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The Leading Eikonal of the Scattering Amplitude of Particles in Gravitational Field at High Energy Using the Partial Wave Method

The scattering amplitudes for two spineless particles colliding at Planckian center-ofmass energies are considered by the partial wave method in quantum gravity. In the framework of the partial method, a scheme for finding the leading eikonal scattering amplitudes is developed and constructed. The connection between the solutions obtained by partial wave method, quasipotential and functional approaches is also discussed. | VNU Journal of Science: Mathematics – Physics, Vol. 33, No. 1 (2017) 41-47 The Leading Eikonal of the Scattering Amplitude of Particles in Gravitational Field at High Energy Using the Partial Wave Method Nguyen Suan Han1,*, Nguyen Nhu Xuan2 1 Department of Theoretical Physics, Hanoi National University, Vietnam 2 Department of Physics, Le Qui Don University, Hanoi, Vietnam Received 12 December 2016 Revised 16 January 2017; Accepted 20 March 2017 Abstract : The scattering amplitudes for two spineless particles colliding at Planckian center-ofmass energies are considered by the partial wave method in quantum gravity. In the framework of the partial method, a scheme for finding the leading eikonal scattering amplitudes is developed and constructed. The connection between the solutions obtained by partial wave method, quasipotential and functional approaches is also discussed. Keywords: Eikonal scattering, partial wave method, gravitational field. 1. Introduction In recent years there have been important advances in our understanding of Planck scattering in quantum field theory and string theory ( M Pl G 1/ 2 is called Planck mass at the energy scale about 1019 GeV ) [1-6]. This understanding give us a scientific basis to investigate the singularity, the formation of black holes and the loss of information near black holes as well as the modification of the string theory in quantum gravity. The research results have confirmed that [1-6] if gravitational interaction is considred, Planck scattering amplitude of two particles at high energy, s M Pl (s is the square of the total energy of two particles in the center of mass system) and small fixed momentum transfer t (t is the square of momentum transfer) has the form Glauber with the scattering phase depends on energy in the limit t / s [1]. The calculation of high-level correction terms to the eikonal leading term of scattering amplitude has been studied by many authors, but this problem remains an .