Pionic Deuterium

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Pionic Deuterium
Thomas Strauch for the Pionic Hydrogen
collaboration
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Experimental program of the Pionic Hydrogen
collaboration

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

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Exotic atoms
Bohr radius
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Atomic cascade of pionic deuterium

• Hadronic interaction
• shift e1s - 2,5 eV
• width G1s 1,2 eV
• Aim
• ??1s /?1s ??1s /?1s
• 3? 1 12? 4

?D(3p - 1s) 3 keV
Deser
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Pionic Deuterium
Width G1s Im apD
directly related to pionproduction at threshold
charge symmetry
detailed-balance
threshold parameter a (s-wave production)

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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-

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Pionic Deuterium
?1s
NLO(LO)
NLO a- appears
NLO()
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?N isospin scattering lengths
bandwidth mainly by LEC f1
bandwidth mainly by LEC f1
J.Gasser et al. Hadronic atoms in
QCDQED Physics Reports 456(2008)167-251
Pionic Deuterium
bandwidth mainly by experiment
Constraint for ?N isospin scattering lengths a
? a
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Experimental setup
High-resolution Bragg crystal-spectrometer
Bragg law
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Experimental setup
spherically bent Bragg crystal bending radius 3m
large area detector 6 CCDs with 600x600
pixel pixelsize 40x40 µm
cyclotron trap superconducting magnets cryogenic
target
N. Nelms et al., Nucl. Instr. Meth 484 (2002) 419
L. M. Simons, Hyperfine Interactions 81 (1993) 253
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Experimental setup
Precision measurement ? low background ?
concrete shielding
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Measurement
Hit pattern on CCD detector
ADC-spectrum
Hit pattern after curvature correction
Cluster analysis
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Measurement
Spectrum after cluster analysis, ADC
cuts, curvature correction, projection onto
x-axis rate 30/h
high-statistics measurement of pD(3p-1s)
earlier measurement without concrete
with concrete
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Molecular formation

• (?d)nl D2 ? (?dd)dee
• radiative deexcitation out of these formations
  would falsify the extracted shift e1s
• ? density dependence
• not seen in ?H, but predicted to be larger in ?D

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Energy calibration
reflection in 1st order
Ga K?1 9257.67 ? 0.066 eV K?2 9224.84 ?
0.027 eV reflection in 3rd order
Deslattes et al. X-ray transition energies, Rev.
of Mod. Phys., Vol 75, Jan 2003
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stability with Ga Ka2
whole measure-time 4 weeks
?E 2,5 meV
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Results transition energies

• corrections
• e.g. index of refraction (3keV / 9keV)
• crystal bending
• penetration depth

no evidence for radiative de-excitation out of
molecular formations
e1s Eexp. - EQED
EQED 3077.9090.008 eV P.Indelicato private
communication
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Results shift e1s
0.002 QED calculation 0.007 pionmass
dominant
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Comparison to earlier measurements
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Extraction of the hadronic width from the line
shape
spectrometer response-function
Doppler- broadening
Lorentzfunction of transition
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Spectrometer response function (RF)

• RF Rocking curve Geometry add. Gauss

Energy resolution ?E 436 3 meV ECRIT-
measurement with He-likeAr
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Doppler broadening

• energy release of Coulomb transitions converted
  into kinetic energy of the pD-atoms

prediction cascade-theory, scaled from pH
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Doppler broadening

• kinetic energy distribution approximation by
  boxes

prediction cascade-theory, scaled from pH
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?2 analysis

• free fit

one box
two boxes
low energy box essential
no evidence for high energy contribution
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Statistical studies MC-simulations
intensity input of high energy
contribution 10 red 25 blue
probability to miss a simulated contribution
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statistical error determination
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Results Width G1s

• ?only one Low-energy-component identified,
• no high-energetic parts
• ?numerous MC-simulations to determine systematic
  errors

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Comparison to earlier measurements

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Pionic Deuterium Final results
23 - 49
2,1 - 4,2
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threshold parameter a
?PT expected uncertainty 30 ? 5 NNLO
calculations
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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
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Pionisches Deuterium

• Appendix

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cascaden effects
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Origin of shift and width
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Pionic Deuterium

• ?1s Pionproduktion an der Schwelle ?NN
  ? NN

Panofsky Rate Pd 2.830.04
Atom
und über optisches Theorem
mit Wirkungsquerschnitt verknüpft
Ladungssymmetrie Zeitumkehr-Invarianz
Pionproduktion Parametrisierung
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Elastic scattering
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Experimental setup
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long range stability
results analysis inclination sensor data
evolution of crystal temperature
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corrections and error for e1s
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Spectrometer responsefunction
Electron Cyclotron Resonance Ion Trap ( ECRIT )
ECRIT cyclotron trap (4) hexapole magnet
(2) high frquency (5)
6.4 GHz 450 W
D. Hitz et al., Rev. Sci. Instr., 71 (2000) 1116

• He-like atoms
• narrow X-rays, few keV
• high rate
• S ? ?H(2p-1s)
• Cl ? ?H(3p-1s)
• Ar ? ?H(4p-1s)
• ?D(3p-1s)

CCD detector
D.F.Anagnostopoulos et al., Nucl. Instr. Meth. B
205 (2003) 9 D.F.Anagnostopoulos et al., Nucl.
Instr. Meth. A 545 (2005) 217
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Kinetic energy ? velocity distribution
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Appendices ?NN threshold parameter ?
?PT at present ?? / ? ? 30 ?
few

NLO
??? ?b
V. Lensky et al., nucl-th/0511054,2005
LO
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Formulae ?D
U.-G. Meißner, U. Raha, A. Rusetsky, Phys. Lett.B
639 (2006) 478
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Deser formula
Coulomb corrections
Single multiple scattering