Redetermination of the strong-interaction width in pionic hydrogen
A. Hirtl, D. F. Anagnostopoulos, D. S. Covita, H. Fuhrmann, H. Gorke, D. Gotta, Alexander Gruber, M. Hennebach, P. Indelicato, Th. Jensen, E.-O. Le Bigot, Yiwei Liu, V. E. Markushin, J. Márton, M. Nekipelov, J.M.F. dos Santos, L. M. Simons, Th. Strauch, M. Trassinelli, J.F.C.A. Veloso, J. Zmeskal
Abstract
Abstract The hadronic width of the ground state of pionic hydrogen has been redetermined by X-ray spectroscopy to be $$\varGamma ^{\pi \mathrm {H}}_{1s}=(856\,\pm \,16_\mathrm{stat}\,\pm \,22_\mathrm{sys})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>π</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>856</mml:mn> <mml:mspace/> <mml:mo>±</mml:mo> <mml:mspace/> <mml:msub> <mml:mn>16</mml:mn> <mml:mi>stat</mml:mi> </mml:msub> <mml:mspace/> <mml:mo>±</mml:mo> <mml:mspace/> <mml:msub> <mml:mn>22</mml:mn> <mml:mi>sys</mml:mi> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> meV. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institute by using the cyclotron trap and a high-resolution Bragg spectrometer with spherically bent crystals. Coulomb de-excitation was studied in detail by comparing its influence on the line shape by measuring the three different transitions K $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , K $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> , and K $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> at various hydrogen densities. The pion-nucleon scattering lengths and other physical quantities extracted from pionic-atom data are in good agreement with the results obtained from pion-nucleon and nucleon-nucleon scattering experiments and confirm that a consistent picture is achieved for the low-energy pion-nucleon sector with respect to the expectations of chiral perturbation theory.