Proton induced Deuteron Breakup reaction studies at COSY

Coordinatore Prof. Filippo Frontera

Proton indu ed Deuteron Breakup

rea tion studies at COSY

Dottorando Tutore

Susanna Bertelli Dr. Paolo Lenisa

The present thesis isdedi ated to the study of the pd Breakup

re-a tion. The study is part of a proje t, realized at the COSY storage

ring, nalized to map pd breakup spin observables in a kinemati al

region where measurements are limited altough strongly ne essary to

ximportant onstraintsforinvestigatingthe roleof thethree-nu leon

for es viathe Chiral Perturbation Theory.

Intherstpartofthework,Idevelopedananalysis haintodetermine

whether adete tionsystem basedonSili onTra king Teles ope,

origi-nally on eivedtoidentifypd elasti events,was apabletoidentifythe

produ ts of the pd Breakup rea tion. This feasibility study has been

su essfullyappliedtoanexistingdatasampletakenattheCOSYring

inFebrauary2008,withaverti allypolarizedprotonbeamof49.3MeV

kineti energy impingingonaDeuterium luster target. In afollowing

phase, the identied pd Breakup events have been employed to tune

an algorithm to measure the analysing power in pd Breakup rea tion

using the neutron asymmetries. This observable represents one of the

probes to onstrain Chiral Perturbation Theory. The analysis of the

available data sample has allowed to outline the experimental

ondi-tionsrequiredforanexhaustiveinvestigationofthe spinobservablesin

pd breakup rea tion. On the other side, the low statisti sand the not

optimalworking onditions of the dete tion system made not possible

to nalize the result on the existing data sample. At present the

de-veloped analysis is being exploited on a new sample of data a quired

during 2011 beam-time.

In parallel, I arried out a study of a new apparatus devoted to the

pd Breakup investigation. In parti ular double spin asymmetries in

pd Breakup oer a ri h laboratory where to test Chiral Perturbation

Theory. For a essing these observables, an experiment where both

re-quired. Inadditionadete tionsystemprovidingalargeazimuthaland

longitudinalphase-spa e overage would be needed.

Forthis reason,I implemented the analysis software, developed inthe

rst stage of my work, for the hara terization and the optimization

of this dedi ated dete tion system on the basis of Monte Carlo

gen-erated data. The results of the analysis served as a guidan e for the

dete tordesign andhavebeen in ludedinaproposal[1℄submitted and

Questo lavoro di tesi è dedi ato allo studio della reazione di

fram-mentazione del Deutone indotta da un fas io di protoni, pd Breakup.

Questo studio ostituis e parte di un progetto di ri er a, realizzato

presso l'anello di a umulazione COSY, nalizzato alla misura delle

osservabili di polarizzazione della reazione di pd Breakup, in una

re-gione inemati a in uile misureesistenti sono limitatesebbene

indis-pensabili per ssare vin oliutiliper investigareil ruolo delle forze he

agis ono tra tre nu leoni 3NF attraverso la Chiral Perturbation

The-ory.

Nella prima parte del lavoro, ho sviluppato una atena di analisi per

stabilire se un sistema di rivelazione basato su sensori di sili io,

on- epiti originariamente per identi are gli eventi del anale pd

elas-ti o, fosse in grado di identi are an he i prodotti della reazione di

pd breakup.

Questo studio di fattibilità è stato appli ato on su esso ad un

am-pione di dati a quisiti presso l'a eleratore COSY nel Febbraio 2008,

in ui sono state indotte ollisioni tra un fas io di protoni

polariz-zato ad un'energia ineti a di 49.3 MeV e un bersaglio di Deuterio.

Nella fase su essiva, gli eventi di pd Breakup identi ati sono stati

utilizzatipermettereapuntounalgoritmoperdeterminarel'analysing

powerdellareazionedipd Breakup usandoleasimmetriedelneutrone.

Questa osservabile rappresenta un test hiave per vin olare la Chiral

Perturbation Theory. L'analisi del ampione di dati a disposizione ha

onsentito di delineare le ondizioni sperimentali ideali per studiare

in maniera esaustiva le osservabili di polarizzazione della reazione pd

Breakup. Tuttavia a ausa della statisti a limitata e delle ondizioni

di lavoro non ottimali del sistema di rivelazione, non è stato possibile

nalizzare un risultato per il ampione di dati esistente. Al momento

ampione didati a quisiti duranteuna presa dati nel 2011.

Inparallelo,hosviluppatol'analisidiunnuovoapparatoespli itamente

dedi atoallostudiodel analepd Breakup. Ledoublespinasymmetries

nel analedipd Breakup ostituis onounri olaboratoriodovetestare

laChiralPerturbationTheory. Pera edereaquesteosservabili,è

ne -essariorealizzareunesperimentoin uiilfas iodiprotonieilbersaglio

di Deuterio siano entrambi polarizzati e il sistema di rivelazione sia

aratterizzato da una estesa opertura longitudinale e azimutale dello

spazio delle fasi.

A questo s opo, ho implementato il software di analisi sviluppato per

laprimapartedellavoroditesi,alnedi aratterizzareeottimizzareil

sistemadirivelazionededi atoutilizzandodatiMonteCarlo. Irisultati

di questa analisi sono serviti ome guida per il design del sistema di

rivelazioneesono stati in lusiinun proposal[1℄ he èstato sottomesso

Abstra t iii

Riassunto v

Introdu tion 3

1 Physi s Motivation 7

1.1 Conventional approa hes to the Nu lear For e problem 8

1.2 The ChiralPerturbation Theory . . . 10

2 Experimental Setup 15 2.1 The COSY fa ility . . . 15

2.1.1 Ele tron Cooler . . . 17

2.2 PAX beam polarimeter . . . 17

2.2.1 Deuterium luster target . . . 17

2.2.2 SILICON TRACKINGTELESCOPES . . . 19

2.2.3 Front-end ele troni s . . . 20

2.2.4 Geometryand Trigger . . . 21

3 Deuteron Breakup events analysis 25 3.1 pd Breakup vs pd elasti . . . 26

3.1.1 Kinemati s of

pd → ppn

. . . 27

3.2 Simulationsand Data . . . 28

3.2.1 RUN SELECTION . . . 29

3.3 Tra k Re onstru tion . . . 30

3.3.2 Tra k "1" re onstru tion . . . 34

3.3.3 Tra k "2" re onstru tion . . . 34

3.3.4 Thirdlayer Calibration . . . 35

3.3.5 Tra k "3" re onstru tion . . . 36

3.4 DeuteronBreakup samples . . . 38

3.5 E ien yof Breakup identi ation . . . 40

3.6 Phase Spa eCoverage . . . 42

3.7 Method development for the analysing power

A

y

in pd

→

ppn . . . 49

3.7.1 Considerations . . . 53

4 Future plans: Dedi ated setup for pd Breakup studies 55 4.1 PAX ExperimentalSetup. . . 55

4.1.1 The COSY beam . . . 56

4.1.2 Polarized Internal Target . . . 57

4.2 PAX Multipurpose Dete tionSystem . . . 59

4.3 pd Breakup event generation . . . 61

4.4 pd Breakup events identi ation . . . 61

4.4.1 Stopped protons: tra k "1" . . . 63

4.4.2 Stopped protons: tra k "2" and "3" . . . 63

4.5 pd Breakup re onstru tion e ien y . . . 65

4.6 Phase spa e overage . . . 67

4.6.1 Considerations . . . 70

Con lusions 71

Appendix A 73

Appendix B 79

Oneof themain issuesin nu learphysi sisdeterminingthe nature

ofthe intera tionsbetweenthe nu leonswhi his ru ialfor

investigat-ing the properties of nu lei. In general observables at the energy

rele-vant to nu lear physi s are well des ribed by a nu leon-nu leon (NN)

potential. Altough mu h has been learned about the NN intera tion,

itis ofinteresttond out whether these for es an alsobeinvolved in

systems where more than two nu leons intera t.

In a three-nu leonsystem it isimportantto investigate howthe

inter-a tion between two nu leons is inuen ed by the presen e of a third

nu leon. This extra ee t is related to a for e whi h is beyond the

two-nu leon intera tion and is known asthree-nu leon for e (3NF).

At present, few-nu leon systems an be studied using

phenomenolog-i al models that, despite some remarkable su esses in des ribing

ex-perimentaldata, leave some open problems, amongwhi h is the loose

onne tion toQCD.

The drawba ks of phenomenologi al models are over ome by

employ-ing the modern theory of nu lear for e Chiral Perturbation Theory

(ChPT). ChPT is an ee tive eld theory (EFT), that allows a

sys-temati approa htostudyinglow-energyhadrondynami sadheringto

the symmetries of QCD.

To provide a better understanding of 3NFs ee ts, dierential ross

se tions and polarization observables have been measured in

nu leon-deuterons attering. Inathree-nu leon(3N) ontinuumthe

experimen-tal data and the theoreti al predi tions reveal both very good

agree-mentand signi antdisagreement.

An alternativeto Nds attering, spin observables in

pd→ppn

deuteron breakup rea tions, due to the ri her kinemati s, oer a fertile

labora-tory wherestudying the 3NFs.

three-nu leonintera tionsandinparti ulartheirspindependen e,amajority

of possible observables need to be measured with high a ura y, sin e

3NFs ee ts are in general very smallin the three-nu leon system. In

parti ular the energy range between 30 and 50 MeV is an ideal range

wherethe3NF ee tsare expe tedtoappear andbesigni antandat

thesametimeitisasuitablerangetotestthepredi tivepowerof hiral

EFT. In this range previous measurements are s ar e and limited and

itwould bevery interesting to have at disposala omplete database.

Thereaser h ofthis thesishas been performedintheframeworkofthe

PAX Collaboration that aims at the produ tion of the rst polarized

antiprotonbeam. In parti ular, inthe past three years, the PAX

Col-laboration has performed a series of tests onprotons at COSY aimed

at investigating spin-ltering and spin-ip as possible me hanisms to

polarizeastoredbeamofprotons. Inthis environmentadedi ated

po-larimeter to measure the stored beam polarization has been installed

inthe COSYring. Thepolarimeterhasbeen implementedbymeansof

a ouple of Sili on-Tra king Teles opes that serve to dete t deuterons

omingfrom pd elasti s attering.

Therst partofmyworkhasbeen devotedtoafeasibilitystudyofthe

useofthe samepolarimetertoidentifydeuteronbreakupevents, whi h

onstituted part of the ba kground with respe t tothe elasti

s atter-ing. To this purpose, I analyzed the data taken during a dedi ated

beamtimein2008 andI developed a hain of sele tion riteriato arry

out the pd Breakup events identi ation. After a lean identi ation

of the deuteron breakupevents,I investigated the possibilityto a ess

the neutron analyzing power by the two outgoing protonsdete ted in

the polarimeter.

This analysis pro edure of pd breakupevents forms partof the

feasib-bility studies for an a epted experiment proposal submitted by the

PAX ollaboration [1℄ to be performed at COSY. The obje tive of

the planned experiment is to provide a means of testing the

predi -tive power of hiral EFT, in luding the ee ts of three-nu leon for es

in few-nu leon systems. Most of the spin orrelation parameters and

the ve tor and tensor analysingpowers inpd breakup rea tions at

30-50 MeV proton beam energy will be measured with large phase spa e

overage.

To this aima dedi ated dete tion system is being developed that will

atthenewlyinstalledPAXsetupatCOSY.Thisdete tordevelopment

wastheobje tofthese ondpartofmythesis. Inparti ularIanalyzed

MonteCarlo dataforthe hara terization and theoptimizationof this

dete tion system. The results of the simulation analysis were adopted

in the proposal[1℄.

The thesis is organized as follows: Chapter 1 reports the motivations

supporting the ne essity of additional measurements in the three

nu- leon se tor; in Chapter 2 the experimental setup used to realize the

feasibility study for pd-breakup is presented; Chapter 3 is devoted to

the pro edure of breakupidenti ationand analysis;in Chapter 4 the

results of Monte Carlo studies for the future dedi ated dete tor are

Physi s Motivation

One of the main issues in Nu lear Physi s is the role of the for es

a tingbetween nu lear onstituentsandfew-nu leonsystemsrepresent

the ideal laboratories where these for es an be investigated. In

par-ti ular it is important to study the dynami s related to the presen e

of a third nu leon, whi his ru ial tounderstand the ontributions of

three-nu leon for es (3NFs).

Evenifthe theoryof3NFswasdevelopedinthe30'softhelast entury

[2℄, still many problems remain open. Presently, the spin stru ture of

the three-nu leon ontinuum exhibits disparate results when

ompar-ing experimentaldata totheoreti al predi tions based on two-nu leon

potentials either with or without the in lusion of three-nu leon

inter-a tions. A detailedreview of the urrent status of the resear h on the

role ofthe three-nu leon for es an be foundin [3℄. The ri h

kinemati- alregioninproton-deuteronbreakuprea tions atlowtointermediate

energy oers agoodtesting groundfor the hiral ee tive eld theory

(EFT), the modern theory of nu lear for es in the low-energyregime.

In parti ular, in the energy range between 30 and 50 MeV, that is of

interest for the experiments presented in this thesis, very s ar e

po-larized experimentaldata exist. This is an ideal range where the

pre-di tive powerof hiral EFT in three-nu leon ontinuum an be tested

by measuring analysingpowers and doublespin observables with high

pre isionover large areas of the phase-spa e.

The hapter is organized as follow: se tion 1 introdu es a survey of

the main approa hes developed tostudy the ontributionofthe

three-nu leon for es (3NFs) in nu lear systems, se tion 2 provides a review

1.1 Conventional approa hes to the Nu lear For e

problem

Sin e the typi al energy s ale in Nu lear Physi s is in the order

of nu lear binding energies, the N-body problem an be des ribed by

thenon-relativisti S hrödingerequation. Inarstapproximation,

ob-servables in this energy range are well des ribed by a nu leon-nu leon

(NN)potential. The onventionalwaytodes ribethenu learfor eis

Figure1.1: The entralnu leon-nu leon(NN)potentialisdisplayed. Thelongestrange

ontribution orresponds to the 1-

π

ex hange, the intermediate range attra tion is

de-s ribedby2-

π

ex hangesandothershorterrange ontributions. Atshorterdistan es,the

NNintera tionisstronglyrepulsive. ThisgureistakenfromRef. [4 ℄.

based onthe meson-ex hangepi ture as proposed by Yukawa[5 ℄. This

approa henri hed by mesoneld theory and dispersion relations

(em-ployed to onstru tthetwo-pionex hange ontribution)broughttothe

development of high pre isionsemi-phenomenologi al nu leon-nu leon

(NN) potentialmodels like AV18[6℄, CDBonn[7 , 8, 9℄, Nijmegen I and

II[10℄. These models des ribe the long-range tail of the nu lear for e

due to ele tromagneti intera tion and the one-pion ex hange

poten-tialandparametrizethemedium-andshort-range ontributions. These

potentials an reprodu e alargesampleofproton-proton and

neutron-protons atteringdataoberservablesup tothepion produ tion

thresh-old with a

χ

2

/datum

∼

1 and provide an a urate representation of most deuteron properties. In Nd s attering dierential ross se tion,

a dis repan y with data is observed as the energy in reases (for the

analysing power this dis repan y is known as

A

y

-puzzle[11℄).

The dieren e between al ulations in luding solely 2NFs and data is

usually interpreted as an indi ation of the existen e of three-nu leon

for es (3NFs). 3NFs are many-body intera tions that have to be

in- ludedbeyondpairfor estodes ribenu leiandnu learrea tions

prop-erly. Systemati studies of the dynami s of systems involving threeor

four nu leons allow pre ise tests of the role and the stru ture of the

3NFs.

The Urbana-Argonne group[12℄ showed that three-nu leon for es have

tobein ludedtodes ribethenu learbindingenergieswhi hareknown

to beunderestimated by two-nu leon potentials.

TheextensionofYukawatheoryto3NFisduetoFujitaandMiyazawa[13℄,

who implemented the meson ex hange idea by sandwi hing the

pion-nu leon s attering amplitude between nu leon lines, thus originating

the 3NF oflongest range.

The des ribed approa his frequentlyused innu learstru ture and

re-a tion al ulations but reveals some de ien ies like the absen e of a

way toassignatheoreti alerror,the di ultytoimplementgaugeand

hiral symmetries, the in onsisten y between three-nu leon for es and

the nu leon-nu leon intera tion models and avery loose onne tionto

Quantum ChromoDynami s (QCD).

These de ien ies an be over ome in hiral Ee tive Field Theory

(EFT), an approa h to study the low-energy hadron onsistent with

the QCD. ChiralEFT is linked to QCDvia itssymmetries and allows

to treat the low-energy properties of hadroni systems in a ontrolled

way. Whenthismethodisappliedtoasystemofthreenu leons,graphs

in luding3NFsappearnaturallyina ompleteagreementwiththe

hi-ralNN intera tions, asdes ribed inthe next se tion.

Theexperimentaldataand thetheoreti al predi tionsforrea tions

in- luding three nu leons at low and intermediate energies are today at

varian e. Insomepartsofthephasespa eforsomeobservables, the

in- lusionofthe3NFinthemodelsleadtoagoodagreementbetweendata

and theory,while inother partsthe agreement isworsened[14 , 15, 16℄.

This ambiguity requiresa omplete and high pre ision database.

The Deuteron breakup oers, with respe t to the elasti hannel, a

ri her kinemati sto study observables in the threenu leon ontinuum

demonstratethe possibile eviden eof the 3NFs.

1.2 The Chiral Perturbation Theory

ChiralPerturbationTheory(ChPT) istheee tivetheoryof

Quan-tum ChromoDynami s (QCD) formulatedby Weinberg[17℄ and

devel-opedintoasystemati toolforstudyingthe propertiesof hadroni

sys-temsatlowenergies inamodel-independentframework. Itisbasedon

thespontaneouslybroken hiralsymmetryofQCD,providingamethod

to improve the results by onsidering higher orders in a perturbative

expansion. Weinberg attemptedageneralizationofthis methodtothe

few-nu leonse tor,fa inganon-perturbativeproblemsin e one hasto

deal with the strong nu leon-nu leon intera tion.

Inthe frameworkofChPTtwokindofintera tionsemerge: long-range

pionex hangesand onta tintera tions,withtheasso iatedlow-energy

onstants(LEC).Dueto hiralsymmetry,apower ounting anbeused

toestimatethe ontributionofindividualgraphstotheNNintera tion.

Weinbergproposed toapply hiralperturbation theorytothe ee tive

potential,dened as the sum of allthe ontributions of irredu ible

di-agrams, instead of applying it to the s attering amplitude, obtained

by solving the orrisponding dynami al equation. In this way, only a

nitenumberofdiagrams ontributesatagiven orderandthe

nonper-turbativity of nu lear systems is taken intoa ount.

In this framework, one an onsider the most general ee tive

La-grangian

L

EF F

forpionsandnu leons onsistentwiththesymmetriesof QCD. Nu lear for es an be determinedfrom

L

EF F

perturbatively via anexpansioninpowers ofQ/

Λ

,whereQreferstoatypi almomentum ofthenu leonsorthepionmassand

Λ

isthe hiralsymmetry-breaking s ale of

≈

1GeV.

The importan e of a parti ular ontribution to the nu lear potential

is xed by the power

ν

of the expansion parameter Q/

Λ

, providing the a ura y at order

ν

. In this sense, the theory an be al ulated atany a ura y and has a predi tive power. The nu lear for e an be

espressed by:

V =

X

ν

V

ν

= V

0

+ V

1

+ V

2

+ ....

(1.1)

expan-Chiralpower ountingexplainsthedominan eofthe 2NF ontribution

that starts at

ν

=0.

•

ν

=0: atthisleadingorder(LO),the2NFisprovidedtwo nu leon-nu leon onta tintera tionswithoutderivates,representedinFig.1.2

by the four-nu leon-leg graph with a small-dot vertex, and by

one pion ex hange, se ond diagram in the rst row of Fig.1.2.

The oupling ostantslinkedtoNN onta tinterationatthis and

higherorders anbederived fromthelow-energynu leon-nu leon

data.

Figure 1.2: The Hierar hy of nu lear for es in ChPT is shown. Solid lines are

nu leons and dashed lines are pions. Solid dots, lled/open squares and ir les

depi tverti esfrom

L

EF F

. Figuretakenfrom ref.[4℄.

•

ν

=1: Theparity onservation pre ludes any ontributions atthis order.

•

ν

=2: The rst orre tions at next-to-leading order (NLO) arise from two-pion ex hange, without new parameters and onta t

•

ν

=3: atnext-to-next-to-leadingorder(

N

2

L0),two-pionex hange

ontributionstogetherwithoneinsertionofthesubleading

ππ

NN verti es has to be onsidered. The related low-energy onstants

c

1,3,4

are determined by

π

N s attering. At this level the rst

ontribution to the 3NF from diagrams appears[18℄. Two-pion

ex hangepartinvolvesnonewparameters,whereasthe twoother

topologies depend on one unknown onstant ea h, whi h an be

xed from three-or more-nu leonobservables.

•

ν

=4: at next-to-next-to-next-to-leading order (

N

3

LO), further

orre tions to the 2NF has to be in luded, onsidering the

sub-leadingtwo-pionex hange,theleadingthree-pionex hangeterms

and the onne ted onta t terms; at this order the four-nu leon

for e(4NF) originates.

In the framework of EFT it is natural to dene a qualitative

expla-nation of the observed hierar hy of two-, three-, more-nu leon for es:

V

2N

≫

V

3N

≫

V

4N

.

Byfar, the 2NF has been worked out and appliedto

N

3

LOinthe NN

system, while the results for three- ormore-nu leonsystems are

avail-able up to

N

2

LO[19℄.

TheLowEnergy Constants(LECs) DandE entering theexpression of

3NF are determinedby tting the

3

H and

4

Hebinding energy[20 ℄ and

either the nd s attering lenght[21℄ or the properties of the nu lei[22℄.

On eD and E are xed, the resultingnu learHamiltonian an be

em-ployed todes ribethe dynami sof few-nu leon systems. This method

has the advantage, withrespe t tothe otherapproa hes, of estimating

un ertainties of the obtained predi tions.

3N s attering observables and in parti ular the breakup rea tion is

a fertile testing ground for the hiral for es. The deuteron breakup

rea tion has been re ently measured at the intermediate energy of

E

N

=65MeV(

E

N

referstokineti energyofthein identnu leonbeam) andsomedata, on erning ross se tions,inkinemati al ongurations

asthenal stateintera tion, symmetri spa estar andquasi-free

s at-tering 1

are available in the range below20 MeV.

Nosystemati data existinthe energyrange between 30and 50MeV.

This energy range is extremely suitable to nd relevant ontributions

1

Inthenalstateintera tionFSI,twonu leonsleavetheintera tionregionwithequal

due to 3NF and at the same time the energies are lowenough tooer

pre ise theoreti al predi tions based on hiral EFT. Data in this

en-ergy range will provide an independent sour e for a determination of

the LECs D andEand thuswillallowa onsisten y he k ofthe

theo-reti al approa h. Moreover, pre ise data in this range willbe relevant

to explore ee ts of the new stru tures whi h appear in the 3NF at

N

3

LOwithoutanyadditionalunknownparameters. Thisisthe energy

range wherethe planned pd breakupdouble-polarized experiment will

take pla e at the COSY-fa ility, see the beam proposal submitted to

the COSY Program Advisory Program[1℄. To map out 3N, pre ision

measurements of some relevant observables as well as a large phase

spa e overage are required; these onditions are fullled using both

polarized beam and target and a large azimuthal overage dete tion

system. Appendix A is devoted to the des ription of the analysis tool

Sampling method, that provides a dire t omparison between

experi-ment and theory and willbe appliedfor the future measurements. In

parti ular the spin observables that an be a essed in a double

po-larized pd breakup experiment are reported. In Chapter 4 the future

Experimental Setup

Theexperimentaldataanalyzed inthis thesishave been taken ina

xed-target experiment performed at the COoler SYn hrotron COSY

of the Fors hungszentrum Juli h (FZJ). In these experiments a

verti- ally polarized proton beam of 49 MeV kineti energy s atters on an

unpolarizeddeuteriumtarget. Inthe s atteringpro essbothpd elasti

and pd breakup events an take pla e. Thesetworea tions are

identi-edbytheSili onTra kingTeles ope(STT)dete tionsystem,whi his

alsopartofthe beampolarimeter. Inthis hapterate hni aloverview

of the various omponents of the experimentalsetup is presented.

2.1 The COSY fa ility

TheCOolerSYn hroton(COSY)attheInstitutforNu learPhysi s

(IKP)of the Resear h Centre of Jueli h (FZJ)is ana elarator whi h

providesprotonanddeuteronbeams(

∆

p/p=

10

−4

-

10

−3

)inthe

momen-tumrangefrom300MeV/ (550MeV/ inthedeuterons ase)upto3.7

GeV/ . The phase spa e ooling of the stored beam isprovided toan

ele tron ooler(up toa momentumof600 MeV/ )and ompleted bya

sto hasti ooling that overs the momentum range above 1.5GeV/ .

Unpolarized and polarized beams originate from external or internal

experiments. Polarizedbeams are produ ed by a polarizedion sour e

whi h provides a ve tor polarized proton beam and deuteron beams

with all possible ombinations of ve tor and tensor polarization. The

Figure2.1: TheCOSY-fa ilitywiththeinje tionandextra tionline;themaininternal

andexternalesperimentsareindi ated.

for a transversely polarized proton beam is

10

10

parti les (

3 · 10

10

for

deuterons) with

70%

of polarization (

70%

ve tor and

50%

tensor po-larization for deuterons). An overview of the COSY-ring is shown in

2.1.1 Ele tron Cooler

TheCOSY ele tron ooler has been optimizedforele tron energies

up to 100 keV, enabling phase spa e ooling up to 183.6 MeV proton

energy. Its basi appli ation is redu ing the large emittan e and the

large momentum spread due to the inje tion stripping pro ess before

the ion beam is a elerated to the requested energy[23 ℄. The ele tron

beam is extra ted from a thermioni athode and ele trostati ally

a - elerated up to the velo ity ion beam. The ele tron beam is driven

by the longitudinal magneti eld provided by toroids and solenoids

through the region of intera tion with the ionbeam and, after energy

re overing by ele trostati de elaration, it enters the olle tor. Two

solenoids with reversed longitudinal eld up- and downstream of the

ooler devi e hinder oupling between horizontal and verti al phase

spa e plane and distortionof the ionspin dire tionin the COSY ring.

Steerer magnets balan e the orbit distortion indu ed by the toroids

and enable the mat h between the ion beam and the ele tron beamin

positionandinangle. Whentheoptimumsettingisfound, theele tron

beam anbetiltedby steering oils onthe driftsolenoidand itslightly

redu ed its ooling for e.

2.2 PAX beam polarimeter

Thebeampolarizationismeasuredusingthe Sili onTra kingT

ele-s opes(STTs)dete tionsystem,pla edattheANKEintera tionpoint,

see Fig.2.1. As des ribed in detail in se tion 3, the beam polarization

an be determined exploiting the left-right asymmetry of the sele ted

deuteronsfromproton-deuteronelasti s attering,wherethedeuterium

is delivered fromthe ANKE Deuterium lustertarget[24℄.

2.2.1 Deuterium luster target

ADeuterium luster targetispla edatthe internaltargetposition

of the ANKE experiment. It provides a target density of

10

13

-

10

15

atoms/

cm

2

and a target beam of 10 mm diameter, entailing a small

beam target overlap. Clusters of

10

3

-

10

4

atoms are delireved from a

Figure 2.2: As hemati view of theDeuteriumClusterTargetis shown. The luster

sour epla edabovetheCOSYbeamprovidesawell-denedtargetbeamofhydrogenor

deuterium lusters. The olle torse tionkeepstheva uumbelow

10

−7

mbar.

range of 15-20 bar, the gas is for ed into the va uum of the skimmer

hamber using the Laval-nozzle of 20

µm

opening diameter. On e insidetheskimmer hamber,the gasexpandsadiabati allyand it ools

down. Inoversaturated gas onditions,the ondensationof atomsinto

lusterstakespla e. Thereareabout

10

3

atoms losetothetriplepoint

per luster. The skimmer provides the separation of the luster beam

from the residual gas whi h is the main omponent of the total gas

load into the skimmer hamber. The target se tion alled olle tor,

see Fig.2.2hosts adierentialpumpingsystem(three ryo-pumpsplus

one turbomole olar pump) whi h limits the gas load into the target

hamber, keeping the va uum below

10

−7

mbar.

Figure2.3: ThetwoSili onTra kingTeles opespla ed olsetothebeam-targetoverlap

regioninthetarget hamberisshown. Thepolarizedprotonbeam(redline)enters the

hamberandhitsthedeuterium lustertarget(yellowline),inje tedfromthetop.

2.2.2 SILICON TRACKING TELESCOPES

Thedete tionsystem onsistsoftwogroupsofsili onstripdete tors

arranged in a teles opelayout aroundthe beam targetoverlap region.

A Sili onTra kingTeles opeis madeby three double-sidedmi rostrip

dete torsofdierentthi kness;therstlayer anbeof65

µm

or300

µm

thi kness, the se ond layer of 300

µm

thi kness and the third layer is a

5100 µ

m sensor tomaximize the number of stopped parti les. This system is able to fullllthe followingtasks:

•

Identi ationofstoppedparti lesbythe

∆

E/Emethod,providing inparti ular the protonidenti ationinthe kineti energy range

2.5 − 40

MeV with a resolution of 150 keV.

•

Parti le tra king over a large energy range, from

2.5

MeV up to minimum ionizingparti les(MIP); vertex resolution of 1 mm.

•

Self-triggering apabilitiesrealizedbyafastamplierwitha peak-ingtimeof

75

nsbymeansofwhi haparti lepassageisregistred fast and provide a trigger; in this way the system behaves like a

stand-alone dete tor.

Theparti leidenti ation, ru ialforthe polarizationmeasurement,is

realizedusingthe

∆

E/Emethodanalysingthe orrelationbetweenthe energy lossin dierent layers, as des ribed in se tion3.

The dete tors used for the rst two layers of the STTs are the BaBar

IVdete torsandhavebeenoriginallydesignedbythe ompanyMi ron

Ltd[25℄fortheBaBarexperiment[26,27,28,29,30℄attheSLAC

PEP-II B fa tory. The size of their a tive area is 51mm

×

62mm and the strip pit his of 400

µ

m.

The p-doped side has 1023 strips, whereas the n-doped side has 631

strips. In order to in rease the ee tive strip pit h up to 400

µ

m, the strips are arranged intogroups that are onne ted tosegments on

the kapton at able used to onne t the dete tor and the front-end

ele troni s (see Fig.2.4for the onne tion s heme).

A va uum-feedthrough for ea h segment is not appli able be ause of

the large number of the readout hannels, one per segment, so the

front-end ele troni s isused inva uum.

Thethi kLithiumdriftedSili ondete torsSi(Li)[31℄usedforthethird

layer has an a tive area of 64 mm

×

64 mm and a strip pit h of 666

µ

m (96 strips per side). They have been developed in the dete tor laboratoryof the Institut fürKernphysik (IKP) ofFZJ. They allowto

stopparti lesuptoanenergyofabout32MeVforprotonsand43MeV

for deuterons.

2.2.3 Front-end ele troni s

The signals oming from the sili on sensors are transported tothe

in-va uum front-end ele troni s by kapton at ables. The VA32TA2

hips are used. The hip provides a low trigger threshold of 100 keV;

two boards 90 mm

×

90 mm (one per dete tor side) with 5 hips are utilized. The front-end ele troni s onsists of 32 hannels logi ally

separated into an amplitude and a trigger part. In the preamplier

stage, a harge signal in the input pad of the hannel is amplied

and then split into the two bran hes. The pre-pro essed signals are

driven by addi tional kapton at ables to the va uum feedthrough

onne tors. The onne tors are pla edonthe ele troni s tofavour the

dismounting of the kapton at ables inorder tofulllthe modularity

request.

Figure2.4: The onne tions hemeofthep-dopedside(a)andn-dopedside(b)ofthe

BaBarIVdete tor.

trigger pattern threshold and alibration pulse amplitudes. The total

read-out hain ontributes toa total dead time of less than 50

µ

s.

2.2.4 Geometry and Trigger

The displa ement of the STTs has been optimized to measure the

beam polarization in proton-deuteron elasti ollisions a ording to

Monte Carlosimulations.

The geometry of the setup has to meetthese requirements:

Figure2.5: Thein-va uumfront-endele troni boardisshown,withtheinput/output

onne torsandthefront-end hipsindi ated.

Figure2.6: Intheleftpi tureonesili on-dete torwiththefront-endele troni boards

andkaptonplat ables isshown;intherightpi ture thenalassemblyfor onedete tor

in ludingthe oolingplatefortheele troni boardisdisplayed. Figurestakenfrom[42 ℄.

•

the setup has to be arranged in an azimuthal symmetry (left-right) in

φ

to use the double-ratio method for the asymmetry measurements,that serve to al ulatethe beam polarizationand

analysingpowers, see Chapter 3.

a eptan e toallow forthe setupalignment.

Figure 2.7: S hemati view of the zx plane of the dete tor (thebeam is along the z

dire tion). Targetpositionanddistan esbewteenlayersareindi ated.

The beam polarizationP isdeterminedusing theleft-rightasymmetry

ǫ

of the s attered deuterons. This asymmetry is proportional to the analysing power

A

y

of the pd elasti s attering through the relation:

ǫ = P · A

y

.

(2.1)

The STT is pla edin the region wherethe pd elasti Figure Of Merit

(FOM)dened by:

F oM =

dσ

dΩ(θ

cm

)

·

(A

y

(θ))

2

,

(2.2)

exhibits the maximum value.

A ording to experimental data at

T

p

= 46.3

MeV, see Fig.2.8, it is taken in onsideration the FOM value at

θ

p

cm

=

110

o

(that in the

labo-ratory is

θ

p

lab

= 80

o

), sin e the rst peak orresponds to angles in the forward s attering region where itis not possibleto pla e the STT.

To optimize the FOM the STT was pla ed 12 mmdownstream along

the beam dire tion. Therst layeris pla edat28mmfromthe enter

of the beam pipe to prote t the dete tor; the distan e between rst

and se ond layer is 20 mm. The distan e between se ond and third

layer is 13.5 mm. The trigger signal was produ ed when at least one

Figure 2.8: In the upper panels the pd elasti dierential roos se tion is

rep-resented in the enter of mass and laboratory system. In the lower panels the

Analysingpower

A

y

andtheFigureofMeritFoMofthepd elasti s atteringinthe enterofmasssystemaredisplayed.

Figure 2.9: The omplete setup of aSili on Tra kingTeles ope is shown. The three

sili on mi rostrips sensors are indi ated as well as the kaptonat ables that link the

Deuteron Breakup events

analysis

The pd

→

ppn Deuteron Breakup hannel has been studied using Monte Carloand experimentaldata.

The ultimategoalof the analysisis the sele tionofpd Breakup andin

parti ular theidenti ationofthe neutron. The identiedpd Breakup

events areusedtodevelop amethodfor al ulatingtheanalysing

pow-ers

A

y

of pd Breakup with respe t to the neutron.

The presented data had been taken during the February 2008 beam

time, when an experiment to test the possibility of using unpolarized

ele trons to depolarize an initially polarized proton beam was

per-formed at the COSY-ring. A polarized proton beam was stored in

COSY and the ele trons of the ele tron- ooler have been employed as

free ele tron target. The depolarization of the beam , aused by the

intera tions with the ele trons, was monitored measuring the beam

polarizationby means of the proton-deuteron elasti s attering events

indu ed at the deuteron luster target [32℄.

In these experimental onditions, proton-deuteron ollisions an give

rise to Deuteron Breakup events. Sin e the experimentalsetup is able

to identify this rea tion, DeuteronBreakup hannel an be studiedas

a omplete independent Physi s ase.

In this hapter the data analysis pro edure to re onstru t Deuteron

Breakup events, insimulatedandexperimentaldata,and inparti ular

the sele tion riteriadeveloped to tag thisrea tion are des ribed. The

identied deuteron breakup events are employed in the method

with respe t tothe neutron.

3.1 pd Breakup vs pd elasti

When a proton beam of 49.3 MeV kineti energy impinges on a

deuteriumtarget, two hannels an be a essible: pd elasti s attering

pd → pd

and Deuteron Breakup

pd → ppn

. In the experimental data these two hannels are present together and need to be separated.

Whilethe phase spa eof the pd elasti hannel iswelldened, the pd

Breakup, being a three-body nal state rea tion, o upies a broader

phasespa ewhi hoverlapstotheelasti one. The basi ideatoisolate

the pd Breakup hannel is to ex lude the pd elasti hannel from the

phase-spa eandgetalltheinfomationsfromthetwooutgoingprotons.

This se ond requirement is ne essary sin e the neutron is invisible for

the used dete tion system and pd Breakup ould be identied when

the two outgoing protons stop inside the dete tor a eptan e. On e

the two protons are stopped, using the four momentum onservation,

the ompletekinemati anbedetermined. Thefour-momentumofthe

missingneutron isgiven by:

n

µ

= p

µ

Beam

+ d

µ

T arget

−

p

µ

1,T elescope

−

p

µ

2,T elescope

,

(3.1) in whi h

p

µ

Beam

is the four-momentum of the in oming proton,

d

µ

T arget

the four-momentum of the deuteron target (it is a xed target, so it

oin ides with the deuteron mass),

p

µ

1,T elescope

and

p

µ

2,T elescope

the

four-momentum of two outgoingprotons dete ted and stopped in the

tele-s opes.

On e the protons from pd Breakup events are sele ted, the Missing Mass:

M

missing

=

q

(E

Beam

p

+ m

d

−

E

p1

−

E

p2

)

2

−

(−

→

p

p

Beam

− −

→

p

p1

− −

→

p

p2

)

2

(3.2)

is used as a ontrol riteria to tag the rea tion and it should peak at

the Neutron mass

939.57

MeV/

c

2

. In equation 3.2,

E

p

Beam

and

−

→

_p

p

Beam

are the total energy and 3-momenta of the in oming proton,

m

d

the

deuteron mass,

1875.61

MeV/

c

2

,

E

p1

,

E

p2

are the total energies of the two outgoing protons,

−

→

_p

p1

and

−

→

_p

p2

are the 3-momenta of the two outgoingprotons.

3.1.1 Kinemati s of

pd → ppn

Ingeneralinarea tion

A + B → 1 + 2 + 3

withtwo initialparti les and three parti lesin thenal state,

3 × (2 + 3)

momenta omponents have to be dened. The momentum-energy onservation laws x four

relations between momenta omponents of the parti les in the initial

and nal state; moreover if the enter of mass system is used, one an

dene three onditions forthe initialstate derived by:

−

→

_p

c.m.

A

+ −

→

p

c.m.

B

= 0,

(3.3)

and three onditions for the nal state:

−

→

_p

c.m.

1

+ −

→

p

c.m.

2

+ −

→

p

c.m.

3

= 0.

(3.4)

Therefore a three-nal state hannel an be des ribed by means of

3 × (2 + 3) − 4 − 3 − 3 = 5

independentvariables.

In the ase of pd Breakup rea tion the ve independent variables

the ja obi momenta p and q, and the ex itation energy of the proton

pair

E

pp

dened as:

E

pp

=

q

(E

p1

+ E

p2

)

2

−

(−

→

p

p1

+ −

→

p

p2

)

2

−

2m

p

,

(3.5) where

E

p1

,

E

p2

,

−

→

_p

p1

and

−

→

_p

p2

are the total energies and the 3-momenta of the twooutgoingprotons and

m

p

is the proton mass.

Figure3.1: Ja obimomentaof

pd → ppn

inthe enter-of-masssystem. p=1/2(p1+p2)

andq=-(p1+p2).

3.2 Simulations and Data

The data analysis is divided in two stages: one on erning Monte

Carlo simulationsand the other experimentaldata.

Inordertoestimatethe expe teddete tor performan es andin

parti -ular to study the re onstru tion e ien y for pd Breakup events and

thepd elasti ontamination,dierentsamplesofsimulatedpd Breakup

and pd elasti events have been analyzed, implementing the February

2008 dete tor onguration.

Thepd elasti s atteringisgeneratedbasedexperimentaldata[33℄. The

lowenergypd Breakupisgeneratedintheframeworkofthepure

phase-spa e GENBOD model with the proton beam kineti energy of 49.3

MeV. The GEANT pa kage [34℄ was used for the dete tor response.

The output of the simulations onsists of a list of events ontaining

hits informations like spatial oordinates, angles and deposited

ener-gies.

Simulated hannel Number of generated events pd

→

pd

10

6

,

T

p

=49 MeV pd

→

ppn

10

6

,

Tp

=49 MeV

Table 3.1: ThistabledisplaysMonteCarloinformations on erningthe hannel

simu-latedandthenumberofgeneratedeventsforea h hannel.

Con erning experimental data, the exe ution of the primary data

analysis, energy alibration orre tion, hits and tra king analysis is

ontrolledbytheRootsorter frameworksoftwaredevelopedatIKP[35℄.

The output is arranged in a list of events with omplete event

identi- ation data (i.e. time, beam polarization index, target polarization,

et .) and hits informations. Ea h hit ontains the information about

the energy loss of the parti le and its position in the dete tor. In the

next se tionthetra kre onstru tionandthepd Breakupidenti ation

te hniques (used either inMonte Carloor data) are des ribed.

3.2.1 RUN SELECTION

The data taking was performed with

10

8

stored protons. For this

analysis seven runs have been analyzed. During ea h run the proton

beam polarization was alternated between state UP (

↑

), DOWN (

↓

) and unpolarized (0). The geometry is represented in Fig.3.2. During

the beam time the third layerin one teles opewasnot working.

Date RUN Start Stop Events

Feb 03,2008 260 16:49 17:00 1360305 Feb 03,2008 262 17:06 17:16 1364067 Feb 03,2008 264 17:16 17:26 1362196 Feb 03,2008 266 17:26 17:36 1350207 Feb 03,2008 267 17:36 17:58 1368407 Feb 03,2008 270 18:15 18:27 1352119 Feb 03,2008 272 18:36 18:50 1174226

Table3.2: Thistable ontainssomeinformationsontherunsofFebruary2008analysed

Figure3.2: Intheuppergure,thezxplaneofthedete torisshown. Theprotonbeam

isdire tedalongthepositivesideofthezaxis. Theprotonbeampolarization isdire ted

along y-axis. The indi ated angles show the geometri al a eptan e of the polar angle

whena s attered parti le impinges on the rst two layers. Inthe lower gure, the yx

plane,lookinginthebeamdire tion,isshown.

3.3 Tra k Re onstru tion

A tra k is dened as a straight line between two orrelated hits

in the rst two layers. Firstly ontiguous signals (within a radius of

1 mm) in the sili on strips are merged together into the so- alled

sili- on hits. Only events with at least two hits inthe rst layers and one

hit in the se ond layer of the dete tor are onsidered. Se ondly the

in azimuthal angle.

Ahitinthe thirdsili onlayerislinked tothere onstru ted tra k if its

distan e from the extrapolatedpointof the tra k is less than 1 m.

Ineventswheretwotra ksaretra ed,themethodofdistan eof losest

approa h is applied to re onstru t the intera tion vertex. Whereas in

eventsinwhi honlyonetra kistra ed,themethodofdistan eof

los-est approa hisappliedbetween the tra k andthebeamlinetolo alize

the vertex point; after that the se ond tra k is tra ed onne ting the

vertex pointto the oordinates of any untra ed hitin the rst layer.

Three tra k typologies are onsidered: tra k "1", if the parti le stops

into the rst layer, tra k "2" and "3", if the parti le stops into the

se ond orthe third layer respe tively, see Fig.3.3.

Figure3.3: S hemati viewofthezxdete torplaneinwhi htra k1,2 and3are

repre-sented.

InMonteCarlo,pd elasti andpd Breakup hannels anbeswit hed

onseparately, whereas indata they are present together; the rst part

of the analysis is dedi ated to the identi ation and separation of the

two rea tions.

The request to suppress the elasti hannel to negligible ontribution

is realized applying a o-planarity ut, shown in Fig.3.4. This ut,

in addition to the request of having no deuterons in the nal state,

2

Θ

+

1

Θ

60

80

100

120

140

160

180

200

|

2

Φ-1

Φ|

50

100

150

200

250

300

350

2

Θ

+

1

Θ

60

80

100

120

140

160

180

200

|

2

Φ-1

Φ|

50

100

150

200

250

300

350

2

Θ

+

1

Θ

60

80

100

120

140

160

180

200

|

2

Φ-1

Φ|

50

100

150

200

250

300

350

Figure 3.4: MonteCarlo: the o-planarity ut. Therelationbetweenthe polarangles

ofthe2-outgoingparti lesversustheirazimuthalangleisdisplayed.Theleftpanelshows

thephasespa eofthepdelasti hannelinsimulations,themiddlepanelshowsthephase

spa e of the pd elasti (red) and pd Breakup hannel (blue) together, the right panel

displaysthe phase spa e of pdBreakup inwhi h theellypse-like area of pdelasti has

beenex luded;inthiswaythemain on entrationofpdBreakupremains.

3.3.1 Parti le Identi ation

Theenergylossinformation arriedby hitsprovidesthesele tionof

the harged parti les by the

∆E

/E and Parti le IDenti ation (PID) methods. These twomethodsare developed ombiningthe energyloss

dete ted in the Sili on Tra king Teles ope and the energy lossof

par-ti les inmatter, asdes ribed by the Bethe-Blo k formula:

−

dE

dx

=

4πnz

2

m

e

v

2

·

(

e

2

4πǫ

0

)

2

·

ln

2m

e

v

2

I

,

(3.6)

where v is the velo ity of the in oming parti le,

ǫ

0

the va uum per-mittivity,

m

e

the ele tron mass, n the ele tron density, z the atomi number and I the average ionizationenergy.

Showing

E

1

, the deposited energy in the rst layer, as fun tion of

E

2

thedepositedenergy inthese ondlayer,one ansee thatdierent

par-ti les populate dierent regions of the phase-spa e (

∆E/E

method). Theborderlineoftheseregionsisbroadsin etheparti lespassthrough

more orless dete tor materialdependingon the in ident angles.

Tosimplify proton/deuteron separation, the PID method an be

ap-plied; in this ase the energy loss are parametrized by the so- alled

parameter dened as follow:

Figure3.5: MonteCarlopdelasti andpdBreakuptogether.Intheleftpanelthe

∆

E/E

plotisshown. InMonteCarloaagtags parti lesas protons(bluepoints)or deuterons

(redpoints); protons and deuteronspopulatedierent lo iof the phasespa e. Looking

atthe deuterons(same isfor protons),theupperband orrespondsto parti lesstopped

inthe

2

nd

layera eptan eandthe lowerband orrespondsto deuteronshavingenough

energytopassthroughthe

2

nd

layer. Heredeuterons anmissthe

3

rd

layeror anenter

the

3

rd

layerandstopbe auseofitsthi kness. Inthisregiondeuteronslayonthestopped

protonsband. Ifthesedeuteronsenterthe

3

rd

layer,they anbeseparatedfromprotons,

otherwisethe separation betweenprotons and deuteronsis notappli able. Inthe rigth

panelthePID utisshown. Usinganenergyparametrizationitispossibleto onvertthe

leftplotintherightoneinwhi htheprotons-deuteronsseparationisrealizedapplyinga

horizontal ut.

Figure 3.6: Experimentaldata. Intheleft panelthe

∆

E/Eplotisshown, aag

indi- atingprotonsordeuteronsisnolongeravailable. Thesele tionofprotonsanddeuterons

anbe arriedoutwithalinear ut(magentaline)whi hdividestheplaneinprotonsand

deuteronslo i. Thesame onsiderationsfortheoverlappingprotons-deuteronsregionsare

appliedhere. Intherigthpanel thePID utisshown, theseparationis realizedusinga

A ut around the horizontal band (see Fig.3.6) allows the separation

between protonsand deuterons.

Afterhavingseparatedthetwo hannels,thefurtherstepoftheanalysis

isaimedtoidentifythetra kswithtwoprotonsstoppedinthedete tor.

3.3.2 Tra k "1" re onstru tion

Whenaparti lestopsintherstlayerislabelledastra k"1". Tra k

"1" is sele ted by means of a geometri al ut in whi h the parti le is

supposedtohaveonehitintherstlayeranditstra k,originatingfrom

the target region, is proje ted in the forward dire tion to he k if it

inter epts these ondlayera eptan e. Sin etheparti leidenti ation

is not appli able in the rst layer, to eliminate the high ba kground

fromdeuteronsstoppedintherstlayer,a o-planarity ut isrequired.

Figure3.7: Sele tionofprotontra k"1". YZplaneofthese ondlayer. The yanpoints

referstothe nominalpositionofthe

2

nd

layer; the pinkpointsareproje tionsof tra ks

withonehitinthe

1

rst

layerthatmissthe

2

nd

layera eptan e. Ifaproje tionbelongs

tothe

2

nd

layera eptan eandno orrelatedhitisfoundthenitislabelledastra k"1".

3.3.3 Tra k "2" re onstru tion

Tra k "2" refers toparti les stopped in the se ond layer of the

IDen-ti ation(PID) methods. Parti les displayed inFig.3.6 are those that

pass the rst layer and give rise to a signal in the se ond layer.

Par-ti les with the highest energy loss in the rst layer have a low energy

loss in the se ond; as the energy of the parti le in reases, the energy

loss inthe se ond layer in reases and the deposited energy inthe rst

layerde reases,sin etheenergylossisproportionalto1/

v

2

. Theupper

Figure 3.8: Experimental data. In the left panel the

∆

E/E plot and in the right

panelthePIDplotaredisplayedinboth aseswithoutthedeuteronslo i;herethemain

on entrationofpdBreakuphasbeenidentied. Protonsstoppedinthese ondlayerare

isolatedsele tingthebandboundedbythepinklines.

bands are populated by deuterons andprotons respe tively stopped in

the se ond layer and their initial kineti energy is determined by the

sum of the deposited energy in the rst two layers. The lower bands

are populated by protons and deuterons that pass through the se ond

layer a eptan e and an enter the third layer. Restri ting our

analy-sis to protons, the sele tion of a tra k "2" proton is arried out with

theserequirements: rsttwolayersred, theparti leshouldlayonthe

stopped protonsregions (see Fig.3.8)and no hits onthe third layer.

3.3.4 Third layer Calibration

Before dis ussing the re onstru tion of Tra k "3", it is here

pre-sented the alibration pro edure of the third layer. The thi kness of

the third layerrequired the use of apa itors to a omplish the

atten-uation of the input signal, therefore the deposited energies have to be

alibrated to get the orre t value. At this aim, the

∆

E/E plots (

2

versus

3

rd

layer)inMonteCarloandexperimentaldatahavebeen

om-pared inorder tomakethem oin ide.

The resultsof this alibrationhas the ee t ofshifting the peak ofthe

MissingMassdistributiontothe orre tvalue, asreportedinFig.3.11.

Figure3.9: The

∆

E/Eplotdisplayingtheenergylossin

2

nd

layerversusenergylossin

3

rd

layerisshownforMonteCarlo(leftpanel)andexperimentaldata(rightpanels). The middlepanelshowsexperimentaldatawithoutthe alibration, theright panelrepresents

experimentaldataaftertheenergy alibration. The alibrationhasbeenrealizedmaking

theenergylossesshownintherstandse ondpanel oin ide.

3.3.5 Tra k "3" re onstru tion

A tra k labelled as "3" is originated by a parti le stopped in the

third layer and is sele ted using the plot representing

E

2

, the energy loss in the se ond layer, as a fun tion of

E

3

, the energy loss in the third layer. The upper band refers to deuterons entering the third

layer. Deuterons that rea h the third layer, due to its thi kness, are

here stopped. The lower band in the

∆

E/E plot refers to protons. Also in this ase a parametrization of the deposited energies an be

used todisantangle protonsand deuteronsand toidentify the stopped

parti les:

c

3

= (E

1

+ E

2

+ E

3

)

1.7

−

E

3

1.7

(3.8)

The sele tionof a"3" tra kprotonis madelookingfor3-hits tra ksin

the proper region of the phase spa e of protons stopped in the third

Figure 3.10: Experimentaldata. Inthe upperbox the

∆

E/Eplot(leftpanel)for

2

nd

and

3

rd

layer anditsparametrization PIDplot (right panel)are shown, onsideringpd

elasti and pd Breakup. Applying the ut identied by the pink line, one an sele t

protons or deuterons. Inthe lower panel

∆

E/E plot and PID plotwithout pdelasti .

Protons labelledas tra k "3"are isolated applyingthe ut indi ated by the pinklines,

whi hsele tstheprotonsstoppedinthe

3

rd

layer.

Figure 3.11: Experimental data: run 260. The Missing Mass distribution is shown

3.4 Deuteron Breakup samples

The ombinationoftwostopped-protonstra ks(1,2or3)generates

veeventsampleslabelled2-1,2-2,3-1,3-2,3-3referringtothenumber

of hits in ea h tra k. These event samples are investigated separately

as they populate dierent lo i of the phase spa e. Every sample is

identied by meansof a ombinationof thesele tion riteriades ribed

above.

•

2-1 sample: This ategory is identied applying the param-eter ut and the tra k "1" geometri al ut. In addi tion the

o-planarity ut is applied be ause of the high ba kground of

deuterons stopped inthe

1

rst

layer.

Figure3.12: 2-1sample. Upperpanels: MonteCarlo.Theleftpanelshowsthesele tion

toidentifytheprotonsstoppedinthe

2

nd

layer, themiddlepanelshows thegeometri al

ut on the proje tion of the tra k to identify protons stopped in the

1

rst

layer. The

right panel displaysthe MissingMass distributions: thered onerefers tore onstru ted

events(21seventsthatenterthegeometri ala eptan ebutnotne essarilystopped),the

green onerefers to generated stopped events (21s eventsthat are stoppeda ording to

simulations),theblueonereferstotheeventsstoppedusingthesele tion riteria. Lower

panels: DATA.Startingfromtheleftthesele tionstoidentifystoppedprotonsinthe

2

nd

and

1

rst

layerareshown. IntherightpaneltheMissingMassforre onstru ted(red)and

•

2-2 sample: This ategory is identied applying the parameter and the o-planarity ut.

•

3-1 sample: This sample is identied applying the 3 parameter (eq.3.8)and thetra k"1" geometri al ut;the o-planarity utis

appliedfor the reasonalready mentionedfor the 2-1sample.

E1+E2 (MeV)

0

5

10

15

20

25

30

35

c (MeV)

20

40

60

80

100

z (cm)

-4

-2

0

2

4

6

8

y (cm)

-6

-4

-2

0

2

4

6

MM31geant

Entries 4543

Mean 939.3

RMS 1.867

)

2

Neutron Mass (MeV/c

910

920

930

940

950

960

970

0

200

400

600

800

1000

1200

1400

1600

MM31geant

Entries 4543

Mean 939.3

RMS 1.867

MM31stop

Entries 5785

Mean 938.2

RMS 3.747

MM31stop

Entries 5785

Mean 938.2

RMS 3.747

MM31rec

Entries 20860

Mean

938.2

RMS

4.861

MM31rec

Entries 20860

Mean

938.2

RMS

4.861

Missing Mass 31

E1+E2 (MeV)

0

5

10

15

20

25

30

35

c (MeV)

20

40

60

80

100

z (cm)

-4

-2

0

2

4

6

8

y (cm)

-6

-4

-2

0

2

4

6

Entries 5785

Mean 939.9

RMS 5.136

)

2

Neutron Mass (MeV/c

910

920

930

940

950

960

970

0

100

200

300

400

500

600

700

Entries 5785

Mean 939.9

RMS 5.136

Missing Mass 31

Entries 22186

Mean

940.9

RMS

7.102

Entries 22186

Mean

940.9

RMS

7.102

0

200

400

600

800

1000

1200

1400

1600

Figure 3.13: 3-1sample: inthe upperpanels: MonteCarlo. Theleftpanel shows the

sele tion to identifythe protons stopped inthe

3

rd

layer. Inthe middlepanel, the ut

forprotonsstoppedintherstlayerisrepresented. TherightpaneldisplaystheMissing

Mass distributions: the red one refersto re onstru tedevents, the green one refers to

generated stoppedevents,the blue one refersto the eventsstoppedusing the sele tion

riteria. Lowerpanels: DATA.Sameplotsasmentionedabovebutdisplayedfor data.In

therightpaneltheMissingMassfor re onstru ted(red)andstopped(blue)31sevents.

•

3-2 sample: This sample is identied applying the 3 parameter (eq.3.8)and the parameter(eq.3.7) sele tion; the requestof the

3.5 E ien y of Breakup identi ation

The Missing Mass of the dierent samples are shown for Monte

Carlo,seeFig.3.14anddata, seeFig.3.15. TheMissingMassisapplied

as a ontrol riteria to tag a breakup event. The number of events

identied for ea h run is displayed in Table 3.2.

Figure3.14: MonteCarlo.TheMissingMassdistributionisshownfortheBreakupevent

samplesinviduallyandtogether(bottomright).RED:theMissingMassforre onstru ted

events(eventsnotne essarystoppedinsidethedete tora eptan e),GREEN:theMissing

Mass for generated stoppedevents(events inwhi hgenerated andre on truted energy

oin ides), BLUE:the MissingMass forstoppedevents(eventsidentiedwithsele tion

Figure 3.15: Experimental data: The Missing Mass distribution is shown for the

Breakup event samples invidually and together (bottom right) for a single run. These

MONTE CARLO

Monte Carlo 21 22 31 32 ALL

Re onstru ted 26280 3765 30131 10122 74595

Truly Geant Stopped 3518 417 6823 2511 17141

Stopped 2361 419 4870 2612 14280

Table3.3: MonteCarlostatisti s:thistable ontainsthenumberofre onstru tedevents

(eventsthatenterthedete tora eptan ebutnitne essarilystopped),trulygeantstopped

events(eventsinwhi hgeneratedandre onstru tedenergies oin ide)andstoppedevents

(eventsthatfulllthesele tion riteria). The ountsarereportedforea hsampleandall

together. DATA RUN 21 22 31 32 ALL 260 4299 188 5785 10730 21002 262 4073 162 5843 10780 20858 264 4178 145 5795 10741 20859 266 4015 189 5771 10409 20384 267 3821 174 5701 10305 20001 270 3489 165 4948 9265 17867 272 3178 131 4841 9055 17205

Table 3.4: Numberof identieddeuteron breakup events for ea hsample and for all

samples onsideredtogetherinexperimentaldata. Thepresen eofthethirdlayerof5mm

in reasesthestoppingeen ybyafa tor3withrespe ttothestoppinge ien yofthe

rst two layers. The 3-3 sampleis not onsidered sin e one of the thirdlayerwas not

workingduringthewholebeamtime.

3.6 Phase Spa e Coverage

The identied Breakup samples populate dierent regions of the

phase spa e. The ja obi momenta of the identied samples are

dis-played in Fig.3.16, 3.17, 3.18, 3.20, 3.21, 3.22, 3.23 to show the phase

MeV/c

20

40

60

80

100 120 140 160 180

0

50

100

150

200

250

P sample 21

P sample 21

MeV/c

20

40

60

80

100 120 140 160 180

0

5

10

15

20

25

P sample 22

P sample 22

MeV/c

50

100

150

200

250

300

0

50

100

150

200

250

Q sample 21

Q sample 21

MeV/c

50

100

150

200

250

300

0

2

4

6

8

10

12

14

16

18

Q sample 22

Q sample 22

Figure3.16: Experimentaldata: Ja obimomentapandqfor 2-1and2-2samples. In

parti ular,qrepresentstheneutroninthe enterofmasssystem.

MeV/c

20

40

60

80

100 120 140 160 180

0

50

100

150

200

250

P sample 31

P sample 31

MeV/c

20

40

60

80

100 120 140 160 180

0

200

400

600

800

1000

1200

1400

1600

P sample 32

P sample 32

MeV/c

50

100

150

200

250

300

0

50

100

150

200

250

300

350

400

Q sample 31

Q sample 31

MeV/c

50

100

150

200

250

300

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

Q sample 32

Q sample 32

Figure3.17: Experimentaldata: Ja obimomentapandqfor 3-1and3-2samples. In