Determination of theS-Wave Scattering Length in Pionic Deuterium with a High Resolution Crystal Spectrometer

Abstract

The pionic deuterium 3P -15 x-ray transition was measured with a quartz crystal spectrometer in combination with a cyclotron trap and charge coupled device detectors. The strong interaction shift and total decay width of the 1S level are e|s (shift) = 2.48~0.10 eV (repulsive), I &s (width) = 1.02~0.21 eV, where the statistical and systematic errors were added linearly. They yield the total pionic deuterium S-wave scattering length: a -d = -0.0264(~0.0011) + i 0 0054. (~0 0011. ) m PACS numbers: 25.80.Hp, 36.10.Gv

Low energyK¯Ninteractions and Faddeev calculation of theK−dscattering length in isospin and particle

“…zero pion mass) limit (however, we should be reminded in this respect that the extraction of this latter quantity is still rather model dependent, see Ref. [33,81] for details, as well as the consequence from the πN partial wave analyses, see for example Ref. [84]).…”

“…But there is a possible way out of this impasse: in Ref. [33,81], by combining the data from the pionic hydrogen and pionic deuterium, the value of the scattering length π − n, or more precisely the isoscalar combination:…”

“…A couple of recent papers have reported an extraction of A π − d from the pionic deuterium atomic transitions, Refs. [33,81,82], using the Deser-Trueman formula [25] to find (Coulomb interaction included):…”

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

“…The threshold and subthreshold parameters are then predicted. We remark that there still is debate about the actual value of the isoscalar S-wave scattering length as extracted from pionic atoms [1] or the various partial-wave amplitudes. As input we use the phase shifts of the Karlsruhe (KA85) group [30], from the analysis of Matsinos [31] (EM98) and the latest update of the VPI group, called SP98 [32].…”

“…In the real world, the situation is complicated by the electromagnetic interactions, which clearly do not conserve isospin (the photon couples to the electric charge). With the advent of high-precision data on pionic hydrogen and deuterium at PSI [1] and neutral pion photoproduction data from MAMI [2] and SAL [3], novel interest has been spurred in separating electromagnetic effects and trying to filter out isospin violating contributions. In addition, in the framework of some models it has been claimed that the presently available pion-nucleon data basis exhibits isospin violation of the order of a few percent [4] [5].…”