Abstract
The inhomogeneous Bethe–Salpeter equation describing the zero-energy scattering of a system composed by two massive scalars exchanging a massive scalar is numerically investigated in ladder approximation, directly in Minkowski space. The solution is obtained by using the Nakanishi integral representation, as performed in Frederico et al. (Phys Rev D 89:016010, 2014) where the method was successfully applied to bound states. The scattering lengths are quantitatively investigated and the results compared with the corresponding ones present in literature.
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Salpeter E.E., Bethe H.A.: A relativistic equation for bound-state problems. Phys. Rev. 84, 1232 (1951)
Nakanishi N.: Partial-wave Bethe–Salpeter equation. Phys. Rev. 130, 1230 (1963)
Nakanishi N.: Graph theory and Feynman integrals. Gordon and Breach, New York (1971)
Task K., Williams A.G.: Solving the Bethe–Salpeter equation for scalar theories in Minkowski space. Phys. Rev. D 51, 7026 (1995)
Kusaka K., Simpson K., Williams A.G.: Solving the Bethe–Salpeter equation for bound states of scalar theories in Minkowski space. Phys. Rev. D 56, 5071 (1997)
Sauli V., Adam J.: Study of relativistic bound states for scalar theories in the Bethe–Salpeter and Dyson-Schwinger formalism. Phys. Rev. D 67, 085007 (2003)
Karmanov V.A., Carbonell J.: Solving Bethe–Salpeter equation in Minkowski space. Eur. Phys. J. A27, 1 (2006)
Carbonell J., Karmanov V.A.: Cross-ladder effects in Bethe–Salpeter and light-front equations. Eur. Phys. J. A27, 11 (2006)
Carbonell J., Karmanov V.A.: Solving the Bethe–Salpeter equation for two fermions in Minkowski space. Eur. Phys. J A46, 387 (2010)
Frederico T., Salmè G., Viviani M.: Quantitative studies of the homogeneous Bethe–Salpeter equation in Minkowski space. Phys. Rev. D 89, 016010 (2014)
Frederico T., Salmè G., Viviani M.: Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane. Phys. Rev. D 85, 036009 (2012)
Frederico T., Salmè G., Viviani M.: Solutions of the Bethe–Salpeter Equation in Minkowski space: a comparative study. Few-Body Sys. 55, 693 (2014)
Newton, R.: Scattering Theory of Waves and Particles. Monographs in Physics. Springer, New York, vol. 2, (2002)
Carbonell J., Karmanov V.A.: Bethe–Salpeter scattering amplitude in Minkowski space. Phys. Lett. B 727, 319 (2013)
Carbonell J., Karmanov V.A.: Bethe–Salpeter scattering state equation in Minkowski space. Phys. Rev. D 90, 056002 (2014)
Frederico, T., Salmè, G., Viviani, M.: in preparation
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Viviani, M., Frederico, T. & Salmè, G. Numerical Studies of the Zero-Energy Bethe–Salpeter Equation in Minkowski Space. Few-Body Syst 56, 369–374 (2015). https://doi.org/10.1007/s00601-015-0966-z
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DOI: https://doi.org/10.1007/s00601-015-0966-z