Tree unitarity in broken supergravity: (II). Double gravitino amplitude

Abstract

High energy tree unitarity is investigated in a spontaneously broken N=1 supergravity theory with a gauge as well as a matter sector through the amplitude for the process gauge boson + gauge boson → gravitino. Both the leading and the next-to-leading energy dependences get cancelled through supercurrent conservation and the super-Higgs mechanism respectively. The surviving energy growth leads to a unitary violation at a critical c.m. energy E_cr~ 4κ⁻¹√3 π(⅙m²_g̅m⁻²_3/2−1/5)^−½. The requirement E_cr≳κ⁻¹ implies the upper bounds 12(2π+1/120)^½ and [96πκ⁻¹m²_3/2m⁻¹_g]^½ respectively on the gaugino -gravitino mass ratio m_g̅m⁻¹_3/2 and the r.m.s. mass (m_S²+m_P²)^½ of the lightest gauge-singlet scalar a nd pseudoscalar.