On superplanckian scattering on the brane

The multidimensional space-time with (D-4) compact extra space dimensions and SM fields confined on a four-dimensional brane is considered. The elastic scattering amplitude of two particles interacting by gravitational forces is calculated at superplanckian energies. Particular attention is paid to a proper account of zero (massless) graviton mode. The renormalized Born pole is reproduced in the eikonal amplitude which makes a leading contribution at small momentum transfers. This singular part of the amplitude coincides with well-known D-dimensional amplitude taken at . The expression for the contribution from massive graviton modes to the eikonal is derived, and its asymptotics in the impact parameter is calculated. Our formula gives the correct four-dimensional expression at , where R_c is the radius of the higher dimensions. The results are also compared with those obtained previously for the scattering of the bulk fields in flat extra dimensions.Received: 9 September 2003, Revised: 2 February 2004, Published online: 2 April 2004