Few-Body Systems

, Volume 40, Issue 3, pp 209-235

First online:

Schwinger Functions and Light-Quark Bound States

  • M. S. BhagwatAffiliated withPhysics Division, Argonne National Laboratory
  • , A. HöllAffiliated withInstitut für Physik, Universität Rostock
  • , A. KrassniggAffiliated withInstitut für Physik, Karl-Franzens-Universität Graz
  • , C. D. RobertsAffiliated withPhysics Division, Argonne National Laboratory
  • , S. V. WrightAffiliated withPhysics Division, Argonne National Laboratory

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We examine the applicability and viability of methods to obtain knowledge about bound states from information provided solely in Euclidean space. Rudimentary methods can be adequate if one only requires information about the ground and first excited state and assumptions made about analytic properties are valid. However, to obtain information from Schwinger functions about higher mass states, something more sophisticated is necessary. A method based on the correlator matrix can be dependable when operators are carefully tuned and errors are small. This method is nevertheless not competitive when an unambiguous analytic continuation of even a single Schwinger function to complex momenta is available.