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Bonn, 04. September 2009

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Pionic Deuterium

| Thomas Strauch

for the Pionic Hydrogen collaboration

Bonn, 04. September 2009 Folie 2

Experimental program of the Pionic Hydrogen collaboration

Pionic Hydrogen R-98.01 ECRIT (response function) Muonic Hydrogen Pionic Deuterium R-06.03


Exotic atoms

Bohr radius: mp

mep13

11

102,2:

103,5:


Atomic cascade of pionic deuterium

Hadronic interaction

shift ε1s ≈ - 2,5 eV

width Γ1s ≈ 1,2 eV

Aim:

1s /1s 1s /1s

3% ~ 1% 12% ~ 4%

D(3p - 1s) 3 keV

Deser:

n

a

r

Ei

LOA

B

nnsns

42/


dppppdnnd

Pionic Deuterium

PMDa Im

Width Γ1s ~ Im aπD

directly related to pionproduction at threshold

charge symmetry detailed-balance

threshold parameter α (s-wave production)

0/ pp


Pion-Nucleon Interaction

Isospin 1/2 or 3/2 system

At threshold: two parameters:

s-wave scattering lengths a1/2 und a3/2

choose isoscalar und isovector scattering lengths a+ und a- :

3/)(

3/)2(

2/32/1

2/32/1

aaa

aaa


Pionic Hydrogen

1s :

1s :

+ NLO(%)

aaa

pp

2)(0

aa

np

Pionic Deuterium 1s : + NLO(~LO)

aaaannppd

NLO: a- appears


N isospin scattering lengths

Constraint for N isospin scattering lengths a & a –

J.Gasser et al.:

Hadronic atoms in QCD+QED

Physics Reports 456(2008)167-251

Pionic Deuterium:

bandwidth mainly by LEC f1

bandwidth mainly by LEC f1

bandwidth mainly by experiment


Experimental setup

High-resolution Bragg crystal-spectrometer

Bragg law:


Experimental setup

spherically bent Bragg crystalbending radius ~ 3m

cyclotron trapsuperconducting magnetscryogenic target

large area detector6 CCDs with 600x600 pixelpixelsize 40x40 µm

N. Nelms et al., Nucl. Instr. Meth 484 (2002) 419

L. M. Simons, Hyperfine Interactions 81 (1993) 253


Experimental setupPrecision measurement:→ low background→ concrete shielding


Measurement

ADC-spectrum

Cluster analysis

Hit pattern onCCD detector

Hit pattern aftercurvature correction


high-statistics measurement

of πD(3p-1s)

Spectrum after

cluster analysis,

ADC cuts,

curvature correction,

projection onto x-axis

rate: ≈ 30/h

Measurement

pressure

/ bar

number

of events

3,3 1500

10 4000

17,5 4800earlier measurementwithout concretewith concrete


Molecular formation

(d)nl + D2 → [(dd)d]ee

radiative deexcitation out of these formations would falsify the extracted shift ε1s

→ density dependence

not seen in H, but predicted to be larger in D


Energy calibration

Ga K1 9257.67 0.066 eV

K2 9224.84 0.027 eV

reflection in 3rd order

Deslattes et al.: X-ray transition energies,Rev. of Mod. Phys., Vol 75, Jan 2003

reflection in 1st order


stability with Ga Kα2

high statistics Ga calibration measurements

810

811

812

813

814

815

816

80 130 180 230 280 330 380 430 480 530 580

No. of measurement

po

sit

ion

on

de

tec

tor

GaKa2

10bar

3,3bar

20bar

whole measure-time : 4 weeks

ΔE ≈ ±2,5 meV


Results | transition energies

corrections:

e.g. index of refraction (3keV / 9keV)

crystal bending

penetration depth…

pressure in bar 3p-1s transition energy in eV

3.3 3075.509 ± 0.028

10.0 3075.594 ± 0.017

17.5 3075.599 ± 0.016

no evidence for radiative de-excitationout of molecular formationsε1s = Eexp. - EQED EQED = 3077.909±0.008 eV

P.Indelicato private communication


Results | shift ε1s

dominant±0.002 QED calculation±0.007 pionmass


Comparison to earlier measurements


Extraction of the hadronic width from the line shape

spectrometer response-function

Doppler-broadening

Lorentzfunctionof transition

LDRFSi

i


Spectrometer response function (RF)

RF = Rocking curve Geometry add. Gauss

Energy resolution:

ΔE = 436 ± 3 meV

ECRIT- measurementwith He-likeAr


Doppler broadening

energy release of Coulomb transitions converted into kinetic energy of the πD-atoms

prediction

cascade-theory,

scaled from πH


Doppler broadening

kinetic energy distribution: approximation by „boxes“

prediction

cascade-theory,

scaled from πH


χ2 analysis

free fit one box two boxes

low energy box essential no evidence forhigh energy contribution


Statistical studies | MC-simulations

intensity input of high energy contribution:

10% : red25% : blue

probability to miss a simulated contribution


statistical error determination


Results | Width Γ1s

→only one Low-energy-component identified,

no high-energetic parts

→numerous MC-simulations to determine systematic errors


Comparison to earlier measurements


Pionic Deuterium | Final results

1s = - 2325 31 meV ( ±3% → ±1,3%)

1s = 1171 meV (±12% → %)+ 23 - 49

+ 2,1 - 4,2

1312.026.0 1026,633,079,24

mia D


threshold parameter α

α = 252 μb+5-11

χPT:expected uncertainty30% → 5%NNLO calculations


Thank you for your attention!

Debrecen – Coimbra – Ioannina – Jülich – Paris – PSI – Vienna

PSI experiments R-98.01 and R-06.03

D. F. Anagnostopoulos, S. Biri, D. D. S. Covita, H. Gorke, D. Gotta, A. Gruber, M. Hennebach,

A. Hirtl, P. Indelicato, T. Ishiwatari, Th. Jensen, E.-O. Le Bigot, J. Marton, M. Nekipelov,

J. M. F. dos Santos, S. Schlesser, Ph. Schmid, L. M. Simons, Th. Strauch, M. Trassinelli,

J. F. C. A. Veloso, J. Zmeskal

PIONIC HYDROGEN collaboration


Pionisches Deuterium

Appendix


cascaden effects


Origin of shift and width


Pionic Deuterium

1s Pionproduktion an der Schwelle NN NN

Ladungssymmetrie Zeitumkehr-Invarianz

dppppdnnd

)( nndnndda

Pionproduktion Parametrisierung:

Atom:

und über optisches Theorem mit Wirkungsquerschnitt verknüpft

Panofsky Rate:Pd = 2.83±0.04

da

...321

20

CCdpp

m

pp

Pa np

dd

11


Elastic scattering


Experimental setup


long range stability

results analysisinclination sensor data

evolution ofcrystal temperature


corrections and error for ε1s


Spectrometer responsefunction

D. Hitz et al., Rev. Sci. Instr., 71 (2000) 1116

CCD detector

He-like atoms

•narrow X-rays, few keV

•high rateS H(2p-1s)

Cl H(3p-1s)

Ar H(4p-1s)

D(3p-1s)

ECRIT

= cyclotron trap (4) + hexapole magnet (2) + high frquency (5)

6.4 GHz450 W

D.F.Anagnostopoulos et al., Nucl. Instr. Meth. B 205 (2003) 9D.F.Anagnostopoulos et al., Nucl. Instr. Meth. A 545 (2005) 217

Electron Cyclotron Resonance Ion Trap ( ECRIT )


Kinetic energy → velocity distribution


Appendices | NN threshold parameter

PTat present / 30%

few %

charge symmetry detailled balance

dppppdnnd )1()0( 1

31

3 IPISNN

V. Lensky et al., nucl-th/0511054,2005

p

nndnndD

m

a

6

1

321

20 ηCβηCασ dπpp

extrapolation to threshold

J. Hüfner, Phys. Rep. 21 (1975) 1

productionD atom

mk /

NLO

LO

[b

]


Formulae D U.-G. Meißner, U. Raha, A. Rusetsky, Phys. Lett.B 639 (2006) 478

+ Coulomb corrections


Deser formula

+ Coulomb corrections

from H 1s

from D 1s

D wave function

Single + multiple scattering

d