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Pia Thöngren Engblom for the PAX Collaboration

University of Ferrara

KTH Royal Institute of Technology

A LOW-ENERGY POLARIZED COMPLETE PROTON-DEUTERON BREAKUP EXPERIMENT

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The 20th International Spin Physics Symposium, SPIN2012, will be heldfrom September 17 to 22, 2012 in Dubna, Russia. The Symposium is opento all scientists, regardless of citizenship and nationality. The Symposium ishosted by the Joint Institute for Nuclear Research.

The scientific program of this Symposium includes the topics related to spinphenomena in particle and nuclear physics as well as those in related fields.The International Spin Physics Symposium series combined together theHigh Energy Spin Symposia and the Nuclear Polarization Conferences since2000.

The spin plays a paramount role in studies of fundamental symmetries,fundamental interactions, particle properties and structure of hadrons.Similarly, spin physics provides decisive progress in the understanding ofnuclear reaction dynamics and of the structures of hadron-nucleon manybody systems. Technical developments and applications of polarized beamsand targets and spin handlings are also important subjects which will greatlycontribute to the future development of particle and nuclear physics.

The preliminary programme includes the traditionallyfor Spin Physics series of conference topics:

Spin Structure of HadronsSpin in Hadronic ReactionsSpin Physics with Photons and LeptonsSpin Physics in Nuclear Reactions and NucleiFundamental Symmetries and Spin Physics beyond the StandardModelAcceleration, Storage, and Polarimetry of Polarized BeamsPolarized Ion and Lepton Sources and TargetsFuture Facilities and ExperimentsMedical and Technological Applications of Spin Physics

OVERVIEW DUBNA PHOTOS

Important Deadlines:Arrival Information: 13 SeptRegistration: 16SeptSPIN2012 dates: 17-22Sept

News:List of participants & time fortalks: updated 10 SeptSocial Program: 23 AugTime-tables: 10 SeptScientific Program: 10 Sept

Copyright © 2011 BLTP JINR | All Rights ReservedPowered by CMS | W3C XHTML 1.0 | W3C CSS 2.0

The 20th INTERNATIONAL SYMPOSIUM onSpin Physics (SPIN2012)

JINR, Dubna, RussiaSeptember 17 - 22, 2012

Home About Contact

September 17 - 22

PROTON DEUTERON BREAKUP @ COSY

SPIN2012 / THÖRNGREN 2

! Polarized proton beam on a vector & tensor polarized deuterium target COSY proposal 202: Measure most of the 22 independent spin observables with high precision & large coverage of phase space

!  Prerequisites: !  Faddeev calculations (Krakow-Bochum group) !  Chiral EFT & collaboration with theorists Epelbam & Nogga !  PAX Double polarized experimental facility !  High precision !  Analysis method, sampling

STATUS 3N IN PD BREAKUP: TENSOR ANALYZING POWERS 50 MEV/A @ KVI


Stephan et al. Phys.Rev.C 82, 014003

CDBonn

CDBonn TM99

VECTOR AND TENSOR ANALYZING POWERS IN . . . PHYSICAL REVIEW C 82, 014003 (2010)

40 80 120

-0.4

-0.2

0

0.2

0.4

Ayy

40 80 120

30 60 90

-0.2

-0.1

0

0.1

40 80 120

-0.1

0

0.1

0.2

Axy

40 80 120S (MeV)

30 60 90-0.4

-0.2

0

0.2

0.4

60 90 120 150

30 60 90S (MeV)

!12 = 40"#1$ #2 = 15", 15"

!12 = 40" !12 = 40" !12 = 80"

!12 = 100"!12 = 100"!12 = 100"!12 = 100"

#1$ #2 = 20", 15" #1$ #2 = 25", 15" #1$ #2 = 15", 15"

#1$ #2 = 30", 25"#1$ #2 = 30", 20"#1$ #2 = 25", 20"#1$ #2 = 20", 15"

FIG. 13. (Color online) Examples of tensor analyzing power results obtained for configurations in which significant effects of the TM993NF are predicted. Meaning of lines and bands as in Fig. 10.

most successful in this case. There are certain places at whicha slight difference between the results of ChPT at N2LOand N3LO exist. Examples of distributions in function ofS obtained for such geometries are shown in Fig. 9. Sincecalculations with the realistic potentials (with and without3NF) agree with ChPT predictions at N3LO (cf. Fig. 10),it can be concluded that at N2LO convergence is not reachedyet. ChPT calculations at N3LO, though not complete, providealso narrower uncertainty bands than at N2LO.

The analysis of the !2/DOF map for tensor analyzingpowers leads to the identification of the regions, whichare responsible for the earlier discussed increase of global!2/DOF value. Problems with the description of Axx andAyy occur mostly at the lowest "12 angles. Examples of suchdistributions of the data along S curve are shown in Figs. 11and 12 and compared to various theoretical predictions. Thesystematic discrepancy between data points and calculatedobservables is not large but significant: roughly of about 0.1.It occurs at the same kinematical region, where the simplifiedanalysis lead to identifying problems with the description ofReT20 [27]. This is not a surprise, since these observables areconnected by a simple relation: Re(T20) = ! 1"

2(Axx + Ayy).

In the right columns of Figs. 11 and 12, Axx and Ayy for thesame angular configuration are shown, which can be combinedtogether to form ReT20 distribution.

In two of the examples presented in Fig. 12 certain sensi-tivity of the theoretical predictions to the Coulomb interactioncan be observed; however, the description of the data becomeseven worse when this important part of interaction is added. Inorder to compensate for that departure a substantial (and actingin the correct direction) effect of 3NF would be required.

The maps obtained for Axy confirm the strongest sensitivityof this observable to differences in assumed dynamics. Two

types of calculations with the realistic potentials combinedwith model 3NF, i.e., 2N+TM99 and AV18+Urbana, showsimilar pattern of inconsistencies with the data, though theeffect is much stronger in the case of 2N+TM99. We presentin Fig. 13 a set of distributions of the tensor analyzing powers,

FIG. 14. Quality of description of vector analyzing powers givenby various models, presented as ! 2 per degree of freedom in functionof the relative energy of the two breakup protons.

014003-13

E. STEPHAN et al. PHYSICAL REVIEW C 82, 014003 (2010)

FIG. 15. The same as in Fig. 14 but for tensor analyzing powers.

where the TM99 3NF effect is significant. Among themthere are configurations in which inclusion of the TM99 3NFimproves the description. Alas, in several other configurationsthe calculations including the 3NF contributions lead to aworse agreement with the experimental data. Coulomb effectspredicted for Axy are rather small, but in some regions theirmagnitude is non-negligible and they can be comparable tothe effects of the TM99 3NF (e.g., for configuration !1 = 30!,!2 = 25!, "12 = 100!, as shown in Fig. 13).

The energy of the relative motion of the two outgoingprotons is an important kinematical variable in pointingout various effects in the cross sections, as presented inRefs. [25,26]. Therefore dependence of #2/DOF on Erel hasalso been studied for the analyzing powers. Figure 14 presentssuch dependencies obtained for vector analyzing powers. Noparticular tendency can be observed and a good descriptionof the data by all theories is confirmed. The influences of3NFs and Coulomb interactions on vector analyzing powersare practically negligible in the whole studied region. A similar#2 analysis for the tensor analyzing powers is shown inFig. 15. Axy is well described by purely NN interactions, whileinclusion of TM99 3NF worsens the agreement, practically inthe whole range of relative energies with exception of thehighest one. In the case of Axx and Ayy the largest discrepancy

between the data and all calculations is present for the lowestErel. The problem with description of Axx at low energies iseven increased when Coulomb interactions are included in thecalculations.

VII. SUMMARY AND OUTLOOK

Vector and tensor analyzing powers have been obtainedfor 82 kinematical configurations of the 1H( "d,pp)n breakupreaction, covering a significant part of the phase space.The experimental results have been compared to varioustheoretical calculations. They comprise predictions based onthe realistic NN (CD Bonn, AV18, Nijm I, and Nijm II)potentials alone and combined with the TM99 and Urbana3NF models. Moreover, the data are confronted with the resultsof the coupled-channels approach based on the CD-Bonn+$potential, with or without Coulomb interactions included.Finally, the results are compared to the observables obtainedwithin the ChPT framework at N2LO including full dynamicsand, currently not complete, calculations at N3LO.

In the majority of the studied configurations and observ-ables all the theoretical predictions agree with each other anddescribe the data very well. In particular this is true for vectoranalyzing powers in the whole studied region of the breakupphase space. The situation is more complicated for the tensoranalyzing powers, for which, in spite of a general success of thetheoretical description, certain discrepancies are observed. ForAxy such discrepancies usually appear or are enhanced whenthe 3N forces, TM99 or Urbana, are included. On the otherhand, problems with describing Axx and Ayy are limited tothe lowest relative energies and are present for all theoreticalapproaches. Effects of Coulomb interactions are small anddistributed rather chaotic in the studied part of the phase space.

Description of the data within the ChPT framework is ofvery similar quality to that of the other approaches. Thereare, however, hints that calculations at N3LO are necessaryto obtain precise results at this energy, therefore completecalculations (including 3NF contributions) at that order wouldbe of high importance. One can also expect an improvementof data description when calculations with explicit $ degreesof freedom in ChPT [62] become available for the breakupreaction. This approach to ChPT leads to a better convergenceof the results and to a reduction of the theoretical uncertainties.

Generally, tensor analyzing powers are more sensitiveto details of dynamics, like effects of 3NF or Coulombinteraction, than vector analyzing powers, what coincides withthe observations inferred from the elastic scattering at thesame energy [17]. In contrast to the data presented here, themeasurements of the breakup reaction at higher energies alsohint at problems with a proper description of the vector ana-lyzing powers [28–31]. The observed discrepancies seem to bestronger in proton analyzing powers than in the deuteron ones.

The overall picture drawn here shows that even thoughin general all presented analyzing powers are quite wellreproduced by modern theoretical approaches, there remainregions of unexplained discrepancies, pointing at still persist-ing flaws in the 3NF models, in particular in their spin structure.This conclusion is supported by data for various polarizationobservables at higher energies [28–31].

014003-14












014003-14












014003-14

VECTOR AND TENSOR ANALYZING POWERS IN . . . PHYSICAL REVIEW C 82, 014003 (2010)

40 80 120

-0.4

-0.2

0

0.2

0.4

Ayy

40 80 120

30 60 90

-0.2

-0.1

0

0.1

40 80 120

-0.1

0

0.1

0.2

Axy

40 80 120S (MeV)

30 60 90-0.4

-0.2

0

0.2

0.4

60 90 120 150

30 60 90S (MeV)

!12 = 40"#1$ #2 = 15", 15"

!12 = 40" !12 = 40" !12 = 80"

!12 = 100"!12 = 100"!12 = 100"!12 = 100"

#1$ #2 = 20", 15" #1$ #2 = 25", 15" #1$ #2 = 15", 15"

#1$ #2 = 30", 25"#1$ #2 = 30", 20"#1$ #2 = 25", 20"#1$ #2 = 20", 15"

FIG. 13. (Color online) Examples of tensor analyzing power results obtained for configurations in which significant effects of the TM993NF are predicted. Meaning of lines and bands as in Fig. 10.

most successful in this case. There are certain places at whicha slight difference between the results of ChPT at N2LOand N3LO exist. Examples of distributions in function ofS obtained for such geometries are shown in Fig. 9. Sincecalculations with the realistic potentials (with and without3NF) agree with ChPT predictions at N3LO (cf. Fig. 10),it can be concluded that at N2LO convergence is not reachedyet. ChPT calculations at N3LO, though not complete, providealso narrower uncertainty bands than at N2LO.

The analysis of the !2/DOF map for tensor analyzingpowers leads to the identification of the regions, whichare responsible for the earlier discussed increase of global!2/DOF value. Problems with the description of Axx andAyy occur mostly at the lowest "12 angles. Examples of suchdistributions of the data along S curve are shown in Figs. 11and 12 and compared to various theoretical predictions. Thesystematic discrepancy between data points and calculatedobservables is not large but significant: roughly of about 0.1.It occurs at the same kinematical region, where the simplifiedanalysis lead to identifying problems with the description ofReT20 [27]. This is not a surprise, since these observables areconnected by a simple relation: Re(T20) = ! 1"

2(Axx + Ayy).

In the right columns of Figs. 11 and 12, Axx and Ayy for thesame angular configuration are shown, which can be combinedtogether to form ReT20 distribution.

In two of the examples presented in Fig. 12 certain sensi-tivity of the theoretical predictions to the Coulomb interactioncan be observed; however, the description of the data becomeseven worse when this important part of interaction is added. Inorder to compensate for that departure a substantial (and actingin the correct direction) effect of 3NF would be required.

The maps obtained for Axy confirm the strongest sensitivityof this observable to differences in assumed dynamics. Two

types of calculations with the realistic potentials combinedwith model 3NF, i.e., 2N+TM99 and AV18+Urbana, showsimilar pattern of inconsistencies with the data, though theeffect is much stronger in the case of 2N+TM99. We presentin Fig. 13 a set of distributions of the tensor analyzing powers,

FIG. 14. Quality of description of vector analyzing powers givenby various models, presented as ! 2 per degree of freedom in functionof the relative energy of the two breakup protons.

014003-13

STATUS 3N IN PD BREAKUP: 135 MEV/A


H.O. Meyer et al., Phys. Rev. Lett. 93, 112502 (2004), T.J. Whitaker IUCF PhD thesis

cannot be measured with vertical deuteron spinalignment.

By combining the yields measured with the appropriatecombinations of the five beam and six target polarizationstates, individual terms in Eq. (1) are singled out. Thedata are evaluated as a function of !!. The other threekinematic variables are ignored; thus their full rangewithin the detector acceptance is included.

Figure 1 shows the longitudinal proton analyzingpower Az as a function of !!. This observable involveslongitudinal target polarization of both signs, combinedwith an average over the five beam states, and thusincludes one-third of the breakup events collected in allspin directions (about 5! 107). The axial vector correla-tion coefficient (Cy;x " Cx;y) versus !!, which uses datawith a vector-polarized beam, combined with sidewaystarget polarization is shown in Fig. 2. Finally, Fig. 3shows the tensor correlation coefficient Czz;z, which isderived from the beam states with tensor polarization,combined with longitudinal target polarization. As ex-pected, all three axial observables presented here crosszero at !! # 0 and !! # ", i.e., for coplanar final-stateconfigurations. The error bars shown represent statisticaluncertainties. An overall normalization uncertaintyarises from the determination of the beam and targetpolarization (1.5% for Az and 4% for the other twoobservables).

When comparing an experimental result with theory,breakup reactions have the inherent problem that thecalculation has to be averaged over all kinematic varia-bles that are not explicitly used in quoting a result. This

average has to be weighted by the cross section and theprobability that the detector registers an event at a givenpoint # in phase space. To do this is often difficult: for thepresent experiment, for instance, the acceptance angle ofthe detector depends on the location of the event along theextended target, there is a lower limit for the energy ofprotons that reach the trigger detector, the joints betweendetector segments may locally reduce the efficiency, andso on.

In order to take instrumental constraints into accountcorrectly, we have developed a new method [11], which is

!"(degrees)

Az

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360

FIG. 1. Longitudinal proton analyzing power as a function of!!. The solid and dashed curves are based on the CD-Bonnand the AV18 NN interaction, respectively. When the TM0

three-nucleon potential is combined with the CD-Bonn inter-action, the dotted curve results.

!"(degrees)

Cy,

x-C

x,y

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 180 360

FIG. 2. Vector correlation coefficient Cy;x " Cx;y as a functionof !!. The curves are explained in the caption for Fig. 1.

!"(degrees)

Czz

,z

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360

FIG. 3. Tensor correlation coefficient Czz;z as a function of!!. The curves are explained in the caption for Fig. 1.

VOLUME 93, NUMBER 11 P H Y S I C A L R E V I E W L E T T E R S week ending10 SEPTEMBER 2004

112502-3 112502-3







!"(degrees)

Az

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360



!"(degrees)

Cy,

x-C

x,y

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 180 360


!"(degrees)

Czz

,z

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360



112502-3 112502-3







!"(degrees)

Az

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360



!"(degrees)

Cy,

x-C

x,y

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 180 360


!"(degrees)

Czz

,z

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360



112502-3 112502-3







!"(degrees)

Az

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360



!"(degrees)

Cy,

x-C

x,y

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 180 360


!"(degrees)

Czz

,z

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 180 360



112502-3 112502-3

cannotbe

measured

with

verticaldeuteron

spinalignm

ent.B

ycom

biningthe

yieldsm

easuredw

iththe

appropriatecom

binationsof

thefive

beamand

sixtargetpolarization

states,individual

terms

inE

q.(1)

aresingled

out.T

hedata

areevaluated

asa

functionof

!!

.The

otherthree

kinematic

variablesare

ignored;thus

theirfull

rangew

ithinthe

detectoracceptance

isincluded.

Figure1

shows

thelongitudinal

protonanalyzing

power

Az

asa

functionof

!!

.This

observableinvolves

longitudinaltargetpolarization

ofboth

signs,combined

with

anaverage

overthe

fivebeam

states,and

thusincludes

one-thirdof

thebreakup

eventscollected

inall

spindirections

(about5!10

7).The

axialvectorcorrela-

tioncoefficient

(Cy;x "

Cx;y )

versus!!

,which

usesdata

with

avector-polarized

beam,

combined

with

sideways

targetpolarization

isshow

nin

Fig.2.

Finally,Fig.

3show

sthe

tensorcorrelation

coefficientCzz;z ,

which

isderived

fromthe

beamstates

with

tensorpolarization,

combined

with

longitudinaltarget

polarization.A

sex-

pected,all

threeaxial

observablespresented

herecross

zeroat!

!#

0and

!!

#"

,i.e.,forcoplanarfinal-stateconfigurations.T

heerror

barsshow

nrepresent

statisticaluncertainties.

An

overallnorm

alizationuncertainty

arisesfrom

thedeterm

inationof

thebeam

andtarget

polarization(1.5%

forAz

and4%

forthe

othertw

oobservables).

When

comparing

anexperim

entalresult

with

theory,breakup

reactionshave

theinherent

problemthat

thecalculation

hasto

beaveraged

overall

kinematic

varia-bles

thatare

notexplicitly

usedin

quotinga

result.This

averagehas

tobe

weighted

bythe

crosssection

andthe

probabilitythat

thedetector

registersan

eventat

agiven

point#in

phasespace.To

dothis

isoften

difficult:forthe

presentexperiment,for

instance,theacceptance

angleof

thedetectordepends

onthe

locationofthe

eventalongthe

extendedtarget,

thereis

alow

erlim

itfor

theenergy

ofprotons

thatreach

thetrigger

detector,thejoints

between

detectorsegm

entsm

aylocally

reducethe

efficiency,andso

on.In

orderto

takeinstrum

entalconstraints

intoaccount

correctly,we

havedeveloped

anew

method

[11],which

is

!"(degrees)

Az

-0.25

-0.2

-0.15

-0.1

-0.05 0

0.05

0.1

0.15

0.2

0.25

0180

360

FIG

.1.L

ongitudinalprotonanalyzing

poweras

afunction

of!!

.T

hesolid

anddashed

curvesare

basedon

theC

D-B

onnand

theA

V18

NN

interaction,respectively.

When

theTM

0

three-nucleonpotential

iscom

binedw

iththe

CD

-Bonn

inter-action,the

dottedcurve

results.

!"(degrees)

Cy,x-Cx,y

-0.1

-0.08

-0.06

-0.04

-0.02 0

0.02

0.04

0.06

0.08

0.1

0180

360

FIG

.2.

VectorcorrelationcoefficientC

y;x "Cx;y

asa

functionof

!!

.The

curvesare

explainedin

thecaption

forFig.1.

!"(degrees)

Czz,z

-0.25

-0.2

-0.15

-0.1

-0.05 0

0.05

0.1

0.15

0.2

0.25

0180

360

FIG

.3.Tensor

correlationcoefficient

Czz;z

asa

functionof

!!

.The

curvesare

explainedin

thecaption

forFig.1.

VO

LU

ME

93,NU

MB

ER

11P

HY

SIC

AL

RE

VIE

WL

ET

TE

RS

week

ending10

SEP

TE

MB

ER

2004

112502-3112502-3

cannotbe

measured

with

verticaldeuteron

spinalignm

ent.B

ycom

biningthe

yieldsm

easuredw

iththe

appropriatecom

binationsof

thefive

beamand


states,individual

terms

inE

q.(1)

aresingled

out.T

hedata

areevaluated

asa

functionof

!!

.The

otherthree

kinematic

variablesare

ignored;thus

theirfull

rangew

ithinthe

detectoracceptance

isincluded.

Figure1

shows

thelongitudinal

protonanalyzing

power

Az

asa

functionof

!!

.T

hisobservable

involveslongitudinal

targetpolarization

ofboth

signs,combined

with

anaverage

overthe

fivebeam

states,and

thusincludes

one-thirdof

thebreakup

eventscollected

inall

spindirections

(about5!

107).T

heaxialvector

correla-tion

coefficient(C

y;x "Cx;y )

versus!!

,which

usesdata

with

avector-polarized

beam,

combined

with

sideways

targetpolarization

isshow

nin

Fig.2.

Finally,Fig.

3show

sthe

tensorcorrelation

coefficientCzz;z ,

which

isderived

fromthe

beamstates

with

tensorpolarization,

combined

with

longitudinaltarget

polarization.A

sex-

pected,all

threeaxial


herecross

zeroat!

!#

0and

!!

#"


heerror

barsshow

nrepresent


An

overallnorm


arisesfrom

thedeterm

inationof

thebeam

andtarget

polarization(1.5%

forAz

and4%

forthe

othertw

oobservables).

When

comparing

anexperim

entalresult

with

theory,breakup

reactionshave

theinherent

problemthat

thecalculation

hasto

beaveraged

overall

kinematic

varia-bles

thatare

notexplicitly

usedin

quotinga

result.This

averagehas

tobe

weighted

bythe

crosssection

andthe

probabilitythat

thedetector

registersan

eventat

agiven

point#in

phasespace.To

dothis

isoften

difficult:forthe



angleof

thedetectordepends

onthe

locationof

theeventalong

theextended

target,there

isa

lower

limit

forthe

energyof

protonsthat

reachthe

triggerdetector,the

jointsbetw

eendetector

segments

may

locallyreduce

theefficiency,and

soon.In

orderto

takeinstrum

entalconstraints

intoaccount

correctly,we

havedeveloped

anew

method

[11],which

is

!"(degrees)

Az

-0.25

-0.2

-0.15

-0.1

-0.05 0

0.05

0.1

0.15

0.2

0.25

0180

360

FIG

.1.

Longitudinalproton

analyzingpow

erasa

functionof

!!

.T

hesolid

anddashed

curvesare

basedon

theC

D-B

onnand

theA

V18

NN


When

theTM

0


iscom

binedw

iththe

CD

-Bonn

inter-action,the

dottedcurve

results.

!"(degrees)

Cy,x-Cx,y

-0.1

-0.08

-0.06

-0.04

-0.02 0

0.02

0.04

0.06

0.08

0.1

0180

360

FIG

.2.

Vectorcorrelation

coefficientCy;x "

Cx;y

asa

functionof

!!

.The

curvesare

explainedin

thecaption

forFig.1.

!"(degrees)

Czz,z

-0.25

-0.2

-0.15

-0.1

-0.05 0

0.05

0.1

0.15

0.2

0.25

0180

360

FIG

.3.

Tensorcorrelation

coefficientCzz;z

asa

functionof

!!

.The

curvesare

explainedin

thecaption

forFig.1.

VO

LU

ME

93,N

UM

BE

R11

PH

YS

ICA

LR

EV

IEW

LE

TT

ER

Sw

eekending

10SE

PT

EM

BE

R2004

112502-3112502-3

cannotbe

measured

with

verticaldeuteron

spinalignm

ent.B

ycom

biningthe

yieldsm

easuredw

iththe

appropriatecom

binationsof

thefive

beamand


states,individual

terms

inE

q.(1)

aresingled

out.T

hedata

areevaluated

asa

functionof

!!

.The

otherthree

kinematic

variablesare

ignored;thus

theirfull

rangew

ithinthe

detectoracceptance

isincluded.

Figure1

shows

thelongitudinal

protonanalyzing

power

Az

asa

functionof

!!

.This

observableinvolves

longitudinaltargetpolarization

ofboth

signs,combined

with

anaverage

overthe

fivebeam

states,and

thusincludes

one-thirdof

thebreakup

eventscollected

inall

spindirections

(about5!

107).T

heaxialvector

correla-tion

coefficient(C

y;x "Cx;y )

versus!!

,which

usesdata

with

avector-polarized

beam,

combined

with

sideways

targetpolarization

isshow

nin

Fig.2.

Finally,Fig.

3show

sthe

tensorcorrelation

coefficientCzz;z ,

which

isderived

fromthe

beamstates

with

tensorpolarization,

combined

with

longitudinaltarget

polarization.A

sex-

pected,all

threeaxial


herecross

zeroat!

!#

0and

!!

#"


heerror

barsshow

nrepresent


An

overallnorm


arisesfrom

thedeterm

inationof

thebeam

andtarget

polarization(1.5%

forAz

and4%

forthe

othertw

oobservables).

When

comparing

anexperim

entalresult

with

theory,breakup

reactionshave

theinherent

problemthat

thecalculation

hasto

beaveraged

overall

kinematic

varia-bles

thatare

notexplicitly

usedin

quotinga

result.This

averagehas

tobe

weighted

bythe

crosssection

andthe

probabilitythat

thedetector

registersan

eventat

agiven

point#in

phasespace.To

dothis

isoften

difficult:forthe



angleof

thedetectordepends

onthe

locationofthe

eventalongthe

extendedtarget,

thereis

alow

erlim

itfor

theenergy

ofprotons

thatreach

thetrigger

detector,thejoints

between

detectorsegm

entsm

aylocally

reducethe

efficiency,andso

on.In

orderto

takeinstrum

entalconstraints

intoaccount

correctly,we

havedeveloped

anew

method

[11],which

is

!"(degrees)

Az

-0.25

-0.2

-0.15

-0.1

-0.05 0

0.05

0.1

0.15

0.2

0.25

0180

360

FIG

.1.

Longitudinalproton

analyzingpow

erasa

functionof

!!

.T

hesolid

anddashed

curvesare

basedon

theC

D-B

onnand

theA

V18

NN


When

theTM

0


iscom

binedw

iththe

CD

-Bonn

inter-action,the

dottedcurve

results.

!"(degrees)

Cy,x-Cx,y

-0.1

-0.08

-0.06

-0.04

-0.02 0

0.02

0.04

0.06

0.08

0.1

0180

360

FIG

.2.

VectorcorrelationcoefficientC

y;x "Cx;y

asa

functionof

!!

.The

curvesare

explainedin

thecaption

forFig.1.

!"(degrees)

Czz,z

-0.25

-0.2

-0.15

-0.1

-0.05 0

0.05

0.1

0.15

0.2

0.25

0180

360

FIG

.3.Tensor

correlationcoefficient

Czz;z

asa

functionof

!!

.The

curvesare

explainedin

thecaption

forFig.1.

VO

LU

ME

93,NU

MB

ER

11P

HY

SIC

AL

RE

VIE

WL

ET

TE

RS

week

ending10

SEP

TE

MB

ER

2004

112502-3112502-3

CDBonn """"CDBonn+TM’

Axial observables

Volume 251, number 2 PHYSICS LETTERS B 15 November 1990

Nuclear forces from chiral lagrangians Steven Weinberg Theory Group, Department of Physics, University of Texas, Austin, TX 78712, USA

Received 14 August 1990

The method of phenomenological lagrangians is used to derive the consequences of spontaneously broken chiral symmetry for the forces among two or more nucleons.

The forces among nucleons have been studied as much as anything in physics. Much of this work has necessarily been phenomenological: scattering data and deuteron properties are used to determine a two- nucleon interaction, which can then be used as an in- put to multi-nucleon calculations. As more and more has been learned about the meson spectrum, efforts have been increasingly aimed at calculating the nuclear potential as an expansion in terms of decreasing range arising from the exchange of one or more mesons of various types, but the number of free parameters rises rapidly as more and more meson types are included, especially if one attempts to extend these calculations to forces involving more than two nucleons. This paper applies methods [ 1 ] based on the chiral symmetry of quantum chromodynamics to derive an expansion of the potential among any number of low energy nucleons in powers of the nucleon momenta, which is related to but not identical with the expansion in terms of increasing range. It is not clear which expansion will be more useful in dealing with the two-nucleon problem, but the expansion in powers of momenta gives far more specific information about multi-nucleon potentials.

The lagrangian that we shall use in this work will be taken as the most general possible lagrangian involving pions and low-energy nucleons consistent with spontaneously broken chiral symmetry and other known symmetries. It is given by an infinite series of

Research supported in part by the Robert A. Welch Founda- tion and NSF Grant PHY 9009850.

terms with increasing numbers of derivatives and/or nucleon fields, with the dependence of each term on the pion field prescribed by the rules of broken chiral symmetry. Other degrees of freedom, such as heavy vector mesons, A's, and antinucleons, are "integrated out": their contribution is buried in the coefficients of the series of terms in the pion-nucleon lagrangian. We shall also integrate out nucleons with momenta greater than some scale Q, which requires that these coefficients in the lagrangian be Q-dependent. Later we will consider how to make a judicious choice of Q; for the moment, it will be enough to specify that Q is substantially less than mp. Any detailed model such as that of Skyrme [2] (also see ref. [3]) that embodies broken chiral symmetry will give results that are consistent with ours, but less general; in particular, we do not specify any particular higher-derivative terms in the lagrangian such as those that are introduced to stabilize skyrmions, but instead we consider all possible terms, with any numbers of derivatives, that are allowed by the symmetries of strong interactions.

Now consider the S-matrix for a scattering process with N incoming and N outgoing nucleons, all with momenta no larger than Q. The non-relativistic nature of the problem makes it appropriate to apply "old-fashioned" time-ordered perturbation theory: there is an energy denominator for every intermediate state, instead of a propagator for every internal particle line. The energy denominators associated with intermediate states involving just N nucleons are small, of order QZ/2mN, as compared with Q for the

288 0370-2693/90/$ 03.50 © 1990 - Elsevier Science Publishers B.V. ( North-Holland ) •

MOTIVATION FROM THEORY


MOTIVATION FROM THEORY


Physics Letters B 295 (1992) 114-121 North-Holland P H ¥ S I C S l_ E T T E R $ 13

Three-body interactions among nucleons and pions

Steven Weinberg Theory Group, Department of Physics, University of Texas, Austin, TX 78712. USA

Received 11 June 1992; revised manuscript 9 September 1992

A chiral invariant effective lagrangian may be used to calculate the three-body interactions among low-energy pions and nucleons in terms of known parameters. This method is illustrated by the calculation of the pion-nucleus scattering length.

Recent articles [ 1,2 ] have described a systematic effective lagrangian framework for the calculation of reactions involving arbi trary numbers of nucleons as well as pions of low three-momentum. To leading order in small momenta , the "potent ia l" for such reactions is given entirely by the tree graphs in which only two of the pions a n d / o r nucleons interact; further, their interaction is calculated using the original effective chiral lagrangian [ 3 ], which consists of terms with only the min imum numbers of derivatives or pion mass factors, supple- mented by contact interact ion terms among nucleons. The corrections to these two-body interactions of second order in small momenta involve not only one-loop graphs, but also a large number of new terms [4] in the lagrangian with addi t ional deri?eatives, so many that not much can be learned about p ion-nuc leon or nucleon- nucleon interactions in this way. Fortunately, these two-body interactions can instead be taken from phenomenological models that incorporate exper imental informat ion on nucleon-nucleon, p ion-nucleon, and p ion -p ion scattering. The only remaining contr ibut ions to the potential of the same order in small momenta consist of graphs in which three particles (or two pairs of part icles) interact, their interactions given by tree graphs calculated from the original effective chiral lagrangian. Thus we can use the three-body interaction calculated in terms of known parameters from the original effective chiral lagrangians together with experimental data on two-body scattering to calculate all corrections to the potential of first and second order in small momenta .

This method will be i l lustrated here in the calculation of the ampl i tudes for pion scattering on complex nuclei. But first, a reminder of some generalities.

Consider the ampl i tude for a process with Nn nucleons and N= pions in the initial state and the same numbers of nucleons and pions in the final state, all with three-momenta no larger than of order rn=. We wish to develop a per turbat ion theory for this ampli tude, based on an expansion in powers of the ratio of these small momenta (and the pion mass) to some momentum scale that is characterist ic of quantum chromodynamics , such as rap. In counting the number of powers of small momenta in any given "old fashioned" ( t ime-ordered) diagram for this process, we must dist inguish between energy denominators of two types. Those of the first type arise from intermediate states that differ from the initial and final states in the number ofp ions a n d / o r in the pion energies, and are therefore of the order of the small momenta or the pion mass. The energy denominators of the second type arise from intermediate states that differ from the initial and final states only in the nucleon momenta , and are therefore much smaller, of the order of the nucleon kinetic energies. A given graph is called irreducible if it contains only energy denominators of the first type. These are graphs for which the initial particle lines cannot all be disconnected from the final particle lines by cutting through any intermediate state containing Nn nucleons and either all the initial or all the final pions. We shall consider disconnected as well as connected irreducible

Research supported in part by the Robert A. Welch Foundation and NSF Grant PHY 9009850.

114 0370-2693/92/$ 05,00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

MODERN THEORY OF NUCLEAR FORCES


!  Chiral effective field theory: Systematic & model independent framework for low-energy few-nucleon physics Few body forces enter naturally with increasing order

! At N2LO - first nonvanishing terms from the chiral Three-Nucleon Force (3NF) Two-pion exchange One-pion exchange Contact interaction

Epelb

aum

et al., PR

C 6

6, 0

64

00

1 (2

00

2)

Epelbaum, Prog. Part. Nucl. Phys. 57 (2006) 57

E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Rev. Mod. Phys. 81 (2009) 1773 R. Machleidt, D.R. Entem, Phys. Rep. 503 (2011) 1 E. Epelbaum, U.-G. Meißner, arXiv:1201.2136 [nucl-th].



!  At N3LO – ! derived longest-range contributions to 3NF

! short-range contributions and the leading relativistic corrections to the three-nucleon force (3NF)

V. Bernard, E. Epelbaum H. Krebs,Ulf-G. Meißner , Phys. Rev. C 77, 064004 (2008)

V. Bernard, E. Epelbaum H. Krebs,Ulf-G. Meißner , Phys. Rev. C 84, 054001 (2011)

BERNARD, EPELBAUM, KREBS, AND MEIßNER PHYSICAL REVIEW C 77, 064004 (2008)

(a) (b) (c) (d) (e)

FIG. 1. (Color online) Various topologies that appear in the 3NF at N3LO. Solid and dashed lines represent nucleons and pions, respectively.Shaded blobs are the corresponding amplitudes. The long-range part of the 3NF considered in this paper consists of (a) 2! exchange graphs,(b) 2! -1! diagrams, and (c) the so-called ring diagrams. The topologies (d) and (e) involve four-nucleon contact operators and are consideredof shorter range.

where the ci are low-energy constants and N, vµ, and Sµ denotethe large component of the nucleon field, the nucleons four-velocity, and the covariant spin vector, respectively. We usestandard notation: U (x) = u2(x) collects the pion fields, uµ =i(u†"µu ! u"µu†),#+ = u†#u† + u# †u includes the explicitchiral symmetry breaking resulting from the finite light quarkmasses, ". . .# denotes a trace in flavor space, and Dµ is thechiral covariant derivative for the nucleon field. Notice furtherthat the first terms in the expansion of U (!) in powers of thepion fields read

U (!) = 1 + i

F!

" · ! ! 12F 2

!

!2 ! i$

F 3!

(" · !)3

+ 8$ ! 18F 4

!

!4 + · · · , (2.2)

where " denote the Pauli isospin matrices and $ is an arbitraryconstant. For further notation and discussion, we refer toRef. [20]; a recent review is given in Ref. [21]. FollowingWeinberg [4,5], we define the dimension % of the Lagrangianvia

% = d + 12n ! 2, (2.3)

where d and n are the number of derivatives or insertions of thepion mass M! and nucleon field operators, respectively. Thepertinent low-energy constants (LECs) of the leading-ordereffective Lagrangian are the nucleon axial-vector couplinggA and the pion decay constant F! . Notice that although allcouplings and masses appearing in the effective Lagrangianshould, strictly speaking, be taken at their SU(2) chiral limitvalues, to the accuracy we are working, we can use theirpertinent physical values. In addition, we have the LECsd16, d18, and d̃28 from the !N Lagrangian at order % = 2. Theellipses in the parentheses in the last line of Eq. (2.1) refer toterms proportional to the LECs d1,2,3,5,14,15 and d̃24,26,27,28,30,which generate !!NN vertices [20] but do not contribute tothe 3NF at N3LO as will be shown later. We also omit inEq. (2.1) pion vertices with % = 2 and proportional to theLECs l3,4, which do not show up explicitly in the formulationbased on renormalized pion fields at the considered order; seeRef. [22] for more details.

For a connected N -nucleon diagram with L loops andVi vertices of dimension %i , the irreducible contribution1

1This is the contribution that is not generated through iterations inthe dynamical equation and that gives rise to the nuclear force.

to the scattering amplitude scales as Q& , where Q is ageneric low-momentum scale associated with external nucleonthree-momenta or M! and

& = !4 + 2N + 2L +!

i

Vi%i . (2.4)

Consequently, at N3LO, which corresponds to & = 4, oneneeds to take into account two classes of connected diagrams:tree diagrams with one insertion of the % = 2 interactionsand one-loop graphs involving only lowest order vertices with% = 0. Notice that it is not possible to draw 3N diagramswith two insertions of % = 1 vertices at this order. We furtheremphasize that similar to the case of the leading four-nucleonforce considered in Refs. [23,24], disconnected diagrams leadto vanishing contributions to the 3NF and will not be discussedin what follows.

The structure of the 3NF at N3LO is visualized in Fig. 1and can be written as

V(4)

3N = V(4)

2! + V(4)

2!-1! + V (4)ring + V

(4)1!-cont + V

(4)2!-cont + V

(4)1/m.

(2.5)

Whereas the 2! -1! , ring, and two-pion-exchange-contact(2! -cont) topologies start to contribute at N3LO, the 2! andone-pion-exchange-contact (1! -cont) graphs already appear atN2LO, yielding the following contributions to the 3NF [6,8]:

V(3)

2! = g2A

8F 4!

$'1 · $q1 $'3 · $q3"q2

1 + M2!

#"q2

3 + M2!

#

%"" 1 · " 3

$!4c1M

2! + 2c3 $q1 · $q3

%(2.6)

+ c4" 1 % " 3 · " 2 $q1 % $q3 · $'2#,

V(3)

1!-cont = !gAD

8F 2!

$'3 · $q3

q23 + M2

!

" 1 · " 3 $'1 · $q3,

where the subscripts refer to the nucleon labels and $qi = $p&i !

$pi , with $p&i and $pi being the final and initial momenta of the

nucleon i. Further, qi ' |$qi |, 'i denote the Pauli spin matrices,and D refers to the low-energy constant accompanying theleading !NNNN vertex. Here and throughout this work, theresults are always given for a particular choice of nucleonlabels. The full expression for the 3NF results by taking intoaccount all possible permutations of the nucleons,2 that is,

V full3N = V3N + all permutations. (2.7)

2For three nucleons there are altogether six permutations.

064004-2

Calculations ready for scattering – Epelbaum & Nogga

(a) 2! exchange graphs (b) 2!-1! diagrams (c) the so-called ring diagrams. (d) (e) shorter range



!  Chiral 3NF at N4LO I: Longest-range contributions

H. Krebs, A.Gasparyan & E.Epelbaum, arXiv:1203.0067

2

(f)(a) (b) (c) (d) (e)

FIG. 1: Various topologies contributing to the 3NF up to and including N4LO: two-pion (2!) exchange (a), two-pion-one-pion(2!-1!) exchange (b), ring (c), one-pion-exchange-contact (d), two-pion-exchange-contact (e) and purely contact (f) diagrams.Solid and dashed lines represent nucleons and pions, respectively. Shaded blobs represent the corresponding amplitudes.

extensively explored. It is, therefore, very interesting to study the impact of the novel structures in the 3NF onnucleon-deuteron scattering and the properties of light nuclei, especially in connection with the already mentionedunsolved puzzles. On the other hand, one may ask whether the resulting (leading) contributions to the structurefunctions accompanying the novel operator structures in the 3NF already allow for their decent description. Stateddi!erently, the question is whether the lowest-nonvanishing-order contributions from the 2!-1! and ring-topologies arealready converged or, at least, provide a reasonable approximation to the converged result. There is a strong reason tobelieve that this is not going to be the case since the contributions due to intermediate "(1232) excitations are not yettaken into account for these topologies at N3LO. In the standard chiral EFT formulation based on pions and nucleonsas the only explicit degrees of freedom, e!ects of the " (and heavier resonances as well as heavy mesons) are hiddenin the (renormalized) values of certain LECs starting from the subleading e!ective Lagrangian. The major part ofthe " contributions to the nuclear forces is taken into account in the "-less theory through resonance saturation ofthe LECs c3,4 accompanying the subleading !!NN vertices [18–22] (see, however, the last two references for someexamples of the "-contributions that go beyond the saturation of c3,4). These LECs turn out to be numerically largeand are known to be driven by the " isobar [20, 23]. As a consequence, one observes a rather unnatural convergencepattern in the chiral expansion of the two-pion exchange nucleon-nucleon potential V 2!

NN with by far the strongestcontribution resulting from the formally subleading triangle diagram proportional to c3 [24]. The (formally) leadingcontribution to V 2!

NN does not provide a good approximation to the potential so that one needs to go to (at least) thenext-higher order in the chiral expansion and/or to include the " isobar as an explicit degree of freedom [20]. Thesituation with the 2!-1! and ring topologies in the 3NF is similar. Based on the experience with the two-nucleonpotential, one expects significant contributions due to intermediate " excitations, see also the discussion in Ref. [25].For the ring topology, this expectation is confirmed by the phenomenological study of Ref. [26]. In order to includee!ects of the "-isobar one needs

• either to go to (at least) next-to-next-to-next-to-next-to-leading order (N4LO) in the standard "-less EFTapproach

• or to include the "-isobar as an explicit degree of freedom.

It should be understood that both strategies outlined above are, to some extent, complementary to each other. Inparticular, N3LO contributions in the "-less theory only take into account e!ects due to single "-excitation but notdue to the double and triple "-excitations (whose inclusion in the "-less approach would require the calculation ateven higher orders). These e!ects are taken into account already at N3LO in the "-full approach. On the otherhand, there are also contributions not related to "-excitations which are included/absent in the "-less approach atN4LO/"-full theory at N3LO. It remains to be seen which strategy will turn out to be most e#cient. The presentpaper represents the first step along this line. We analyze here the longest-range contribution to the 3NF in thestandard, "-less approach at N4LO in the chiral expansion. This topology is particularly challenging due to (i) theneed to carry out a non-trivial renormalization program as explained in section III and (ii) the need to re-considerpion-nucleon scattering in order to determine the relevant LECs. Our paper is organized as follows. In section II, wespecify all terms in the e!ective Lagrangian that are needed in the calculation. The general structure of the two-pionexchange 3NF is discussed in section III. Here, we also briefly summarize the already available results at N2LO andN3LO and give explicit expressions for the N4LO contributions. In section IV we analyze pion-nucleon scattering atorder Q4 in the chiral expansion with Q referring to the soft scale of the order of the pion mass and use the availablepartial wave analyses to determine the relevant LECs. In section V, the numerical results for the two-pion exchange

Toplogies contributing to the 3NF including N4LO: (f) contact diagrams

COSY proposal 202

N

N N Measure doubly polarized pd breakup reactions � Low energy range

30-50 MeV � Large coverage � High precision

  3 Nucleon (3N) interaction ~ 0.5-1 MeV   3N effects vary with observable & kinematics   Ideal energy range for chiral EFT to be valid   Few previous measurements exist 30-50 MeV


22 OBSERVABLES


13

formalism is based on G.G. Ohlsen, Rep. Prog. Phys. 1972 35 717-801 [34]. The

traditional coordinate system used is according the Madison convention with the beam in

the z-direction, the y-axis pointing upwards, and the x-axis sideways completing a right

hand coordinate system [39].

The notation for the observables and spin alignment components are as follows: The

vector and tensor analyzing powers are Ai and Ajk, respectively, with i, j, k = x, y, z.Vector correlation parameters are Ci,j , tensor vector correlation parameters are denoted

Cik,j , with the first index referring to the deuteron polarization, and the second represents

the proton polarization state. The proton vector moments are denoted px,y,z. The deuteronvector components are given by qx,y,z and the tensor moments are qjk with j, k = x, y, z.

The unpolarized cross section is denoted σ0, and the polarized cross section σ is given

by

σ = σ0(1 + pyAy(p) + pzAz(p) +3

2qyAy(d) +

3

2qzAz(d)

+3

4(qxpx + qypy)(Cx,x + Cy,y) +

3

4(qxpx − qypy)(Cx,x − Cy,y)

+3

4(qypx − qxpy)(Cy,x − Cx,y) +

3

2qxpzCx,z +

3

2qzpx Cz,x +

3

2qzpzCz,z

+1

6(qxx − qyy)(Axx −Ayy) +

1

2qzzAzz +

2

3qxzAxz

+1

6(qxx − qyy)py(Cxx,y − Cyy,y) +

1

2qzzpzCzz,z +

1

2qzzpyCzz, y

+2

3qxypxCxy,x +

2

3qxzpyCxz,y +

2

3qyzpxCyz,x

+2

3qxypzCxy,z +

2

3qyzpzCyz,z +

1

3(qxzpx + qyzpy)(Cxz,x + Cyz,y)) (7)

2.4.2 Vector and Tensor Moments

We label the absolute polarization of the proton P , and the magnitude of the vector po-

larization of the deuteron Q. The azimuthal and polar angles of the proton spin alignment

is (Φp,βp), The azimuthal of the outgoing particle is denoted φ, or in the case of elastic

scattering it refers to the scattering plane.

The vector moments of the proton spin:

px = P sin(βp) cos(Φp − φ) (8a)

py = P sin(βp) sin(Φp − φ) (8b)

pz = P cos(βp) (8c)

Analogous for the vector moments of the deuteron spin, with the direction of the

deuteron spin alignment given by (Φd,βd):

qx = Q sin(βd) cos(Φd − φ) (9a)

qy = Q sin(βd) sin(Φd − φ) (9b)

qz = Q cos(βd) (9c)


15

Table 3: Tabulated here are the 15 spin correlation observables and 7 analyzing powers

possible in proton deuteron breakup showing the required polarization alignment directions

of beam and target and some combinations thereof. For p (proton) and d (deuteron); U

means alignment up (vertical), S is sideways (parallell to the x-axis) and A is along the

beam direction (longitudinal).

The last two columns refer to the situation when the deuteron spin alignment axis is at

45 degrees which can be accomplished by running current through two guide field coils

simultaneously. With the longitudinal (±z) and vertical (±y) guide field coils on, denoted

dAU, and switched in ± polarity, four directions are achieved. Another four alignments are

obtained with the longitudinal and sideways (±x) combinations, denoted dAS. There are

five observables (here marked in bold font) that are parity forbidden in elastic scattering

and goes to zero in breakup reactions in coplanar kinematical configurations. In the

last two columns also a few observables are included requiring longitudinally polarized

beam. The tensor-vector correlation coefficient Cyz,z is accessible only using longitudinally

polarized beam and diagonal target spin alignment.

PolObs pU dU pU dS pU dA pA dU pA dS pA dA pU dAU pU dAS

Ay(p) X X X X X

Az(p) X X X pA dAU pA dASAy(d) X X X X X X

Az(d) X X X X

Axx −Ayy X X X X X X

Azz X X X X X X X X

Axz X X

Cx,x + Cy,y X X

Cx,x − Cy,y X X X X

Cy,x −Cx,y X X

Cx,z X X pA dAU pA dASCz,x X X X

Cz,z X pA dAU pA dASCxx,y − Cyy,y X X X X

Cxz,x +Cyz,y X X

Czz,z X X X pA dAU pA dASCzz,y X X X X X

Cxy,x X X X X

Cxz,y X X

Cyz,x X X

Cxy,z X X pA dAU pA dASCyz,z pA dAU pA dAS

15

















Ay(p) X X X X X

Az(p) X X X pA dAU pA dASAy(d) X X X X X X

Az(d) X X X X


Azz X X X X X X X X

Axz X X

Cx,x + Cy,y X X


Cy,x −Cx,y X X

Cx,z X X pA dAU pA dASCz,x X X X

Cz,z X pA dAU pA dASCxx,y − Cyy,y X X X X

Cxz,x +Cyz,y X X

Czz,z X X X pA dAU pA dASCzz,y X X X X X

Cxy,x X X X X

Cxz,y X X

Cyz,x X X

Cxy,z X X pA dAU pA dASCyz,z pA dAU pA dAS

15

















Ay(p) X X X X X

Az(p) X X X pA dAU pA dAS

Ay(d) X X X X X X

Az(d) X X X X


Azz X X X X X X X X

Axz X X

Cx,x + Cy,y X X


Cy,x −Cx,y X X

Cx,z X X pA dAU pA dAS

Cz,x X X X

Cz,z X pA dAU pA dAS

Cxx,y − Cyy,y X X X X

Cxz,x +Cyz,y X X

Czz,z X X X pA dAU pA dAS

Czz,y X X X X X

Cxy,x X X X X

Cxz,y X X

Cyz,x X X

Cxy,z X X pA dAU pA dAS

Cyz,z pA dAU pA dAS

A METHOD TO COMPARE BUP WITH THEORY


The Sampling Method (iv)

! The # of occupied xi elements = the total # of events collected in the region ! during the experiment !

! The list of xi’s = the list of phase space coordinates for all collected events!!!

0

0

The theoretical calculation provides us with a value

( )at any point in phase space. For comparison withexperiment we have to average over the region

( ) ( ) ( ) ( ) (( )( ) ( )

th

th thth i

O x

x x O x dx N x OO xx x dx

!

" #" #

= =$$

)( )

Here ( ) is the # of events collected in element irrespective of polarization. Since we are free to choosethe size of x, we decrease it until all N( )are either 0 or 1

i

i

i i

i

xN x

N x x

x

%%

J.Kuros-Zolnierczuk, P.Thörngren, H.O. Meyer et al., FBS 34, 259 (2004), nucl-th/0402030

x is the set of parameters needed to determine the kinematics, at any point of phase space

! For a kinematically complete experiment: The correctly averaged theoretical value is the mean

A Simple Recipe: The Sampling Method

( )( )( )

thth th kO xO O

N!

!= = "

22

( )( ) 1

th th

thO O

ON

!!

"# =

"

Few Body Syst. 34, 259 (2004), nucl-th/0402030

! The error, the standard deviation that arises from the randomness of the experimental phase space points, is

For a kinematically complete experiment, over some region ! of phase space - The correctly averaged theoretical value is the mean

J. Kuros -"o#nierczuk, P. Thörngren-Engblom, H.O. Meyer, T.J. Whitaker, H. Wita#a, J. Golak, H. Kamada, A. Nogga and R. Skibi$ski, Few-Body Systems 34, 259 (2004)

CHOICE OF INDEPENDENT PARAMETERS


A set of five parameters needed to determine the kinematics of 3B

J. Kuros -"o#nierczuk, P. Thörngren Engblom, H.O. Meyer, T.J. Whitaker, H. Wita#a, J. Golak, H. Kamada, A. Nogga and R. Skibi$ski, Few-Body Systems 34, 259 (2004)

p = % ( p1 - p2 ) q = - ( p1 + p2 ) { p, &p, 'p, &q, 'q }

2011 Oct 9-14 STORI'11 FRASCATI 31 !"#$#!%&% #'()*+!%&%','(-./')012.32'./'+435678'9673:.;/2'7/<'+4356.'&#'')='>0?8/@86/ &A

!"#$$%&'()*+,-./*01.1$!"#$$%&'()*+,-./*01.1$

B C.D6,<.E6/2.;/75'-0726'2-736'

B A'7/@562'7/<'E;EF'''!"#$!%#$&"#$&%#$$"

B *C'7G.E4:075'21EE6:81'!''!"#$!%#$!&#$"

B H./<'8656D7/:'./<6-6/<6/:'-787E6:68'I'

;J268D7J56

!"$'$"$(")$*$"$(%)!

+,-./0$1.1234,

"$'$5$("6$7$"8)

%$'$7$("6$9$"8)

p2

p

q

p1

:-;<=2(>6#>8)

!6#$!8#$!"$'

?@#$?6#$6A@$B2C$

!"!"#$%&'()*+,-*./0*1.02.3*425

p1

p1

p

n

GRID EXAMPLES OF SENSITIVITY STUDIES •  Theoretical framework N2LO & calculations: Epelbaum & Nogga


GRID SPACING p # of steps 20 (p # of steps 9 (p [deg] 5..90 (p # steps 18 (p [deg] 10..180 'p,q # steps 37 'p,q [deg] 0..360 # of grid points 4,435,560

Using the sampling method & phase space simulation

CXZ,Y (AY,XZ)


cxzy3b-0.4 -0.2 0 0.2 0.4

1

10

210

310

410

510

cxzy3b

dcxzy-0.06 -0.04 -0.02 0 0.02 0.04 0.06

10

210

310

410

dcxzy

2040

6080

100120

140160

180

050

100150

200250

300350

-0.05-0.04-0.03-0.02-0.01

00.010.02

cxzy>0.03)!(q) 49 MeV ("(q) #cxzy(3N) vs

1020

3040

5060

7080

90

050

100150

200250

300350

-0.08-0.06-0.04-0.02

00.020.040.060.08

cxzy>0.03)!(p) 49 MeV ("(p) #cxzy(3N) vs

10 20 30 40 50 60 70 80 90

020

4060

80100

120140

160180-0.1

-0.05

0

0.05

0.1

cxzy > 0.03)!(p) p 49 MeV (#cxzy(3N) vs

13

formalism is based on G.G. Ohlsen, Rep. Prog. Phys. 1972 35 717-801 [34]. The

traditional coordinate system used is according the Madison convention with the beam in

the z-direction, the y-axis pointing upwards, and the x-axis sideways completing a right

hand coordinate system [39].

The notation for the observables and spin alignment components are as follows: The

vector and tensor analyzing powers are Ai and Ajk, respectively, with i, j, k = x, y, z.Vector correlation parameters are Ci,j , tensor vector correlation parameters are denoted

Cik,j , with the first index referring to the deuteron polarization, and the second represents

the proton polarization state. The proton vector moments are denoted px,y,z. The deuteronvector components are given by qx,y,z and the tensor moments are qjk with j, k = x, y, z.

The unpolarized cross section is denoted σ0, and the polarized cross section σ is given

by

σ = σ0(1 + pyAy(p) + pzAz(p) +3

2qyAy(d) +

3

2qzAz(d)

+3

4(qxpx + qypy)(Cx,x + Cy,y) +

3

4(qxpx − qypy)(Cx,x − Cy,y)

+3

4(qypx − qxpy)(Cy,x − Cx,y) +

3

2qxpzCx,z +

3

2qzpx Cz,x +

3

2qzpzCz,z

+1

6(qxx − qyy)(Axx −Ayy) +

1

2qzzAzz +

2

3qxzAxz

+1

6(qxx − qyy)py(Cxx,y − Cyy,y) +

1

2qzzpzCzz,z +

1

2qzzpyCzz, y

+2

3qxypxCxy,x +

2

3qxzpyCxz,y +

2

3qyzpxCyz,x

+2

3qxypzCxy,z +

2

3qyzpzCyz,z +

1

3(qxzpx + qyzpy)(Cxz,x + Cyz,y)) (7)

2.4.2 Vector and Tensor Moments

We label the absolute polarization of the proton P , and the magnitude of the vector po-

larization of the deuteron Q. The azimuthal and polar angles of the proton spin alignment

is (Φp,βp), The azimuthal of the outgoing particle is denoted φ, or in the case of elastic

scattering it refers to the scattering plane.

The vector moments of the proton spin:

px = P sin(βp) cos(Φp − φ) (8a)

py = P sin(βp) sin(Φp − φ) (8b)

pz = P cos(βp) (8c)

Analogous for the vector moments of the deuteron spin, with the direction of the

deuteron spin alignment given by (Φd,βd):

qx = Q sin(βd) cos(Φd − φ) (9a)

qy = Q sin(βd) sin(Φd − φ) (9b)

qz = Q cos(βd) (9c)

In[205]:= FullSimplify�3 � 2 � qz � Az_d�Out[205]= �

3 Q Az_d

2 2

In[206]:= FullSimplify�3 � 4 � �qx � px � qy � py� � SCxxCyy�Out[206]= �

3 P Q SCxxCyy

4 2

In[207]:= FullSimplify�3 � 4 � �qx � px � qy � py� � DCxxCyy�Out[207]=

3 DCxxCyy P Q Cos�2 Φ�4 2

In[208]:= Simplify�3 � 4 � �qy � px � qx � py� � DCyxCxy�Out[208]= 0

In[209]:= Simplify�3 � 2 � qx � pz � Cx_z�Out[209]= 0

In[210]:= Simplify�3 � 2 � qz � px � Cz_x�Out[210]= �

3 P Q Cz_x Sin�Φ�2 2

In[211]:= Simplify�3 � 2 � qz � pz � Cz_z�Out[211]= 0

In[212]:= Simplify�1 � 6 � �qxx � qyy� � DAxxAyy�Out[212]= �

1

8DAxxAyy Qt Cos�2 Φ�

In[213]:= 1 � 2 � qzz � AzzOut[213]=

Azz Qt

8

In[214]:= 2 � 3 � qxz � AxzOut[214]=

1

2Axz Qt Sin�Φ�

In[215]:= Simplify�1 � 6 � �qxx � qyy� � py � DCxxyCyyy�Out[215]= �

1

8DCxxyCyyy P Qt Cos�Φ� Cos�2 Φ�

In[216]:= 1 � 2 � qzz � pz � Czz_zOut[216]= 0

In[217]:= Simplify�1 � 2 � qzz � py � Czz_y�Out[217]=

1

8P Qt Cos�Φ� Czz_y

In[218]:= Simplify�2 � 3 qxy � px � Cxy_x�Out[218]=

1

2P Qt Cos�Φ� Cxy_x Sin�Φ�2

In[219]:= 2 � 3 � qxz � py � Cxz_yOut[219]=

1

2P Qt Cos�Φ� Cxz_y Sin�Φ�

polp_pold_cs_UP_LONGSIDE.nb | 3

Differential observable of potential interest for Time Reversal Invariance test experiment at COSY

CXZ,Y (AY,XZ)


20 40 60 80 100120140160180

050

100150

200250

300350

-0.05-0.04-0.03-0.02-0.01

00.010.02

(q) 49 MeV!(q) "cxzy(3N) vs

20 40 60 80 100120140160180

050

100150

200250

300350

-0.016-0.014-0.012

-0.01-0.008-0.006-0.004-0.002

00.002

(q) 49 MeV!(q) "cxzy vs #

20 40 60 80100120140160180

050

100150

200250

300350

0.00040.00060.0008

0.0010.00120.00140.00160.0018

0.002

(q) 49 MeV!(q) "cxzy(2N-3N) vs #FOM of

10 20 30 40 50 60 70 80 90

050

100150

200250

300350

-0.08-0.06-0.04-0.02

00.020.040.060.08

(p) 49 MeV!(p) "cxzy(3N) vs

10 2030 40

50 6070 80

90

050

100150

200250

300350

-0.02-0.015

-0.01-0.005

00.005

(p) 49 MeV!(p) "cxzy vs #

10 20 30 40 50 60 70 80 90

050

100150

200250

300350

0.00050.001

0.00150.002

0.00250.003

(p) 49 MeV!(p) "cxzy(2N-3N) vs #FOM of

CXZ,Y (AY,XZ)


50 55 60 65 70 75 80 85 90-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

cxzy3b:th_p {((th_q>80&&th_q<110)||th_q>140)&&th_p>50&&(p<60||p>160)}

0 10 20 30 40 50 60 70 80 90

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

cxzy3b:th_p {th_q>80&&th_q<110||th_q>140}

10 20 30 40 50 60 70 80 90

020

4060

80100

120140

160180-0.08-0.06-0.04-0.02

00.020.040.060.08

(p) p 49 MeV!cxzy(3N) vs

10 20 30 40 50 60 70 80 90

020

4060

80100

120140

160180-0.02

-0.015-0.01

-0.0050

0.005

(p) p 49 MeV!cxzy vs "

10 20 30 40 50 60 70 80 90

020

4060

80100

120140

160180

0.0005

0.001

0.00150.002

0.0025

0.003

(p) p 49 MeV!cxzy(2N-3N) vs "FOM of

3N 2N

Using cuts in phase space for sensitivity studies of n2lo

3N 2N

&p &p

@ 49 MEV - CYY,Y


20 40 60 80 100120140160180

050

100150

200250

300350-0.2

-0.1

0

0.1

0.2

0.3

0.4

cyyy>0.03)!(q) 49 MeV ("(q) #cyyy(3N) vs

10 20 30 40 50 60 70 80 90

050

100150

200250

300350-0.2

-0.1

0

0.1

0.2

0.3

cyyy>0.03)!(p) 49 MeV ("(p) #cyyy(3N) vs

10 20 30 40 50 60 70 80 90

020406080100120140160180

-0.1

0

0.1

0.2

0.3

0.4

cyyy > 0.03)!(p) p 49 MeV (#cyyy(3N) vs

&q

0 20 40 60 80 100 120 140 160 180

0.04

0.06

0.08

0.1

0.12

0.14

cyyy3b:th_q {cyyy3b>0&&phi_p>70&&phi_p<270&&phi_q>70&&phi_q<270&&p>60&&th_p>50}

0 20 40 60 80 100 120 140 160 180

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

cyyy3b:th_q {cyyy3b>0&&phi_p>70&&phi_p<270&&phi_q>70&&phi_q<270}

3N 3N


@ 49 MeV - Axz

10 20 30 40 50 60 70 80 90

050100150200250300

350-0.1

-0.05

0

0.05

0.1

(p) 49 MeV!(p) "Axz(2N) vs

1020

3040

5060

7080

90

050100150200250300350

-0.01-0.005

00.005

0.010.015

(p) 49 MeV!(p) "Axz vs #

10 2030

405060

708090

050100150200250300350

0.00050.001

0.00150.002

0.00250.003

0.0035

(p) 49 MeV!(p) "Axz(2N-3N) vs #FOM of

10 20 30 40 50 60 70 80 90

020406080100120140160180-0.1

-0.05

0

0.05

0.1

(p) p 49 MeV!Axz(2N) vs

10 20 30 40 50 60 70 80 90

020406080100120140160180

-0.01

-0.005

0

0.005

0.01

0.015

(p) p 49 MeV!Axz vs "

10 20 30 40 50 60 70 80 90

020406080100120140160180

0.00050.001

0.00150.002

0.00250.003

0.0035

(p) p 49 MeV!Axz(2N-3N) vs "FOM of

@ 49 MEV - AXZ VS (Q

21

htempEntries 117672

Mean 90.69

Mean y 0.1073

RMS 38.63

RMS y 0.07824

0 20 40 60 80 100 120 140 160 1800

0.02

0.04

0.06

0.08

0.1

0.12

0.14

htempEntries 117672

Mean 90.69

Mean y 0.1073

RMS 38.63

RMS y 0.07824

axz2b:th_q {axz2b>0&&(p<60||p>120)&&th_p>30&&(phi_p<60||(phi_p>120&&phi_p<240)||phi_p>300)&&(phi_q<60||(phi_q>120&&phi_q<240)||phi_q>300)}

0 20 40 60 80 100 120 140 160 1800

0.02

0.04

0.06

0.08

0.1

axz2b:th_q {axz2b>0&&(phi_q<70||phi_q>300)}

&q

Using cuts in phase space for sensitivity studies comparing 3N & 2N calculations at n2lo

3N 2N

3N 2N

SPIN2012 / THÖRNGREN

@ 49 MEV – CXX VS (P


htempEntries 117305Mean 67.24Mean y -0.3635RMS 14.25RMS y 0.1851

40 50 60 70 80 90

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

htempEntries 117305Mean 67.24Mean y -0.3635RMS 14.25RMS y 0.1851

cxx2b:th_p {cxx2b<0&&(p>130||p<30)&&th_p>40&&th_q<100&&q>60}

&p

3N ~ 2N

COSY – COOLER SYNCHROTRON AND STORAGE RING

inauguration of COSY in 1993


EDM PAX

WASA ANKE

EXPERIMENTAL SETUP PAX interaction point


Low beta quadropoles BRP

ABS Scattering chamber

COSY Cooler synchrotron & storage ring 600 - 3700 MeV/c Polarized proton & deuterons


POLARIZED HYDROGEN/DEUTERIUM TARGET Figure from Diploma thesis of C. Barschel

Dissociator H2!2H

Nozzle Skimmer Collimator

Sextupoles

Sextupoles

HF transitions

!. E!"#$%&#'()* S#(+"

!.". Target Section Overview

!e target section provides a polarized hydrogen or deuterium gas target for the PAX spin-"lteringexperiments. It is composed of the following main components: the Atomic Beam Source (ABS),the target chamber with the storage cell, the Target Gas Analyzer (TGA) and the Breit-RabiPolarimeter (BRP). A schematic view of the components is shown in Fig. !.#. High areal densitiesof up to $ ! #%#& atoms/cm' are required for spin-"ltering. !ey are achieved by injecting nuclearspin polarized hydrogen or deuterium atoms produced by an ABS into a storage cell [##%]. !e BRPmeasures the polarization of an e(usive beam extracted from that cell.

Fig. !.".: Schematic drawing (le)-hand side) the Polarized Internal Target (PIT)[###] with the Atomic BeamSource (ABS, Sec. !.'), the target cell (Sec. !.&), the Breit-Rabi Polarimeter (BRP, Sec. !.!) and the TargetGas Analyzer (TGA, Sec. !.$). !e right-hand side shows a &D plot of the H-beam laboratory setup as usedduring the calibration measurements (source: technical drawing from IKP, Forschungszentrum Jülich).

!.#. Atomic Beam Source

!e ABS, formerly used in the HERMES experiment [*$, ##', ##&], has been modi"ed for the spin-"ltering studies of the PAX experiment [###]. !e vacuum system had to be modi"ed because ofspace limitations of the future setup. !e transitions in the appendix chamber of the ABS had tobe removed because of the low target holding "eld requirement, and to increase the intensity byshortening the distance to the storage cell. !e scheme of the ABS components is shown in Fig. !.'.

For di(erential pumping the ABS is separated into ! chambers (I-IV) and evacuated with +turbomolecular pumps. !e pumping speed is approximately #% %%% l/s. !is powerful pumping

&!


SCATTERING CHAMBER 400 mm

Guide field coils (x, y, z) Atomic beam

Stored beam 36 Silicon double sided strip detectors 97x97 mm 3 layers: 2 x 300µm; 1.5 mm pitch 0.76 mm < 1 mm vertex reconstruction

Appendix A P. Thörngren Engblom

6

reverse process, the depolarization of a polarized proton beam by a co-moving beam of electrons with a slight velocity difference corresponding to an energy for which the cross section for spin flip was expected to be advantageous. Our recently published experimental result24, (an upper limit of 107 b at a c.m. energy of 1 eV), disproved the former prediction by 16 orders of magnitude25 and is in agreement with a recent theoretical calculations with lower cross sections. The former papers were withdrawn after the experimental upper limit became known, and a numerical error was corrected26. The conclusion is that the only viable method for polarizing a stored antiproton beam is through spin filtering.

4.2.2. Spin Filtering at COSY (Exp. No. 199)

At COSY the polarization build-up of a stored proton beam passing through a polarized internal target is pursued mainly to commission the equipment needed for the spin-filtering studies at the AD and to study machine-related effects in a storage ring. The transverse and the longitudinal spin-dependent total cross sections will be measured with high accuracy. Vacuum improvements, beam lifetime and acceptance studies have been carried out and a low ! (0.3 m) section was recently installed and commissioned at COSY in order to optimize the conditions for filtering. The experimental facility comprises an Atomic Beam Source (ABS) for producing the target gas, a so-called Breit-Rabi Polarimeter to measure the polarization of the target gas and an openable storage target cell. To this aim the HERMES target has been brought to COSY and a new openable storage cell has been designed and manufactured. The detector setup for the polarimeter is based on silicon strip detectors in a telescope arrangement. In 2010 the target interaction region was commissioned and the openable storage target cell was installed, see Fig. 1.

Paolo Lenisa and Frank Rathmann(for the PAX collaboration)

!

The measurement of the diffused sample of the gas fromafter subsequent openings (see experiments in low-energy storage ringsignificant increase in the luminosity

Figure 5: Left panel: front view of the openable storage cell in the closed and openof the target polarization after various opening and closing procedures of the target cell: no change was evidenced.

Summer 2010: installation of the PAX

In summer 2010, the PAX target the PAX interaction point at COSY (Fig

Figure 6: Left panel: PAX installation at the COSY ring. Shown in yellow are the existing COSY straight section quadrupole magnets. Four additional quadrupoles (blue) have been recuperated from the CELSIUS ring. The atomic beam source is mounted above the target chamber. panel: Picture of the PAX interaction region.

The PAX target chamber hosting the storage cell has been equipped with three sets of coils providing magnetic holding fields in and functionality, the coils have been mounted on the edges of the chamber

Paolo Lenisa and Frank Rathmann

"!

The measurement of the diffused sample of the gas from the cell showed no loss of see Fig. 5). This result represents an important achievement for

energy storage rings as the use of this kind of storage the luminosity.

: front view of the openable storage cell in the closed and opened position. Rightof the target polarization after various opening and closing procedures of the target cell: no change was evidenced.

Summer 2010: installation of the PAX experimental setup at the interaction region

has been moved and installed, together with the target chamber, at COSY (Fig. 6).

installation at the COSY ring. Shown in yellow are the existing COSY straight section quadrupole magnets. Four additional quadrupoles (blue) have been recuperated from the CELSIUS ring. The atomic

nted above the target chamber. The Breit-Rabi polarimeter is mounted outwards of the ring.icture of the PAX interaction region.

The PAX target chamber hosting the storage cell has been equipped with three sets of coils providing magnetic holding fields in x, y and z direction. For reasons of space optimization and functionality, the coils have been mounted on the edges of the chamber (Fig. 7)

Jülich, 25.03.2011

no loss of polarization an important achievement for all

storage cell can lead to a

d position. Right panel: behaviour of the target polarization after various opening and closing procedures of the target cell: no change was evidenced.

interaction region

been moved and installed, together with the target chamber, at

installation at the COSY ring. Shown in yellow are the existing COSY straight section quadrupole magnets. Four additional quadrupoles (blue) have been recuperated from the CELSIUS ring. The atomic

Rabi polarimeter is mounted outwards of the ring. Right

The PAX target chamber hosting the storage cell has been equipped with three sets of Helmholtz direction. For reasons of space optimization

(Fig. 7).

Fig. 1 Left: Closed and opened storage target cell. Right: The polarization as measured by the BRP after open and closing of the cell, showing no change of polarization.

4.2.3. Spin filtering at AD

The AD ring is the only facility world wide that provides the possibility to do spin-filtering experiments with antiprotons. At present there is virtually no knowledge of the spin dependence of the antiproton-proton interaction and the foreseen experiment opens up a whole new field in hadron physics. There is no certain theoretical estimate of the polarization buildup of a stored antiproton beam and the planned experiments at CERN are necessary for 24 D. Oellers et al., Phys. Lett. B, in press, arXiv:0902.1423 25 A.I. Milstein, S.G. Salnikov, V.M. Strakhovenko, Nucl. Instr. Meth. B 266, 3453 (2008) 26 H. Ahrenhövel, Eur. Phys. J. A. 39 (2009) 133, T. Walcher et al., Eur. Phys. J. A 39 (2009) 137

Openable teflon storage cell

BEAM TIME ESTIMATES

•  Assumptions: •  statistical uncertainy of 0.002 •  # stored polarized protons ) 109

•  target thickness of 5 * 1013 atoms/cm2

•  duty factor of 0.9 •  polarization of the beam P ) 0.5 •  target polarization Q + 0.8. •  # of events of the order of 5 * 107 with roughly 106 events per ten

degree bin in the azimuthal angle '.


SUMMARY - TOTAL BEAM TIME


Polarized proton beam 49 MeV 30 MeV

,tot breakup 212.2 mb 145 mb Acceptance 5 % 8 %

Measuring time ) 5 days/tgt scenario ) 3 days/tgt scenario Beam time/energy 2 weeks 2 weeks

•  With longitudinal and vertical beam polarization:

Four run periods of two weeks each, separated by at least four months.

SUMMARY

•  pd breakup at 30-50 MeV where few previous measurement exist •  Measure most observables with large phasespace coverage –

direct comparison of experiment & theory  Would provide precise data for constraints of chiral EFT in a relevant energy range 30-50 MeV

•  Independent determination of Low Energy Constants D & E

•  New effects of 3NF that appear at N3LO can be accessed


More information: COSY Proposal 202, PTE et al., Measurement of Spin Observables in the pd Breakup Reaction, http://www2.fz-juelich.de/ikp/publications/PAC39/PAX_proposal202.1_202.pdf

•  Theory: E Epelbaum & A Nogga •  PAX Experiment: S Barsov, Z Bagdasarian, S Bertelli, M

Contalbrigo, D Chiladze, A Kacharava, P Lenisa, N Lomidze, B Lorentz, G Macharashvili, K Marcks von Würtemberg, S Merzlyakov, S Mikirtytchiants, A Nass, D Oellers, F Rathmann, R Schleichert, H Ströher, PTE, M Tabidze, S Trusov, C Weidemann, M Zhabitsky for PAX and ANKE Collaborations

•  COSY accelerator group: D Prasuhn & B Lorentz et al.


SPIN

Spin is at the heart of the nuclear force # multiple observables to tell us about nature A highly selective tool # studies of fundamental symmetries


Company from 1953, and in the middle of the 1950's, Tippe Tops could be found in cereal boxeslike Post Rice Krinkles in the USA. According to Dan Goodsell from www.theimaginaryworld.comTippe Tops could be found in cereal boxes from companies like Nabisco, General Mills and Postfrom the 1950's and up into the 1970's.

A famous picture also exists from the opening of the institute of physics at the University of Lundin Sweden in 1951, where Wolfgang Pauli and Niels Bohr are looking at a Tippe Top. Bohr wasvery interested in the physics of the top, and it is believed that also Winston Churchill enjoyed thetop.

Picture from around 1954 of two cereal boxes containing TippeTops. The picture is reproduced with permission from Dan

Goodsell of www.theimaginaryworld.com.

Picture of Wolfgang Pauli and Niels Bohr studying a Tippe Top.The picture is taken at the opening of the new institute ofphysics at the University of Lund on May 31 1951. Credit:

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