new experimental approach to modern three-nucleon forces

New experimental approach to modern three-nucleon forces

P. Thörngren

for the PAX Collaboration

27/9/2010 / SPIN2010 - Spin Physics in Nuclear Reactions and Nuclei 1/ P. Thörngren 22

ResourcesResources

• Experiment: PAX collaboration, bup group formed: – Susanna Bertelli, Marco Contalbrigo, Andro

Kacharava, Paolo Lenisa, Bernd Lorentz, Gogi Macharashvili, Alex Nass, Frank Rathman, Mirian Tabedzi, Pia Thörngren

• Theory: Evgeny Epelbaum & Andreas Nogga• COSY accelerator group


Θcm[deg] Θcm[deg]

pd elastic 135 & 200 MeV 3NFs pd elastic 135 & 200 MeV 3NFs B.v. Przewoski et al., PRC 74, 064003 (2006), arXiv:nucl-ex/0411019

θcm[deg] θ cm[deg]

Each pixel corresponds to one of the 868 data points A pixel is colored blue if 3NF improves the agreement

θ cm[deg] θ cm[deg]θ cm[deg]θ cm[deg]

http://lanl.arxiv.org/abs/nucl-ex/0411019


Three-nucleon forces (3NF)

• Today: Conflicting messages from comparisons of data to all 3NF models: – See e.g. Przewoski et al., Kistryn et al., Sekiguchi et al.

How to proceed ?

Primakoff&Holstein PR55 (1939)Wigner (1933)

Fujita&Miyazawa Prog.Th.P. 17 (1957)

Pudliner et al., PRC 56 (1997)

Coon&Han FBS 30 (2001)

Nemoto et al., FBS 24 (1998)Chimielevski etal., Deltuva et al., PRC67 (2003)

Coon & Glöckle, PRC23 (1981)


pd breakup data at 65 MeV/A

• Recent data:

• Kistryn et al., Cross sections (previous talk)

• Stephan et al., Analyzing powers (next talk)

• Previous Data: – Low et al., PRC 44, 2276 (1991)– Allet et al., PRC 50, 602 (1994)– Qin et al., NPA 587, 252 (1995)– Allet et al., FBS 20, 27 (1996)– Zejma et al., PRC 55, 42 (1997)– Bodek et al., FBS 30, 65 (2001)

• Theory: NN high precision realistic models, CDBonn NijmI, II, AV18, Nijm93, ChEFT-N2LO

• 3NF: TM, TM’, UIX


Zejma pol(p) beam 65 MeV – σ & Ay

FPS = Forward Plane Star

θ1= θ2=35.2o

φ = 12 180o NN calculations


Zejma 65 MeV BP

S 75

.4, 7

5.4,

180

deg

rees

(lab

)

SSS

54, 5

4, 1

20 d

egre

es (l

ab)


… cont. 65 MeV/A

• 3 NF Sensitive regions for

cross section & Ay:

• θ1,2=10, 20 degrees

• φ=0..60 degrees

Figure from Kuros et al., PRC 66, 024004 (2002)

Light shaded band: NN

Dark shaded band:NN + TM

Dashed line: CDBonn + TM’

Solid line: AV18 + UrbanaIX

Dat

a: Z

ejm

a et

al


Recent experiments in breakupRecent experiments in breakupSakai, NPA 790, 122c-128c (2007)

”The more data accumulated themore confusion revealed. ”

Guidance by theory needed


3NF from chiral effective field theory

• Guidance from theory

• High precision data of several observables over

large areas of phase space are needed for theory

Primakoff&Holstein PR55 (1939)Wigner (1933)

Epelbaum, Nogga, Glöckle, Kamada, Meißner, Witała, PRC 66, 064001 (2002)


Chiral Effective Field Theory (ChEFT)

• Chiral Effective Field theory: – Systematic & model independent framework for low-

energy hadron 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

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

Epelbaum et al., PRC 66, 064001 (2002)


ChEFT @ N2LO & 3NF at 65 MeVChEFT @ N2LO & 3NF at 65 MeV

NLO (blue) and N2LO (red) bandpd breakup data are from J. Zejma et al., Phys. Rev. C 55 (1997) 42Epelbaum, Prog. in Part. and Nucl. Physics 57 (2006) 654–741

symmetric space star symmetric forward star

TPE OPE Contact


Goals for Letter-of-Intent at COSYGoals for Letter-of-Intent at COSY

– Provide experimental evidence of the Three-Nucleon Forces – Provide precise data for constraints of Chiral EFT– pd breakup at 30-50 MeV offers

• Systematic double polarized measurements at 30-50 MeV– an ideal energy range for testing ChEFT– few previous measurement exist

» (c.f. E.Stephan talk for analyzing powers at 50 MeV/A)• Independent determination of D & E• New effects of 3NF that appear at N3LO can be accessed


Three-body final stateThree-body final state

• five-dimensional phase space

• 4 angles and mom: θp, θq, φp, φq, p

• If azimuthal symmetry θp, θq, ∆φ, p

• Find relevant independent parameter &

observable

∆ϕ = ϕ (p) - ϕ (q)

Jacobi momenta

p = ½ (p1 – p2)

q = – (p1 + p2)p2

p

q

p1

Scurve(E1,E2)

θ1, θ2, ∆ϕ =30, 31, 180 deg

G.G.Ohlsen, NIM 179 (1981) 283


Systematic Approach to 3particle Phase Systematic Approach to 3particle Phase Space – The Sampling MethodSpace – The Sampling Method

� Problems: 1) What observable to analyze as function of what independent

variable? 2) How to ”correct” the experimental data with respect to the

true acceptance and variations of detection efficiencies?� Solution� For a kinematically complete experiment: The correctly

averaged theoretical value is the mean

� The error is the standard deviation that arises from the randomness of the experimental phase space point

( )( )( )

thth th kO xO O

Nγ

γ= = ∑

16

Cy,x-Cx,y and Czz,z as a function of ∆ϕ

solid line:D-Bonn dashed: AV18 dotted: CD-Bonn+TM´

H.O. Meyer et al., PRL 93,112502 (2004)


LoI 202 - PAX facility at COSY

Low

Low beta quadropolesBRP

ABS

27/9/2010 / SPIN2010 - Spin Physics in Nuclear Reactions and Nuclei 1/ P. Thörngren 18 18

Target chamber, storage cell and detection system

Openable storage cell10 µm teflon wallsSilicon strip detectors

Atomic beam

Stored beam

Guide field coils(x, y, z)

400 mm


Detection systemDetection system

3 layers: 2 x 300µm; 1.5 mm

36 Silicon strip detectors 97x97 mm double sided

pitch 0.76 mm < 1 mm vertex reconstruction

HERMES detectors PAX detectors

Openable storage cell10 µm teflon walls


Polarization ObservablesPolarization Observables

• Observables with polarized proton beam and PAX PIT:

– Ay(p), Ay(d),Axz,Axx-Ayy, Azz + spin correlation coefficients

• 2 hyperfine states injected– |2> |3> -1 tensor; <5% vector– |1> |2> 0 tensor; 2/3 vector

• Holding fields (Helmholtz like) coils: x,y,z directions

• Spin alignment axis at 90 or 45 degrees– Two holding fields activated simultaneously– Transverse/Vertical (x/y) & Longitudinal (z):


Polarization observablesPolarization observables


COSY-LoI 202: COSY-LoI 202: Sensitivity at 30 MeVSensitivity at 30 MeV


COSY-LoI 202: COSY-LoI 202: Sensitivity at 50 MeVSensitivity at 50 MeV


Preliminary Grid StudiesPreliminary Grid Studies

Axz (pos) vs ɵq Axz (pos) vs ϕ q; ɵq=70-150deg

|dA|>0.01 ~ 45% of generated events (profile histograms)


Preliminary Grid Studies Axx-AyyPreliminary Grid Studies Axx-Ayy


SUMMARY SUMMARY

• Measure double polarized pd breakup at 30-50 MeV – Vector & tensor analyzing powers– Spin correlation coefficients using both polarized beam and target

• COSY-experiment will provide– Systematic measurements at 30-50 MeV, at an ideal energy for

testing the predictive power of ChEFT and 3NF– Independent determination of LEC D & E– New effects of 3NF that appear at N3LO can be accessed– Possible implications for spectra of light nuclei

Comparison to THEORY

Using the sampling method

Thank you for your attention !


Minutes of the 37th Meeting of the

COSY Programme Advisory Committee (PAC)

Sep 7/8, 2009 IKP, Forschungszentrum Julich

• Letter-of-Intent #202:New theoretical developments, in particular by the

theory groups at Bonn and Julich concerning a consistent treatment of three-nucleon forces within chiral perturbation theory, provide a solid framework for the analysis of this reaction….

The PAC recognizes the opportunity for presumably the most complete studies of this 3-body break-up channel. Whereas previous dedicated experiments were too often inconclusive or inconsistent with respect to the nature and magnitude of three-nucleon forces, the large kinematical domain to be explored in this experiment together with a large number of observables (aiming at a complete set of observables) give the potential for significant, and possibly definitive, advances in this domain.


3Nucleon Force - What is it?3Nucleon Force - What is it?

• IUCF Workshop Sep 1998 - Working Session II:– Question: What do we mean by 3NF, and where is the best

place to look for experimental evidence?• H. Witala (working session notes):

– ”In a pragmatic view, with nucleon DOF only H=T + ΣVij + V1,2,3 where the second term is all pairwise i.a. summed over the 3N. The rest is 3NF and takes into account any distorsion of NN potential energy caused by the presence of the third nucleon.”

V

Size of the 3NF interaction:

∆V ~ V2/Mc2 → 0.5 – 1 MeV


Traditional Configurations • FSI – the relative energy of two nucleons is zero (or very

small)• QFS quasifree – one of the nucleons at rest in the

laboratory frame• STAR – three nucleons with equal momenta in one plane

with the beam• SSS Symetric Space Star – the nucleon plane

perpendicular to the beam• COLLinear – one nucleon at rest in cm → the other two

back to back


Binding Binding Energy of Energy of 33He He and and 33HH

-9

-8

-7

-6

-5AV 18 Nijm I Nijm II CD Bonn Nature

BE

[MeV

]

3H (NN) 3H (NN+TM)3He (NN) 3He (NN+TM)

BE [MeV] NN-potential 3H(NN) 3H(+TM) 3He(NN) 3He(+TM)

AV 18 -7.62 -8.48 -6.92 -7.76 Nijm I -7.74 -8.39 -7.08 -7.72 Nijm II -7.66 -8.39 -7.01 -7.72 CD Bonn -8.01 -8.48 -7.27 -7.72 Nature -8.48 -8.48 -7.72 -7.72

A.N

ogg a et al.,P hys. Re v. L

ett. 85 (2000 ) 944

…so all is well….?


The Experiment at COSY – LoI 202The Experiment at COSY – LoI 202

COSY circumference: 184 mProton & deuteron beams used with electron & stochastic coolingBeam: ~ 109 stored protons P ~ 0.7; Injection pmin = 293 MeV/c → T = 45 MeVMaximum pmax = 3.7 GeV/c

Polarized p beam 30 – 50 MeV

Polarized deuterium target

PAX ia point at COSY: βx = βy = 0.3 m


Atomic Beam Source & Storage Cell; Atomic Beam Source & Storage Cell; P ~ 0.8

Dissociator H2→2HSextupoles

HF transitions

Sextupoles

HF transitions

Strong Field Transition STF (D)

Nozzle Skimmer Collimator

MFT/WFT (H+D) STF (H) Breit Rabi Polarimeter

Target Gas AnalyzerTarget Cell


Sampling Method - Using a Grid & Sampling Method - Using a Grid & Multidimensional InterpolationMultidimensional Interpolation

• Requirement:

– Calculate a theoretical value for each event

Drawback: X time consuming

• Solution:

– Construct a grid covering phase space

– Use multidimensional interpolation

Kuros et al., Few Body Syst. 34, PTE et al. 259 (2004), nucl-th/0402030

Four-dimensional

24=16 corners / grid cell

Five-dimensional:

25=32 corners / grid cell


Polarization ObservablesPolarization Observables


Table II

Cuts: > 0.01 mb/sr2 along S

Ekin >15 MeV (3 MeV@Elab=13 MeV)

–Kuros et al., PRC 66, 024003, 024004 (2002)


ϕ

θ

Φβ

Coordinate system

new experimental approach to modern three-nucleon forces

Documents