b/(GeV

2

/c

4

)

]

COSY-11

pp + ηp

3 - body

Figure2.5: (Left panel) Distribution of the square of the proton-proton (

s

pp

) invariant mass determined experimentally for the

pp → ppη

rea tion. Solid and dashed lines orrespond to al ulationsunder the assumption ofa

3

P

0

→

1

S

0

s

transition a ordingto themodelsdes ribed in[39℄and[12℄,respe tively. Thedottedlineshowstheresultof al ulationswithin lusionofthe

1

S

0

→

3

P

0

s

ontribution as suggestedin [12℄. (Right panel) The samedata as in the left panel but omparedwiththree-body al ulations[10,11℄. Thesolidlinewasdeterminedwitharigorous

massdistribution. Seekingfor thebetter des riptionthey postulate thattheshapeof the

enhan ement an be reprodu ed by folding the relative momentum of the proton-proton

subsystem withthe available phasespa e [12℄ suggesting that the enhan ement ould be

the onsequen eof the

pp

P-wave inthe nalstate. Cal ulations assuming a

3

_P

0

→

1

S

0

s

transition orrespond to the dashed urve and the result of al ulations with the in lusion of the

1

_S

0

→

3

P

0

s

ontribution is depi ted by the dotted line. Although the dotted line orresponding to al ulations based on the

strongerP-wave ontribution is inquite good agreement to the experimental determined

dierential distribution of the proton-proton invariant mass, it underestimates the

to-tal ross se tion data taken for the

pp → ppη

rea tion near the kinemati al threshold (Qlower than 30MeV)[1℄.

Onthe otherhand, thedis ussed ee t an inprin iple be assignedto hanges of the

produ tion amplitude, sin e in al ulations by V. Baru et al. [39℄, and by K. Nakayama

and ollaborators[12℄ the produ tion amplitude wasnearly onstant.

Ananalysisguidedbytheassumptionofalinearenergydependen eoftheprodu tion

am-plitudewasperformedbyA.Delo[13℄. Thesquaredinvariant massdistributions

s

pp

and

s

pη

′

determined for the

pp → ppη

rea tionmeasuredat anex ess energyof Q=15.5MeV are ompared to al ulationsperformedbyA.Deloingure2.6.

0

20

40

60

80

100

120

3.52

3.54

3.56

3.58

s

_pp

[

GeV

2

/c

4

]

d

σ

/ds

pp

[

µ

b/(GeV

2

/c

4

)

]

COSY-11

0

20

40

60

80

100

2.2

2.22

2.24

2.26

s

_p

_η

[

GeV

2

/c

4

]

d

σ

/ds

p

η

[

µ

b/(GeV

2

/c

4

)

]

_COSY-11

Figure2.6:Distributionsofthesquareoftheproton-proton(

s

pp

)(left)andproton-

η

(

s

pη

)(right) invariant masses determined experimentally for the

pp → ppη

rea tion ( losed squares). The experimentaldataare omparedto al ulationsperformedassumingthelinearenergydependen e

oftheprodu tionamplitudeasproposedbyA.Delo[13℄ depi tedbysolidlines.

dependen e inthe leading

3

_P

0

→

1

S

0

s

partial wave amplitude [13℄. Those al ulations are in ontradi tion to the suggestion of Nakayama [12℄, giving eviden e that higher partial

waves playonly amarginal role.

Atthispoint,theobservedenhan ement ouldbeexplainedbythreedierent

hypothe-ses:

i)asigni ant role ofproton-

η

intera tioninthe nalstate, ii)an admixture of higherpartial waves or

iii)anenergy dependen e of the produ tion amplitude.

Based on the

pp → ppη

data only,it is not possible to verifyany ofthose models. These ontingen ies motivated the work presented in this thesis whi h is an analysis of a high

statisti s

pp → ppη

′

rea tion measurement inordertodeterminethedistributionofevents

overthephasespa eforanex essenergyofQ=15.5MeVthesame oneassele tedbefore

forthe

pp → ppη

rea tion. The omparisonofthe dierential distributions forthe proton-protonandproton-meson invariant massesinthe

η

and

η

′

produ tion ouldhelpto judge

between postulated explanations of the observed ee t and may allow for a quantitative

estimationof the proton-

η

and proton-

η

′

intera tion.

Theexperimentalfa ility,themethodoftheanalysis,anda hievedresultsforthe

pp → ppη

′

The measurement of the

pp → ppη

′

rea tion was ondu ted using the ooler syn hrotron

COSYandthe COSY-11 dete torsetup. Both fa ilitieswill bedes ribedinthis hapter.

3.1 Cooler Syn hrotron COSY

TheCOolerSYn hrotron(COSY)[17℄ islo atedattheInstituteofNu learPhysi s ofthe

Resear hCentre Jüli hinGermany. Thefa ility wasdesigned toa elerate polarizedand

unpolarized proton and deuteron beams in the momentum range from 0.3 GeV/ up to

3.7 GeV/ . The sket h of the whole a elerator omplex is presented in gure 3.1. The

totallengthofthe syn hrotronringis184meter. Therearetwostraight40meter se tions,

andtwo bendingse tions with24dipole magnets.

Theexperimental installationsat thesyn hrotron anbe lassied astwogroups;

a)thedete torsinstalledinsidetheCOSYring: WASA[40,41℄,COSY-11[14 16℄,PISA[42℄,

EDDA [43℄,COSY-13 [44℄,and ANKE[45℄ and

b) outside of the COSY ring at external beam lines: COSY-TOF [46℄, JESSICA [47℄,

NESSI[48℄,GEM [49℄,MOMO[50℄, andHIRES [51℄.

Someof those experiments arealready ompleted and no longer in operation (labelled in

bla k)and the others arestill inoperation (labelled ingreen) ingure3.1.

TheCOSYsyn hrotron isequipped withele tronandsto hasti oolingdevi eswhi h

areusedto de reasethemomentumand spatial spreadof thebeam [52℄.

In the ase of ele tron ooling, theele trons with velo ities equal to the nominal proton

beam velo ity areinje ted at astraight se tionof the syn hrotron. Thisoperation auses

thatfaster protons arede elerated andslowerones area elerated.

Sto hasti ooling uses an ele tromagneti devi e, theso alledpi k-up unit, whi h

mea-sures the beam deviation from the nominal position at one point of the a elerator and

orre ts it by transmitting a orre tion signal through the shortest way to the ki ker

unit at theother side of the beam pipe. It auses not only a shift to the nominal beam

orbit, but also de reases the spread of the transversal and longitudinal momentum

Figure3.1: S hemati view of the oor plan of the COSY syn hrotron. Marked in violet are

internal-beam [14,40,4245℄ and external-beam [4651℄ dete tor setups. Fa ilities COSY-TOF,

WASAandANKElabelledingreenarepresentlystillinoperation. Thepositionsofele tronand

3.2 COSY-11 dete tor setup

Themeasurementofthe

pp → ppη

′

rea tionisbasedontheregistrationofthetwooutgoing

protonsandre onstru tionoftheir momenta. The

η

′

mesonisidentiedusingthemissing

masste hnique.

S2

Si

Figure3.2:S hemati viewoftheCOSY-11dete tionfa ility[14℄. Note,thatonlythosedete tors

whi h were used during the measurement of the

pp → ppX

rea tion are presented. Protons originating from the

pp → ppX

rea tion are bent in the dipole magneti eld, and leave the va uum hamberthroughtheexitwindow. Afterwardstheyaredete tedinthetwodrift hambers

D1andD2,inthes intillatorhodos opesS1andS2,andinthes intillatorwallS3. Thes intillation

The COSY-11 fa ility is one of the internal dete tor setups installed inside the COSY

syn hrotron tunnel at a bending se tion of the ring. It is mounted next to one of the

dipolemagnets, and benetsfrom thedipole magneti eldwhi h isused for theparti le

separationfrom the beam.

A s hemati view of the COSY-11 apparatus is presented in gure 3.2. The gure

illustratesalso s hemati allythe tra ks of protons outgoing fromthe

pp → ppX

rea tion. Twooutgoing protonspossessingsmallermomentathan thebeammomentum, arebent in

the dipole magneti eld towards the dete tor system. They leave the va uum hamber

throughout the exit window made out of a 30

µ

m layer of aluminum and 300

µ

m of a arbon ber arriermaterial withan averaged densityof 2.1 g/ m

3

[14℄ and are dete ted

usingthe drift hambersD1 andD2, the s intillator hodos opesS1 andS2, andthe

s in-tillationwall S3 1

.

The target 2

used during the experiment, was realized as a beam of

H

2

mole ules grouped inside lusters of up to about

10

6

atoms. The average density of the target

wasaround

5 · 10

13

atoms/ m

2

[63℄. Itwasinstalledinfrontofthedipolemagnetasit an

be seens hemati allyin gure3.2.

Thedrift hambersD1andD2wereusedfor thedetermination oftheparti les

traje -tories. Those two planar drift hamber sta ks are spa ed by 70 m [14,64℄. Their a tive

areais1680mmwide and433mmhigh. Drift hamberD1(standing losertothebending

magnet) onsistsofsixdete tion planes. The rsttwo withverti al wires,two withwires

in lined by

+31

o

and two in lined by

−31

o

. The D2 drift hamber is built in the same

s heme, but itisextendedbytwo additional planeswith verti alwires.

Thewiresinadja entplanesofea hpairareshiftedbyhalfofthe ellwidthtoresolve

theleft-right position ambiguitywithrespe tto thesense wire. The hosen onguration

of thedete tion planes allows to perform the measurement of the horizontal and verti al

oordinates and enables aunique multi-hitevent identi ation[64℄.

A harged parti le rossingthedrift hambers produ es gasionization insidethedrift

ells, lled with a gas mixture of one to one argon and ethane at atmospheri pressure.

Theele trondrift time to the sensewireis ameasureof thedistan ebetween thepassing

parti le tra k and the sense wire (see se tion 4.1). Inthe ase of parti le tra ks oriented

perpendi ularto the dete tionplanes,themaximumdrifttime orrespondingto the

max-imumdrift path of20 mm equalsto 400 ns.

1

Inthemeasurementofthemesonprodu tioninthequasi-free

pd → pnp

spectator

X

rea tiondedi ated neutron[55 58℄and spe tator [59 61℄dete torswereinstalledinaddition. Theywerehowevernot used

forthemeasurementdes ribedinthisthesis.

2

Determined parti le traje tories inthe data analysisare tra ed through themagneti

eldofthedipoleba ktothetarget. Therefore,itispossibletore onstru tthemomentum

ve torsof outgoing parti lesat the rea tion point. The re onstru tion of themomentum

ve torsof the registered parti les ombined withthe information about thetime-of-ight

between the S1andthe S3dete tors allows forthe al ulation oftheparti lemassandby

thistheparti le type identi ation.

The S1 s intillating hodos ope is built out of sixteen identi al, verti ally arranged

modules, read out from both sides (top and bottom) by photomultipliers. The modules

with

45 × 10 × 0.4

m

3

dimensionsarearrangedwithsmallverti aloverlap(

1

mm[14,65℄) inorder to avoid "not overed" spa e in the geometri al a eptan e. The S1 dete tor is

usedasthe "start"for thetime-of-ight measurement.

The S2 s intillating hodos ope, similar asS1, onsistsof sixteen s intillation modules

withthedimension of

45 × 1.3 × 0.2

m

3

[14℄.

TheS3s intillatingdete tordeliversthe "stop"informationfor thetime-of-ight

mea-surement. It is built from one non-segmented s intillating wall with the dimension of

220 × 100 × 5

m

3

. Itisviewedbyamatrix of 217photomultipliers [14,66,67℄,o upying

theedgesof equilateral triangles withthesidesof11.5 m.

TheS4s intillation ountertogetherwiththesili onpaddete tor(depi tedingure3.2

asSi)areusedforregistrationofthere oilprotonsfromtheproton-protonelasti s attering

[14℄. The sili on pad dete tor [14℄ onsists of 144 pads with dimensions of

22.0 × 4.5 ×

0.28

mm

3

. Ea h padis readout separately.

3.3 Trigger logi

In the experiment two independent trigger bran hes were used, in order to dete t the

pp → ppη

′

and

pp → pp

rea tions. Themain triggerusedfor the

pp → ppη

′

rea tionwasbasedon thefollowing onditions:

T

pp→ppη

′

= (S1

_µ≥2

∨ S1

_µ=1,high

∨ S2

_µ≥2

∨ S2

_µ=1,high

) ∧ S3

_µ≥2

,

(3.1)

where

µ

denotesthemultipli ityofsegmentsintheS1andS2s intillationhodos opes,and the number of photomultipliers whi h have red in the S3 dete tor. The subs ript

high

stands for ahigh amplitude signalintheS1 and S2dete tors whi h was implemented for

triggeringevents whentwoparti les rossthesame segment [67℄. The hardwarethreshold

forthehighamplitude wassethighenough to redu ethenumberof singleparti leevents

onsiderably, and low enough to a ept most events (almost 100

%

) with two protons passingthroughone segment ofS1 [67℄.

between signals fromthe S1 and S4dete tors:

T

pp→pp

= S1

µ=1

∧ S4,

(3.2)

wheretheS1hodos opewasusedforthe registrationofforwards atteredprotons andthe

S4s intillationdete tor wasregistering re oilprotons.

The dete tors were positioned to over a large part of the kinemati s of the

pp → pp

elasti s attering. Due to the high rate of the

pp → pp

rea tion only every 128'th event was registered for the further analysis. The number of the elasti s attering events was

In this hapter the method used to alibrate the COSY-11 dete tors and their relative

settingswill bepresented. Inparti ular,the time-spa erelationof thedrift hambersand

thepro edureof time-of-ight alibration willbedes ribed. Inaddition, thepro edureof

monitoring the relative beam-targetsetting will be dis ussed.

4.1 Spa e-time relation for drift hambers

Thedrift hambersD1andD2 onsistof6and8planesofwires,respe tively. Theyprovide

theinformation about thedrift time of ele trons (tothe sense wires) produ ed along the

traje toryof hargedparti lespassingthroughthe hambers. Inordertore onstru tthose

traje tories one needs to establisharelation between drift timeanddistan e between the

parti letra kand thesensewire (Fig. 4.1(left)).

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0

100 200 300 400 500 600 700 800

drift time + offset

[

ns

]

distance from the sense wire

[

cm

]

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0

100 200 300 400 500 600 700 800

drift time + offset

[

ns

]

∆

X

MEAN

[

cm

]

Figure4.1: (Left panel) Time-spa e alibration - relation betweenthe distan e from the sense

wireand the drifttime. (Rightpanel) Corre tions of thetime-spa e relation, where themiddle

histogramrepresentsthemeanvalueof

∆X

,theupperandlowerhistogramsvisualizeonestandard deviation(

σ

)ofthe

∆X

distribution. Seethetextfortheexplanationof

∆X

.

Due to the sensitivity of the drift velo ity to the atmospheri pressure, humidity and

gas mixture hanges [68℄, the data used for the alibration pro edure were divided into

time intervals of about 3-8 hours, with a similar number of olle ted events. The

al-ibration fun tion was determined for ea h interval applying the pro edure of iterative

improvements[67℄. Startingwithanapproximatedfun tionofthespa e-timerelation, the

straightlinetotheobtainedpointswasttedandfurtheron,assumingthatit orresponds

totherealparti letra k,thedeviation

∆X

,betweenthemeasureddistan eoftheparti le tra k from the sense wire and the one from the tting pro edure was al ulated. Next,

having a ertain amount of data, one oulddetermine amean value of

∆X

asa fun tion of the drift time (presented in gure 4.1 (right)). The

∆X

M EAN

was subsequently used fora orre tion ofthe time-spa e relation. Next,theimproved fun tionhasbeen usedfor

thetra k re onstru tion similarly as intherst step. The whole pro edure wasrepeated

until the orre tionsweresmallerthan thestatisti alun ertainty ofthe

∆X

M EAN

. Theaveragedspatialresolutionofthedrift hambersa hieved intheexperimentdis ussed

inthis thesis amountedto 250

µ

m(rms).

4.2 Time-of-ight alibration of s intillator dete tors

Thes intillatordete torsS1andS3"start"and"stop",respe tively,areusedforthe

time-of-ight measurement. S1 onsists of 16 s intillator plates with photomultiplier readout

from both sides, and S3 is a s intillator wall read out by a 217 photomultipliers matrix.

Inorder toobtaintheproperinformation about thetime-of-ightbetween both dete tors,

one needs to determine time "osets" for all photomultipliers i.e. therelative dieren es

intransition time ofthe signal fromthephotomultiplier to theTDC unit.

Letusdenote

t

S1

asthe real time whenaparti le rosses theS1 dete torand

t

S3

when it rossesS3. Then, thetime-of-ight an be al ulated asfollows:

tof

S1−S3

= t

S3

− t

S1

. ThemeasuredTDC valuesfor a singlephotomultiplier inS1 andS3 dete tors read:

T DC

S1

= t

S1

+ t

y

+ t

S1

walk

(P M ) + t

S1

of f set

(P M ) − t

trigger

,

(4.1)

T DC

S3

= t

S3

+ t

pos

+ t

S3

walk

(P M ) + t

S3

of f set

(P M ) − t

trigger

.

(4.2) Inboth equations thetimestamp

t

trigger

(denotingthetimeofthetriggersignal) is iden-ti al. The index

y

orresponds to the distan e between hit position and the edge of the s intillator lose to the given photomultiplier in the S1 dete tor and

pos

stands for the distan e between the hit position and the photomultiplier in the S3 dete tor. The

ab-breviation

t

walk

denotes the orre tions for the

time − walk

ee t, i.e. the signal time dependen e onthe signalamplitude [69℄. Anydependen eof

t

y

is an elledbytakingthe averagebetweenthetimesmeasuredbytheupperandlowerphotomultipliers[67℄andthis

an be al ulated from theknowntraje tories. Thus, theonly unknown variablesare the

time osets

t

of f set

for both dete tors. For a rst approximation, the time dieren e in the S1 dete tor an be a hieved by taking into a ount signals from the parti les

ross-ing the overlapping parts of the modules. Next, for the S3 dete tor the time oset an

(

tof

rec

). Then, iteratively, using the obtained S3 oset one an determine the time o-sets for the S1 dete tor. After two iterations, the time osets for both dete tors an be

established. Asan example,the distribution

∆t(P M

S3

ID

)

determined as

∆t(P M

S3

ID

) = tof

S1−S3

(P M

ID

S3

) − tof

rec

fora groupof photomultipliers of theS3 dete torarepresentedingure4.2.

-4

-3

-2

-1

0

1

2

3

4

75

80

85

90

95 100 105 110

photomultiplier ID

∆

t(PM

S3

ID

)

[

ns

]

Figure4.2: Distribution of thetime dieren e betweenthe time

tof

rec

al ulated from the re- onstru tedparti lemomentum andthemeasured time

tof

S1−S3

betweentheS1 dete torand a parti ular photomultiplier in the S3 dete tor, as afun tion of the photomultiplier ID in the S3

dete tor. As a hieved afterse ond iteration, theguredepi tsonly afra tion ofPM's ofthe S3

dete tor(75-112).

ThetimeosetsforthephotomultipliersintheS3dete torareobtainedonthebasisofthe

timedieren es between

tof

S1−S3

and

tof

rec

presentedin gure4.2. Theywere adjusted su hthat thisdieren e isequal to zero.

4.3 Monitoring of relative beam-target settings

Possible hangesofthepositionwherethebeam rossesthetarget ouldhavesigni antly

inuen edthe momentumre onstru tion and asa onsequen e ouldworsen the

determi-nation of the mass of the undete ted parti le. Therefore, it is important to monitor the

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0

0.2 0.4 0.6 0.8

1

1.2 1.4 1.6

p

_II

[

GeV/c

]

p

⊥

[

GeV/c

]

Figure4.3:Thedistributionoftheperpendi ular

p

⊥

versusparallel

p

k

momentum omponentsfor

pp → pp

elasti s atteringeventsatabeammomentumof3.260GeV/ . Thesolidline orresponds to thekinemati al ellipse. Changes of theevent density along thekinemati al ellipse ree t the

angulardependen e ofthe rossse tionforthe

pp → pp

rea tion.

The mean value of the distan e between the expe ted kinemati al ellipse and the

exper-imental points (shown in gure 4.3) may be used as a measure for the deviation of the

enterofthe intera tionregion fromits nominalposition(

∆center

). Api torial denition of

∆center

is presented in gure 4.4 and the beam-target geometri al onditions are de-pi ted ingure4.5. By assuming a wrong intera tion enter there onstru tion results in

a wrong momentum determination and the

pp → pp

events are not entered around the expe tedkinemati al ellipse.

Figure4.4: Pi torial denition of the deviation of the enter of the intera tion region from its

Figure4.5:S hemati viewoftherelativetargetandbeamsettings. Leftpaneldepi tstheview

from above, right presents aside view.

σ

X

and

σ

Y

denote the horizontal and verti al standard deviationsof theassumed Gaussiandistributions of theproton beamdensity, respe tively.

∆

X

bt

denotes thedistan e betweenthe enters of the proton target and beam. The gureis adapted

from[70℄.

Inthe left panel ofgure4.6 themean distan eof experimental

pp → pp

eventsfrom the expe tedkinemati alellipseisshownasafun tionof

∆center

assumedintheanalysis. As anbe seen,the enter ofthe intera tion region diersby0.45 m fromthenominalone.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.4 -0.2

0

0.2

0.4

0.6

0.8

∆

center

[

cm

]

distance from the ellipse

[

GeV/c

]

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0

10000

20000

measurement time

[

minutes

]

distance from the ellipse

[

GeV/c

]

Figure4.6:(Leftpanel)Thedistan ebetweentheexpe tedellipseandthe enterofexperimental

distributionon the(

p

⊥

,

p

k

) plot(gure 4.3)versusthe deviation of the enter of theintera tion regionfrom itsnominalposition(

∆center

). (Rightpanel)Thedeviationofthedistan efrom the kinemati alellipseasafun tion ofthetimeofthemeasurement. Themeanvalueofthedistan e

fromtheellipsehasbeenplottedfor13hours intervals. Intheanalysisthevalueof

∆center

was setto0.45 m.

statisti al error in the determination of the mean value of the distan e from the ellipse.

Thevariations areatalevelof

10

−3

and,as an be inferredfromtheplotpresentedinthe

leftpanelofgure4.6, orrespondtoshiftsoftheintera tion enterbylessthan 0.01mm.

Thus, thevariations ofthe enter of the intera tion region an be safelynegle ted in the

5. Identi ation of the

pp

→ ppη

′

rea tion

Inthefollowing hapterthemethodofidentifyingthe

pp → ppη

′

rea tionwillbedes ribed.

5.1 Identi ation of protons

Themeasurement was basedon the registration oftwo outgoing protons originating from

the

pp → ppX

rea tion.

10

10

2

10

3

10

4

10

5

0

1

2

3

4

(invariant mass)

2

[

GeV

2

/c

4

]

events

pions

protons

deuterons

Figure5.1: Distribution of the squared invariant mass of the registered parti les. (Note the

logarithmi s aleonverti alaxis.) Signalsfrommeasuredpions,protons,anddeuteronsareeasily

distinguished.

After hoosing only two-tra k events, theprotons were identied by thedetermination of

theirrest masses. The parti lemasswas al ulateda ording tothe following formula:

m

2

=

p

~

2

_{(1 − β}

2

₎

β

2

,

(5.1)

where

~

p

and

β

are denoting the momenta and velo ities of parti les, respe tively, whi h were determined in an independent way (

p

~

from the urvature of the traje tory in the

dipoleand

β

fromthetime of ight between S1 and S3). The distribution of thesquared massesoftheparti lesisshowningure5.1. Clearlyvisiblearesignalsfrompions,protons

anddeuterons.

For the further analysis, parti les with re onstru ted masses in the range from 0.2 to

1.5GeV

2

/

4

wereassumedto beprotons.

5.2 Identi ation of the

η

′

meson

Inthepresentexperimentthede ayprodu tsofthe

η

′

mesonwerenotmeasured, therefore

itwasimpossibletoidentifyitsprodu tiononanevent-by-eventbasis. Eveninexperiments

dete tingallde ayprodu tsanunambiguousidenti ationofasingle"

η

′

produ tionevent"

isnot possible, but theba kground would be mu h smaller.

0

2000

4000

6000

0.95

0.955

0.96

0.965

missing mass

[

GeV/c

2

]

events / 0.25 MeV/c

2

Figure5.2:Missingmassspe trumforthe

pp → ppX

rea tionmeasuredatabeammomentum of

P

B

=

3.260 GeV/ . The peakoriginating from the

pp → ppη

′

rea tionis learly seenon top

ofamulti-pionprodu tionba kground. Thedashedline orrespondsto at withase ondorder

polynomialtothedataoutsidethesignalfrom the

η

′

meson.

Thenumber of

pp → ppη

′

events wasdetermined using themissingmasste hnique. This

method is based on the knowledge of the protons four-momenta before and after the

Identi ationof the

pp → ppη

′

rea tion 37

four-momenta of the proton beam, proton target, and rst and se ond outgoing proton,

respe tively, one an usethe following formula, inthe ase of the

pp → ppX

rea tion, to al ulatethe mass

m

X

of the unregisteredparti le:

m

2

_X

= E

_X

2

_{− ~p}

2

_X

= (P

b

+P

t

−P

1

−P

2

)

2

=

= (E

b

+ E

t

− E

1

− E

2

)

2

− (~p

b

+ ~

p

t

− ~p

1

− ~p

2

)

2

.

(5.2) In gure 5.2 the missing mass spe trum determined experimentally for the

pp → ppX

rea tionfor the whole datasampleis presented. The spe trumin ludes abroad

distribu-tionfrommulti-mesonprodu tionandthewelldenedpeakoriginatingfromthe

η

′

meson

produ tion.

Thesmoothbehaviouroftheexperimentalmulti-pionprodu tionba kground,whi h ould

be veried byMonte Carlosimulations studies (see se tion9.2), allows for asimple

poly-nomial t. The knowledge of the smooth behaviour of the ross se tion [60,71℄, assures

thatintherangeof the signal, themulti-pion ba kground should be at.

The dashed line in gure 5.2 orresponds to a se ond order polynomial tted to the

ex-perimental ba kground. Indeed, it an be seen that the t reprodu es the shape of the

ba kground satisfa torywell.

0

500

1000

1500

0.95

0.955

0.96

0.965

missing mass

[

GeV/c

2

]

events / 0.25 MeV/c

2

Ingure5.3 the experimental missingmassspe trumafter theba kground subtra tion is

presented. Theba kgroundwasapproximated byase ondorderpolynomialtasdepi ted

ingure5.2byadashedline. Thetotalnumberofregisteredandre onstru ted

pp → ppη

′

rea tionsamountsto about 15000.

Here, the statisti sa hieved in the measurement is only illustrated and thepossibilityof

the ba kground determination is shown. A detailed dis ussion of the subtra tion of the

multi-pion produ tion ba kground for dierential ross se tions will be omprehensively

Inorder to determine theabsolute values ofthe dierential rossse tions, theluminosity

(

L

) integrated over the measurement time has to be established. For that purpose, the analysis of the

pp → pp

rea tion, in order to establish the number of elasti s attering eventswasperformed.

A s hemati view of theCOSY-11 dete torsetup with superimposed tra ks of elasti ally

s atteredprotons isshowningure6.1.

Si

123....

...48

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

-8

0

-6

0

-4

0

-2

0

0

20

40

60

80

x

S1

[cm]

Figure6.1:S hemati viewoftheCOSY-11apparatuspresentingthedete torsusedforthe

reg-istrationofthe

pp → pp

elasti s attering. Thesuperimposedlinesshowanexampleoftraje tories from elasti ally s attered protons with the laboratory angles

θ

1

and

θ

2

. One an ompare this guretogure3.2. The

x

S1

axisindi atesthesizeofdete tormodules(forfurtherdes riptionsee text).

One an evaluate theluminosity(

L

)a ording tothe formula:

∆N (θ

₂

∗

)

∆Ω

∗

_(θ

∗

2

)

=

dσ

∗

dΩ

∗

(θ

∗

2

) · L,

(6.1) where

dσ

∗

dΩ

∗

(θ

∗

2

)

denotes the knowndierential rossse tion [72℄ and

∆N (θ

∗

2

)

indi ates the number of elasti ally s attered protons at a solid angle

∆Ω

∗

around theproton emission

angle

θ

∗

2

in the entre-of-mass system. In thefurther analysis, the available range of the

θ

₂

∗

angle(

44

o

to

66

o

)wasdividedinto 11binswithawidth of

2

o

. Thetra ksofelasti ally

s atteredprotonsresultinginsignalsinthe S1dete torwitha oin ident signalinS4from

the se ond proton overs the horizontal axis of the S1 dete tor, marked in gure 6.1 as

x

S1

,from 40 m to 75 m, whi h orrespondsto a

θ

∗

2

anglerange from

44

o

to

66

o

.

0

5000

10000

15000

20000

25000

30000

-0.4

-0.2

0

0.2

0.4

distance from ellipse

[

GeV/c

]

48

o

<

Θ

*

₂

<

50

o

events

Figure6.2:Proje tionoftheeventdistributionalongthekinemati alellipsefora entre-of-mass

protons attering angle of

θ

∗

2

in therange from

48

o

to

50

o

, orresponding to therangein the S1

dete torfrom

x

S1

= 67.0 cm

to

x

S1

= 70.0 cm

.

As an example, the distribution of elasti ally s attered protons at the

θ

∗

2

angular range from

48

o

to

50

o

is presented in gure 6.2. This distribution shows the proje tion of the

experimental data along the kinemati al ellipse. The number of events (redu ed by the

ba kground indi ated bythedashed line)isusedfor the al ulation of theluminosity.

Thesignalfrom elasti allys attered protons an be learly separatedfromthe at

multi-pions attering ba kground. Thesolidangle

∆Ω

∗

usingtheMonte-Carlomethod,asfollows:

∆Ω

∗

=

4π N

accepted

2 N

0

[sr],

(6.2)

where

N

0

stands for the number of proton-proton elasti s attering events in the orre-sponding angular range and

N

accepted

onstitutes the number of events inthe onsidered binof the

θ

∗

2

angle, whi h ould be registeredandidentied. In parti ular,theanalysisin thefollowing manner wasdone. First,

N

0

= 2 · 10

7

events hasbeen generated, al ulating

theresponse of the COSY-11 dete tors, and then those events have been analysed using

pro eduresappliedfor theexperimentaldataevaluationinorderto determinethenumber

of

N

accepted

eventsfor ea h

θ

∗

2

angleinterval.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

40

60

80

Θ

₂

∗

[

_degrees

]

d

σ

/d

Ω

[

mb/sr

]

p

_beam

= 3262.5

[

MeV/c

]

EDDA

COSY-11

Figure6.3:Dierential rossse tionfor theproton-protonelasti s attering. Theresult ofthis

thesis( losed ir les)measuredatabeammomentumof

P

B

= 3.260

GeV/ wass aledinamplitude tothe rossse tionmeasuredbytheEDDA ollaborationshownbyopensquares[72℄.

Figure 6.3 indi ates the angular distribution of the dierential ross se tion for elasti

proton-proton s attering obtained in the experiment ( losed ir les). The amplitude of

thatdistribution was ttedto the dataof the EDDA experiment in luding only one free

parameter being the integrated luminosity (see eq. 6.1). The extra ted integrated

lumi-nosityfortheexperimentdes ribedinthisthesisamountsto

L

= (5.859 ± 0.055) pb

−1

The knowledge of the luminosity value will allow for the overall normalization of the

deriveddierential rossse tionasafun tion ofthe

s

pp

and

s

pη

′

invariantmasses,angular distributions andtotal rossse tion whi h will be dis ussed in hapter 10.

beam momentum

Inordertoperformrealisti simulationsofthestudiedrea tions,inparti ulartodetermine

thea eptan eandto al ulatethe ovarian ematrix,itismandatorytoknowtheabsolute

valueandthespreadofthebeammomentum. Thedis ussedmeasurementofthe

pp → ppη

′

rea tion was nominally performed at the same value of ex ess energy Q as the

pp → pp

rea tion measurement with Q =15.5 MeV whi h orrespondsto a nominal proton beam

momentum of

P

B

= 3.257

GeV/ .

The pre ision of the absolute beam momentum adjustment of the COSY syn hrotron is

about

10

−3

[73℄ whi hinthis ase orrespondsto

∼

3 MeV/ .

The beam momentum dependen e of the mean value of the missing mass distribution

presented in gure 5.3, was studied in order to determine the a tual value of the beam

momentum more a urate.

Thebeammomentumwas al ulatedusing theformula:

m

X

=

√

s − 2m

p

=



2m

2

_p

+ 2m

p

q

P

2

B

+ m

2

p



1/2

− 2m

p

,

(7.1) where

√

s

denotes the total energy inthe entre-of-mass frame,

P

B

stands for theproton beam momentum, and

m

p

orrespondsto the proton mass.

The beam momentum of

P

B

= 3.260

GeV/ has been determined by adjusting the

P

B

su h that the mean value of the missing mass peak is equal to the

η

′

meson mass. The

determined value of the beam momentum diers by 0.003 GeV/ from the nominal one.

This deviation is in agreement with results of analogous analysis performed in previous

measurements[67℄.

Thedeterminedvalueoftheex essenergyamountsto(Q=16.39

±

0.01

±

0.4)MeV, where the errors indi ate statisti al and systemati un ertainty, respe tively. The

domi-nating systemati un ertainty was established in [9℄ and the statisti un ertainty of the

ex essenergy wasdetermined using the following formula:

∆Q =

s

 dQ

dP

B



2

· (∆P

B

)

2

,

(7.2)

0

0.002

0.004

0.006

0.008

0.01

-2.5

0

2.5

∆

P

_B

[

MeV/c

]

intensity a. u.

Figure7.1:Spe trumofthebeammomentumdistributionintegratedoverthewholemeasurement

time. Thevalueof

∆P

B

= 0

orrespondstoabeammomentum of3.260GeV/ . Thedashedlines markthebeammomentumdispersionfortheextended9millimetertargetusedinthisexperiment.

Afterthedetermination oftherealvalueoftheabsolutebeammomentum,nowitsspread

willbedetermined. One an al ulate thebeammomentumspe trumfromthefrequen y

spe trumof the COSYbeam (S hotky spe trummeasured during the experiment) using

thebelow formula[74℄:

∆f

f

= η

B

·

∆P

B

P

B

,

(7.3)

where

f

and

P

B

denote beam frequen y and beam momentum, respe tively,

η

B

is a pa-rameterwhi hdependsonthe beamopti s,i.e. theele tri andmagneti eldsinthe

syn- hrotron. Duringthe experiment,the

η

B

parameter wasestablishedto be

η

B

=0.12 [75℄. The spe trum of the beam momentum obtained during the experiment is shown in

g-ure7.1.

Thedispersionofthe beammomentumdependsonthemagneti eldalongthering.

Pro-tons on the outer routes have a "longer way" than those on the inner side of thebeam,

and the traje tories are dierent from the nominal value. When at a ertain point the

parti lepositiondeviatesby

∆x

fromthenominal(

x

0

)position andpossessestherelative momentumdeviation

∆P

B

/P

B

,one anrelatethisvaluebymeansoftheknowndispersion