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Register a new userTransition electromagnetic form factor and current conservation in the Bethe-Salpeter approach
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The transition form factor for electrodisintegration of a two-body bound system is calculated in the Bethe-Salpeter framework. For the initial (bound) and the final (scattering) states, we use our solutions of the Bethe-Salpeter equation in Minkowski space which were first obtained recently. The gauge invariance, which manifests itself in the conservation of the transition electromagnetic current Jq = 0, is studied numerically. It results from a cancellation between the plane wave and the final state interaction contributions. This cancellation takes place only if the initial bound state BS amplitude, the final scattering state and the operator of electromagnetic current are strictly consistent with each other, that is if they are found in the same dynamical framework. A reliable result for the transition form factor can be obtained in this case only.
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Using the solutions of the Bethe-Salpeter equation in Minkowski space for bound and scattering states found in previous works, we calculate the transition electromagnetic form factor describing the electro-disintegration of a bound system.
Using our solutions of the Bethe-Salpeter equation with OBE kernel in Minkowski space both for the bound and scattering states, we calculate the transition form factors for electrodisintegration of the bound system which determine the electromagnetic current J of this process. Special emphasis is put on verifying the gauge invariance which should manifest itself in the current conservation. We find that for any value of the momentum transfer q the contributions of the plane wave and the final state interaction to the quantity J.q cancel each other thus providing J.q=0. However, this cancellation is obtained only if the initial Bethe-Salpeter amplitude (bound state), the final one (scattering state) and the current operator are strictly consistent with each other. A reliable result for the transition form factor can be found only in this case.
For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q^2. At JLab domain (Q^2=10 GeV^2/c^2), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.
The electromagnetic form factors calculated through Euclidean Bethe-Salpeter amplitude and through the light-front wave function are compared with the one found using the Bethe-Salpeter amplitude in Minkowski space. The form factor expressed through the Euclidean Bethe-Salpeter amplitude (both within and without static approximation) considerably differs from the Minkowski one, whereas form factor found in the light-front approach is almost indistinguishable from it.
We present a new method for solving the two-body Bethe-Salpeter equation in Minkowski space. It is based on the Nakanishi integral representation of the Bethe-Salpeter amplitude and on subsequent projection of the equation on the light-front plane. The method is valid for any kernel given by the irreducible Feynman graphs and for systems of spinless particles or fermions. The Bethe-Salpeter amplitudes in Minkowski space are obtained. The electromagnetic form factors are computed and compared to the Euclidean results.
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