Pion-Nucleon Interaction

The pionic hydrogen experiment (PSI-Experiment R-98-01) aims at a precision determination of the hadronic shift (ε1s) and width (Γ1s) of the ground state in pionic hydrogen by measuring the 4p 1s, 3p 1s and 2p1s X-ray transitions by means of ultimate resolution X-ray spectroscopy. The measurements were performed at the low-energy pion channel of the Paul Scherrer Institute and data taking has been completed recently.

The quantities ε1s and Γ1s are directly connected to the pion-nucleon isoscalar and isovector scattering lengths, which in turn can be confronted with results from continuing theoretical efforts within the framework of Chiral Perturbation Theory. The width Γ1s is connected to the pion-nucleon coupling constant fπNallowing an accurate determination of the Goldberger-Treiman discrepancy, which constitutes a measure of chiral symmetry breaking due to non-vanishing quark masses. From the shift and the width together, the isoscalar scattering length is extracted serving to extrapolate to the Cheng-Dashen-point, yielding the pion-nucleon sigma term.

The final value of the shift ε1s was already obtained and the result is

ε1s = +7.120 ± 0.008 ± 0.006 eV,

which corresponds to an error of 0.2%, whereas the extraction of Γ1s from the data is still in progress.

In a PhD thesis in our institute an elaborate analysis
method to extract Γ1s from the data, based on extensive Monte Carlo studies, was developed and first applied to the 4p1s transition in pionic hydrogen. A preliminary value for the strong interaction width of the ground state in pionic hydrogen was given and it reads:

Γ1s = 765 ± 56 meV.

This corresponds to an error of 7.3% and, by using the 4p1s transition only, already constitutes an improvement, compared to the predecessor experiment,http://www.oeaw.ac.at/smi/typo3/#_ftn3 where an error of 9% was given.

Fig. 40: Sketch of the setup of the pionic hydrogen experiment at the PSI.The analysis routine takes into account the instrument's response function, measured using narrow X-ray transitions, produced in an electron cyclotron resonance ion trap (ECRIT)http://www.oeaw.ac.at/smi/typo3/#_ftn4 as well as a the changing kinetic energy distribution of the formed pionic hydrogen atoms, leading to a Doppler broadening of the emitted X-rays.

The kinetic energy distribution is approximated by so-called Doppler boxes, an approach which was verified in a measurement of muonic hydrogenhttp://www.oeaw.ac.at/smi/typo3/#_ftn5. Muonic hydrogen is similar to pionic hydrogen, but the muon is not affected by strong interaction. With the response function given, it therefore offers a unique opportunity to study the influence of the kinetic energy distribution on the line shape of emitted X-rays.

The above mentioned analysis method is being applied to the 3p1s and 2p1s transitions also and will substantially decrease the systematic error of the hadronic width of the ground state in pionic hydrogen. Finally, a relative error of 2-3% is envisaged for Γ1s.

Outlook

Currently the analysis method, developed in our institute, is applied to all measured transitions from all measurement periods. The analysis is scheduled to be completed in the middle of 2009, which also represents the end of the pionic hydrogen experiment.

Additionally, the analysis method is used for the determination of the hadronic width from the measured 3p → 1s transition in pionic deuterium. The analysis is performed at a collaborating institute and will be finished in the middle of the year 2009 as well.