Inverting the Nakanishi Integral Relation for a Bound State Euclidean Bethe–Salpeter Amplitude

Abstract : The extraction of the weight function g of the Nakanishi integral representation of the Bethe–Salpeter amplitude is investigated. We studied the numerical inversion of the discretized Nakanishi kernel in the case of an Euclidean bound state. The discretized kernel is regularized by adding the identity operator times a small regularisation parameter ε to avoid numerically unstabilities. We have found that the weight function g as well as the associated light-front valence wave function are unstable against variation of ε. These results suggest that the extraction of the Nakanishi weight function from an Euclidean amplitude, is an ill-defined problem. Without further assumptions on the solution or/and without developing more elaborate methods, the Nakanishi weight function, as well as the corresponding light-front valence wave function, cannot be safely determined.
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Submitted on : Wednesday, August 24, 2016 - 11:31:30 AM
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T. Frederico, J. Carbonell, V. Gigante, V. A. Karmanov. Inverting the Nakanishi Integral Relation for a Bound State Euclidean Bethe–Salpeter Amplitude. Few-Body Systems, Springer Verlag, 2016, 57 (7), pp.549-555. ⟨10.1007/s00601-016-1057-5⟩. ⟨in2p3-01355800⟩

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